23.10.1995
 RNDr. Jiří Souček, DrSc. (MUUK): Role topologických podmínek ve variačním počtu pro vektorová zobrazení
 30.10.1995
 Prof. Maria E. Schonbek (University of California): On the decay of higher order derivatives of solutions to the Navier-Stokes equations
 30.9.1996
 Prof. RNDr. Miloslav Feistauer, DrSc. (KNM): "Coupling" ve vnejsich ulohah mechaniky kontinua
 7.10.1996
 RNDr. Josef Malek, CSc. (MUUK): Vlastnosti reseni nekterych modelu dokonale plasticity
 3.4.2000
 Mgr. Jaroslav Hron (MÚ UK): Směsi tekutin a pevných látek a jejich použití při modelování měkkých tkání
 10.4.2000
 Doc. RNDr. Josef Málek, CSc. (MÚ UK): Regularita a tekutiny s nekonstantní vazkostí
 17.4.2000
 RNDr. Vít Dolejší, Ph.D. (KNM MFF UK): Adaptivní metody pro simulaci proudění stlačitelného vazkého plynu
 24.4.2000
Seminář se nekoná - Velikonoce
 1.5.2000
Seminář se nekoná
 8.5.2000
Seminář se nekoná
 15.5.2000
Seminář se nekoná
 22.5.2000
Seminář se nekoná.

Zájemci jsou zváni na:

## Slavnostní seminář k 150. výročí narození profesora Čeňka Strouhala

V pondělí 22.5.2000 od 16:30 hodin ve Strouhalově posluchárně (F1) v budově MFF, Ke Karlovu 5, Praha 2.

 9.10.2000
 Mgr. Dalibor Pražák (MÚ UK): Finite fractal dimension to global attractor for nonlinear wave equation
 16.10.2000
 Dr. Miroslav Rozložník (ÚIVT AV): Iterative solution of augmented systems from the potential fluid flow problem Abstract: Mixed-hybrid finite element discretization of the Darcy's law and the continuity equation which describe the potential flow problem in porous media leads to augmented symmetric indefinite systems of linear equations. In this talk we give an overview of various possible approaches for solving such systems. We consider the minimum residual method, the Schur complement approach and the dual variable approach based on the construction of the null-space basis of the off-diagonal block in the system matrix.
 23.10.2000
 RNDr Pavel Krejčí, DrSc (MÚ AV): Konstituční zákony plasticity, fronty na maso a hysterezní operátory Abstract: Tématem budou matematické souvislosti mezi Skorochodovým problémem z teorie hromadné obsluhy, evolučními variačními nerovnicemi, Kurzweilovým integrálem a Madelungovými zákony paměti materiálu.
 30.10.2000
 Dr Ing Michal Beneš (Katedra matematiky FJFI ČVUT): Mathematical Modelling of Solidification Phenomena in Pure Substances. Part I.
 6.11.2000
 Dr. Michael Fried (Institute of Applied Mathematics, University Freiburg): Mathematical Modelling of Solidification Phenomena in Pure Substances. Part II.
 13.11.2000
 Professor Taoufik Sassi (INSA-Lyon Scientific and Technical University): A priori and a posteriori error estimates for unilateral contact problems Abstract: Inthe first part, we propose and study different mixed variational methods in order to approximate with finite elements the unilateral problems arising in contact mechanics. A priori error estimates are established and several numerical studies corresponding to the different choices of the discretized unilateral conditions are achieved.In the second part, we define and study a natural residual a posteriori error estimator for the variational inequality modelling unilateral contact. The new estimator is particularly well-adapted to a contact problem which is approximated with a domain decomposition technique involving general non-matching meshes.
 20.11.2000
 Mgr. Dalibor Pražák (MÚ UK): Konečně-dimenzionální dynamika disipativních systémů s omezeným zpožděním.
 27.11.2000
 Prof. RNDr. Jan Kratochvíl, DrSc. (Katedra fyziky Stavební fakulty ČVUT): Models of formation of dislocation structure in deformed metal crystals.
 4.12.2000
 RNDr. Eduard Feireisl, DrSc (MÚ AV): Stlačitelné Navier-Stokesovy rovnice s obecnou konstitutivní rovnicí pro tlak.
 11.12.2000
 Professor Kari Kärkkäinen (Department of Math. Information Technology, University of Jyväskylä): Discrete version of a total linearization method applied to a class of free boundary problems. Abstract: In this work we consider a numerical approach to implement a total linearization method for various free boundary problems. In total linearization method the idea is to linearize the weak formulation of original equations with respect to the shape in continuous case and then to discretize these equations in order to create an efficient iterative method to solve a free boundary problem. In particular, this kind of approach generates superlinearly convergent method also in discrete case, if the mesh is refined during the iteration appropriately. Further, the linearised equations contain a new function, which describes the change to the domain and is supported only on the free boundary.Here we consider a slightly different approach. First we discretize weak formulations and then apply the total linearization to them. The sensitivities are calculated in elementwise manner and the restriction of the calculation to the elements beside the free boundary is established. In particular, we use these shape sensitivities to linearise the weak formulations of free boundary problem. The advantage of this approach is the easier computation during the implementation so that it can be applied quite general free boundary problems. A detailed implementation is presented along with test calculations on model free boundary problems
 18.12.2000
 Doc. Ing. Tomáš Roubíček, DrSc. (MÚ UK): Matematické modely feromagnetik
 8.1.2001
 Prof. RNDr. Jaroslav Haslinger, DrSc (KFK MFF UK): Materiálová optimalizace pomocí konstrukce G-uzávěrů
 26.2.2001
 Doc. RNDr. Josef Málek, CSc. (MÚ UK): Nestlačitelné tekutiny s vazkostí závislou na tlaku. Globální existence slabého řešení.
 5.3.2001
 Dr. Kunibert G. Siebert (IAM, Albert-Ludwigs-Universität Freiburg): ALBERT - Adaptive Finite Element Software for Scientific Computations and Applications Abstract: Adaptive finite element methods are a modern, widely used tool which make realistic computations feasible, even in three space dimensions. We describe the basic ideas and ingredients of adaptive FEM and the implementation of our toolbox ALBERT. The design of ALBERT is based on the natural hierarchy of locally refined meshes and an abstract concept of general finite element spaces. As a result, dimension independent programming of applications is possible. Numerical results from applications in two and three space dimensions demonstrate the flexibility of ALBERT.
 12.3.2001
 Prof. RNDr. Jiří Neustupa, CSc (Katedra matematiky, Strojní fakulta ČVUT): Nové podmínky pro lokální regularitu slabého řešení Navierových-Stokesových rovnic
 19.3.2001
 Mudr. Jan Krásný, Mudr. Renata Brunnerová, Mudr. Jana Chvojková, Mudr. Sylva Procházková (Oční klinika FN Královské Vinohrady, Praha): Strabismus a refrakční chirurgie u dospělých pacientů. Abstract: V období posledních čtyř let jsme vyšetřili pět desítek dospělých pacientů se strabismem nebo-li šilháním, kteří poté podstoupili refrakční výkon - operační postup měnící dalekozrakost či krátkozrakost na emetropii, tzn. zrušení nutnosti nošení korekční pomůcky ( brýle či kontaktní čočky). Metodiky jsou LASIK (Laser in Situ Keratomileusis) či CLE (Clear Lens Extraction), někdy v kombinaci s AK (Astigmatic Keratotomy). Strabismus jsme řešili operativně u cca 25% pacientů. V průběhu pooperačního sledování zatím u necelých 50% pacientů nebyla úchylka po refrakčním výkonu větší než 5 st. Postavení očí bylo kosmeticky plně vyhovující a tedy nebylo ani indikací k operační úpravě. Posledních 25% pacientů je ve sledování vzhledem k časovému faktoru nutnému po operačním refrakčním výkonu. Z ortoptických rozborů ( strabologické vyšetření postavení očí - úhel šilhání a posouzení funkcí obou očí ve smyslu přítomnosti a stupně prostorového vidění ) před a po refrakčním výkonu vyplynulo. U všech i jen částečně akomodativních esotropií (konvergentní strabismus, kde úchylka šilhání je podmíněná refrakční vadou, převážně zastoupená dalekozrakostí, pouze ojediněle krátkozrakostí) se po refrakčním výkonu zmenšila úchylka. U divergentního šilhání se úchylka minimálně změnila, a to pouze u malých úchylek do několika stupňů, nad pět stupňů se úchylka nezmenšila ani nezvětšila. Změna úchylky byla bez zjevné závislosti na velikosti refrakční vady a jejímu poklesu, pokud jsme byli schopni posoudit. U některých pacientů se po normalizaci zrakové vady na praktickou emetropii, která byla již trvale bez korekční pomůcky , objevil určitý stupeň binokulárního vidění, tzn. souhra obou očí v senzorické činnosti umožňující hloubkové prostorové vidění. Před operačním refrakčním výkonem tito pacienti střídali, tzn. používali jedno nebo druhé oko, nebyli schopni prostorového hloubkového vidění.EpikrízaKardinální otázka zní, zda existuje mezi refrakční změnou a změněným stupněm šilhání určitá matematicky vyjádřitelná závislost, zda lze vyjádřit možnost nástupu určitého stupně prostorového vidění.
 26.3.2001
 Prof. Dr. Michael Růžička (Freiburg University): On Electrorheological Fluids. Abstract: Electrorheological fluids change dramatically their mechanical properties in dependence on an applied electrical field. We derive an system of partial differential equations which describes the motion of such fluids. This elliptic or parabolic system possesses so called non-standard growth conditions. We discuss the underlying structure, which naturally leads to generalized Sobolev spaces W1,p(x)(Ω) and present first existence, uniqueness and regularity results for the steady and the unsteady problem.Reference: M. Růžička, Electrorheological Fluids: Mathematical Modelling and Existence Theory, LNM 1748, Springer
 2.4.2001
 Prof. Dr. Christoph Schwab (ETH Zürich): Generalized p-FEM for homogenization problems
 9.4.2001
 Prof. Ing. Václav Tesař, CSc (University of Sheffield a ČVUT): MIKROFLUIDIKA - co to je za nový obor a jak může změnit svět, ve kterém žijeme Abstract: Mikroinženýrství, součástky vyráběné technikou původně vyvinutou pro mikroelektroniku. Mikrofluidika: řízení proudění tekutin. Fluidika: jak řídit pohyb tekutiny bez pohyblivých součástek. Problém extrémně nízkých Reynoldsových čísel, nelze využívat setrvačnost tekutiny. Tlakové působení. Využití elektroosmotickýchsil. Jak prakticky vypadá mikrofluidický ventil, jak se navrhuje a jak se vyrábí (leptáním). Aplikace: Mikrochemie. Míchání reaktantu založené na hydrodynamické nestabilitě. Kombinatorická chemie: hledání katalyzátoru a enzymu. Jiné uplatnění: analýza DNA a objektivní diagnóza nemoci. Automobily bez spalovacího motoru: palivové články a příprava paliva pro ně.
 16.4.2001
Seminář se nekoná - Velikonoce
 23.4.2001
 Professor Jonathan J. Healey (Keele University, United Kingdom): Hydrodynamic stability course I and II Abstract: Very few exact solutions are known for the equations of fluid motion, and these are usually steady and only for the simplest flow geometries. However, these simple flows can often be regarded as idealizations of more complicated flows that arise in practical situations. Typically, as flow speed increases, a smooth laminar flow is observed to break down to a turbulent state with important consequences for fluid drag on solid surfaces, heat transfer and fluid mixing. This transition to turbulence remains a major challenge in classical mechanics. Nonetheless, progress has been made in understanding the first stages of transition through a study of the behaviour of small disturbances present in a prescribed steady flow, in particular whether they grow or decay i.e. the flow's stability. This course introduces the theoretical techniques required to undertake such a study, and includes applications to certain classical examples like thermal instability, centrifugal instability, gravitational instability and shear instability. A more advanced case where instability is brought about through an *increase* in viscosity is also treated, and the course includes an outline of triple-decked stability theory', which underpins much contemporary theoretical research in boundary layers. There will also be discussion of the initial value problem, transient algebraic growth and absolute/convective instability.
 30.4.2001
 Professor Jonathan J. Healey (Keele University, United Kingdom): Hydrodynamic stability course III and IV
 7.5.2001
Seminář se nekoná
 14.5.2001
 Prof. RNDr. M. Feistauer, DrSc., RNDr. V. Dolejší, Ph.D. (KNM UK): Nespojitá Galerkinova metoda
 21.5.2001
 Prof. RNDr. J. Kratochvíl, DrSc. (FS ČVUT): Fyzika skluzových pásů (vrstev)
 28.5.2001
Professor Bernard Ducomet
(CEA Bruyeres, France):
Asymptotic behaviour for nuclear fluids and thermoviscoelasticity

# Seminář začne vyjímečně již v 14:00

 8.10.2001
 Professor Dr. Jens Frehse (University of Bonn, Germany): An analysis of the Stokes-like system for a mixture of compressible fluids
 15.10.2001
 Doc. Ing. Ivan Samohýl, CSc. (VŠCHT Praha): Konstitutivní rovnice pro rychlost chemických reakcí a difuzi
 22.10.2001
 Prof. Ing. František Maršík, DrSc. (ÚT AVČR a MFF UK): Rozšířená nerovnovážná termodynamika chemicky reagujících směsí Abstract: Podle předpokladů rozšířené nerovnovážné termodynamiky závisí konstitutivní vztahy vedle obvyklých proměnných (vnitřní energie-teplota, deformace) i na disipativních procesech, probíhajících v systému. Jde především o toky tepla, toky difuzní a disipativní část tenzoru napětí. Takto formulovaná teorie dovoluje jednotným způsobem popsat chemicky reagující visko-plastické materiály, včetně materiálu Maxwellova typu. Definice chemického potenciálu je rozšířena i pro konečné deformace a je ukázána vzájemná souvislost mezi chemickými reakcemi (fázovými přechody) a tenzorem napětí pro případ homogenního isotropního materiálu.
 29.10.2001
Seminář se nekoná
 5.11.2001
 Doc. RNDr. Josef Málek, CSc. (MFF UK): Je nekluzká hranice v dynamice nestlačitelných tekutin čertův vynález?
 12.11.2001
 Doc. RNDr. Josef Málek, CSc. (MFF UK): Metody teorie regularit v existenční teorii rovnic mechaniky tekutin
 19.11.2001
 Mgr. Milan Pokorný, Ph.D. (MFF UK): Eulerovsko-lagrangeovský popis newtonovských tekutin a jeho problémy
 26.11.2001
 Professor Patrick Penel (UTV Toulon, France): New stability results for 1D-compressible Navier-Stokes equations
 3.12.2001
 Ing. Martin Vohralík (FJFI ČVUT): Smíšeně-hybridní model proudění puklinovým prostředím skalního masívu - teorie, modelové problémy a simulace reálné situace
 10.12.2001
 Professor K.R. Rajagopal (Texas A&M University, College Station, USA): A Thermodynamic Framework for Anisotropic Liquids
 17.12.2001
 Professor Karl Kunisch (University Graz, Austria): Optimal semismooth Newton's method in optimal control
 7.1.2002
 Prof. RNDr. Jaroslav Haslinger, DrSc. (MFF UK): Tvarová optimalizace v kontaktních úlohách s Coulombovským třením
 25.2.2002
 Professor K.R. Rajagopal (Texas A&M University, College Station, USA): A Thermodynamic Framework for Anisotropic Liquids, part II
 4.3.2002
 Professor M. Arndt (University Bonn, Germany): Modelling and numerical simulation of martensitic transformation
 11.3.2002
 Professor F.J. Barthold (University of Braunschweig): Variational design sensitivity analysis - Theory and Computation
 18.3.2002
 Profesor Ing. O. Wein, DrSc. (Ústav chemických procesů AV ČR): Reologické konstitutivní modely a experimentálně dostupná realita
 25.3.2002
 RNDr. Zdeněk Fiala, CSc. (ÚTAM AV ČR): Lomová mechanika - úloha s pohyblivou hranicí (fyzikální aspekty)
 1.4.2002
Seminář se nekoná - velikonoční svátky
 8.4.2002
 RNDr. Jiří Souček, DrSc. (MFF UK): Matematické principy kvantové teleportace a kvantových počítačů
 15.4.2002
 Prof. Dr. Christoph Schwab (ETH Zürich, Switzerland): Sparse finite elements for elliptic partial differential equations with stochastic data
 22.4.2002
 Doc. Ing. Tomáš Roubíček, DrSc. (MFF UK): Optimální řízení ustáleného proudění nestlačitelných tekutin
 29.4.2002
 Professor Jonathan J. Healey (Keele University, United Kingdom): Hydrodynamics Stability, Theoretical Analysis and Applications I
 6.5.2002
 Professor Jonathan J. Healey (Keele University, United Kingdom): Hydrodynamics Stability, Theoretical Analysis and Applications II
 13.5.2002
 Prof. RNDr. Jan Kratochvíl, DrSc. (MFF UK): Počítačová simulace mechanismů únavy kovů
 20.5.2002
Seminář se nekoná - 15 30 v K1 se koná setkání s prof. Choquetem
 21.10.2002
 Professor Alfred Wagner (RWTH Aachen, Germany): The optimal shape of a liquid drop supported by an elastic membrane
 28.10.2002
Seminář se nekoná - státní svátek
 4.11.2002
 Professor Victor Starovoitov (Lavrentyev Institute of Hydrodynamics, Novossibirsk, Russia): Penalty methods and problems of liquid-solid interaction
 11.11.2002
 Professor Claude Bardos (Ecole normale supérieur Cachan, France): "N tends to infinity" limit of quantum particles
 18.11.2002
 Ing. Petr Louda (FS ČVUT): Úvod do modelování turbulence pro aplikace CFD v technice
 25.11.2002
 Professor Danielle Hilhorst (Université Paris Sud, Orsay): Singular limit of an inhomogeneous reaction-diffusion equation Abstract: It is well-known that some classes of nonlinear diffusion equations give rise to sharp internal layers (or interfaces) when the diffusion coefficient is small enough or the reaction coefficient is very large the motion of such interfaces is often driven by their curvature. We consider here the inhomogeneous reaction-diffusion equation u_t = div(h(x) grad u) + h/e2 u (1-u2) in O x (0,T) where O is a smooth bounded domain in RN. We suppose that the functions h and k are smooth and strictly positive and that the parameter e is small enough. We consider the corresponding initial value problem together with homogeneous Neumann boundary conditions and we prove a propagation of interface result, and a result for the generation of interfaces. This is joint work with Hiroshi Matano and Reiner Schaetzle.
 2.12.2002
 Dr. Lars Diening (University of Freiburg, Germany): Generalized Lebesgue spaces, Singular Integrals and Applications in Fluid Mechanics
 9.12.2002
 RNDr. Pavel Krejčí, DrSc. (MÚ ČAV): O jednom modelu singulárních oscilací
 16.12.2002
 RNDr. Jiří Svoboda, CSc. (Ústav fyziky materiálů AV ČR, Brno): Využití extremálního termodynamického principu k modelování úloh lineární nerovnovážné termodynamiky
 6.1.2003
 Prof. Ing. František Maršík, DrSc. (MFF UK): Revize teorie varu a kavitace na základě termodynamických fluktuací
 17.2.2003
 Eduard Feireisl, Sonja Goj, Josef Málek (MÚ AV ČR a MÚ UK): Fluids: Analysis and Rheology
 24.2.2003
Seminář se nekoná
 3.3.2003
 Dr. Martin Kruzik (Institute of Information Theory and Automation (UTIA AV CR)): Model hystereze v mikromagnetismu
 10.3.2003
 Dipl.Math. Marcel Arndt (University Bonn (SRN)): Multiscale atomistic-continuum simulation of shape memory alloys
 17.3.2003
 Dr.Ing.Eduard Rohan (Katedra mechaniky, Fakulta aplikovanych ved a Nove technologie - vyzkumne centrum, Zapadoceska univerzita v Plzni): Moznosti modelovani mekkych tkani s prihlednutim k mikrostrukture
 24.3.2003
 Dipl.-Math. Sonja Goj (University Bonn and MFF UK): A Stokes-like system for mixtures
 31.3.2003
 Professor Adelia Sequeira (Technical University of Lisbon, Portugal): Steady Flows of Viscoelastic Fluids with Shear Dependent Viscosity Abstract: The mathematical theory of the equations of motion of incompressible viscoelastic fluids of differential and rate type in bounded and unbounded domains has been studied in several articles published in the last years. However, as far as we know, generalizations of these models incorporating shear-thinning or shear-thickening properties have not been considered from the mathematical point of view. This lecture is devoted to the investigation of the existence and uniqueness of solutions to the system of non-linear partial differential equations governing the motion of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain, with a non-Newtonian viscosity depending on the second invariant of the rate of deformation tensor. Considering the equations in a suitably decomposed form, we establish, for small and sufficiently regular data, existence of a unique solution using a fixed point argument in an appropriate functional setting. This model includes the classical Oldroyd-B fluid as a particular case. Applications to blood rheology will also be considered in this lecture.
 7.4.2003
 Angel Manuel Ramos (Complutense University of Madrid, Spain): Numerical solutions for multiobjective control problems in PDE's
 14.4.2003
 Professor Arthur Shavit (Technion-Israel Institute of Technology): The Structure of Thermodynamics
 21.4.2003
Seminář se nekoná - velikonoční svátky
 28.4.2003
 Professor Jonathan J. Healey (Keele University, United Kingdom): On the nature of the absolute instability of the rotating disk boundary layer
 5.5.2003
 Professor Gerhard Rein (Institut für Mathematik, Universität Wien, Austria): Stability of Newtonian Stars and Galaxies / Gravitational Collapse of Relativistic Galaxies
 12.5.2003
 RNDr. Eduard Feireisl, DrSc (MÚ AV): Global existence for the full system of the Navier-Stokes equations for a compressible viscous heat conducting fluid.
 19.5.2003
 výjimečně již od 14:00 v K1 -------------------- Professor James S. Byrnes (Prometheus Inc., Newport, USA): A Home for Wayward Mathematicians. Abstract: Přednáška je organizována Seminářem z matematické analýzy (vedoucí: J. Král, J. Lukeš, I. Netuka, J. Veselý).
 6.10.2003
 doc. ing. Tomáš Roubíček, DrSc. (MFF UK): Nestlačitelné tekuté ionizované směsi Abstract: Bude prezentován model nestlačitelné tekutiny složené z elektricky nabitých komponent interagujících se samobuzeným elektrostatickým polem a navzájem přes chemické reakce, které mohou být navíc teplotně závislé. Bude diskutována termodynamická konzistence modelu a důkaz existence slabého řešení ve dvou speciálních případech: nulového Reynoldsova čísla a konstantní teploty.
 13.10.2003
 Ing. Anna Machová, CSc. (Ústav termomechaniky AV ČR): Atomární simulace růstu defektů metodou molekulární dynamiky (MD) Abstract: Přehled problémů, které je možné technikou MD řešit (včetně výsledků z Ústavu termomechaniky), návaznosti na modely kontinua, klasickou termodynamiku a kvantovou mechaniku
 20.10.2003
 RNDr. Michal Kočvara, DrSc. (ÚTIA AV ČR): Formulace a numerické řešení problému strukturální optimalizace pomocí semidefinitního programování Abstract: Cílem přdnášky je ukázat, že semidefinitní programování (optimalizační úlohy s omezením typu maticových nerovností) tvoří vhodný rámec pro formulaci a řešení úloh strukturální (tvarové, materiálové, topologické) optimalizace tuhých těles. Na konkrétní úloze tzv. volné optimalizace materiálu s omezeními na stabilitu ukážeme výhody a těžkosti s tím spojené.
 27.10.2003
 RNDr. Jiří Kolafa, CSc. (Ústav fyzikální chemie VŠCHT): Molekulární modelování a simulace metodami Monte Carlo a molekulová dynamika. Abstract: Molekulární modelování: od kapalin k bílkovinám, konstrukce silového pole. Molekulová dynamika jako numerické řešení Newtonových pohybových rovnic. Vzorkování konfiguračního prostoru metodou Monte Carlo.
 3.11.2003
 ing. Zdeněk Brož (FJFI ČVUT): Počítačové modelování kardiovaskulárního systému Abstract: Úkolem kardiovaskulárního systému člověka je distribuce krve a tím i kyslíku a mnoha jiných životně důležitých látek. Jeho důkladná znalost nám nejen umožňuje léčit některá srdeční onemocnění, ale i lépe pochopit důsledky jeho nedostatečné funkce. Numerická simulace umožňuje studium jeho vlastností a slouží k neinvaznímu vyšetření pacienta a tudíž může být jedním z velice užitečných nástrojů pro stanovení diagnózy kardiovaskulárního onemocnění a následně doporučení nejlepšího způsobu léčby.
 10.11.2003
 ing. Michal Landa, CSc. (Ústav termomechaniky AV ČR): Vyšetřování vlastností materiálů ultrazvukem
 17.11.2003
Seminář se nekoná
 24.11.2003
 Doc. RNDr. Jiří Langer, CSc. (ÚTF MFF UK): Kosmologie a reliktní záření Abstract: Letos na jaře byly publikovány první výsledky ze sondy WMAP, které značně upřesnily naše znalosti historie vesmíru.
 1.12.2003
 Prof. RNDr. Jiří Horáček, DrSc. (ÚTF MFF UK): O integrálních rovnicích v teorii rozptylu
 8.12.2003
 SPECIÁLNÍ PŘEDNÁŠKA (18:00 K1): Prof. RNDr. Jiří Neustupa, CSc. (FSI ČVUT): Spojitá větev silných řešení Navierových-Stokesových rovnic v omezené oblasti Abstract: Některé otevřené problémy v teorii Navierových-Stokesových rovnic. Přínos a vliv profesora Nečase. Souvislost Eulerových a Navierových-Stokesových rovnic. Existence a jednoznačnost spojité větve silných řešení Eulerových a Navierových-Stokesových rovnic v omezené oblasti na časovém intervalu, jehož délka nezávisí na viskozitě.
 15.12.2003
 doc. RNDr. Jiří Souček, DrSc. (MÚ UK): Brownův pohyb, Ornsteinův-Uhlenbeckův proces a jejich kvantové analogy
 5.1.2004
 RNDr. Zdeněk Fiala, CSc. (ÚTAM AV ČR): Kinematika kontinua a nekonečně dimenzionální Riemannovy variety Riemannových metrik Abstract: Teorie konečných deformací bude vyložena z pohledu diferenciální geometrie. Zavedení metriky do prostoru deformačních tenzorů umožňuje významně rozšířit možnosti tohoto přístupu. Časovou derivaci lze pak definovat jako kovariantní derivaci a logaritmický tenzor přetvoření získá jasný geometrický význam.
 23.2.2004
 doc. RNDr. Jiří Souček, DrSc. (MÚ UK): Eulerovy rovnice - geodetiky na grupě nestlačitelných difeomorfismů I
 1.3.2004
 doc. RNDr. Jiří Souček, DrSc. (MÚ UK): Eulerovy rovnice - geodetiky na grupě nestlačitelných difeomorfismů II
 8.3.2004
 prof. RNDr. Miloslav Feistauer, DrSc. (KNM MFF UK): Nespojitá Galerkinova metoda pro simulaci stlačitelného proudění
 15.3.2004
 RNDr. Zbyněk Jaňour, DrSc. (Ústav termomechaniky ČAV): Modelování mezní vrstvy atmosféry Abstract: Pro popis procesů v nejnižší vrstvě atmosféry, v tzv. mezní vrstvě jsou navrženy pohybové rovnice v rotující soustavě souřadné, jsou diskutovány podstatné vlastnosti turbulentního proudění v atmosféře, včetně problému uzávěru a jsou zavedeny modely turbulence. Pro případ mezní vrstvy atmosféry na omezené oblasti jsou diskutovány okrajové podmínky a zavedena Boussinesquova aproximace. Na vybraných příkladech jsou demonstrovány další problémy modelování.
 22.3.2004
 prof. RNDr. Jan Kratochvíl, DrSc. (MÚ MFF UK): Bifurkace řešení rovnic krystalové plasticity a jejich fyzikální význam
 29.3.2004
 prof. Florian Theil (University of Warwick, UK): Mathematical Analysis of Single Slip Elastoplastic Microstructures Abstract: We consider rate-independent crystal plasticity with constrained elasticity and state the variational formulation of the incremental problem. For generic boundary data, even the first time-increment does not admit a smooth solution and fine structures are formed. Solutions with microstructures are constructed by forming laminates between two different deformation gradients. For the concrete case of a simple shear test it can be shown that these generalised time-discrete solutions converge to solution of the time continuous evolution problem.
 5.4.2004
 ing. Milan Jirsák, CSc. (VZLU, Letňany): Tekutinové modelování přenosových dějů v povrchové vrstvě atmosféry Abstract: Zásady simulace proudění v povrchové vrstvě atmosféry ve větrných tunelech. Měřítka a hranice podobnosti. Kvalita simulace v tunelu VZLU/KU ČVUT a možnosti aplikace. Podobnostní parametry a technika aplikačních měření, ukázky koncentračních polí komínových vleček aj.
 12.4.2004
Seminář se nekoná - velikonoční svátky
 19.4.2004
 RNDr. Tomáš Ledvinka, Ph.D. (ÚTF MFF UK): Simulace srážek černých děr Abstract: Einsteinova teorie gravitace předpověděla existenci stabilních černých děr. Astrofyzikové však pozorovali na obloze nejen projevy samotných černých děr, ale také jevy, jež si vysvětlují jako ohňostroje doprovázející srážky černých děr nebo neutronových hvězd, tedy objektů z nichž zhroucením stelární černé díry vnikají. Právě ted' se navíc rozbíhají nové přístroje, které by měly právě takové procesy zaznamenat - gravitační detektory. Srážka černých děr představuje v principu jednoduchý problém, kdy dvě černé díry splynou v jednu větší. Nelinearita Einsteinových rovnic, která zaručuje stabilitu původích i výsledné černé díry je ale také zdrojem dosud nepřekonaných potíží při hledání analytického i numerického řešení popisujícího srážku černých děr. V semináři budou popsány některé způsoby jimiž se během posledních desetiletí hledalo numerické řešení problému a problémy, které doposud zabránily nalezení uspokojivého řešení.
 26.4.2004
 Prof. Piotr Mucha (University of Warsaw, Poland): Cylindrical flows and geometrical constraint Abstract: I would like to analyze cylindrical symmetric (axial) flows in bounded domain. The motion is described by the steady Navier-Stokes equations with slip boundary conditions admitting flows across the boundary. Under a geometrical restriction on the shape of the boundary we are able to find a priori bound on the vorticity applying the maximum principle. The obtained estimate has a linear character as the standard energy bound although the boundary data are inhomogeneous. The simply connectedness of the domain is not required.
 3.5.2004
 Prof. Pablo Pedregal (Universidad Castilla - La Mancha, Ciudad Real, Spain): On the optimal design of a plate of variable thickness Abstract: In the framework of the model of Kirchhoff for symmetric plates, we seek to minimize the compliance of such a plate in terms of its pointwise thickness. The problem in a fully two-dimensional situation (which is obviously the interesting one) seems to be out-of-the-reach of current analytical techniques. Thus, some simplifications need to be imposed to start understanding the problem. One first level of simplification consists in admitting only designs (thicknesses) depending on one variable. This turns out to be a non-convex optimization problem that can be explored by using Young measures. A second level of simplification amounts to examining the one-dimensional situation. In this case, by means of a suitable variational reformulation, one can show existence of optimal solutions that can even be compute numerically by using optimality conditions in a more-or-less elementary way. In the talk, we will try to cover all of these situations.
 10.5.2004
 Professor Agnieszka Kalamajska (University of Warsaw, Poland): New geometric conditions for quasiconvex functions
 17.5.2004
 Doc. Ing. Tomáš Roubíček, DrSc., RNDr. Martin Kružík, Ph.D. (MFF UK a ÚTIA ČAV Praha): Mesoskopický model materiálu s pamětí tvaru Abstract: Bude presentován rychlostně nezávislý model martensitické transformace při velkých deformacích včetně stručného popisu numerické strategie i výsledků počítačových simulací modelového příkladu experimentu s monokrystaly.
 11.10.2004
 Prof. RNDr. Miloslav Feistauer, DrSc. (MFF UK): Interakce tuhého tělesa a tekutiny
 18.10.2004
 Doc. RNDr. Jiří Souček, DrSc. (MFF UK): Význam kvantové mechaniky v matematice
 25.10.2004
 doc. ing. Tomáš Roubíček, DrSc. (MFF UK): Rychlostně nezávislý model delaminace
 1.11.2004
 Dr. Agnieszka Swierczewska (TU Darmstadt, Germany): Large Eddy Simulation of turbulent flows: Existence of weak solutions
 8.11.2004
 Dr. Piotr Gwiazda (Universytet Warszawski, Poland): Measure-valued solutions to Savage-Hutter granular flow model
 15.11.2004
 RNDr. Zdeněk Fiala, CSc. (ÚTAM AV ČR): Objektivní časová derivace v kinematice velkých deformací jako kovariantní derivace
 22.11.2004
 Mgr. Jan Stebel (KNM MFF UK): Tvarová optimalizace pro zobecněné Navier-Stokesovy rovnice
 29.11.2004
 Mgr. Tomáš Pergler (Katedra geofyziky MFF UK): Modelování postseismických a koseismických jevů v Zemi pomoci metody konečných prvků a spektrálního rozkladu
 6.12.2004
 Mgr. Tomáš Vít (ÚT AV ČR): Vliv teplotního gradientu na proudění tekutiny podél zakřivené stěny
 13.12.2004
 Professor Gunther Peichl (University of Graz): Variational approach to shape derivatives for a class of Bernoulli problems
 20.12.2004
 Professors Jens Frehse and K.R. Rajagopal (University of Bonn and Texas A&M University, College Station): Seminář organizovaný u příležitosti nedožitých 75. narozenin prof J. Nečase
 3.1.2005
 Mgr. Vít Průša (MÚ UK): Stabilita proudení ve válcové trubici Abstract: V první části přednášky budou na příkladu jednoduchých proudění (Poiseuilleovo a Hagen-Poiseuilleovo proudění) představeny některé ze základních přístupů k problému stability proudění (energetická metoda, lineární teorie stability, lineární teorie stability s použitím pseudo-vlastních čísel) a budou stručně shrnuty výsledky dosažené aplikací těchto teorií. Druhá část přednášky bude věnována diskusi stability pulsačního Hagen-Poiseuilleova proudění. Problém bude zkoumán užitím lineární teorie stability.
 10.1.2005
 Doc. Ing. Jiří Nedoma, CSc. (Ústav informatiky AV ČR): Numerické modely pole napjatosti ve svrchních částech zemského tělesa, vliv tektoniky a čtvrtohorního zalednění Abstract: Budou uvedeny modely založené na tektonice litosferických desek a teorii kontaktních úloh ve vazko-pružnosti a vazko-plasticitě se třením.
 28.2.2005
 Prof. Dr. Carsten Cartensen (Department of Mathematics, Humboldt Unversity of Berlin): Analysis, numerics and optimization of multiphase problems.
 7.3.2005
 RNDr. Eduard Feireisl, DrSc (MÚ AV): Fluid dynamics models in astrophysics.
 14.3.2005
 Prof. RNDr. Jaroslav Haslinger, DrSc (KNM MFF UK): Aproximace a numerická realizace kontaktních úloh se třením.
 21.3.2005
 Prof. RNDr. Jiří Neustupa, CSc (MÚ AV): Stabilita stacionarniho reseni Navierovy-Stokesovy rovnice ve vnejsi oblasti.
 28.3.2005
Seminář se nekoná - velikonoční svátky
 4.4.2005
 Professor L. M. Brown (Cavendish Laboratory, Cambridge): Unifying concepts in dislocation plasticity.
 11.4.2005
 RNDr. Martin Kružík, Ph.D. (ÚTIA ČAV Praha): Oscilace a koncentrace v posloupnostech gradientu.
 18.4.2005
 Professor Jonathan J. Healey (Keele University, United Kingdom): An unusual instability with exponential growth outside a boundary layer.
 25.4.2005
 Prof. Piotr Mucha (University of Warsaw, Poland): On asymptotic structure of solutions to the Navier-Stokes equations in 2D pipe.
 2.5.2005
 Dr. Radan Sedláček (Fakultaet fuer Mashinenwesen, TU-Muenchen): Variační formulace problému vzniku mikrostruktury v plasticitě.
 9.5.2005
 RNDr. Dalibor Pražák, PhD. (KMA MFF UK): O dimenzi atraktoru pro některé rovnice nenewtonských tekutin Abstract: Zabýváme se asymptotickým (pro velké časy) chováním homogenní nestlačitelné tekutiny nenewtonského typu, kde zobecněná viskozita závisí na normě symetrického gradientu a případně na tlaku. Všimneme si podrobněji (1) metody Lyapunovských exponentů a (2) metody trajektorií coby dvou možných přístupů k otázce konečnosti dimenze atraktoru, včetně explicitních odhadů.
 16.5.2005
Seminář se nekoná (od 13:00 obhajoby a SZZ oboru Matematické modelování)
 23.5.2005
 Prof. Dr. Francesco Bassi (Universita di Bergamo, Italy): High-Order Discontinuous Galerkin Solution of the Compressible Navier-Stokes Equations.
 10.10.2005
 Prof. Dr. Fredi Troeltzsch (TU Berlin, Germany): Regularization techniques for optimal control problems with state constraints Abstract: In important applications of optimal control to partial differential equations, inequality constraints are imposed on the state of the control system. For instance, in optimal heating problems the temperature must obey certain bounds (steel production, crystal growth, local hyperthermia in tumor therapy). The Lagrange multipliers for with these inequality constraints are in general Borel measures that occur in the associated adjoint PDE. By a Lavrentiev regularization, measures can be avoided by the construction of more regular Lagrange multipliers. In the talk, this technique is explained and applied to the numerical analysis of state-constrained optimal control problems. Some practical applications are presented.
 17.10.2005
 Doc. RNDr. Josef Málek, CSc. (MÚ UK): Nestlačitelné materiály rychlostního typu s materiálovými koeficienty, které závisí na tlaku a rychlosti smyku Abstract: Biologické či geologické tekutiny, gely a některé potraviny lze modelovat jako nehomogenní nestlačitelné (vazkopružné) materiály rychlostního typu, přičemž materiálové koeficienty mohou záviset na rychlosti smyku a tlaku (i teplotě). Cílem přednášky je odvození vhodného termodynamicky konsistentního modelu. Přednáška je založena na společných publikacích s K.R. Rajagopalem.
 24.10.2005
 Professor Francesco Mollica (Universite di Ferrara, Italy): Modelling and testing of polymeric foams in tension and compression Abstract: Polymeric foams are interesting materials in that they can undergo large deformations, in large part reversible, are compressible and display a markedly different behaviour in tension and compression. The reason for this behaviour is to be looked for in the microstructure: in compression the cell walls and struts composing the microstructure buckle, thus the material is able to deform at a very low, almost constant applied external stress. In tension, on the other hand, the cells walls and struts are being pulled, thus exhibiting a stiffer stress - strain curve. Continuum modelling of the mechanical behaviour of foams has been undertaken by many researchers (e.g., recently, Murphy and Rogerson, 2002; Attard and Hunt 2004), who have used compressible hyperelasticity to fit the experimental data available in the literature. These models are mainly compared only with experiments in compression or only with experiments in tension. It is proposed in this work to test the material behaviour of a commercial polyurethane foam both in tension and in compression and after that to find an appropriate model. In order to capture the difference between tension and compression it is convenient to use the implicit constitutive equation approach developed by Rajagopal (2005).
 31.10.2005
 Dr. Radan Sedláček (Fakultaet fuer Mashinenwesen, TU-Muenchen [17:20 - 18:20]): Model plastické deformace založený na pohybu spojitě rozložených dislokací Abstract: Zakladem navrhovaneho modelu plasticke deformace je klasicka teorie spojite rozlozenych dislokaci. K tomu, aby bylo mozno formulovat pohybovou rovnici pro dislokace, evolucni rovnice pro jejich hustotu a orientaci, a z techto odvodit rychlost plasticke deformace, je treba klasickou teorii modifikovat. Vysledny konstitutivni model ve spojeni s rovnicemi mechaniky kontinua je vhodny k simulaci plasticke deformace na mikroskopicke urovni, nebot obsahuje vlastni charakteristickou delku, ktera umoznuje reprodukovat experimentalne pozorovanou zavislost plasticke odezvy na rozmerech materialu. Pokud se tyce numerickeho reseni, zda se, ze jista analogie Lagrangeovskeho popisu je pro vysledne rovnice prirozenejsi a numericky stabilnejsi nez puvodne uzivany Eulerovsky pristup.
 7.11.2005
 Dr. Joerg Wolf (Humboldt Universitat Berlin, SRN): Existence of Weak Solutions to the Equations of Non-stationary Motion of Non-Newtonian Fluids with Shear dependent Viscosity
 14.11.2005
 Dr. Lars Diening (University of Freiburg): Finite elements for the p-Stokes system Abstract: We study the approximation error of the Finite-Element solution to the $p$-Stokes System. As auxiliary result we will generalize the interpolation theory of Finite Elements to the Sobolev-Orlicz spaces. The method is easy but very general and works for almost all standard Finite Elements.
 21.11.2005
 Professor Johannes Zimmer (University of Bath, Great Britain): On dynamic models of phase transitions Abstract: Travelling waves in a one-dimensional chain of atoms will be investigated. The aim is to allow for nonconvex energy densities, which occur in the theory of phase transforming solids, such as martensitic crystals. The existence of solitary waves with a prescribed asymptotic strain will be shown under certain assumptions on the asymptotic strain and the wave speed. Connections to previous results will be discussed.
 28.11.2005
 Ing. Hanuš Seiner (Ústav termomechaniky AV ČR, Praha, externí doktorand katedry materiálů FJFI ČVUT): Nelineární akustika materiálů s martenzitickou transformací Abstract: Tématem přednášky je matematický popis chování materiálů s martenzitickou transformací, konkrétně slitin s tvarovou pamětí, prostřednictvím mechaniky nelineárních vln. Martenzitická transformace je bezdifuzní fázová transformace prvního druhu, při které vznikají z mateřské austenitické fáze smykovým mechanismem různé varianty dceřinné fáze martenzitické. Pohyb fázového rozhraní materiálem pak lze interpretovat jako solitární vlnu (soliton). Na základě této interpretace je možno zkoumat podmínky existence či mobilitu fázového rozhraní v závislosti na teplotě a na vnějším aplikovaném napětí. V přednášce budou tyto postupy demonstrovány na jednoduchém diskrétním modelu se dvěma stupni volnosti (Maugin 1990) a výsledky potom kvalitativně porovnány jak s pokročilejšími termodynamickými modely (např. Truskinovsky 2003), tak s experimentálními výsledky.
 5.12.2005
 Prof. Dr. Mária Lukačová (TU Hamburg-Harburg): Numerical modelling of shallow flows on rotating plane including topography effects. Abstract: Typical examples of shallow flows are rivers with their flood plains, flows in lakes generated by wind blows as well as propagation of tsunamis in oceans. The goal of this contribution is to present results of numerical modelling of the shallow water equations by higher order finite volume schemes which belong to the class of genuinely multidimensional well-balanced schemes. In particular, we will concentrate on the so-called finite volume evolution Galerkin (FVEG) method. A special attention need to be payed to approximate source terms. The aim is to construct such a method that computes exactly equilibrium states, i.e. stationary states. In particular we can prove that our method preserves exactly steady stationary states (the so-called lake at rest state) as well as stationary jets in the rotational frame.
 12.12.2005
 Prof. Dr. Christian Schmeiser (University of Vienna): Existence and stability of kinetic profiles for shock waves of scalar hyperbolic conservation laws Abstract: Kinetic transport equations, whose macroscopic limits are hyperbolic conservation laws, can be expected to possess travelling wave solutions regularizing shock waves of the latter. Some recent results on the existence and dynamic stability of these kinetic shock profiles will be discussed. In particular, BGK kinetic models for general conservation laws as well as a model for electron flow in semiconductor crystals will be considered.
 19.12.2005
 VB Abstract:
 2.1.2006
 Dr. Jaroslav Hron (University of Dortmund): A monolithic multigrid FEM solver for fluid structure interaction and numerical benchmarking Abstract: A monolithic, fully coupled approach using the ALE formulation is used to discretize and solve the problem of time dependent interaction between an incompressible viscous fluid and an incompressible elastic solid. For the discretization the FEM method is used while the solver is based on approximate Newton method combined with multigrid solver for the solution of the linear systems. To investigate accuracy, performance and efficiency of the solver a simple problem configuration is introduced as a benchmark.
 9.1.2006
 Prof. Dr. Michael Hinze (Technical University Dresden): PDE constrained optimization I Abstract: This is a first lecture of the course that continues on Tuesday Jan 10, 15:40 in K4 by its second part, and finishes on Thursday Jan 12, 14:00 in K3.
 27.2.2006
 Michal Beneš, Eduard Feireisl, Josef Málek NCMM: Centrum Jindřicha Nečase pro matematické modelování Abstract: Cílem tohoto nestandartního semináře (valné hromady) je přiblížit poslání a cíle "Nečasova Centra pro matematické modelování", shrnout obsahovou i finanční stránku projektu, strukturu centra a především otevřít prostor pro vědeckou činnost centra.
 6.3.2006
 Prof. Piotr Mucha (University of Warsaw): Stefan problem with Gibbs-Thomson correction Abstract: I would like to investigate the quasistationary Stefan problem with Gibbs-Thomson correction. The main subject will be the proof of existence of unique solutions for arbitrary initial surface. The system is equivalent to the parabolic equation of the third order, hence a suitable approach is required to obtain the optimal result from the regularity point of view. The considerations will be done in the L_p-spaces.
 13.3.2006
 Dr. Petr Knobloch, Ph.D. (KNM MFF UK): Numerické řešení rovnic konvekce-difúze metodou konečných prvků Abstract: If convection strongly dominates diffusion, the solutions of convection-diffusion equations typically contain interior and boundary layers and solutions of Galerkin finite element discretizations exhibit in general unwanted spurious oscillations. To enhance the stability and accuracy of these discretizations, various stabilization strategies have been developed during the past three decades. One of the most efficient procedures is the streamline upwind/Petrov-Galerkin (SUPG) method developed by Brooks and Hughes. Unfortunately, the SUPG method does not preclude spurious oscillations localized in narrow regions along sharp layers. Although these oscillations are usually small in magnitude, they are not permissible in many applications. Therefore, various terms introducing artificial crosswind diffusion in the neighborhood of layers have been proposed to be added to the SUPG formulation in order to obtain a method which is monotone or which at least reduces the local oscillations. This procedure is referred to as discontinuity capturing (or shock capturing). The literature on discontinuity-capturing methods is rather extended and the various numerical tests published in the literature do not allow to draw a clear conclusion concerning their advantages and drawbacks Therefore, our aim is to provide a review of discontinuity-capturing methods and to compare these methods computationally by means of several test problems.
 20.3.2006
 Prof. Dr. Wolfgang Wendland (University of Stuttgart): Boundary Element Methods: Boundary Integral Equations and Variational Problems Abstract: This is the first lecture of the short course that continues on Tuesday March 21, 15:45 (at K2) by the second part "Finite Elements on the Boundary" and finishes on Thursday, March 23, 14:00 (at K3) by the lecture "Efficient Solution Algorithms and Some Industrial Applications".
 27.3.2006
 Prof. RNDr. Jan Malý, DrSc. (KMA MFF UK): Problémy s řetízkovým pravidlem v teorii ODR a PDR Abstract: Otázka za jakých předpokladů platí v nějakém smyslu vzorce o derivování složené funkce, vyvstává v teorii soustav obyčejných diferenciálních rovnic, v DiPerna-Lionsově teorii toků (flows), teorii Hamilton-Jacobiho rovnic i v zákonech zachování. Konkrétně, derivujeme výraz $(h\circ u) B$, kde $h\in C^1$, $u\in L^{\infty}$ a $B\in BV$.
 3.4.2006
 Prof. Dr. Barbara Wohlmuth (University of Stuttgart): Mortar discretizations and their applications Abstract: This is the first lecture of the short course that continues on Tuesday April 4, 15:45 at K2 by the second part and finishes on Thursday, April 6, 14:00 at K3.
 10.4.2006
 doc. ing. Tomáš Roubíček, DrSc. (MFF UK): Ionizované nestlačitelné směsi Abstract: Formulace modelu nestlačitelných chemicky reagujících ionizovaných směsí a důkaz existence řešení jak pro newtonovský případ tak pro speciální nenewtonovské případy.
 17.4.2006
Seminář se nekoná - Velikonoce
 24.4.2006
 Prof. RNDr. Jan Malý, DrSc. (KMA MFF UK): Problémy s řetízkovým pravidlem v teorii ODR a PDR - část II Abstract: Otázka za jakých předpokladů platí v nějakém smyslu vzorce o derivování složené funkce, vyvstává v teorii soustav obyčejných diferenciálních rovnic, v DiPerna-Lionsově teorii toků (flows), teorii Hamilton-Jacobiho rovnic i v zákonech zachování. Konkrétně, derivujeme výraz $(h\circ u) B$, kde $h\in C^1$, $u\in L^{\infty}$ a $B\in BV$.
 1.5.2006
Seminář se nekoná - státní svátek
 8.5.2006
Seminář se nekoná - státní svátek
 15.5.2006
 RNDr. Antonin Slavik, Ph.D. (KDM MFF UK): An introduction to product integration Abstract: Product integral might be considered as a multiplicative analogy of the classical additive integral. The notion is useful especially in the field of ordinary differential equations, but has also applications in mathematical physics, probability and statistics. The presentation will take less than half an hour.
 22.5.2006
 Dr. Soeren Bartels (Humboldt Universitaet zu Berlin, Germany): Approximation of Harmonic Maps -- Gradient Flow Approaches vs. Iterative Minimization Abstract: Harmonic maps are stationary points of the Dirichlet energy among vector fields with values in the unit sphere. Owing to the nonconvex constraint, harmonic maps are non-unique and fail to admit higher regularity properties. Moreover, the constraint prohibits the use of standard tools for their numerical approximation. In this talk we discuss stability and weak convergence of three numerical approaches to the reliable approximation of harmonic maps.
 29.5.2006
 Professor Giovanni Pallotti, Dr., Ing. (Mech. Eng.), Dr.(Phys.) (University of Bologna): Mechanical Properties of Great Arterial Wall and Clinical Implication
 2.10.2006
15:40
 Prof. Luisa Consiglieri (Department of Mathematics FCUL, Lisboa, Portugal): A (p-q) coupled system in elliptic nonlinear problems with nonstandard boundary conditions
17:20
Introduction of the guests and members of the Nečas Center for Mathematical Modeling
 9.10.2006
INAUGURAL SEMINAR OF the Nečas Center
 16.10.2006
15:40
 Prof. Dr. Dietmar Kröner (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany): Well balanced schemes for conservation laws Abstract: There are many numerical schemes for hyperbolic conservation laws, which have some problems, if there is a source term and if a stationary solution has to be computed. There are many ideas to overcome this problem. One of them goes back to Greenberg et al. and needs a special structure of the source term. We will present this idea and extend it to problems in multi space dimensions and to systems with nonconservative source terms in 1D. Furthermore we will give a convergence proof for this method, if applied to the initial boundary value problem for scalar conservation laws in 1D. In that case the definition of entropy process solutions for initial boundary value problems will be used.
 23.10.2006
15:40
 Prof. Dr. Herbert Amann (Mathematical Institute University of Curych, Curych, Switzerland): Parabolic equations on singular manifolds Abstract: We report on a new, rather simple and flexible approach to the study of linear and nonlinear parabolic equations on manifolds with corners, cusps, edges etc. The basic technique is illustrated for reaction-diffusion equations on a manifold with a cusp or a cuspoindal wedge.
17:20
 Prof. Dorin Bucur (Département de Mathématiques Université de Metz, Metz, France): Γ-convergence and domain dependence of solutions of PDE's (part 1 of 4)
 30.10.2006
15:40
 Prof. Dorin Bucur (Département de Mathématiques Université de Metz, Metz, France): Γ-convergence and domain dependence of solutions of PDE's (part 3 of 4)
17:20
 Prof. Frank Ettwein (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany): Micropolar electrorheological fluids: existence of weak solutions in a degenerate stationary case
 6.11.2006
15:40
 Prof. Ziemmer (Dep. of Mathematical Sciences, University of Bath, UK): On waves in discrete models of elasticity and plasticity
17:20
 Prof. Pavol Quittner (Dep. of Applied Mathematics and Statistics Comenius University, Bratislava, Slovakia): Qualitative theory of semilinear parabolic equations and systems (part 9 of 12)
 13.11.2006
15:40
 Prof. Konstantina Trivisa (Dep. of Mathematics University of Maryland, College Park MD, USA): Hyperbolic Systems of Conservation Laws: Wellposedness and Qualitative Behavior of the Solutions
17:20
 Prof. Pavol Quittner (Dep. of Applied Mathematics and Statistics Comenius University, Bratislava, Slovakia): Qualitative theory of semilinear parabolic equations and systems (part 11 of 12)
 20.11.2006
15:40
 Prof. Dr. Werner Varnhorn (Fachbereich für Mathematik und Informatik Universität Kassel, Kassel, Germany): The Navier Stokes equations with Lagrangian differences 1 Abstract: The steady motion of a viscous incompressible fluid in a bounded domain can be described by the nonlinear Navier Stokes equations (N). We describe an approximation method for (N) by using Lagrangian differences. The method leads to a sequence of unique approximate solutions containing a convergent subsequence with limit function v solving (N) weakly.
17:20
 Prof. Dr. Werner Varnhorn (Fachbereich für Mathematik und Informatik Universität Kassel, Kassel, Germany): The Navier Stokes equations with Lagrangian differences 2 Abstract: Replacing the nonlinear convective term in the Navier Stokes equations (N) by central Lagrangian differences we obtain an energy conserving approximation. The resulting regularity properties of the limit function v (compare Part 1) are sufficient for the limit procedure in the nonlinear term. Some details of the proofs are carried out.
 27.11.2006
15:40
 Ing. R. Liska (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha): Arbitrary Lagrangian Eulerian (ALE) Method for Laser Plasma Simulations
16:10
 Ing. T. Oberhuber (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha): Numerical scheme for the Willmore flow
17:00
 Ing. R. Straka (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha): Model of coal combustion in a furnace
17:30
 Ing. V. Minárik (Research Team3, Faculty of Nuclear Science of the Czech Technical University, Praha): Mathematical Model of Dislocation Dynamics
 4.12.2006
15:45
 Prof. Dr. Robert Finn (Stanford University): The capillarity problem for compressible fluids Abstract: Current literature on fluid configurations under capillary attractions generally is based on postulates introduced in 1830 by Gauss. By neglecting bulk energy variations within the fluid, these postulates lead to an essentially geometrical problem. I will present an example indicating that bulk energy terms can indeed be significant, and I will derive and examine the equations obtained by taking account of energy changes imposed by fluid compressibility. The formal character of the mathematical problem then changes, but remains geometrical. Solutions of the new equations share some striking features that occur with the classical equations, but also new exotic behavior appears that was previously not encountered. Experimental tests of the predictions may be feasible.
17:15
 Prof. Dr. Friedemann Schuricht (Universität zu Köln): A new mathematical foundation for contact interactions in continuum physics Abstract: The investigation of contact interactions, such as traction and heat flux, that are exerted by contiguous bodies across the common boundary is a fundamental issue in continuum physics. However, the traditional theory of stress established by Cauchy and extended by Noll and his successors is insufficient for handling the lack of regularity in continuum physics due to shocks, corner singularities, and fracture. The talk presents a new mathematical foundation for the treatment of contact interactions. Based on mild physically motivated postulates, which differ essentially from those used before, the existence of a corresponding interaction tensor is established. While in earlier treatments contact interactions are basically defined on surfaces, here contact interactions are rigorously considered as maps on pairs of subbodies. This allows the action exerted on a subbody to be defined not only, as usual, for sets with a sufficiently regular boundary, but also for Borel sets (which include all open and all closed sets). In addition to the classical representation of such interactions by means of integrals on smooth surfaces, a general representation using the distributional divergence of the tensor is derived. In the case where concentrations occur, this new approach allows a more precise description of contact phenomena than before.
 11.12.2006
15:45
 Dr. Lars Diening (University of Freiburg, Germany): Convergence of Adaptive Finite Element Methods for the p-Laplace Abstract: We study adaptive finite element methods for the $p$-Laplacian Equation using piecewise linear, continuous functions. The error is measured by means of the quasi-norm of Barrett and Liu. We provide residual based error estimators without a gap between the upper and lower bound. We show linear convergence of the algorithm which is similar to the one of Morin, Nochetto, and Siebert. Moreover, we show that the algorithm produces (almost) optimal meshes with respect to the degress of freedom. This extends the results of Stevenson to the non-linear case. All results are obtained without extra marking for the oscillation.
17:15
 Dr. Giuseppe Tomassetti (University of Rome, Italy): Derivation of the Reissner-Mindlin plate theory from Gamma convergence
 18.12.2006
16:00
 Prof. RNDr. Jaroslav Kurzweil, DrSc. (MU AV ČR): Matematikovy vzpomínky na čtyřicátá až šedesátá léta Abstract: Přednáška bude doplněna o vystoupení kvarteta violončelistů a zpěv písní vánočních
 8.1.2007
15:45
 RNDr. Eduard Feireisl, DrSc. (Mathematical Institute AS CR, Prague): Fluid dynamics problems on domains with rapidly oscillating boundaries: Is it always optimal when Young measures reduce to Dirac masses?
 19.2.2007
15:40
 Prof. A. Novotny (Universite du Sud Toulon-Var (France)): Low Mach number limits to the complete Navier-Stokes-Fourier system
 26.2.2007
15:40
 Prof. Dr. Anna-Margaret Saendig (IANS, Univeritaet Stuttgart, Germany): Variational methods for nonlinear boundary value problems in elasticity
17:20
 Prof. Antonín Novotný (Universite du Sud Toulon-Var, France): Low Mach number limits to the complete Navier-Stokes-Fourier system
 5.3.2007
15:40
 Prof. Dr. Ch. Grossmann (TU Dresden, Germany): Domain decomposition methods
17:20
 Prof. Dr. R. Farwig (TU Darmstadt, Germany): From the Theory of Very Weak Solutions to Regularity of Weak Solutions of the Instationary Navier-Stokes System Abstract: The three lectures deal with the theory of very weak solutions to the stationary and instationary Stokes and Navier-Stokes equations. Very weak solutions define a new class of solutions with no differentiability and not necessarily finite energy, but with uniqueness properties. The aim of this series of lectures is to apply this theory to questions of regularity of weak solutions of the Navier-Stokes equations in the sense of Leray-Hopf and to prove local or even global in time regularity beyond Serrin s condition.
 12.3.2007
15:40
 Doc. RNDr. L. Pick, DrSc. (KMA MFF UK): Optimal Sobolev Embeddings and Interpolation
17:20
 Dr. J. Schneider (NCMM, Prague): Function Spaces of Varying Smoothness
 19.3.2007
15:40
 Dr. C. Schwarz (TU Muenchen, Germany): Continuum dislocation-based plasticity: numerical implementation and short-range interactions Abstract: In this talk, the latest advances on the continuum dislocation-based model of plastic deformation will be presented, both concerning the numerical implementation and the modelling. In this deterministic model, the description of evolving fields of curved dislocations is embedded in the rigorous framework of small strain continuum mechanics. The model explains the size-dependent plastic response of crystalline materials at the scale of micrometers.
17:20
 Dr. D. Wachsmuth (Institute of Mathematics, TU Berlin, Germany): Optimal control of the unsteady Navier-Stokes equations Abstract: The talk is concerned with the study of optimal distributed control problems for the non-stationary Navier-Stokes equations. The control $u$ in our problem is vector-valued. Thus, box-constraints are not the only possible choice of a control constraint. Therefore, we consider pointwise convex control constraints of the form $u(x)in U(x)$, where $U$ is an set-valued mapping with convex and closed images. We present necessary as well as sufficient optimality conditions for that general type of constraint. The first-order necessary conditions imply a representation of locally optimal controls by projections, a fact which leads to new regularity results. In the presence of box-constraints and under the assumption of sufficient optimality conditions, locally optimal controls are stable with respect to small perturbations. This stability result directly gives the local quadratic convergence of the SQP-method for our optimal control problem. The talk closes with an outlook on open questions, which are connected to regularity issues of the Navier-Stokes system.
 26.3.2007
15:40
 Prof. Dr. Dietmar Kröner (Dep. of Applied Mathematics of University Freiburg, Freiburg, Germany): Phase transitions for liquid vapor flows Abstract: Vapor together with liquid phases occur in many applications like cavitation problems, two phase flows in micro devices, cooling and boiling processes and breakup of liquid jets. Since e.g. turbine blades and ship propellers can be destroyed by cavitation this research is of high industrial interest. Both phases are transported by the flow and undergo phase transitions. The governing mathematical equations are expressed by the basic conservation laws for mass, momentum (, and energy) together with suitable equations of state for all phases. Additionally, for the mass transfer across the phase boundaries special treatment is necessary. A very important issue is the simultaneous treatment of phase transition and compressible flow. Up to now the dynamics of pure phase transition (free boundary value problems, Stefan problems, Cahn-Hilliard problem, Landau-Ginzburg equation etc.) as well as the dynamics of compressible (viscous) flow have been studies very extensively but separately. The most basic experiment on liquid vapor flows considers the dynamics of a single vapor bubble in a container filled with liquid. If the outer pressure of the liquid is decreased to vapor pressure then the liquid vapor interface starts to move: We have a dynamic phase boundary with mass transfer. In more complex settings this occurs during the process of cavitation. Lord Rayleigh discovered that pressure waves emitted during the process of cavitation near rigid walls may damage the walls. This can be observed on the surface of ship propellers. Mathematical models for liquid vapor phase transitions can be divided into two classes: diffuse interface and sharpe interface models. The first class takes into account the internal structure of a phase boundary and resolves it as a steep but continuous transition. In the second class phase boundaries are discontinuous transitions of the thermodynamical variables. We will consider the mathematical model which is given by the compressible Navier-Stokes-Korteweg equations which consists of the classical Navier_Stokes equations and additional higher order derivatives of the density on the right-hand side of the momentum equations, multiplied by a small parameter $lambda$. In this lectures we will present an overview of theoretical results concerning existence, the interface conditions for the pressure in the limit if $lambda$ tends to zero and about some numerical experiments.
 2.4.2007
15:40
 MUDr. Vladimir Prochoda (FTN Krc): Modelovani kancerogeneze bunky kolorektalniho karcinomu Abstract: Strucny popis geneze kolorektalniho karcinomu - vyvoj, stadia a casova osa. Charakterizace 3 modelu pro popis chovani kancerogeneze kolorektalniho karcinomu v ruznych stadiiich ( 1/ kancerogeneze bunky kolorektalniho karcinomu 2/ vyvoj kolorektalniho karcinomu do urovne karcinoma in sinu 3/ distribucni model pro distribuci ndoru do kompartmentu) - vztah a prolinani techto stadii. Pozornost bude venovana predevsim na exploataci moznosti matematickeho nebo jinak abstrahovaneho modelovani s naslednou aplikaci do tvaru enginu, ktery by bylo mozno virtualne zpracovavat na PC. Hlavn podminkou je vytvorit ciselne rady pro nezavisle promenne /ovlivnujici faktory geneze/ a zavisle promenne /ukazatele geneze/. Problematika se bude tykat i vytvoreni formulaci pro zpetne vazby procesu.
 9.4.2007
Seminář se nekoná - Velikonoce
 16.4.2007
15:40
 Prof P. Podio-Guidugli (Dipartimento di Ingegneria Civile, Universita di Roma, Italy): Remarks on the notion of aggregation state for complex materials Abstract: In standard continuum mechanics, a material body is termed simple' if its mechanical response depends only on the history of its deformation gradient. As to their aggregation state, simple materials are sorted into solids and fluids according to a well-known algebraic criterion proposed by W.Noll. There is no such criterion for complex' (i.e., not simple) materials. In this talk, I shall try and propose one, based on certain specifications of the internal working.
 23.4.2007
15:40
 Dr. A. Timofte (Institute of Mathematics, Romanian Academy, Bucharest): Two-scale homogenization for evolutionary variational inequalities Abstract: This topic (subject of a joint work with Alexander Mielke) is devoted to the two-scale homogenization for a class of rate-independent systems described by the energetic formulation or equivalently by an evolutionary variational inequality. In particular, we treat the classical model of linearized elastoplasticity with hardening. The associated nonlinear partial differential inclusion has periodically oscillating coefficients, and the aim is to find a limit problem for the case that the period tends to 0.
17:20
 Dr. Jonathan Healey (Department of Mathematics, Keele University, Keele, United Kingdom): Destabilizing fluid flows by confinement
 30.4.2007
Seminář se nekoná
15:40
 No program for this date.
 7.5.2007
15:40
 prof. Dr. P. J. Rabier (Dep. of Mathematics, University od Pittsburgh, USA): Degree theory for nonlinear Fredholm mappings of index 0 (lecture 1 of 5) Abstract: This mini-course will discuss the Fredholm and related properties of partial differential operators on unbounded domains and their applications to linear and nonlinear PDEs. The course is divided in 5 lectures, briefly described below. Since most technical details will not be addressed during the lectures due to time limitation, a list of relevant references dealing with such details will be provided with each lecture. 7.5. Lecture 1: "Degree theory for nonlinear Fredholm mappings of index 0" 9.5. Lecture 2: "Fredholm and properness properties of elliptic operators on R^N" 28.5. Lecture 3: "Nonlinear problems with infinitely many solutions" 29.5. Lecture 4: "Decay transference and applications" 30.5. Lecture 5: "The index of evolution operators"
17:20
 Prof. Jan Sokolowski (Laboratoire de Mathmatiques, Universite Henri Poincare Nancy I, France): Shape optimization for spectral problems - singular boundary perturbations Abstract: In a joint research with S.A. Nazarov we perform the asymptotic analysis of eigenvalues and eigenfunctions of elliptic spectral problems with respect to singular perturbations of small size, in the form of cowerns, boundary cracks and knops. The asymptotics are justified by the method of compound asymptotic expensions.
 14.5.2007
15:40
 no program for this date
 21.5.2007
15:40
 Prof. Dr. Torsten Linss (TU Dresden, Germany): Parameter robust methods for systems of singularly perturbed problems
17:20
 Dr. Soeren Bartels (Humboldt-Universitaet zu Berlin, Germany): Aspects in the Modelling, Analysis, and Simulation of Thermoviscoplasticity at Small Strains Abstract: Materials that undergo plastic deformations dissipate mechanical energy into heat. Then, possible changes in temperature influence, in turn, the yield stress which determines the threshold for plastic slip behaviour. In this talk, a simple mathematical model at small strains is proposed and theoretical aspects in the proof of existence of weak solutions are discussed. In particular, sophisticated estimates for the temperature variable are required in order to pass to the limit of Galerkin approximations. Implementation issues such as necessity of numerical integration, usage of weakly acute triangulations, and treatment of a non-smooth potential are adressed. Preliminary illustrative numerical experiments will be shown. This is joint work with Tomas Roubicek.
 28.5.2007
16:15
 prof. Dr. P. J. Rabier (Dep. of Mathematics, University od Pittsburgh, USA): Nonlinear problems with infinitely many solutions (lecture 3 of 5) Abstract: This mini-course will discuss the Fredholm and related properties of partial differential operators on unbounded domains and their applications to linear and nonlinear PDEs. The course is divided in 5 lectures, briefly described below. Since most technical details will not be addressed during the lectures due to time limitation, a list of relevant references dealing with such details will be provided with each lecture. 7.5. Lecture 1: "Degree theory for nonlinear Fredholm mappings of index 0" 9.5. Lecture 2: "Fredholm and properness properties of elliptic operators on R^N" 28.5. Lecture 3: "Nonlinear problems with infinitely many solutions" 29.5. Lecture 4: "Decay transference and applications" 30.5. Lecture 5: "The index of evolution operators"
 18.6.2007
15:40
 Lecture room K1 Doc. RNDr. Josef Malek, CSc. (Mathematical Institut, Charles University, Prague): Blood as an example of non-Newtonean material Abstract: The aim of this talk is to recall basic facts concerning non-Newtonean fluid mechanics, and to illustrate why the blood when considered as a single continuum can be modeled as a viscoelastic shear thinning incompressible fluid.
16:45
 Dr. Frederic Weller (IWR, Universitaet Heidelberg, Germany): Thrombosis & Hemostasis (I): Biology & kinetic considerations Abstract: Hemostasis is responsible to stem blood loss after injury by platelet plug formation. Although being life essential, a major part of deaths in the western society is due to thrombotic events provoked by disorders of the hemostatic system. Therefore, a better understanding of the underlying mechanisms is needed. The first talk presents the biological background and focuses on the kinetics (without taking flow into account). The mechanisms of platelet adhesion/aggregation and the chemical processes are explained in quite detail, the latter both from a cascade and from a cell-based view. Then, the ODE-model of Kenneth Mann serves to study feedback mechanisms, threshold behavior and impairement of thrombin production in the bleeding disorder hemophilia. These findings help to understand hemostatic tests.
17:50
 MUDr. Radek Chabiniok (IKEM, Prague): Thrombosis: A radiological point of view Abstract: The objective of the talk is to show a few practical examples of radiological techniques used in diagnostics of diseases affecting blood vessels and complications of these diseases. Images such as pulmonary embolism acquired by computerized tomography, artery stenoses observed during angiographicexaminations, the nonviable fibrous scar after the myocardial infarction acquired by magnetic resonance imaging will be presented.
 7.9.2007
10:00
Prof. K.R. Rajagopal
(Texas A&M University, College Station, USA):
Thermodynamics of Materials Undergoing Dissipative Processes
Abstract:

## different date and place: this FRIDAY

at UI AV CR, Pod Vodarenskou vezi 2, Praha 8, room c. 318 metro C; tram 10,17,24; bus 103,145,156,177,186,187 - Ladvi, see. SEMINAR Oddeleni vypocetnich metod
 8.10.2007
15:30
RNDr. Eduard Feireisl, DrSc.
(Mathematical Institute, AS CR):
Mathematical theory of multicomponent reactive flows
Abstract: Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

17:00
Doc. RNDr. Martin Kruzik, PhD.
(Institute of Information Theory and Automation, AS CR):
Gamma-convergence methods and applications
Abstract: Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

18:15
Prof. Alexander G.Ramm
(Department of Mathematics, Kansas State University, USA):
Creating materials with desired refraction coefficient
Abstract: A method is given for calculation of a distribution of small impedance particles, which should be embedded in a bounded domain, filled with material with known refraction coefficient, in order that the resulting new material would have a desired refraction coefficient. The new material may have some desired wave-focusing properies. For example, it can scatter plane wave mostly in a fixed solid angle. The inverse scattering problem with scattering data given at a fixed wave number and at a fixed incident direction is formulated and solved.

Part of workshop Analysis of Multiphase Problems

### place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha

 15.10.2007
15:40
 Prof. Matthieu Hillairet (Laboratoire MIP, Universite Paul Sabatier, Toulouse): Problem of collision between solid bodies in a viscous fluid Abstract: In the last decade, several studies in fluid-structure interactions showed that collisions between solid bodies in a fluid raise numerous difficulties in the mathematical treatment of such models. In my talk, I shall detail these difficulties and recent results when considering an incompressible fluid.
17:15
 Prof. em. H. Amann, Dr. Dr. h. c. (Institut fur Mathematik, Universitat Zurich): Maximal regularity for parabolic systems in weak settings (lecture no. 3)
 22.10.2007
15:40
 Prof. Bodo Werner (Fachbereich Mathematik, Uni Hamburg, Germany): Microscopic Car Following Traffic models - Road works and macroscopic observations Abstract: here
17:15
 Prof. em. H. Amann, Dr. Dr. h. c. (Institut fur Mathematik, Universitat Zurich): Maximal regularity for parabolic systems in weak settings (lecture no. 5)
 29.10.2007
15:40
 Prof. Joachim Naumann (Humboldt Universitat, Berlin): On the Existence of Weak Solutions to the Equations of Stationary Motion of Perfectly Plastic Fluids Abstract: abstract (pdf)
 5.11.2007
15:40
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 1 of 6)
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 2 of 6)
 12.11.2007
15:40
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University, Prague): Rate independent processes in viscous solids and their thermodynamics Abstract: So-called generalized standard solids (of Halphen-Nguen type) involving also activated typically rate-independent processes such as plasticity, damage, or phase transformations, will be described as a system of a force-equilibrium equation and variational inequality for internal parametr variable. Various definitions of weak solutions will be examined, especially from the viewpoint of ability to combine rate-independent processes and other rate-dependent phenomena, as viscosity or inertia. If those rate-dependent phenomena are suppressed, then the system becomes fully rate-independent and then the concept of the so-called energetic solution fully applies. In general case, compromises are needed in definitions, in data qualification, and in results, too. Eventually, thermodynamically consistent coupling with temperature and (inevitably rate-dependent) heat transfer will be scrutinized, too.
 19.11.2007
15:40
 Ing. Miroslav Sedlacek, CSc. (Stavebni fakulta, CVUT): Zakladni parametry odvalovaciho principu Abstract: This lecture will be presented in Czech language.
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 5 of 6)
 26.11.2007
15:40
 Doc. RNDr. Josef Malek, CSc. DSc. (Mathematical Institute of Charles University, Prague): On unsteady flows of Fluids with Pressure, Shear-rate and Temperature Dependent Material Moduli, that slip at solid boundaries Abstract: We rigorously investigate the mathematical properties of unsteady three-dimensional internal flows of incompressible fluids with pressure, shear-rate and temperature dependent viscosity and heat conductivity. The model is expressed through a system of partial differential equations representing the balance of mass, the balance of linear momentum, the balance of energy and the equation for the entropy production. Assuming that we have Navier s slip at the impermeable boundary we establish the long-time existence of a (suitable) weak solution when the data are large. This result includes the classical Navier-Stokes-Fourier system for a Newtonean incompressible fluid with the viscosity and the heat conductivity depending on the temperature as a special case. The talk is based on joint works with M. Bulicek, E. Feireisl and K. R. Rajagopal.
17:20
 Prof. em. Dr.-Ing. Dr. h.c. Wolfgang L. Wendland (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart): Boundary Integral Equations and Pseudodifferential Operators (lecture 6 of 6)
 3.12.2007
15:40
 Prof. Bob (R. S.) Anderssen (CSIRO Mathematical and Information Sciences, Canberra): The Double Clumping Model of Wheat-Flour Dough Extension Abstract: The response of a wheat-flour dough to the flow and deformation performed on it during mixing is a sequence of hysteretic extension-rupture-recoil-relax events. On recording mixers, such as the Farinograph and Mixograph, this sequence of events is clearly visible in high resolution recordings. Because of its pin arrangement, the viscoelastic flow of the dough is simplest in the Mixograph and the upward branches of the stress-strain hysteretic events can be recovered. The importance of these upward branches is that they can be viewed as in situ measurements of the extensional flow of a dough, which is normally assessed using an extensograph to record the extensional flow (as an extensogram) of a dough sample taken from the mixer at a particular stage of the mixing. Traditionally, extensograph testing is utilized as a plant breeding assay to assess whether the flour from a new wheat variety will make a good bread or cake. The models, on which such deliberations are based, are rules-of-thumb correlations between the global structure of extensograms and the baking performance of good breads and cakes. In many ways, the rules-of-thumb simply reduce to being indirect measurements of the protein content of wheat-fours. From the baker?s perspective, extensograph testing, in conjunction with the rules-of-thumb, can be used to determine the optimal blending of expensive (high protein) and inexpensive (low protein) flours to achieve a given bread or cake quality. A major goal of plant breeding is the development of technology which will allow a new variety to be bred in three to five years rather than five to ten years. This can only be achieved if a more definitive understanding is available about the relationship between the molecular genetics of wheat-flours and the quality of the breads or cakes that they produce. This leads naturally to the need to understand the molecular dynamics of a dough during an extensograph test.
 10.12.2007
15:40
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institut, Charles University, Prague): On existence of solution to incompressible Navier-Stokes-Fourier system with nonlinear heat flux and Cauchy stress Abstract: We derive under which assumptions on Cauchy stress and heat flux (both of them can be nonlinear functions of velocity gradient and temperature gradient, respectively) one has apriori estimates so strong that the definition of weak solution is meaningful. In addition, if we assume some monotonictity properties of Cauchy stress and heat flux we establish the existence of weak solution to N-S-F system whenever the weak formulation makes a good sense.
17:20
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institute of Charles University, Prague): On existence of solution to heat equation with nonlinear heat flux, $L^1$ right hand side and nonintegrable convective term Abstract: The exitence theory for heat equation with nonlinear flux with $L^1$ right hand side was established by using the so-called method of $L^{infty}$ truncation function (developed by Boccardo and Murat). However, if we assume that the convective term is nonintegrable one can not use this method. There is also second method, the so-called method of Lipschitz approximation, that perfectly works if flux has some $r-1$ growth and we have $r$-estimates. But for this problem such estimates are not available. We show that a delicate combination of both methods leads to the proof of point-wise convergence of temperature gradient.
 17.12.2007
15:30
Prof. Dr. Eberhard Zeidler
(Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany):
Euler and the mathematical principles of modern natural philosophy I, II
Abstract:

## !!! Special memorial seminar, starts at 15:30 at the Building of the Faculty of Mathematics and Physics at Malostranska square 25. !!!

 7.1.2008
15:40
 Prof. Dr. Christian Rohde (University of Stuttgart): Modelling of Liquid-Vapour Flows: Diffuse Interface versus Sharp Interface and Mesoscopic versus Macroscopic Models
17:20
 Doc. RNDr. Jiri Langer, CSc. (UTF, MFF UK, Prague): Je hospodin hospodarny? (in czech)
 18.2.2008
15:40
 Prof. Jens Frehse (Institut fur Angewandte Mathematik, University of Bonn): Diagonal elliptic and parabolic systems with superquadratic Hamiltonians Abstract: We consider elliptic or parabolic systems (ut ) − ∆u = H (∇u) + f where u is a vector function, periodic in the space variables. Under additional special structure conditions for H (the ?Hamiltonian?) and natural smoothness conditions on the data we prove the existence of regular solutions ? without smallness conditions ? in the case that H ( ∇u) grows like a polynomial in |∇u|. Up to now, in the case of systems of equations, only Hamiltonians growing at most quadratically in |∇u| have been treated. The work has been done in collaboration with Alain Bensoussan (Dallas, USA).
 25.2.2008
15:40
 priv.doz. RNDr. Martin Kruzik, PhD. (UTIA, ASCR, Prague and Dep. of Physics, Civil engineering, CVUT, Prague): Oscillations and concentrations generated by A-free mappings and weak lower semicontinuity of integral functionals Abstract: We use a generalization of Young measures to describe oscillations and concentrations in sequences of maps in $L^p(\O;\R^m)$ satisfying a linear differential constraint ${\mathcal A}u_k=0$. Applications to sequential weak lower semicontinuity of integral functionals along ${\mathcal A}$-free sequences and to weak continuity of determinants are given, too. This is a joint work with I. Fonseca (CMU, Pittsburgh)
17:20
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University, Prague): Rate independent processes in viscous solids Abstract: Abstract: Generalized standard solids with internal parameters describing activated typically rate-independent processes such as plasticity, damage, or phase transformations, ferromagnets or ferroelectrics, will be described as a system of a force-equilibrium equation and variational inequality for internal parametr variable. Various definitions of weak solutions will be examined, especially from the viewpoint of ability to combine rate-independent processes and other rate-dependent phenomena, as viscosity or inertia. The talk will emphasize mathematical aspects (contrary to modelling itself, as already exposed on Nov.12, 2007)
 3.3.2008
15:40
 Prof. Dr. A. Mielke (WIAS & HU Berlin): Analysis of Rate-Independent Materila Models: I. Classical rate-independent models including elastoplasticity Abstract: Some physical processes like dry friction, elastoplasticity, damage, hysteresis in ferromagnets and shape-memory alloys can be modeled by rate-independent material laws. We provide mathematical models for such processes and discuss general existence results based on the energetic formulation which is based on the dissipation distance and the stored-energy funtional. Several applications are given and the uestion of convergence of solutions under Gamma convergence of the unctionals is addressed. The latter theory provides convergence of umerical schemes and homogenization results.
 10.3.2008
15:40
 Prof. Dr. A. Mielke (WIAS & HU Berlin): Analysis of Rate-Independent Materila Models: III. Applications in material models Abstract: Some physical processes like dry friction, elastoplasticity, damage, hysteresis in ferromagnets and shape-memory alloys can be modeled by rate-independent material laws. We provide mathematical models for such processes and discuss general existence results based on the energetic formulation which is based on the dissipation distance and the stored-energy funtional. Several applications are given and the uestion of convergence of solutions under Gamma convergence of the unctionals is addressed. The latter theory provides convergence of umerical schemes and homogenization results.
17:20
 Dr. Chiara Zanini (Dep. of Mathematics and Computer Sciences, University of Udine, Italy and Institute of Physics AS CR, Prague): Mathematical models of quasistatic crack propagation Abstract: We consider the propagation of a single crack along a prescribed crack path and discuss two notions of evolution of brittle fractures inspired by Griffith s theory. The first one corresponds to the energetic solution for rate-independent processes introduced by Mielke, and is based on a global stability criterion. The second one, more recent, uses a different selection criterion and is based on local minimality. We compare these two notions in an explicit example.
 17.3.2008
15:40
 Prof. Dr. P. Exner (Dep of Theoretical Physics, Nuclear Physics Institute, ASCR): Klasicke a kvantove isoperimetricke problemy resene pomoci nerovnosti pro delky tetiv Abstract: Prednaska je motivovana isoperimetrickymi problemy, jez vznikaji v kvantove mechanice i v klasicke fyzice. Budeme se zabyvat Schrodingerovymi operatory v L2(R2) se singularni pritazlivou interakci, jejimz nosicem je uzavrena krivka. Abstract
 31.3.2008
15:40
 Prof. Philippe Laurencot (Universite Paul Sabatier, Toulouse): Large time behavior for diffusive Hamilton-Jacobi equations
17:20
 Doc. RNDr. J. Malek, DSc. (Mathematical Institute, Charles University, Prague): Large data existence result for inhomogeneous incompressible heat-conducting fluids
 14.4.2008
15:40
 Prof. Philippe Laurencot (Universite Paul Sabatier, Toulouse): Large time behavior for diffusive Hamilton-Jacobi equations
16:20
 Ing. Jan Zeman, PhD. (Klokneruv ustav, CVUT, Praha): Homogenization of fibrous composites with phase debonding: Rate-independent formulation and numerical solution using FETI-based approach Abstract: Load-induced debonding at internal interfaces is considered to be the dominant damage phenomenon in fibrous reinforced composites, reducing the overall material properties and reduced structural integrity. In the present lecture, a rate-independent multi-scale model of debonding processes is presented, following the ideas introduced recently by Mielke, Roubicek and co-workers. It is shown that the rate-independent setting not only offers a convenient framework for studying the qualitative properties of the solution, but also naturally leads to efficient discretization schemes. As a particular example, we examine a numerical algorithm based on the Finite Element Tearing and Interconnecting (FETI) method. The performance of the algorithm is illustrated on selected numerical examples.
 21.4.2008
15:40
 Dr.Giuseppe Tomassetti (Uni. Rome II Tor Vergata): Coupling dynamic micromagnetics with the heat equation Abstract: In standard micromagnetics the specific magnetization is subject to the saturation constraint, which reflects the assumption that the temperature is well below the Curie point. There exist, however, interesting evolution processes, some of them of technological importance, where temperature instantaneously rises above the Curie point in a very small portion of the body. Modeling these processes requires a suitable nonisothermal extension of micromagnetics. In this talk, which is based on an ongoing collaboration with Paolo Podio-Guidugli and Tomas Roubicek, it will illustrated how to produce such an extension using standard tools from continuum thermomechanics. Both modeling and analytical issues will be discussed.
 28.4.2008
15:40
 Dr Jonathan J. Healey (School of Computing and Mathematics, Keele University, UK): Instabilities of mixing layers
17:20
 Dr. Lucia Scardia (MPI MIS Leipzig): Damage as Gamma-limit of microfractures in linearized elasticity Abstract: A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.
 5.5.2008
15:40
 Prof. Dr. E. Miersemann (Mathematisches Institut, Universitat Leipzig, Germany): On liquid layers in cavities
 12.5.2008
15:40
 Dr. M. Bulicek (Mathematical Institut, Charles University, Prague): On the existence of an entropy solution to scalar hyperbolic conservation laws with discontinuous flux Abstract: We will present an observation how the theory on existence of soution to scalar hyperbolic conservation laws can be extended to the case when the flux function has a finite number of monotone jumps. We will also introduce a natural notation for entropy and measure-valued entropy solution for such fluxes.
 19.5.2008
15:40
 Mgr. Josef Kristan (NCMM, Prague): Modelling of elementary processes of plastic deformation of crystalline materials
 26.5.2008
15:40
 Dr. M. Lund (Institute of Organic Chemistry and Biochemistry, ASCR): Coarse-Grained Models for Molecular Systems
16:20
 Prof. Ing. Frantisek Marsik, DrSc. (Institute of Thermodynamics, ASCR): Modeling of biochemistry of bone reconstruction
16:40
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute, Charles University): Incompressible ionized non-Newtonean fluid mixtures
17:00
 Doc. RNDr. Josef Malek, CSc. (Mathematical Institute, Charles University): Incompressible chemically-reacting fluids
 6.10.2008
15:40
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Stabilized finite element methods for thermally coupled incompressible flows Abstract: The talk is concerned with stabilized finite element methods for the incompressible Navier-Stokes problem with thermal coupling. Turbulent flows are simulated based on an unsteady Reynolds-averaged Navier-Stokes (URANS) model. In the discrete case, an equal-order interpolation is applied to all unknowns. Some aspects of classical residual-based stabilization techniques like streamline-upwind stabilization (SUPG), pressure stabilization (PSPG), stabilization of the divergence-free constraint (div-div stabilization) and the treatment of boundary and interior layers will be addressed. Finally, some applications to indoor-air flow simulation are given.
17:20
 Prof. Hans Christian Oettinger (ETH Zurich, Department of Materials, Institute of Polymers, Zurich, Switzerland): Mathematical Structure of Thermodynamics and Its Preservation in Coarse Graining Abstract: Coarse graining is NOT a necessary evil required to solve problems which are computationally too large. Coarse graining rather is the art to simplify to the essentials and hence to provide understanding. Systematic coarse graining procedures are therefore needed, which are the topic of statistical equilibrium and nonequilibrium thermodynamics. We show that any coarse graining step should be accompanied by an increase in irreversibility and is potentially accompanied by the same kind of historical confusion that was created by the passage from reversible to irreversible equations. The relevant thermodynamic structure and the coarse graining recipes suggested by statistical mechanics are described in detail and are illustrated by the example of hydrodynamics. We employ systematic coarse graining techniques to derive hydrodynamic equations from Grad s ten-moment equations. The coarse graining procedure is designed such that it manifestly preserves the thermodynamic structure of the equations. A number of mathematical challenges associated with structure-preserving coarse graining of evolution equations for thermodynamic systems as a generalization of Hamiltonian dynamic systems and reduction techniques are presented. Coarse graining is a key step that should always be considered before attempting to solve an equation.
 13.10.2008
15:40
 Prof. Dr. Maria Lukacova (Institute of Numerical Simulation, Hamburg University of Technology, Germany): Finite volume evolution Galerkin method : theory and application for geophysical flow
17:20
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Local projection stabilization methods for singularly elliptic problems Abstract: The concept of variational multiscale methods (VMS) is the starting point of the talk. The first goal is to describe the link of local projection stabilization (LPS) techniques to the VMS framework. Then we present recent results on the a-priori analysis for LPS methods applied to the basic linear advection-diffusion-reaction problem. Moreover, a critical comparison to the standard streamline-diffusion stabilization will be given.
 20.10.2008
15:40
 Prof. Dr. Gert Lube (Institut fuer Numerische und Angewandte Mathematik (NAM), Georg-August-Universitat Gottingen, Germany): Calibration of subgrid viscosity models for turbulent incompressible flows Abstract: We start with some requirements for the large eddy simulation (LES) of incompressible flows. Then we consider the variational multiscale approach to LES and discuss a parameter identification problem for the corresponding subgrid-scale model. Finally, we present some recent results for the LES with a collocated finite volume code applied to standard benchmark problems and give some conclusions for the finite element case.
 27.10.2008
15:40
 Seminar canceled
 3.11.2008
15:40
 Dr. Johannes Zimmer (Dep. of Mathematical Sciences, University of Bath, UK): From conservative lattice models for elasticity to macroscopic dissipation Abstract: We consider travelling waves in a one-dimensional chain of atoms with nearest neighbour interaction. The elastic potential is piecewise quadratic and the model is thus capable of describing phase transitions. We show that for suitable fixed subsonic waves, there is a family of heteroclinic travelling waves (connecting both wells of the energy). Though the microscopic picture is Hamiltonian, we derive non-trivial so-called kinetic relations on the continuum scale; they can be related to the dissipation generated by a moving phase boundary. It turns out that the microscopic asymmety determines here the macroscopic dissipation. This is joint work with Hartmut Schwetlick (Bath).
17:20
 Prof. Roger Lewandowski (University Rennes 1, France): Simple results for 3D NSE in periodic case Abstract: Part I - Some remarks on Sobolev spaces for periodic functions
 10.11.2008
15:40
 Dipl.-Math. Marita Thomas (Humboldt Universitat zu Berlin): Existence analysis of rate-independent damage processes Abstract: We analyze a model describing partial damage of a solid within its energetic formulation. This approach involves the free energy functional of the body and the dissipation potential expressing the evolution of damage. We provide an existence result in the small strain as well as in the finite strain setting and give examples on energy densities covered by our theory.
17:20
 Prof. Roger Lewandowski (University Rennes 1, France): Simple results for 3D NSE in periodic case Abstract: Part III - Deconvolution models, still in the periodic case
 17.11.2008
15:40
 seminar canceled
 24.11.2008
15:40
 Prof. RNDr. Jiri Mls, CSc. (Prirodovedecka fakulta UK): Pretvareni nasycenych porovitych teles Abstract: 1. nasycene porosni prostredi jako dvoufazovy system, 2. rozlisovaci uroven, 3. Darcyuv zakon, 4. pretvareni, 5. Biotova teorie.
17:20
 Dr. Sebastian Franz (TU Dresden): Superconvergence for singularly perturbed problems with parabolic layers
 1.12.2008
14:00
 Prof. Dr. Barbara Wohlmuth (University of Stuttgart, Germany): Stabilized semi-smooth Newton algorithms for variational inequalities Abstract: Numerical simulation for partial differential equations plays an important role in many fields. Although efficient solution strategies are well known for simple settings, more complex models involving non-smooth nonlinearities are still quite challenging. In this talk we present some applications from structural mechanics and finance where variational inequalities play an important role. Surprisingly frictional contact problems with plasticity fit into the same mathematical framework as American options. We propose fast and robust numerical approaches based on the concept of domain decomposition, adaptivity and stabilized time integration.
15:40
 Prof. Dr. Christof Eck (University of Bielefeld, Germany): Existence results for contact problems with friction Abstract: Contact problems in elasticity belong to the classical topics of applied mathematics, but there are still many questions unsolved, in particular if friction is taken into account. The main difficulty is the combination of the unilateral contact condition with the Coulomb friction law that leads to a non-monotone and non-compact formulation. This requires special approaches to prove the existence of solutions. The most successful approach to analyze contact problems with Coulomb friction was established by Jindrich Necas together with Jiri Jarusek and Jaroslav Haslinger in a seminal paper On the solution of the variational inequality to the Signorini problem with small friction. (Boll. Un. Mat. Ital. B 5(17), pp. 943-958). It consists in the approximation of the problem by some convex problem, the proof of some addition regularity of the solution by a certain translation technique and the application of a fixed point argument. This approach was first applied to static contact problems with Coulomb friction. It was later extended to many other types of frictional contact problems, as e.g. quasistatic contact problems and dynamic problems for viscoelastic and viscoplastic materials. Some results also include the transport of heat generated by friction. In the lecture we present this approach and give a survey on the available existence results for static, quasistatic and dynamic frictional contact problems.
16:50
 Prof. RNDr. Igor Bock, Ph.D. (Slovak University of Technology Bratislava, Slovakia): Dynamic Contact Problems for von Karman Plates Abstract: We deal with systems consisting of a nonlinear hyperbolic variational inequality for a deflection and a nonlinear elliptic equation for the Airy stress function. The systems describe moderately large deflections of thin elastic and viscoelastic plates with an inner obstacle and in a dynamic action. The dynamic contact problems are not frequently solved in the framework of variational inequalities. Mainly for the elastic problems there is only limited amount of results available. The aim of the presentation is to extend these results to von K arm an plates. We neglect the rotational inertia member in the elastic case. We will consider the short memory and the long memory material in the case of a viscoelastic plate. The fist one is expressed by a pseudo-hyperbolic unilateral problem. The long memory material will be considered as an integro-differential variational inequality with a singular kernel.
 8.12.2008
15:40
 Prof. Martin Hairer (University of Warwick, UK): Ergodic Theory for Stochastic PDEs I. Abstract: The aim of these lectures is to present a reasonably self-contained theory of ergodicity for stochastic processes that is sufficiently flexible to allow to deal with infinite-dimensional problems like the stochastic Navier- Stokes equations, stochastic reaction-diffusion equations, etc. In the first lecture, we will introduce the main objects and problems, and remind the audience of the classical theory of Harris chains. We will go through elementary sketches of proofs of some of the main results of this theory. In the second lecture, we will argue that the theory of Harris chains is not suitable for infinite-dimensional problems and we will lay down the foundations for a modified theory that is more flexible. The remainder of the course will be devoted to the applications of this theory to a class of stochastic PDEs. In the third lecture, we will sketch the proof of a general ergodicity result. The final lecture will be devoted to showing how to leverage the bounds obtained in the third lecture to obtain an exponential convergence result.
17:20
 Prof. Martin Hairer (University of Warwick, UK): Ergodic Theory for Stochastic PDEs II.
 15.12.2008
15:40
 Doc. RNDr. Lubos Pick, CSc., DSc. (Charles University, Prague): Sobolev Spaces and their Optimality in Embeddings - Old and New Abstract: We develop a new method that enables one to test whether a given Sobolev embedding can or cannot be improved in the framework of the rearrangement-invariant spaces. The method is applicable to various tasks including Sobolev embeddings, boundary trace embeddings, logarithmic Sobolev inequalities etc.
17:00
 Doc. RNDr. Lubos Pick, CSc., DSc. (Charles University, Prague): The Gateway to Compactness Abstract: We focus on finding the frontier (if only such a thing exists) between boundedness and compactness of a Sobolev embedding. We apply the result to obtaining a manageable condition equivalent to saying that a Sobolev embedding involving a pair of rearrangement - invariant spaces is compact.
 5.1.2009
15:40
 Dr. Atsushi Suzuki (Faculty of Mathematics, Kyushu University, Japan): Preconditioned conjugate gradient solver for the Stokes equations Abstract: The Stokes equations are fundamental equations of incompressible fluid. Discretized problem of the Stokes equations by finite elements consists of an indefinite matrix. We use conjugate gradient (CG) method with preconditioners to utilize the property of symmetry of the matrix. Since the matrix is not positive definite, there is a possibility of break down of the algorithm. However, if we do not encounter the break down, we can obtain approximate solution in the CG method. We can also employ indefinite matrix as a preconditioner. This simple algorithm helps to develop large-scale 3-D computational codes. Understanding of the CG procedure as variational problems in Krylov subspaces and results of numerical computation will be shown.
17:10
 Doc. Ing. Dr. Miroslav Rozloznik (Institute of Computer Sciences, Czech Academy of Sciences, Prague): Saddle point problems and the conjugate gradient method with indefinite preconditioning Abstract: In this talk we consider the solution of saddle-point problems that arise in many application areas such as computational fluid dynamics, electromagnetism, optimization and nonlinear programming. Particular attention has been paid recently to the iterative solution of these systems and to various preconditioning techniques. Several structure-dependent schemes have been proposed and analyzed. Indeed, the block pattern of saddle-point systems enables to take into account not only simple preconditioning strategies and scalings, but also preconditioners with a particular block structure. Here we analyze the null-space projection (or constraint) indefinite preconditioner. Since it was shown that the behavior of most of nonsymmetric Krylov subspace methods can be in this case related to the convergence of preconditioned conjugate gradient method (PCG) we study in detail its theoretical properties and propose simple procedures for correcting its possible misconvergence. The numerical behavior of the scheme is discussed and the maximum attainable accuracy of the approximate solution computed in finite precision arithmetic is estimated. This contribution is a joint work with V. Simoncini. M. Rozloznik and V. Simoncini, Krylov subspace methods for saddle point problems with indefinite preconditioning, SIAM J. Matrix. Anal. Appl.(2002), Vol. 24, No. 2, pp. 368--391.
 12.1.2009
15:40
 Mgr. Vit Prusa, Ph.D. (Mathematical institute of Charles University): Stability of fluid flow - recent developments Abstract: The lecture will briefly introduce some basic notions and classical approaches used in theory of stability of fluid flow, and subsequently it will summarize some well-known fundamental results. After the introductory part, some weaknesses of the presented approaches will be pointed out, and the rest of the lecture will be devoted to some recent approaches to stability, namely to so called transient growth theory and self-sustaining processes theory. These fruitful approaches were developed on an engineering (read as non-rigorous ) level, and are probably still lacking a rigorous mathematical background, therefore the aim of the second part of the lecture is to attract attention to these approaches and possibly stimulate rigorous investigation of these approaches.
17:20
 Prof. Ing. Frantisek Marsik, DrSc. (Institute of Thermomechanics, Czech Academy of Sciences): Stability of viscous flow-Thermodynamic point of view Abstract: Thermodynamics of open systems offers a new concept for description of real material objects. The basic ideas come out the time irreversibility of processes and stability of states. The II. Law of Thermodynamics can be interpreted as an evolution law of all material systems, which are in interaction with their surroundings. The most important quantity is the entropy, which is defined by the balance law of entropy. The production of the entropy gives information about the processes into the systems. The convexity of the thermodynamic potentials (e.g. entropy, total enthalpy etc.) inform us about the stability of the system states. Under the appropriate outer conditions the fluctuations can to drive the systems to an instability. The consequence is the creation or decay of dissipative structures. When the new dissipative structure appears, the system is going further from the thermodynamic equilibrium to the new stable state. However, if the dissipative structure disappears the systems tends to the thermodynamic equilibrium without any transport processes. This approach is applied to the derivation of thermodynamic stability criteria for Blasius, Poisseulle and Couette flows . Moreover, the fluid flow stability enhancement by temperature gradient is discussed for heated Coanda flow. All theoretical conclusions are compared with physical experiments.
 2.3.2009
15:40
 Prof. Tomas Roubicek (MFF UK Praha): Delamination problems Abstract: Contact problems of elastic solids with activated, rate-independent delamination on the contact boundary (also called debonding or adhesive contacts) will be addressed. Models at large or small strains will be presented first in a quasistatic formulation based on the concept of energetic solutions. In particular, a brittle delamination model (i.e. only either completely rigidly glued contact or fully debonded contact allowed) is exposed and shown to be a limit of a delamination with elastically responding glue that can be thus understood as a regularization which is also suitable to numerical implementation. Further extension to dynamical contact problems in visco-elastic solids and its possible thermodynamics will be briefly outlined, too. The talk will include also results from joint works with M.Kocvara, A.Mielke, L.Scardia, and C.Zanini.
17:20
 Mgr. Libor Pavlicek (MFF UK Praha): Uvod do Di Perna-Lionsovy teorie Abstract: Pracovni seminar NCMM.
 9.3.2009
15:40
 dr. Giuseppe Tomassetti (Univ. Roma II Tor Vergata): Theories of shearable beams and plates as gamma limit of three-dimensional micropolar elasticity Abstract: In this talk I will outline some recent developments on the mathematical justification of theories of shearable rods and plates. In particular, I will discuss what happens when micropolar elasticity is adopted as parent theory from which the plate theory is deduced. In particular, I will show that for beams and plates quite different scalings are in order.
17:20
 Mgr. Libor Pavlicek (MFF UK): Uvod do Di Perna-Lionsovy teorie II. Abstract: Student seminar of the Necas Center
 16.3.2009
15:40
 Dr. Joerg Wolf (University of Magdeburg): On the pressure of the Navier-Stokes equations from different points of view Abstract: The Navier-Stokes equations and related system describe an incompressible viscous fluid, where the volume is preserved. Therefore the pressure p has to be introduced as an additional unknown quantity. From the theory of the non-stationary Stokes system using the well-known properties of the Stokes operator under suitable conditions the pressure for the Navier-Stokes equation can be introduced. However, in general this method does not work, for example if the viscosity ν is non-constant. In this first lecture will introduce different methods for introducing a global and local pressure in general situations.
17:20
 Mgr. Libor Pavlicek (MFF UK Praha): Uvod do Di Perna-Lionsovy teorie III. Abstract: Student seminar of the Necas Center
 23.3.2009
15:40
 Prof.Dr. Soeren Bartels (Institute for Numerical Simulation, University of Bonn): Approximation of Harmonic Maps and Wave Maps Abstract: Partial differential equations with a nonlinear pointwise constraint defined through a manifold occur in a variety of applications: The magnetization of a ferromagnet can be described by a unit length vector field and the orientation of the rod-like molecules that constitute a liquid crystal is often modeled by a vector field that attains its values in the real projective plane thus respecting the head-to-tail symmetry of the molecules. Other applications arise in geometric modeling, quantum mechanics, and general relativity. Simple examples reveal that it is impossible to satisfy pointwise constraints exactly by lowest order finite elements. For two model problems we discuss the practical realization of the constraint, the efficient solution of the resulting nonlinear systems of equations, and weak accumulation of approximations at exact solutions.
17:20
 Prof. Piotr Mucha (University of Warsaw): Analysis of equations arising from the theory of crystal growth Abstract: I would like to introduce some simple models of equations which determine evolution of crystals. They base on singular and degenerated parabolic systems. A model problem can be represented by the equation of the total variation u_t - partial_x (u_x/|u_x|)=0 on R times (0,T). Analysis of this type of equations requires a new approach to define such quantity as smooth function , compositions of multi-functions. Then we will be able to obtain solutions so good that we will call them almost classical . Although in the system there appears formally a product of two Dirac deltas.
18:30
 Mgr. Miroslav Bulicek, Ph.D. (MUUK): Partial regularity for Navier-Stokes equations by De Giorgi s method Abstract: Student seminar of the Necas center.
 30.3.2009
15:40
 Prof. Antonin Novotny (University of Toulon): Singular limits in the thermodynamics of viscous fluids - part I/IV
17:20
 Prof. Antonin Novotny (University of Toulon): Singular limits in the thermodynamics of viscous fluids - part II/IV
18:30
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institute of the Charles University): Partial regularity for Navier-Stokes equations by De Giorgi s method - part II Abstract: Student seminar of the Necas center.
 6.4.2009
15:40
 Prof. Maurizio Grasselli (Politecnico di Milano): Asymptotic behavior of dissipative evolution equations - Part I/IV Abstract: Semigroups of operators, trajectories and orbits, phase space, equilibria, invariant sets, omega-limit sets. bounded absorbing sets, attracting sets, compactness and asymptotic compactness, global attractors and their properties. Slides: 1 and 2, 3 and 4
17:20
 Prof. Antonin Novotny (University of Toulon): Singular limits in the thermodynamics of viscous fluids - part IV/IV
18:30
 Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institute of the Charles University): Partial regularity for Navier-Stokes equations by De Giorgi s method - part III Abstract: Student seminar of the Necas center.
 13.4.2009
15:40
seminar cancelled
Abstract: Easter Monday
 20.4.2009
15:40
 dr. Zdenek Fiala (UTAM AV CR): Geometrical interpretation of the logarithmic strain and the Zaremba-Jaumann time derivative Abstract: After a brief review of some concepts in computational solid mechanics (objective time derivative, logarithmic strain, logarithmic time derivative), we adress the finite deformations from the viewpoint of natural geometry of the set of all symmetric, positive-definite real matrices $Sym^+$ to find a geometrical interpretation of the Zaremba-Jaumann time derivative and the logarithmic strain. Since the right Cauchy-Green deformation tensors $mathbf{C}=mathbf{F}^ ext{T}mathbf{F}$ are symmetric, positive-definite matrices, a deformation process is represented by a time-parameterized trajectory $mathbf{C}_t: o Sym^+$. As an open convex cone in the ambient space of all symmetric matrices $sym$, which is an inner product vector space, the set $Sym^+$ inherits this way its Riemannian geometry to become a constant negatively-curved manifold. From the viewpoint of continuum mechanics, the Riemannian metric naturaly enters $Sym^+$ via the stress power. We can then employ the tools of differential geometry to find out that the Zaremba-Jaumann derivative is related to geometrically consistent linearization via the covariant derivative, and the logarithmic strain to geodesics in $Sym^+$, which prove to be matrix exponentials. Adopting this interpretation we can consider initially-deformed and undeformed states in a unified way, resulting in particular to generalization of the logarithmic strain, and in general to some universal conclusions concerning the incremental approach. Moreover, within this interpretation we geometrically distinguish stress, deformation, and rate-of-deformation tensors.
17:20
 Dr. Riccarda Rossi (Univ. Brescia, Italy): A variational approach to doubly nonlinear and rate-independent evolutions Abstract: A wide class of dissipative phenomena can be modelled by doubly nonlinear abstract evolution equations in Banach spaces, featuring a convex dissipation functional and an energy functional. When the dissipation functional is positively homogeneous of degree 1, the related doubly nonlinear equation models rate-independent evolutions, arising in several branches of continuum mechanics, often in connection with hysteresis problems. In many relevant applications, the driving energy functional may be nonsmooth and nonconvex. Hence, the resulting rate-independent evolutions have jumps, which require additional modelling. Consequently, a new approach has been proposed, based on the analysis of such systems as limit of suitable viscous evolutions (given by doubly nonlinear equations with a superlinear dissipation functional). Combining variational and reparametrization techniques, in collaboration with Alexander Mielke and Giuseppe Savare we have developed the notion of parametrized rate-independent evolution , which shall be presented in this talk.
18:30
 Dr. Petr Kaplicky (MFF UK Praha): On W^{1,p} estimates for elliptic equations in divergence form Abstract: We refer beautiful method of proving L^p theory for large class of elliptic PDE s from article L. A. Caffarelli, I. Peral: On W^{1,p} estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 51 (1998), no. 1, 1--21.
 27.4.2009
16:00
 Prof. RNDr. Jan Kratochvil, DrSc. (FSv CVUT Praha): Modeling of microstructure formation in materials exposed to severe plastic deformation Abstract: It is well documented that severe plastic deformation produces ultrafine grained materials with extraordinary mechanical properties. Very high strength and relatively good ductility is attributed to their fine microstructure. One of methods suitable for experimental and theoretical studies of the microstructure evolution during severe plastic deformation is the high pressure torsion (HPT). The proposed crystal plasticity model outlines a possible mechanism of ultrafine structure formation as observed in HPT experiments. The HPT deformation can be interpreted as a plastic flow though the adjustable crystal lattice. In the deformation process the lattice is settled to provide the energetically most effective plastic flow, analogously as a riverbed adjusts to a water flow. HPT deformation as seen in the radial direction can be roughly described as a plastic flow through a channel with crystal lattice structure. The flow is exposed to the boundary conditions: zero velocity at the bottom and a prescribed velocity at the upper surface. The model reveals rotations of slip systems caused by the imposed shear strain. An axial compression and a shear stress of twist govern this process. Local variations in the crystal lattice orientation are responsible for the microstructure fragmentation. The accompanied continuous reconstruction of the deformation substructure is probably the main reason of the observed strengthening.
17:30
 Prof. Kumbakonam Rajagopal (Texas A&M University): The elasticity of elasticity Abstract: In this note we assert that the usual interpretation of what one means by elasticity is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular. Reference: K. R. Rajagopal, The elasticity of elasticity, Z. Angew. Math. Phys. 58 (2007) 309-317.
 4.5.2009
15:40
 Prof. Gerhard Huisken (Universitat Tubingen, Germany): Mean curvature flow with surgery Abstract: A family of hypersurfaces is said to move by mean curvature if at every point the speed in normal direction is given by the mean curvature of the surface. This quasilinear parabolic system decreases area and tends to uniformize the shape of the evolving surfaces. It has a similar analytic behavior as the Ricci flow of Riemannian metrics, that was recently used by Hamiltoon and Perelman for the proof of the Poincare conjecture. The lecture explains recent work by Huisken and Sinestrari on mean curvature flow with surgeries that can extend the flow through singularities in a controlled way. In particular it is shown that a certain class of hypersurfaces called 2-convex exhibits the same structure of singularities and surgeries as 3-dimensional Ricci flow.
17:20
 Prof. Roger Lewandowski (University Rennes 1): Regularity and uniqueness results for the k-u system Abstract: We first introduce the turbulence model that couples the mean velocity and the mean pressure of a flow field with its turbulent kinetic energy thru eddy viscosities. After the recall of the classical existence result, we show a regularity and uniqueness result in the steady-state case.
18:30
 Dr. Petr Kaplicky (MFF UK Praha): On W^{1,p} estimates for elliptic equations in divergence form - part II Abstract: We refer beautiful method of proving L^p theory for large class of elliptic PDE s from article L. A. Caffarelli, I. Peral: On W^{1,p} estimates for elliptic equations in divergence form. Comm. Pure Appl. Math. 51 (1998), no. 1, 1--21.
 11.5.2009
15:40
 Antonio Andre Novotny (National Laboratory for Scientific Computing, Rio de Janeiro): Topological Sensitivity Analysis Abstract: The topological asymptotic analysis provides the sensitivity of a given shape functional with respect to an infinitesimal singular domain perturbation. Therefore, this sensitivity can be naturally used as a descent direction in an optimization algorithm. The concept of topological derivative is an extension of the classical notion of derivative. It has been rigorously introduced in 1999 by Sokolowski & Zochowski. Since then, the notion of topological derivative has proved extremely useful in the treatment of a wide range of problems in mechanics, optimization, inverse analysis and image processing and has become a subject of intensive research. In this seminar it will be presented some recent developments and also some applications of the topological derivative in image processing, inverse problems, topology optimization design of load bering structures and, finally, in the synthesis and optimal design of microstructures to meet a specified macroscopic behavior.
 18.5.2009
15:40
 Prof. A. M. Saendig (University of Stuttgart): Regularity results for nonlinear convection-diffusion problems Abstract: The knowledge of analytical existence and regularity results for solutions of nonlinear nonstationary convection-diffusion equations is important for their numerical treatment. In particular, error estimates for Discontinous Galerkin Methods demand a high classical regularity of the solution [2]. This regularity is not guaranteed, if the domain is nonsmooth or if the boundary conditions change. Starting from weak solutions in anisotropic Sobolev spaces L2(I,V) [3], we analyse their regularity for Dirichlet boundary conditions in polygonal domains using the theory of semigroups in Lp [4]. Problems with changing boundary conditions can be handled analogously. Essential is, that we benefit from the introduction of Sobolev spaces with attached asymptotics in the linear stationary case [1], which reflects also the behavior of the solutions to nonlinear nonstationary convection-diffusion problems near corner points of a polygon under certain conditions. Full abstract
 5.10.2009
15:40
 Dr. Lars Diening (IAM, University of Freiburg, Germany): Finite element analysis of the p-Stokes system Abstract: We derive apriori estimates for the finite element solutions of the p-Stokes system. The estimates for the velocity are optimal and presented in terms of quasi-norms. We also prove convergence of the pressure.
 12.10.2009
15:40
 Prof. RNDr. Josef Malek, DSc. (MUUK, Charles University, Prague): On compressible and incompressible generalized Newtonian fluids
17:20
 Dr. Martin Heida (IAM University of Heidelberg, Germany): Modeling Vapor Transport in Cold Dry Soil Abstract: We consider vapor transport in cold dry soil with high temperature fluctuations. Such systems occur in permafrost soil in the northwest of Tibet. A model is set up consisting of two temperature fields, air density, vapor saturation and water content as free variables. In contrast to most numerical models the assumption on constant full vapor saturation is dropped. Instead, the air phase allows for over- and undersaturation. Mathematical solvability results for suitable assumptions on the coefficients and boundary conditions will be demonstrated.
 19.10.2009
15:40
 prof. Hans-Goerg Roos (TU Dresden): Finite element methods for convection-diffusion problems Part I Abstract: Convection-diffusion equations are a fundamental subproblem for models in various applications. Typically, diffusion is less significant than convection: on a windy day the smoke from a chimney moves in the direction of the wind and the influence of the diffusion is small. Finite element discretizations of convection-diffusion equations are not trivial because stability problems arise and layer phenomena lead to difficulties with the interpolation error. In part I of our lecture we discuss several finite element techniques on standard meshes. Because on standard meshes it is difficult to resolve layer structures we analyze in part II the use of layer-adapted meshes. Contents of part I and II: Standard meshes 1. A review of classical FE analysis and the difficulties for convection-diffusion problems 2. Stabilization methods 2.1 Residual based stabilization 2.2 Symmetric stabilization: CIP and LPS 3. Operator fitted methods  Contents of part III and IV: Layer-adapted meshes 1. Solution-decomposition and classification of meshes 2. Galerkin-FEM on layer-adapted meshes 3. Stabilization 4. Solution recovery  Parts I and II will form the contents of 4 lectures delivered on 19 and 26 October in the lecture hall K1 at 15:40 (Seminar on Continuum Mechanics) and on 22 and 29 October in the lecture hall K3 at 14:00 (Seminar on Numerical Mathematics). The parts III and IV will be the subject of the course which will be delivered during 1 - 14 March 2010.
17:20
 Mgr. R. Chabiniok (INRIA Rocquencourt, France): Biomechanical model of the heart function: validation and clinical applications Abstract: First we describe an approach that we propose to model the electromechanical behavior of the heart. The modeling of the heart tissue is based on an electrically-activated contraction law formulated via multiscale considerations and is consistent with various key physiological and thermomechanical requirements. Then we present several steps of the model validation and some clinical applications, in particular: 1. Validation in 1D using experimental data of cardiac muscle fiber contraction, and in 3D using clinical data or data from specially designed experiments. 2. Physiological simulations of the infarcted heart with possible study of the heart remodeling after the infarction. 3. Clinical application on modeling of cardiac resynchronization therapy (CRT).
 26.10.2009
15:40
 Prof. Hans-Goerg Roos (TU Dresden): Finite element methods for convection-diffusion problems Part II
 2.11.2009
15:40
 Prof. Joga I. Rao (Department of Mechanical Engineering, New Jersey Institute of Technology, USA): MODELING THE THERMO-MECHANICS OF SHAPE MEMORY POLYMERS (part 1) Abstract: Shape memory polymers have the ability to retain a temporary shape, which can be reset to the original shape with the use of a suitable trigger, typically an increase in temperature or exposure to light. These temporary shapes can be very complex and the deformations involved large. These materials are finding use in a large variety of important applications; hence the need to model their behavior. The first talk will provide an overview of the different types of shape memory polymers, in particular crystallizable or glassy shape memory polymers and light activated polymers. In crystallizable shape memory polymers the temporary shape is fixed by a crystalline phase, while return to the original shape is due to the melting of this crystalline phase. In glassy polymers the temporary shape is fixed by the formation of a glassy phase and the return to the original shape is initiated by heating above the glass transition temperature. For light activated shape memory polymers exposure of the polymer to UV light at a specific frequency initiates the formation of cross-links that are responsible for the temporary shape. Exposure to UV light of a different frequency is responsible for cleavage of these cross-links and return to the original shape. In this talk we will discuss the underlying mechanisms and our approach to formulating constitutive equations to model the thermo-mechanical behavior of these polymers. The modeling is done within the framework of natural configurations utilizing a full thermodynamic approach. The application of the models developed to different boundary value problems of interest will be discussed.
17:20
 Prof. Joga I. Rao (Department of Mechanical Engineering, New Jersey Institute of Technology, USA): MODELING THE THERMO-MECHANICS OF SHAPE MEMORY POLYMERS (part 2) Abstract: The second talk will focus on the details of the model for crystallizable shape memory polymers and its relation to models developed for the other kinds of shape memory polymers. Particularly we will discuss each aspect of the model. Initially these materials are elastomers. On cooling, crystallization is initiated and the rate at which crystallization takes place is related to the thermodynamics. Natural configurations of this newly formed crystalline are prescribed based on experimental data. An important aspect of these materials that is overlooked in models developed is the anisotropic response of the material after the onset of crystallization. The anisotropy in the behavior is directly included in the model and depends on the deformation in the original material at the onset of crystallization. Finally the reverse transition from a semi-crystalline material back to an elastomer is included in a similar manner. The predictions of the model are compared with experimental data available. A variety of boundary value problems are solved using the model developed. The model has also been included into a large deformation finite element code by creating a user defined subroutine, which is then used to solve complex boundary value problems.
 9.11.2009
15:40
 Doc. RNDr. Eduard Feireisl, DrSc. (Institute of Mathematics, Academy of Sciences, Praha): Propagation of acoustic waves on general unbounded domains with applications to incompressible limits of the Navier-Stokes system Abstract: We discuss the problem of propagation of acoustic waves and their oscillations in the so-called incompressible limit for the Navier-Stokes system. We derive Lighthill's acoustic analogy and study its basic properties. Finally, a necessary and sufficient condition will be given for the acoustic waves to decay locally to zero.
 16.11.2009
15:40
 Prof. Dr. Yasushi Taniuchi (Department of Mathematics, TU Darmstadt): On the uniqueness of almost periodic-in-time solutions to the Navier-Stokes equations in unbounded domains Abstract: We present a uniqueness theorem for almost periodic-in-time solutions to the Navier-Stokes equations in $3$-dimensional exterior domains $Omega$. It is known that there exists a small almost periodic-in-time solution in $C(R;L^{3}_w(Omega))$ to the Navier--Stokes equations for a small almost periodic-in-time force. Here $L^n_w(Omega)$ denotes weak $L^n$ space. Thus far, with respect to the uniqueness of almost periodic-in-time solutions to the Navier--Stokes equations in exterior domain, roughly speaking, it has been only known that a small almost periodic-in-time solution in $BC(R;L^{3}_w)$ is unique within the class of solutions which have sufficiently small $L^{infty}( L^{3}_w)$-norm, i.e., that if $u$ and $v$ are $L^3_w$-solutions for the same force $f$, and if both of them are small, then $u=v$. In this talk, we will show that a small almost periodic-in-time solution in $BC(R;L^{3}_wcap L^{6,2})$ is unique within the class of all almost periodic-in-time solutions in $BC(R;L^{3}_wcap L^{6,2})$, i.e., we will show that if $u$ and $v$ are almost periodic-in-time solutions in $BC(R;L^{3}_wcap L^{6,2})$ for the same force $f$, and if one of them are small, then $u=v$.
 23.11.2009
15:40
 Dr. Radek Erban (Mathematical Institute, University of Oxford): Stochastic and Multiscale Modelling in Biology I Abstract: Some recent advances in the development and analysis of methods for stochastic and multiscale modelling of biological systems will be presented. The biological examples will cover problems ranging over different length and time scales, including processes on the molecular level (e.g. genes and proteins), cellular level (e.g. cell motility) and population level (e.g. social insect behaviour). Many subcellular biological processes can be described in terms of diffusing and chemically reacting species. Several stochastic simulation algorithms (SSAs) suitable for the modelling of such reaction-diffusion processes will be analysed. The connections between SSAs and the deterministic models (based on reaction-diffusion partial differential equations (PDEs)) will be presented. I will consider chemical reactions both at a surface (e.g. a membrane with receptors) and in the bulk. I will show how the microscopic parameters should be chosen to achieve the correct macroscopic reaction rate. This choice is found to depend on which SSA is used. The movement of unicellular organisms can also be viewed as a stochastic process - a biased random walk. Examples include chemotaxis of bacteria or amoeboid cells and in both cases, cells detect extracellular signals (attractants or repellents) and alter their behaviour accordingly. I will discuss the derivation of macroscopic PDEs (collective behaviour) from individual based models of unicellular organisms. I will also present modelling of animal groups with a focus on the behaviour of locusts. Systematic analysis of the experimental data reveals that individual locusts appear to increase the randomness of their movements in response to a loss of alignment by the group. I will show how properties of individual animal behaviour can be implemented in the self-propelled particle model to replicate the group-level dynamics seen in the experimental data.
17:20
 Dr. Radek Erban (Mathematical Institute, University of Oxford): Stochastic and Multiscale Modelling in Biology II Abstract: This is a continuation of my talk Stochastic and Multiscale Modelling in Biology I . I will discuss further the challenges of mathematical modelling of biological systems mentioned in my first talk. In all model systems considered, I will discuss connections and differences between deterministic models (mean-field ODEs/PDEs) and stochastic simulation algorithms. I will also present multiscale modelling approaches linking models with a different-level of detail together.
 30.11.2009
15:40
 Prof. Louisette Priester (Universite Paris 11, France): Stress relaxation at grain boundaries: Models and experiments. Consequences on material plasticity Abstract: Grain boundaries (and more generally interfaces) play a fundamental role in most properties of crystalline materials, and particularly in their mechanical behaviour. The study of the elementary processes that occur at grain boundaries is necessary to understand the plastic deformation of the material and constitutes a prerequisite to control, then to improve its global properties. To approach intergranular phenomena, we first have to know the equilibrium structure of grain boundaries at three levels that are strongly linked: geometrical, mechanical and atomic. Then we must describe their defects, mainly their linear defects that are responsible for their mechanical behaviour. The interfacial strains and stresses are generally approached in terms of discrete dislocations, however, as a preliminary, we will briefly evoke how the continuum theory of defects may apply to grain boundary. During plastic deformation, interactions between lattice dislocations and grain boundaries necessary occur giving rise to intergranular dislocations. The stresses associated to these dislocations must be relieved in order that the deformation may go on. The main object of this seminar is to describe the interaction and the relaxation phenomena at grain boundaries. We will first present the existing models, then we will see how they are confirmed (or invalidate) by some simulations and transmission electron microscopy observations. It will be proved that all the reactions (entrance of lattice dislocations in grain boundaries and relaxation processes) depend on the fine grain boundary structure: then, the answer to the deformation differs from one grain boundary to the other. The latter statement involves that the role of different grain boundaries in the global deformation of the material must also differ. In the last part of the seminar, we will try to see how the macroscospic plasticity may be affected by the microscopic phenomena. This implies to relate the individual behaviours to the collective ones (grain boundary network) that depend, in particular, on the grain boundary distribution. These efforts constitute a first step towards a grain boundary engineering, a concept that is still in its infancy.
 7.12.2009
15:40
 4.1.2010
15:40
 Prof. Zdenek Strakos (Institute of Computer Science, ASCR): Moments, Krylov subspace methods and model reduction with application in ellipsometry Abstract: Joint work with Dr. Petr Tichy. Reduced order modeling plays a central role in approximation of large-scale dynamical systems, and techniques based on Krylov subspaces are used in that area for decades, see, e.g. [2] and the recent monograph [1]. Krylov subspace methods can not only be viewed as tools for model reduction. Many of them by their nature represent model reductions based on matching moments. In order to explain the deep link between matching moments and Krylov subspace methods, we start with a modiﬁcation of the classical Stieltjes moment problem, and show that its solution is given: in the language of orthogonal polynomials by the Gauss-Christoﬀel quadrature; in the matrix form by the conjugate gradient method (see [4]). In order to allow straightforward generalizations, we use the Vorobyev vector moment problem [3], and present some basic Krylov subspace methods from the moment matching model reduction point of view [5]. The second part of the talk will be devoted to application in numerical modeling of the diﬀraction of light on periodic media [6]. References [1] A. C. Antoulas, Approximation of large-scale dynamical systems, vol. 6 of Advances in Design and Control, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2005. [2] K. Gallivan, E. Grimme, and P. Van Dooren, Asymptotic wave-form evaluation via a Lanczos method, Appl. Math. Lett., 7 (1994), pp. 7580. [3] Y. V. Vorobyev, Methods of moments in applied mathematics, Translated from the Russian by Bernard Seckler, Gordon and Breach Science Publishers, New York, 1965. [4] Meurant, G. and Strakos, Z., The Lanczos and conjugate gradient algorithms in ﬁnite precision arithmetic, Acta Numerica, 15 (2006), pp. 471542. [5] Strakos, Z., Model reduction using the Vorobyev moment problem, Numerical Algorithms, 51, (2008), pp. 363376. [6] Hench, J. and Strakos, Z., The RCWA method - a Case study with open questions and perspectives of algebraic computations, Electronic Transactions on Numerical Analysis, 31 (2009), pp. 331357.
 11.1.2010
15:40
 Mgr. Tomas Ligursky (Mathematical Institute of the Charles University, Praha): Theoretical analysis of discrete contact problems with Coulomb friction Abstract: A discrete model of a two-dimensional Signorini problem with Coulomb friction and a coefficient of friction $mathcal{F}$ depending on the spatial variable will be analysed. It will be shown that a solution exists for any $mathcal{F}$ and is globally unique if $mathcal{F}$ is sufficiently small. The Lipschitz continuity of this unique solution as a function of $mathcal{F}$ as well as as a function of the load vector $boldsymbol{f}$ will be obtained. Furthermore, local uniqueness of solutions for arbitrary $mathcal{F} > 0$ will be studied. The question of existence of locally Lipschitz-continuous branches of solutions with respect to the coefficient $mathcal{F}$ will be converted to the question of existence of locally Lipschitz-continuous branches of solutions with respect to the load vector $boldsymbol{f}$. A condition guaranteeing the existence of locally Lipschitz-continuous branches of solutions in the latter case and results for determining their directional derivatives will be given. Finally, the general approach will be illustrated on an elementary example, whose solutions are known exactly.
 1.3.2010
15:40
 Prof. Hans-Goerg Roos (TU Dresden): Solution-decomposition and classification of meshes Abstract: First lecture of the mini-course Finite element methods for convection-diffusion problems II: Layer-adapted meshes Next lectures: March 4 (Seminar on Numerical mathematics, room K3, 2nd floor), 14:00: Galerkin-FEM on layer-adapted meshes March 8, 17:20: Nitsche-Mortaring and stabilization on layer-adapted meshes March 11 (SNM, K3), 14:00 Solution recovery and non-stationary problems
17:20
 Dr. Adrian Hirn (University of Heidelberg): Approximation of the p-Stokes equations with equal-order finite elements Abstract: Non-Newtonian fluid motions are often modeled by the p-Stokes equations where the extra stress tensor exhibits p-structure. In this talk we study the discretization of the p-Stokes equations with equal-order finite elements. Here, the stabilization of the pressure-gradient, which is essential due to the violation of the discrete inf-sup condition, is based on the local projection stabilization method. In this talk, a priori error estimates are derived and numerical simulations are shown.
 8.3.2010
15:40
 Dr. Tomas Bodnar (Faculty of Mechanical Engineering, Czech Technical University, Prague): On the implementation of a new viscoelastic shear-thinning model for blood flow simulations Abstract: The talk will summarize the first experience with the implementation of a new viscoelastic model specially designed for blood flow simulations. This model is based on the thermodynamic framework approach developed by Rajagopal & Srinivasa and further extended for blood flow simulations by Anand & Rajagopal. K. Rajagopal, A. Srinivasa, A thermodynamic frame work for rate type fluid models, Journal of Non-Newtonian Fluid Mechanics 80 (2000) 207-227. M. Anand, K. R. Rajagopal, A shear-thinning viscoelastic fluid model for describing the flow of blood, International Journal of Cardiovascular Medicine and Science 4 (2) (2004) 59-68.
17:20
 Prof. Hans-Goerg Roos (TU Dresden): Nitsche-Mortaring and stabilization on layer-adapted meshes Abstract: Third lecture of the mini-course Finite element methods for convection-diffusion problems II: Layer-adapted meshes Last lecture: March 11 (Seminar on Numerical Mathematics, room K3, 2nd floor), 14:00 Solution recovery and non-stationary problems
 15.3.2010
15:40
 Prof. Jens Frehse (Hausdorff Center for Mathematics, University of Bonn): Improved Lp-estimates for the strain velocities in hardening problems Abstract: Problems of elastic plastic deformation with kinematic or isotropic hardening and von Mises flowrule are considered. It is shown that the velocities of the stresses, strains and hardening parameters satisfy an improved Lp-property that is , , ∇ L∞(0,T;L2+2δ(Ω)) with some δ > 0. For dimension n = 2 this implies continuity of in spatial direction, furthermore it can be used as tool to prove boundary differentialbility σ,ξ L∞(L1+ϵ) and σ,ξ L∞(0,T;1∕2+δ′,2), where 1∕2 + δ′ is the order of fractional Nichol’skii differentiability. For large values of the Hardening modulus we achieve δ = 1∕3.
 22.3.2010
15:40
 Dr. Riccarda Rossi (University of Brescia, Italy): Analysis of rate-independent model of adhesive contact with thermal effects Abstract: In this talk we present a joint work with T. Roubicek on the analysis of a model for adhesive contact, which encompasses both thermal effects and a rate-independent evolution for the adhesive parameter. After describing the model, we present some existence and approximation results.
 29.3.2010
15:40
 Prof. Dr. Torsten Linss (TU Dresden): Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems Abstract: In the first part of the lectures we consider stationary reaction-diffusion equations of the type while the second part is concerned with its time-dependent analogue Both are equipped with homogeneous Dirichlet boundary conditions and, in case of the time-dependent problem, with appropriate initial conditions. The parameter ε >0 is small, while the reaction cofficient c is assumed to satisfy c ≥ γ2 with some positive constantγ. The efficiency of standard numerical methods deteriorates as the perturbation parameter ε approaches zero. This is because layers form. These are regions where the solution varies rapidely. In the present talk, bounds for the Greens function associated with the differential operators and are derived. These bounds are applied to obtain a posteriori error estimators in the maximum norm for difference schemes and for FEM. These estimators are robust with respect to the perturbation parameter. They can be applied to design adaptive mesh-movement algorithms that give numerical methods which converge uniformly with respect to the perturbation parameter ε. Numerical results will be presented to illustrate the theoretical findings. The lecture will be delivered also at the Seminar on Numerical mathematics on 1st April, 14:00, seminar room K3.
17:20
 Prof. Dr. Soeren Bartels (Institute for Numerical Simulation, University of Bonn): Robust Approximation of Phase Field Models past Topological Changes Abstract: Phase field models are often used to describe the evolution of submanifolds, e.g., the Allen-Cahn equation approximates motion by mean curvature and more sophisticated phase field models provide regularizations of the Willmore flow and other geometric evolution problems. The models involve small regularization parameters and we discuss the dependence of a priori and a posteriori error estimates for the numerical solution of the regularized problems on this parameter. In particular, we address the question whether robust error estimation is possible past topological changes. We provide an affirmative answer for a priori error estimates assuming a logarithmic scaling law of the time averaged principal eigenvalue of the linearized Allen-Cahn or Ginzburg-Landau operator about the exact solution. This scaling law is confirmed by numerical experiments for generic topological changes. The averaged eigenvalue about the approximate solution enters a posteriori error estimates exponentially and therefore, critical scenarios are detected automatically by related adaptive finite element methods. The devised scheme extracts information about the stability of the evolution from the approximate solution and thereby allows for a rigorous a posteriori error analysis. This is joint work with Ruediger Mueller (HU Berlin) and Christoph Ortner (U Oxford).
 12.4.2010
15:40
 Prof. Endre Suli (University of Oxford): An adaptive finite element approximation of a variational model of brittle fracture Abstract: The energy of the Francfort--Marigo model of brittle fracture, posed as a free-discontinuity problem over the space of special functions of bounded variation, can be approximated, in the sense of $Gamma$-convergence, by the Ambrosio--Tortorelli functional. In this talk we formulate and analyze an adaptive finite element algorithm for the computation of local minimizers of the Ambrosio--Tortorelli regularization of the Francfort--Marigo model. We combine a Newton-type method with an adaptive mesh-refinement algorithm driven by an a posteriori error bound. We present theoretical results that demonstrate the convergence of our algorithm. The theoretical results are illustrated by numerical experiments. The lecture are based on joint work with Siobhan Burke and Christoph Ortner at the University of Oxford.
17:20
 Dr. Ewelina Kaminska (Warsaw University, Poland): Analysis of nonlocal model of compressible fluid in 1-D Abstract: The talk will be devoted to a nonlocal modification of the compressible Navier-Stokes equations in mono dimensional case with a boundary condition characteristic for the free boundary problem. From the formal point of view the system is an intermediate between the Euler and Navier-Stokes equations. Under certain assumptions, imposed on initial data and viscosity coefficient the local and global existence of solutions can be proved. Moreover, we have a uniform in time bound on the density of fluid.
 19.4.2010
15:40
Incompressible fluids with pressure and shear-rate dependent viscosity
Abstract:

15:40 Prof. Josef Malek (Faculty of Math. and Phys., Charles University in Prague)
Introduction

15:55 Mgr. Martin Lanzendorfer (Institute of Computer Science, AS CR)
On the existence analysis of fluids whose viscosity depends on the pressure and the shear rate

16:25 MSc. Adrian Hirn (IWR, University of Heidelberg)
Finite element approximation of flows of fluids with shear rate and pressure dependent viscosity

16:45 MSc. Stefan Knauf (IWR, University of Heidelberg)
Numerical simulations for ball bearings containing fluids with pressure-dependent viscosity

 26.4.2010
15:40
 Dr. Tomas Furst (Palacky University, Olomouc, Czech Republic): Richards equation and finger-like solutions: an impossibility result Abstract: The understanding and description of water movement in unsaturated porous media rates among the most challenging (and still not fully resolved) problems with important applications in oil recovery, environment protection, nuclear waste deposition, etc. Traditionally, fluid motion in porous media has been described in the framework of continuum mechanics which has lead to various forms of the celebrated Richards equation (1931). However, this approach runs into several problems, which will be addressed in the seminar. Most thoroughly, the problem of finger flow (observed as early as 1960) will be addressed. Finger flow represents a widely observed (rather generic than exceptional) mode of water infiltration into an initially dry porous medium. Recently, there has been a considerable discussion about the possibility of obtaining finger-like solutions to the Richards equation. In the seminar, it will be demonstrated that Richards equation, in principle, cannot admit finger-like solutions for three-dimensional homogeneous unsaturated porous media flow, subject to monotone boundary conditions. This will be demonstrated for any reasonable type of homogeneous porous material; the result will not be dependent on any particular constitution assumptions. Moreover, it will be explained why hysteresis of the retention curve does not play any role in the proof. An alternative approach to finger flow modeling will be discussed which uses the ideas of cellular automata.
17:20
 Dr. Rostislav Vodak (Palacky University, Olomouc, Czech Republic): Two models of non-linear diffusion in leather processing Abstract: 1. Processing of raw hide into leather comprises more than thirty chemical, physical and mechanical processes which need to be performed optimally in order not to damage the valuable raw material. Before the transport to tanneries, hide is usually conserved by salt. Even the process of salination is subject to optimisation because its incorrect course may lead to a considerable economic loss. Although raw hide represents a complicated (water-saturated) porous medium, the process of salination can be modeled by molecular diffusion. However, the concentrations involved are so high (up to 10 %) that the infiltration of salt into the water-saturated hide induces a counter-flow of fresh water out of the sample. This so called self-induces convection makes the mathematical model far more interesting. In the seminar, a one-dimensional form of the model will be presented. Existence of a weak solution to the system will be proved by means of the Schaefer Fixed Point Theorem. Moreover, a minimum principle for salt concentration will be derived. 2. Removing of the preserving salt is followed by a de-hairing operation, which is performed by sodium sulphide under strongly alkaline conditions of calcium hydroxide. After de-hairing, the white hide contains an excess of calcium hydroxide, which has to be removed again by decantation washing. In terms of mathematical modeling, decantation washing represents diffusion accompanied by desorption, which makes the model non-linear. In the seminar, existence and uniqueness of a weak solution to the model will be presented, and its stabilization for time converging to infinity will be shown.
 3.5.2010
15:40
 Prof. Endre Suli (University of Oxford): Existence of global weak solutions to kinetic models of dilute polymers Abstract: We report on recent progress concerning the existence of global-in-time weak solutions to a general class of microscopic-macroscopic bead-spring models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The model consists of the unsteady incompressible Navier-Stokes equations in a bounded domain, for the velocity and the pressure of the fluid, with an elastic extra-stress tensor as the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass diffusion term. We establish the existence of global-in-time weak solutions to the model for a general class of spring-force potentials including, in particular, the widely used finitely extensible nonlinear elastic (FENE) potential. A key ingredient of the argument is a special testing procedure in the weak formulation of the Fokker-Planck equation, based on a convex entropy function. This is joint work with John W. Barrett (Imperial College London).
 10.5.2010
15:40
 Dr. Anna Marciniak-Czochra (IWR, University of Heidelberg): Boundedness of solutions of a haptotaxis model Abstract: we prove existence of global solutions of the haptotaxis model of cancer invasion for arbitrary nonnegative initial conditions. Uniform boundedness of the solutions is shown using the method of bounded invariant rectangles applied to the reformulated system of reaction-diffusion equations in divergence form with a diagonal diffusion matrix. Moreover, the analysis of the model shows how the structure of kinetics of the model is related to the growth properties of the solutions and how this growth depends on the ratio of the sensitivity function (describing the size of haptotaxis) and the diffusion coefficient. One of the implications of our analysis is that in the haptotaxis model with a logistic growth term, cell density may exceed the carrying capacity, which is impossible in the classical logistic equation and its reaction-diffusion extension.
 17.5.2010
15:40
 Prof. Enrique Zuazua (Basque Center for Applied Mathematics): canceled
 31.5.2010
15:40
 Prof. Akif Ibragimov (Department of Mathematics & Statistics, Texas Tech University): Stability analyzes of non-linear flows in porous media and application Abstract: Note: The seminar will exceptionally take place in the lecture room K3.
 4.10.2010
15:40
 Prof. Gerard Meurant (Commissariat a l Energie Atomique (CEA), former Research Director): Matrices, moments and quadrature I Abstract: The aim of this series of lectures is to describe and explain the beautiful mathematical relationships between matrices, moments, orthogonal polynomials, quadrature rules and the Lanczos and conjugate gradient algorithms. The main topic is to obtain numerical methods to estimate or in some cases to bound quantities like I[f]=u^T f(A)v where u and v are given vectors, A is a symmetric nonsingular matrix and f is a smooth function. There are many instances in which one would like to compute bilinear forms like u^T f(A)v. A first application is the computation of some elements of the matrix f(A) when it is not desired or feasible to compute all of f(A). Computation of quadratic forms r^T A^{-i}r for i=1,2 is interesting to obtain estimates of error norms when one has an appro ximate solution of a linear system Ax=b and r is the residual vector b-Ax. Bilinear or quadratic forms arise naturally for the computation of parameters in problems like least squares, total least squares and regularization methods for solving ill--posed problems. We will describe the algorithms and give some examples of applications. Particular topics addresssed: Orthogonal polynomials and properties of tridiagonal matrices, the Lanczos and conjugate gradient (CG) algorithms and computation of Jacobi matrices, Gauss quadrature and bounds for bilinear forms u^T f(A)v, and applications (bounds for elements of $f(A)$, estimates of error norms in CG, least squares and total least squares, discrete ill--posed problems). The presentation is available at http://www.karlin.mff.cuni.cz/ncmm/texts/Meurant_Lecture1.pdf
17:20
 Prof. Giulio Schimperna (Universita di Pavia): On a class of fourth order degenerate parabolic equations Abstract: I will present some existence, regularity, and long-time behaviour results for a fourth order parabolic equation related to the evolution of thin films. Applications to the Cahn-Hilliard model with degenerate mobility are also discussed. More precisely, after showing existence of at least one (weak) solution by means of an approximation - a priori estimates - passage to the limit argument, I will analyze the generalized dynamical process associated to the equation and prove the existence of a weak trajectory attractor. In case a viscosity term is added and slightly more restrictive conditions on the nonlinearities are assumed, this trajectory attractor can be intended with respect to the strong phase-space topology. Finally, I will present sufficient conditions for having strict positivity of the solution, entailing in particular uniqueness. The result presented in the talk have been obtained in collaboration with Sergey Zelik (university of Surrey).
 11.10.2010
15:40
 Prof. Vladislav Mantic (Universidad de Sevilla): Debonding at the fibre-matrix interface under transversal biaxial loads: an application of Interfacial and Finite Fracture Mechanics to crack initiation and propagation at micro scale in composites Abstract: Under loads normal to the direction of the fibres, composites reinforced by long fibres suffer failures that are known as matrix or interfibre failures, typically involving interface cracks between matrix and fibres, the coalescence of which originates macrocracks in the composite. A micromechanical model, based on the Interfacial and Finite Fracture mechanics and also on a numerical Boundary Element model, is presented aiming to explain the mechanism of appearance and propagation of the damage. To this end, the plane strain problem of a single circular cylindrical inclusion embedded in an unbounded matrix subjected to a far field uniaxial and biaxial transverse load is studied. First, a theoretical model for the simultaneous prediction of the initial size of a crack originated at the inclusion-matrix interface and of the critical remote load required to originate this crack is presented. Isotropic and linear elastic behaviour of both materials, with the inclusion being stiffer than the matrix, is assumed. The interface is considered to be strong (providing continuity of displacements and tractions across the interface surface) and brittle. A new dimensionless structural parameter, depending on bimaterial and interface properties together with the inclusion radius, which plays a key role in characterizing the interface crack onset, is introduced. A size effect inherent to this problem is predicted and analysed. Then, the crack growth along the inclusion-matrix interface and its subsequent kink towards the matrix is studied by means of a numerical model. Experiments show an excellent agreement between the predictions generated and the evolution of the damage in an actual composite.
17:20
 Prof. Gerard Meurant (Commissariat a l Energie Atomique (CEA), former Research Director): Matrices, moments and quadrature II Abstract: The presentation is available at http://www.karlin.mff.cuni.cz/ncmm/texts/Meurant_Lecture2.pdf
 18.10.2010
15:40
 Dr. Christos Panagiotopoulos (Universidad de Sevilla): Boundary Element Method for linear elasticity and implementation of an energetic approach to the delamination problem Abstract: Boundary Element Method (BEM) as a numerical tool for solving (initial)-boundary values problems with a focus on engineering mechanics will be introduced first. Some new trends in the BEM programming will be discussed. A novel application of the BEM to the delamination onset and growth by means of the energetic solution formulation will be presented together with some numerical results.
 25.10.2010
15:40
 Priv.-Doz. RNDr. Martin Kruzik, PhD. (Institute of Information Theory and Automation, AS CR): Quasiconvexity at the boundary and weak lower semicontinuity of integral functionals Abstract: We show that the so-called quasiconvexity at the boundary, originally defined by J.M. Ball and J. Marsden to state necessary conditions for minimizers in nonlinear elasticity, plays a crucial role in the description of weak lower semicontinuity of integral functionals depending on gradients. As a consequence, we get higher integrability properties of some quasiaffine mappings.
17:20
 Prof. Gerard Meurant (Commissariat a l Energie Atomique (CEA), former Research Director): Matrices, moments and quadrature 3 Abstract: The presentation is available at http://www.karlin.mff.cuni.cz/ncmm/texts/Meurant_Lecture3.pdf
 1.11.2010
15:40
 RNDr. Miroslav Bulicek, PhD. (Mathematical Institute of the Charles University, Prague): C^alpha-regularity for a class of non-diagonal elliptic systems with p-growth Abstract: We consider any weak solution to a system of nonlinear elliptic PDE s in $W^{1,p}$ setting that represents an Euler equation to a certain variational problem. Assuming that such a solution satisfies, in addition, the Noether equation, we identify new structural assumptions on the nonlinearity that guarantees Holder continuity of the solution. The new method is applicable also to a class of non-diagonal non-convex problems.
17:20
 Prof. Gerard Meurant (Commissariat a l Energie Atomique (CEA), former Research Director): Matrices, moments and quadrature 4
 8.11.2010
15:40
 Prof. Dr. Alexander Mielke (Weierstrass Inst. Berlin & Humboldt Universitat zu Berlin, Germany): Rate-independent plasticity as Gamma limit of a slow viscous gradient flow for wiggly energies Abstract: In a joint work with Lev Truskinovsky it is shown that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco-elastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete to continuum limit. In the course of these limits a non-convex elastic problem transforms into a convex elastic problem while the quadratic rate-dependent dissipation of visco-elastic solid transforms into a singular rate-independent dissipation of an ideally plastic solid. In order to emphasize ideas we employ in our proofs the simplest prototypical system describing transformational plasticity of shape-memory alloys. The approach, however, is sufficiently general and can be used for similar reductions in the cases of more general plasticity and damage models.
 15.11.2010
15:40
 Prof. Ing. Tomas Roubicek, DrSc. (Charles University, Prague & Academy of Sciences of the Czech Republic): Plasticity at small strains with or without hardening Abstract: Small-strain plasticity in its quasistatic formulation based on the energetic-solution concept will be presented, with the focus to the limit to the Prandt-Reuss elastic/perfectly plastic model when hardening parameters go to zero. Beside mere isothermal quasistatic evolution, also thermodynamical augmentation of these models will be discussed for isotropic materials undergoing thermal expansion. Numerical analysis will be outlined. The talk will be accompanied by sample computational experiments performed by S. Bartels (Univ. Bonn).
17:20
 RNDr. Miroslav Bulicek, Ph.D. (Charles University, Prague): On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions Abstract: We establish the large-data and long-time existence of a suitable weak solution to an initial and boundary value problem driven by a system of partial differential equations consisting of the Navier-Stokes equations with the viscosity $nu$ increasing with a scalar quantity $k$ that evolves according to an evolutionary convection diffusion equation with the right hand side nu(k)|D(v)|^2 that is merely L^1-integrable over space and time. We also formulate a conjecture concerning regularity of such a solution.
 22.11.2010
15:40
 Dr. Vit Prusa (Charles University, Prague): Flow of an electrorheological fluid in a journal bearing Abstract: Electrorheological fluids have numerous potential applications in vibration dampers, brakes, valves, clutches, exercise equipment, etc. The flows in such applications are complex three dimensional flows. Most models that have been developed to describe the flows of electrorheological fluids are one dimensional models. Here, we discuss the behaviour of two fully three dimensional models for electrorheological fluids. The models are such that they reduce, in the case of simple shear flows with the intensity of the electric field perpendicular to the streamlines, to the same constitutive relation, but they would not be identical in more complicated three dimensional settings. In order to show the difference between the two models we study the flow of these fluids between eccentrically placed rotating cylinders kept at different potentials, in the setting that corresponds to technologically relevant problem of flow of electrorheological fluid in journal bearing. Even though the two models have quite a different constitutive structure, due to the assumed forms for the velocity and pressure fields, the models lead to the same velocity field but to different pressure fields. This finding illustrates the need for considering the flows of fluids described by three dimensional constitutive models in complex geometries, and not restricting ourselves to flows of fluids described by one dimensional models or simple shear flows of fluids characterized by three dimensional models.
 29.11.2010
15:40
 Prof. Maria Lukacova (University of Mainz, Germany): Large time step finite volume schemes for shallow water flows Abstract: We present two new large time step methods within the framework of the well-balanced finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for low Froude number shallow water flows with source terms modelling the bottom topography and Coriolis forces, but results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We present two variants of large time step FVEG method: a semi-implicit time approximation and an explicit time approximation using several evolution steps along bicharacteristic cones. The behaviour of the methods will be discussed through a series of numerical experiments. This is a joint work with A. Hundertmark and F. Prill.
17:20
 Dr. Stefan Kroemer (Mathematisches Institut, Universitaet zu Koeln, Germany): Dimension reduction for functionals on solenoidal vector fields Abstract: We study integral functionals constrained to divergence-free vector fields in $L^p$ on a thin domain, in the limit as the thickness of the domain goes to zero. The Gamma-limit with respect to weak convergence in $L^p$ turns out to be given by the associated functional with convexified energy density wherever it is finite. Remarkably, this happens despite the fact that relaxation of nonconvex functionals subject to the limiting constraint can give rise to a nonlocal functional as illustrated in an example.
 6.12.2010
15:40
 Prof. Andreas Fischer (TU Dresden, Germany): Newton Methods for Generalized Nash Equilibrium Problems Abstract: In the generalized Nash equilibrium problem (GNEP) both the objective function and the feasible set of each player may depend on the other players strategies. In general, to find even one solution is a challenging task. Solutions of GNEPs can be characterized by necessary conditions. Based on this we provide two Newton methods, analyze their features and their range of applicability. In particular, we address the issue of the non isolated solutions that can cause severe difficulties within an application of standard methods. The talk is based on joint work with Francisco Facchinei and Veronica Piccialli.
17:20
 Prof. Maria Lukacova (University of Mainz, Germany): Efficient Fluid-Structure Algorithms with Application in Hemodynamics Abstract: The aim of this talk is to present recent results on numerical modelling of non-Newtonian flow in compliant stenosed vessels with application in hemodynamics. For the structure problem the generalized string equation for radial symmetric tubes is used and extended to a stenosed vessel. We consider two FSI algorithms: firstly, the global iterative approach with respect to the domain deformation and secondly, the kinematic splitting that is used to split a coupled fluid-structure problem in an efficient and stable way. Stability of the new FSI schemes will be studied theoretically as well as experimentally. At the end we present numerical experiments for some non-Newtonian models, comparisons with the Newtonian model and the results for hemodynamic wall parameters; the wall shear stress and the oscillatory shear index. This is a joint work with A. Hundertmark and G. Rusnakova
 13.12.2010
15:40
 Dr. Trygve Karper (Norwegian University of Science and Technology, Trondheim, Norway): Convergent finite element methods for compressible Stokes flow Abstract: In the literature one can find a variety of numerical methods appropriate for viscous compressible flow. However, there are very few results with reference to the convergence properties of these methods. For instance, it is an open problem whether any numerical method for the compressible Navier-Stokes equations (in more than one dimension) converges as discretization parameters tend to zero. In this talk, I aim at discussing why proving convergence of numerical methods for viscous compressible flow is so hard. I will also present some recently developed methods that are provably convergent for compressible Stokes flow (neglecting convection). These methods solves half of the problems, but still seem inadequate for the problem with convection.
 3.1.2011
15:40
 Prof. Josef Malek (Mathematical Institute of the Charles University, Prague): Necas Center in 2011
16:00
 Dr. Ondrej Soucek (Charles University in Prague, Faculty of Mathematics and Physics): Advances and open problems in physical glaciology Abstract: Glaciology is a physical discipline describing the flow and evolution of ice masses on the Earth. The evolution of grounded glaciers - ice-sheets - is primarily controlled by the climate forcing via surface temperature and precipitation/ablation rates and by the geothermal heat flux from the Earths interior. Given these inputs, the dynamics of ice-sheets on sufficiently long time and spatial scales may be viewed as a thermomechanically coupled free-surface flow of a non-Newtonian fluid subject to gravity forcing. A large number of physical processes needs to be taken into account to provide a sufficiently realistic glacier model, some of which are still only poorly understood. Typical example is a generation and transport of meltwater in the ice matrix and its interaction with the glacier flow, that would require a mixture continuum thermodynamics rather than a single-component theory. Of the same importance are processes at the glacier base, such as the interaction of basal ice and meltwater with a sedimentary glacier bed, which strongly affects basal boundary conditions. For sufficiently low local temperatures, no-slip (frozen bed) Dirichlet boundary condition is applied, while in regions where basal temperature exceeds the local pressure-melting point, a rapid sliding occurs, governed by a Newton-type sliding law. As shown in recent numerical studies, such a type of thermally-conditioned boundary conditions may become a trigger of large-scale intrinsic instabilities of the whole ice-sheet, which is a phenomenon indicated by geological evidence. From a numerical point of view, glacier physics remains a challenging topic as even relatively crude and simplistic formulations of glacier flow problem remain rather intractable by standard numerical techniques such as finite-elements. Various approximations of the flow equations based on scaling analysis have been adopted, in order to reduce the huge computational demands.
17:10
 Dr. Jan Haskovec (Johann Radon Institute for Computational and Applied Mathematics, Linz, Austria): Stochastic Particle Approximation to the Keller-Segel model in 2D Abstract: We construct an approximation to the measure valued, global in time solutions to the Keller-Segel model of chemotaxis in 2D, based on systems of stochastic interacting particles. The main advantage of our approach is that it captures the solution even after the possible concentration events (blow-ups). We present a numerical method based on this approach, discuss the related technical issues and show some numerical results. The first step toward the convergence analysis of our method consists of considering a regularized particle scheme and showing that one recovers the solution of the regularized Keller-Segel system when the number of particles tends to infinity. The proof is based on the BBGKY-approach known from classical kinetic theory. The second step is to describe the limit when the regularization parameter tends to zero, which is technically much more involved and requires an application of the framework of time dependent measures with defects. Subsequently, we pass to the limit when the number of particles tends to infinity and show that the resulting object is compatible with the measure valued solutions of the Keller-Segel system, in the sense that solutions of the latter generate solutions of the former. However, from fundamental reasons it is impossible to make a rigorous statement about the equivalence of these two. Finally, we provide a detailed description of the dynamics of the particle system consisting of two particles only, and explain why the analysis of systems with three or more particles remains an open problem. This is a joint work with Christian Schmeiser (University of Vienna).
 10.1.2011
15:40
 Doc. RNDr. Eduard Feireisl, DrSc. (Institute of Mathematics AS CR): Suitable weak solutions to the compressible Navier-Stokes system Abstract: We introduce a class of suitable weak solutions to the Navier-Stokes system of equations governing the motion of a compressible viscous fluid. These solutions satisfy the relative entropy inequality introduced by several authors, and, in particular, they enjoy the weak-strong uniqueness property.
17:20
 Dr. Ondrej Soucek (Mathematical Institute of the Charles University): Shallow Ice Approximation Abstract: We present in detail the traditional physical approach towards the Shallow Ice (SI) scaling approximation of the Navier-Stokes-Fourier system for the ice-flow problem. The simplest possible (still physically relevant) setting is considered. Ice is described as a single-component continuum and described by a model of a heat-conducting non-Newtonian power-law fluid. The ice-sheet geometry is described by two smooth boundaries, the first one representing the upper free surface with a prescribed mass-production rate and surface temperature, the bottom representing the glacier base, where the heat flux is prescribed and the sliding law is specified by a Newton-type boundary condition. A-priori scaling is introduced into the stress-tensor and other field quantities and a corresponding dimensionless form of the governing equations and boundary conditions is derived. The SI approximation is obtained from the differential form of the Navier-Stokes-Fourier system as a leading-order limit of the perturbation expansion for the flatness parameter and the Froude number approaching zero.
 28.2.2011
15:40
 Prof. Lorenzo Freddi (Dipartimento di Matematica e Informatica, Universita di Udine): From 3D non-linear elasticity to 1D elastic models for thin-walled beams Abstract: Geometrically, a thin-walled beam is a slender structural element whose length is much larger than the diameter of the cross-section which, on its hand, is larger than the thickness of the thin wall. Beams of this kind have been used for a long time in civil and mechanical engineering and, most of all, in flight vehicle structures because of their high ratio between maximum strength and weight. Because of their slenderness thin-walled beams are quite easy to buckle and to deform and hence, in several circumstances, their study has to be conducted by means of nonlinear theories. In this talk, starting from three-dimensional nonlinear elasticity, we rigorously derive a hierarchy of one-dimensional models for a thin-walled beam, in the spirit of what has been done by Friesecke, James and Muller for plates. The different limit models are distinguished by the different scaling of the elastic energy, which, in turn, depends on the scaling of the applied loads. We can identify three main regimes. In the first the limit model is an inextensible string. In the second we obtain a Cosserat model for a thin-walled beam. Finally, in the third regime we deduce one dimensional linear/quasi-linear models for thin-walled beams.
17:20
 Dr. Chiara Zanini (Dipartimento di Matematica e Informatica, Universita di Udine): Quasistatic delamination models for Kirchhoff-Love plates Abstract: The talk will address a quasistatic rate-independent brittle delamination problem and also an adhesive unilateral contact problem on a cylinder with a prescribed normally-positioned surface inside. By letting the height of the cylinder go to zero, we obtain two quasistatic rate-independent crack models with prescribed path for Kirchhoff-Love plates. (This is essentially based on a joint work with L.Freddi, R.Paroni, and T.Roubicek.)
 7.3.2011
15:40
 Prof. Dr. Christian Grossmann (TU Dresden, Institute of Numerical Mathematics): Convergence of Interior-Exterior Penalty Methods in Optimal Control
 14.3.2011
15:40
 Dr. Agnieszka Swierczewska-Gwiazda (Institute of Applied Mathematics and Mechanics, University of Warsaw, Poland): On flows of implicitly constituted fluids characterized by a maximal monotone graph Abstract: We study flows of incompressible fluids in which the deviatoric part of the Cauchy stress and the symmetric part of the velocity gradient are related through an implicit equation. Although we restrict ourselves to responses characterized by a maximal monotone graph, the structure is rich enough to include power-law type fluids, stress power-law fluids, Bingham and Herschel-Bulkley fluids, etc. We are interested in the development of (large-data) existence theory for internal flows subject to no-slip boundary conditions. We study first Stokes-like problems, and later we consider complete problems including the convective term. Doing so, we pay the attention to the tools involved in the analysis of the problem.
 21.3.2011
15:40
 Dr. Tomasz Piasecki (Institute of Mathematics, Polish Academy of Sciences): Stationary compressible flow with slip boundary conditions Abstract: I am going to discuss the issue of existence of stationary solutions to the Navier Stokes Equations for compressible, barotropic flow in a cylindrical domain. More precisely, we are interested in strong solutions in a vicinity of given laminar flows. I will show existence of such solution when the perturbed flow is a constant flow or a Poiseuille profile. In the latter case we need some assumptions on the viscosity, but these turn out natural and does not provide any serious limitations. A main problem to face in the proof is the lack of compactness in the continuity equation. To overcome this diffuculty we can introduce a kind of Lagrangian coordinates. In the new system the continuity equation simplifies enabling us to apply the Banach Fixed Point Theorem.
 28.3.2011
15:40
 priv. doc. RNDr. Martin Kruzik, PhD (UTIA, Czech Academy of Science, Prague): Young measures supported on regular matrices Abstract: We completely and explicitly describe Young measures generated by matrix-valued mappings ${Y_k}_{kinN} subset L^p(O;R^{n imes n})$, $OsubsetR^n$, such that ${Y_k^{-1}}_{kinN} subset L^p(O;R^{n imes n})$ is bounded, too. Moreover, the constraint $det Y_k>0$ can be easily included and is reflected in a condition on the support of the measure. These results allow us to relax minimization problems for functionals $J(Y):=int_O W(Y(x)),md x$, where $W(F)$ tends to infinity if the determinant of $F$ converges to zero. This phenomenon typically occurs in problems of nonlinear-elasticity theory for hyperelastic materials if $Y:= abla y$ for $yin W^{1,p}(O;R^n)$, for instance. We touch this particular situation with the additional condition $det abla y>0$, as well. This is a joint work with Barbora Benesova and Gabriel Patho.
 4.4.2011
15:40
 Prof. Ing. Tomas Roubicek, DrSc. (Mathematical Institute of Charles University): Perfect plasticity at small strains and its thermodynamics Abstract: A thermodynamically consistent model of perfect plasticity is presented and an existence of its energetic solutions is proved.
 11.4.2011
15:40
 Dr. Riccarda Rossi (University of Brescia, Italy): Analysis of doubly nonlinear evolution equations driven by nonconvex energies Abstract: In this talk, based on a joint collaboration with Alexander Mielke and Giuseppe Savare , we present existence results for doubly nonlinear equations featuring nonsmooth and nonconvex energies. We prove existence by passing to the limit in a time-discretization scheme, based on the Minimizing Movement approach by Ennio De Giorgi. We present some applications.
 18.4.2011
15:40
 Doc. RNDr. Ondrej Cadek, CSc. (Department of Geophysics, Faculty of Mathematics and Physics, Charles University in Prague): Geofyzikalni modely vyvoje Zeme a dalsich teles slunecni soustavy Abstract: Geofyzikalni studium vyvoje Zeme a dalsich teles slunecni soustavy je zalozeno na numerickem reseni rovnic popisujicich prenos tepla ve vysokoviskozni kapaline. Krome tradicni Bousinesqovy aproximace se dnes jiz standardne vyuziva take rozsirena Bousinesqova aproximace (zahrnujici disipacni a adiabaticke zahrivani a teplo uvolňujici se pri fazovych prechodech) a anelasticka aproximace (uvazujici narust hustoty s hloubkou). Jelikoz se jedna o velmi pomale procesy, lze v pohybove rovnici bezpecne zanedbat setrvacny clen. Vyznamnou komplikaci pri reseni rovnic zpravidla predstavuje viskozita, ktera se muze menit v rozmezi sesti i vice radu. Viskozita je obecne chapana jako funkce tlaku, teploty a napeti (a pripadne dalsich parametru, jako je napr. velikost zrna) a je casto zavedena tak, aby simulovala i dalsi typy deformaci, jako je krehke poruseni a plasticita. Dalsim specifikem geofyzikalnich modelu jsou fazove prechody, ať uz souvisejici s tavenim materialu nebo s jeho prechodem do vysokotlake faze s odlisnymi fyzikalnimi vlastnostmi. Chovani geofyzikalnich systemu je obvykle studovano ve dvourozmerne kartezske geometrii, stale castejsi jsou ale dnes i trojrozmerne sfericke modely. Nektere soucasne modely se snazi pracovat s volnou hranici a zahrnout deje, ktere souvisi s jeji deformaci (eroze, sedimentace). Z geofyzikalnich problemu resenych na katedre geofyziky MFF budou diskutovany tri priklady: 1) model litosfericke desky zanorujici se do plaste (priklad komplikovane reologie materialu s fazovymi prechody), 2) simulace geologickeho vyvoje Ceskeho masivu v prubehu variske orogeneze (model zahrnuje nekolik nemisitelnych petrologickych fazi, krehke chovani svrchni kury a volnou erodujici hranici) a 3) generace podpovrchoveho oceanu na Saturnove mesici Enceladu v dusledku slapoveho zahrivani (trojrozmerny sfericky model, zahrnujici viskozni i viskoelastickou deformaci). Spoluautori: Hana Cizkova, Petra Maierova a Marie Behounkova z teze katedry
17:20
 Dr. Ondrej Sramek (University of Colorado at Boulder, Department of Physics, Boulder, Colorado, USA): Modeling of two-phase flow in geophysics: compaction, differentiation and partial melting Abstract: Partial melting and migration of melts play an important role in the formation and evolution of the Earth other terrestrial bodies. Transport of heat, rock rheology and distribution of major, minor, as well volatile chemical species are all affected by the presence and migration of magmas. Partial melting and melt extraction are central processes for the formation of the oceanic crust and are responsible for the depletion of the bottom part of the lithosphere in incompatible elements. Migration of molten material played a major role in the dynamic evolution of the early Earth and even now plays a fundamental role in the transport of matter as well as heat in partially molten regions of deeper mantle (e.g., at the coremantle boundary). The separation of the denser metal from the lighter silicates is the most extensive differentiation process in the course of Earths evolution and the evolution of terrestrial planetary bodies in general. This process also implies the presence of distinct phases, in solid and liquid states. Gravitational energy which is released upon differentiation is a major source of heat that must be considered when assessing the thermal history of a forming planet. It is therefore essential to properly take into account the energy exchange that takes place in a multiphase medium on a large spatial scale in order to investigate early planetary evolution and to constrain the differentiation time scales. In my talk I will present a recently developed general model of two-phase flow and deformation in a two-phase medium. The model offers a self-consistent description of the mechanics and thermodynamics of a mixture of two viscous fluids, in the form of continuum mechanical equations in the limit of a slow creeping flow. The difference in pressures that exists between the two phases is generated i) by the surface tension at the interfaces between the phases which are included in the description, and ii) by the isotropic deformation (i.e., compaction or dilation) of the individual phases upon flow. In most geologic applications, one of the phases (named the liquid phase) is much less viscous than the other phase (the solid phase), which greatly simplifies the equations. I will show some results of modeling of a terrestrial planet differentiation, and of the coupling between melting and deformation.
 25.4.2011
15:40
 Easter Monday - seminar canceled
 2.5.2011
15:40
 Ing. Mgr. Tomas Bodnar, Ph.D. (Department of Technical Mathematics, Czech Technical University of Prague): Viscoelastic fluid flows at larger than small Weisenberg numbers Abstract: The talk addresses one of the classical problems related to the mathematical modeling and numerical simulation of viscoelastic flows. A short overview of problems arrising during the simulation of viscoelastic fluid flows at moderate and high Weisenberg numbers is presented. An alternative point of view on the treatment of these issues is offered. A new simple test case is proposed to demonstrate the problem and it s possible solution. In the conclusion, a new formulation of the Johnson-Segalman model is proposed to be solved.
 9.5.2011
15:40
 Dr. Giuseppe Tomassetti (Dipt. Ingegneria Civile, Univ. di Roma II - Tor Vergata): Energetic solution of the torsion problem in strain-gradient plasticity Abstract: We consider elasto-plastic torsion in a thin wire in the framework of the strain-gradient plasticity theory recently proposed by Gurtin and Anand. This theory takes into account the socalled geometricallynecessary dislocations through a dependence of the free energy on the Burgers tensor G=curl E , where E is the plastic part of the linear strain. For the rate-independent case with null dissipative length scale, we construct explicitly an energetic solution of the evolution problem. We use this solution to estimate the dependence of the torque on the twist and on the material scale. Our analysis highlights some size effect, showing that thinner wires are stronger. This work is in collaboration with Maria Chiricotto and Lorenzo Giacomelli.
 16.5.2011
15:40
 Dr. Jan Valdman (University of Iceland, Reykjavik, Iceland and Max-Planck Institute Leipzig): Computations and a posteriori error estimates in elastoplasticity Abstract: download abstract
 23.5.2011
15:40
 Dr. Martin Heida (Institute for Applied Mathematics, University of Heidelberg, Germany): An introduction to homogenization theory Abstract: Homogenization theory deals with modeling of processes in media with complex micro structures, whenever this particular micro structure influences the macroscopic behavior. The homogenization theory has become a huge domain in mathematical modeling and this talk aims to give a short overview over the goals and methods in this field. We will mostly restrict to periodic micro structures and discuss formal and rigorous methods like asymptotic expansion, two-scale convergence and periodic unfolding. As an outlook we will also look at the homogenization methods for stochastic geometries.
 3.10.2011
15:40
 Prof. E. Fernandez-Cara (Dpto. EDAN, University of Sevilla, Spain): Global Carleman inequalities and control results for systems from continuum mechanics Abstract: This talk deals with the theoretical and numerical solution of several control problems for several PDEs from mechanics. I will present some results that rely on global Carleman inequalities and Fursikov-Imanuvilov s approach. In the linear case, according to this strategy, the (original) controllability problems can be reduced to the solution of appropriate higher-order differential problems. For similar nonlinear problems, this can be used in combination with fixed point theorems and/or iterative methods. I will also present some numerical experiments that show that this approach is very useful.
 10.10.2011
15:40
 Ucastnici studentske letni staze v NCMM Nepracuj v Tescu, ziv se vedou Abstract: Prezentace vysledku studentske letni staze v NCMM. Program prezentace: 15:40 Barbora Benesova: SIAM Student Chapter Prague 16:00 Dominik Mokris: Uvodni slovo ke stazim; Isogeometricka Analyza 16:20 Jan Kuratko: Vypocet hodnosti Sylvesterovy matice 16:40 Martin Rehor: Materialy ve squeezeflow geometrii 17:00 ------- Coffee Break 17:10 Miroslav Kuchta: Lapetus 17:30 Marek Netusil: Benchmarky pro anisotropni materialy 17:50 Adam Janecka: Tekutiny s viskozitou zavislou na tlaku pri povrchovem zatizeni
 17.10.2011
15:40
 Prof. E. Fernandez-Cara (Dpto. EDAN, University of Sevilla, Spain): The control of evolution PDEs: some recent results and open problems, Part 1 of 3 Abstract: Texts for the lectures can be downloaded: Introduction, L1-OptimalControl.pdf, L2-HeatandWaves, L3_Others.pdf. Lecture 1: Introduction. Optimal control and controllability. Basic definitions and fundamental results. Optimal control results for some nonlinear problems and related open questions. Numerical approximation, numerical results and applications.
 24.10.2011
15:40
 Prof. E. Fernandez-Cara (Dpto. EDAN, University of Sevilla, Spain): The control of evolution PDEs: some recent results and open problems, Part 2 of 3 Abstract: Texts for the lectures can be downloaded: Introduction, L1-OptimalControl.pdf, L2-HeatandWaves, L3_Others.pdf. Lecture 2: Controllability of parabolic equations. Unique continuation, Carleman estimates and observability. On the controllability of semilinear and nonlinear problems. Additional results and open questions: the Stokes and Navier-Stokes systems, stochastic controllability, etc.
17:20
 Prof. E. Fernandez-Cara (Dpto. EDAN, University of Sevilla, Spain): The control of evolution PDEs: some recent results and open problems, Part 3 of 3 Abstract: Texts for the lectures can be downloaded: Introduction, L1-OptimalControl.pdf, L2-HeatandWaves, L3_Others.pdf. Lecture 3: Controllability of linear hyperbolic equations and systems. Unique continuation, observability, the multipliers method and the geometric control condition. Semilinear hyperbolic equations. Additional results and open questions: linear elasticity, visco-elastic fluids, etc.
 31.10.2011
15:40
 MUDr. Ales Hejcl, Ph.D. a Dr. med. MUDr. Amir Zolal, Ph.D. (Neurochirurgicka klinika Univerzity J.E. Purkyne a Masarykovy nemocnice, Usti nad Labem): Intrakranialni aneuryzma: vyvoj, hemodynamika a terapie z pohledu neurochirurga
17:20
 RNDr. J. Hron, PhD. a RNDr. Martin Madlik, Ph.D. (Matematicky Ustav UK): Intrakranialni aneuryzma: hemodynamika a CFD z pohledu matematickeho modelovani
 7.11.2011
15:40
 Prof Vlastimil Krivan (Biology center, Ceske Budejovice): The Lotka-Volterra predator-prey model Abstract: In my talk I will review some crucial steps, based on mathematical reasoning, that laid foundations of today s ecology. I will start with the Lotka-Volterra predator-prey model and will review some subsequent research. I will focus on research by F. G. Gause, a Russian biologist, who made some crucial extensions of the Lotka-Volterra model. In particular, I will discuss his idea about using differential equations with discontinuities, a concept that was developed by A.F. Filippov much latter . I will show, how such models arise naturally in ecology and how they can be used to unify two major ecological fields: evolutionary and population ecology. Presentation can be downloaded from: Krivan_2011.pdf
17:20
 Prof Willi Jaeger (University of Heidelberg, Germany): Multiscale Systems in Lifesciences - Mathematical Modelling and Simulation - Lecture 1
 14.11.2011
15:40
 prof. Antonio DeSimone (SISSA, Trieste, ITALY): Mechanics of motility at microscopic scales: challenges and opportunities for mathematical modeling Abstract: We will review recent progress on the mathematical modeling of crawling and swimming motility in cells, and discuss open problems and promising directions for future research.
 21.11.2011
15:40
 Prof. Sergey Repin (V.A. Steklov Institute of Mathematics at St. Petersburg, Russia): Estimates of deviations from exact solutions of some nonlinear problems in continuum mechanics Abstract: In the talk, we discuss estimates measuring the difference between exact solutions of boundary value problems and arbitrary functions from the corresponding (energy) space. The estimates must be computable, consistent and possess necessary continuity properties. In the context of PDE theory, deriving such type estimates present one of the general problems, which unlike, e.g., regularity theory is focused on studying neighborhoods of exact solutions. Being applied to numerical approximations these estimates imply a unified way of a posteriori error estimation. They can be also used for the analysis of modeling errors and errors caused by incomplete knowledge on the problem data. The talk contains a short introduction devoted to historical background, overview of the results obtained in the last decade (in particular for elliptic variational inequalities) and some recent results related to models with linear growth energy (as, e.g., Hencky plasticity) Literature: S. Repin. A posteriori error estimates for PDE s, deGruyter, Berlin, 2008. M. Fuchs and S. Repin. A Posteriori Error Estimates for the Approximations of the Stresses in the Hencky Plasticity Problem, Numer. Funct. Analysis and Optimization, 32(2011), 6, 610-640. S. Repin and S. Sauter. Estimates of the modeling error for the Kirchhoff-Love plate model. C. R. Math. Acad. Sci. Paris 348 (2010), no. 17-18, 10391043.
17:20
 Prof. Vladislav Mantic; Prof. Roman Vodicka (University of Seville, School of Engineering; Technical University of Kosice, Civil Engineering Faculty): A variational formulation for elastic domain decomposition problems solved by SGBEM with non-conforming discretizations Abstract: The solution of Boundary Value Problems of linear elasticity using a Domain Decomposition approach (DDBVPs) with non-overlapping subdomains is considered. A new variational formulation based on a potential energy functional for DDBVPs expressed in terms of subdomain displacement fields is introduced. The coupling conditions between subdomains are enforced in a weak form. A novel feature of the potential energy functional is a distinct role of subdomains on both sides of the interface. The solution of a DDBVP is given by a saddle point of the potential energy functional. The present formulation of DDBVPs is solved by Symmetric Galerkin Boundary Element Method (SGBEM) considering non-conforming meshes along interfaces between subdomains if required. Finally, some numerical results are presented incuding the cases with non-conforming discretizations of curved interfaces. An excellent accuracy and convergence behaviour of our implementation of SGBEM for DDBVPs is shown providing some stability condition is fulfilled.
 28.11.2011
15:40
 Prof. Henryk Petryk (Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw, Poland): Incremental energy minimization and microstructure formation in dissipative solids Abstract: In elastic or pseudo-elastic solids with fully reversible microstructural changes, the energy minimization is a standard approach based on the concept of stability of equilibrium in a dynamic or thermodynamic sense. It is well known that the loss of ellipticity, rank-one convexity or quasi-convexity of a nonlinear elastic energy function can lead to formation of fine microstructures in the material. However, that approach does not take into account the dissipation of energy that invariably accompanies the transition between equilibrium states. To include the effect of rate-independent dissipation, one can minimize the total incremental energy supplied quasi-statically to the system, which incorporates both free energy and dissipation contribution to the deformation work increment. It is shown that the incremental energy minimization up to the first and second-order terms can yield an exact solution in the first-order rates, provided an appropriate symmetry restriction is imposed on the constitutive law. Loss of quasi-convexity by the rate-potential means that the mechanical work can be extracted from a deforming material element embedded in a continuum being unperturbed elsewhere, which is associated with formation of energetically preferable microstructures. Details of the approach are discussed and illustrated by examples.
17:20
 Prof. Stanislaw Stupkiewicz (Institute of Fundamental Technological Research (IPPT), Polish Academy of Sciences, Warsaw, Poland): Interfacial energy and size effects in evolving martensitic microstructures Abstract: Shape memory alloys (SMA) undergo phase transformation of martensitic type which is the main mechanism responsible for the interesting effects observed in these materials. The transformation is accompanied by formation and evolution of martensitic microstructures which govern the functional properties of SMA. Evolution of microstructure occurs at different scales, and micromechanical models have been developed aimed at description of this multiscale phenomenon. A promising new area of research is to include into such models the effects of interfacial energies present at different scales of martensitic microstructures. In this work, interfacial energy of two origins is accounted for, namely the atomic-scale energy of phase boundaries (taken from the materials science literature) and the elastic micro-strain energy at microstructured interfaces (e.g. at the austenitetwinned martensite interface). The latter is a bulk energy at a finer scale, however, at a higher scale it can be interpreted as the interfacial energy. This energy is predicted using micromechanical considerations. Size-dependent interfacial energy contributions introduce size effects into the multiscale modelling framework. Evolution of microstructure is then determined by applying a general evolution rule in the form of minimization of incremental energy supply. The incremental energy, being the sum of the increments in the free energy and dissipation, comprises both the bulk and the interfacial energy contributions at all levels of the microstructure. As an example, size effects are studied for the pseudoelastic CuAlNi and NiTi shape memory alloys. In particular it is shown that characteristic dimensions of the microstructure can be predicted without introducing any artificial length-scale parameters.
 5.12.2011
15:40
 Dr. Vit Prusa (Mathematical Institute, Charles University in Prague): On a new class of models for fluids stemming from the implicit constitutive theory Abstract: Implicit constitutive theory is a new methodological framework for developing material models. The main idea is, in the case of fluids, that one has to abandon the approach based on the fact that the Cauchy stress tensor T can be expressed as a function of the symmetric part of the velocity gradient D, and has to search for the constitutive relation in the form of an implicit tensorial relation between T and D, f(T,D)=0. We will discuss the ideas that led to the formulation of the theory, introduce some models that has been developed using the theory, and we will in brief analyze their properties.
 12.12.2011
15:40
 Dr. Adrian Hirn (IWR, Heidelberg University): Stabilized finite elements for fluids with shear-rate- and pressure-dependent viscosity Abstract: Non-Newtonian fluid motions are frequently modeled by a power-law ansatz that provides a nonlinear relation between the fluid s viscosity and shear rate. Such fluids play an important role in many areas of application such as engineering, blood rheology, and geology. This talk deals with the finite element (FE) approximation of the corresponding equations of motion. In order to cope with the instabilities of the Galerkin FE method resulting from violation of the inf-sup stability condition or dominating convection in case of high Reynolds numbers, we propose a stabilization method that is based on the well-known local projection stabilization method. For shear thinning fluids, we derive a priori error estimates quantifying the convergence of the method. The established error estimates provide optimal rates of convergence with respect to the supposed regularity of the solution. Finally, we consider viscosities depending on both the shear rate and pressure. We analyze the Galerkin discretization of the governing equations.
 19.12.2011
15:40
 prof. E. Feireisl (Institute of Mathematics, Academy of Sciences of the Czech Republic): Weak solutions and weak strong uniqueness for the Navier-Stokes-Fourier system Abstract: We introduce a concept of weak solution based on Second law of thermodynamics for the full Navier- Stokes-Fourier system describing the motion of a general viscous, compressible, and heat-conducting fluid confined to a bounded spatial domain with energetically insulating boundary. We show that the weak solutions comply with the principle of weak strong uniqueness, meaning they coincide with the strong solution emanating from the same initial data as long as the latter exists.
 9.1.2012
15:40
 Doc. RNDr. Petr Chvosta, CSc. (Katedra makromolekularni fyziky, MFF UK): Matematika a fyzika Brownova sveta Abstract: Jedna se o neformalni uvodni seznameni se soucasnym teoretickym vyzkumem fyzikalnich jevu na urovni reality, ktera se rozprostira na pomezi makrosveta a mikrosveta. V prednasce budou zdurazneny specificke dynamicke a energeticke principy Brownova sveta a nektere jejich neintuitivni dusledky. Adekvatnim matematickym nastrojem se zde jevi teorie stochastickych procesu, specialne teorie difuze a s ni souvisejici Fokker-Planckova rovnice. Diskuze se dotyka nove interpretace druhe hlavni vety termodynamiky a vyzaduje, mimo jine, revizi zakladnich termodynamickych pojmu jako jsou entropie, teplo a prace. Jednim z cilu zakladniho vyzkumu je navrzeni novych principu transformace vsudypritomneho termalniho pohybu na usmerneny makroskopicky pohyb. Takove tzv. Brownovy motory, tj. mechanismy hrajici v mezoskopicke oblasti roli znameho makroskopickeho Carnotova tepelneho stroje, priroda jiz patrne davno objevila a vyuziva je napriklad pri vnitrobunecnem transportu.
 27.2.2012
15:40
V case seminare od 16:00 se kona prednaska Dr. Karla Janecka, RSJ algorithmic trading.
Abstract: Prednasku organizuje SIAM SC a kona se v ramci oslav 60. vyroci MFF UK. [viz. informacni letak]
 5.3.2012
15:40
 prof. Ing. Tomas Roubicek, DrSc. (MU UK): Models of adhesive contacts delaminating at mixity modes Abstract: After introducing a basic concept of quasistatic rate-independent adhesive contacts and surveying some results about it, a refinement by reflection of the mode of delamination will be exposed. As a matter of fact, engineering models distinguishes Mode I (=opening, with rather small activation energy needed) from Mode II (=shearing, with usually much bigger activation energy). Mixity mode combining both modes occurs most typically, rather than a pure Mode I or II. Some mixity-sensitive models bear rigorous mathematical and numerical analysis. Two-dimensional computational experiments will be presented, too. Eventually, some rate-dependent effects like healing or viscosity or inertia will be mentioned. The presentation will reflect collaboration with L.Freddi, M.Kruzik, A.Mielke, V.Mantic, R.Paroni, R.Rossi, L.Scardia, M.Thomas, and C.Zanini, including computational simulations from M.Kocvara, C.G.Panagiotopoulos, R.Vodicka, J.Zeman.
 12.3.2012
15:40
 Prof. Dr. Claus-Dieter Munz (Institut fur Aerodynamik und Gasdynamik, Universitat Stuttgart): Discontinuous Galerkin schemes with reconstruction Abstract: Reconstruction is usually thought of a building block in volume schemes, but may also be combined with discontinuous Galerkin (DG) schemes. In this approach, the degrees of freedom of a piecewise polynomial approximation of degree N are directly based on the DG variational formulation, while reconstruction is used to raise the polynomial degree of the approximation to M>N and thus increase the order of accuracy of the solution. In this talk, I will give an overview of reconstructed DG schemes with an explicit time discretization. Within an implicit treatment of time I propose the use of reconstruction to estimate the local discretization error of a steady state DG solution. An iterated defect correction is then applied to improve the accuracy of the steady solution.Within this approach one only needs the inversion of the basic lower-order DG scheme. The main advantage is that the defect correction does not a ffect the DG scheme beside a modi cation of the right hand side, and the matrix of the linear system to be solved remains unchanged. Due to the fact that computational e ffort for higher order schemes strongly increases with the order the defect correction scheme may be considerably more efficient. Numerical results for Euler and Navier-Stokes equations are shown.
 19.3.2012
15:40
 Prof. Endre Suli (Mathematical Institute, University of Oxford): Existence of global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids Abstract: We prove the existence of global-in-time weak solutions to a general class of coupled bead-spring chain models that arise from the kinetic theory of dilute solutions of nonhomogeneous polymeric liquids with noninteracting polymer chains, with fi nitely extensible nonlinear elastic spring potentials. The class of models under consideration involves the unsteady incompressible Navier--Stokes equations with variable density and density-dependent dynamic viscosity in a bounded domain in two or three space dimensions for the density, the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is de fined by the Kramers expression through the associated probability density function that satisfi es a Fokker--Planck-type parabolic equation, a crucial feature of which is the presence of a centre-of-mass di ffusion term and a nonlinear density-dependent drag coefficient.
 26.3.2012
15:40
 prof. Tarak Ben Zineb (LEMTA, Lorraine University, CNRS, Francie): A constitutive model for Fe-based SMA considering martensitic transformation and plastic sliding coupling: Application to finite element structural analysis Abstract: In this paper, a finite-element numerical tool adapted to Fe-based SMA structural analysis is proposed. The algorithm is based on an earlier developed constitutive model which describes the effect of phase transformation, plastic sliding and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking non linear interaction of quantities related to inter- and intra-granular incompatibilities as well as interaction of mechanical and chemical quantities into account. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Fe-based SMA during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the non linear partial derivative constitutive equations was implemented into the Abaqus finite element code via the UMAT subroutine. After tests to verify the homogeneous and heterogeneous thermo-mechanical loading, an example of Fe-based SMA application was studied which corresponded to an Fe-based SMA tightening system made up of fish plates for crane rails. The results we obtained were compared to experimental ones.
 2.4.2012
15:40
 Prof. K. R. Rajagopal A thermodynamical framework for chemically reacting systems Abstract: In this talk I present a very general thermodynamic framework that is capable of describing a large class of bodies undergoing entropy producing processes. Attention will be focused on bodies that are undergoing chemical reactions and the framework takes stoichiometry into account. As a special sub-case, we describe the response of viscoelastic materials that undergo chemical reactions. One of the quintessential features of this framework is that the second law of thermodynamics is formulated by introducing the Gibbs potential, which is the natural way to study problems involving chemical reactions. The Gibbs potentialbased formulation also naturally leads to implicit constitutive equations for the stress tensor. The assumption of maximization of the rate of entropy production due to dissipation, heat conduction, and chemical reactions is invoked to determine an equation for the evolution of the natural configuration, the heat flux vector and a new set of equations for the evolution of the concentration of the chemical constituents. To determine the efficacy of the framework with regard to chemical reactions we consider the reactions occurring during vulcanization of rubber. The theoretically predicted distribution of mono,di and polysulfidic cross-links by using the framework agree reasonably well with available experimental data.
 9.4.2012
15:40
 . Seminar se nekona
 16.4.2012
15:40
 Mgr. Jan Stebel, PhD (NTI FM TU Liberec): Numerical solution of Stokes problem and of its generalization within implicit constitutive theory Abstract: Rheology of some classes of non-Newtonian fluids is characterized by an implicit relation of the Cauchy stress and the symmetric velocity gradient. This leads to a generalized Stokes problem in which the stress becomes an independent unknown and the constitutive relation plays the role of an additional constraint. For successfull numerical solution it is crucial to find stable finite elements that take into account the twofold saddle-point structure of the problem. I will describe several formulations of the generalized Stokes problem, discuss the choice of finite element spaces and present some numerical results.
 23.4.2012
15:40
 Prof. Dr. Ing. Eduard Rohan (Fakulta aplikovanych ved, Katedra mechaniky, ZCU): Modeling double porosity media using hierarchical homogenization Abstract: Models of fluid saturated porous media (FSPM) are widely used in geomechanics, civil engineering and biomechanics; in the last application, FSPM models can approximate bone mechanics, or tissue perfusion, to name a few examples. Asymptotic analysis of PDEs with strongly oscillating coefficients forms a mathematically sound basis for modeling complicated interactions in heterogeneous materials with respect to their microstructure. Assuming scale separation, this approach can be adapted for simultaneous modeling of materials on the micro-, meso- and macroscopic scales. In the lecture, various models of FSPM will be presented which were obtained using hierarchical homogenization, or using homogenization of PDEs with scale-dependent coefficients. Also different origins of the fading memory effects observed at the macroscopic scale will be discussed.
 30.4.2012
15:40
 . Seminar se nekona
 7.5.2012
15:40
 . Seminar se nekona
 14.5.2012
15:40
 Mgr. Stanislav Sysala, Ph.D. (Institute of Geonics AS CR, v.v.i., Applied mathematics and computer science): Preliminary modelling of rock pillar failure processes based on continuum mechanics Abstract: Firstly, we briefly describe the Aspo Pillar Stability Experiment (APSE). The APSE experiment was carried out to examine the failure process in a heterogeneous and slightly fractured granite rock mass when subjected to coupled excavation-induced and thermal-induced stresses. The APSE experiment has been related to an underground nuclear waste repository research. Secondly, we map the pillar failure process and describe some effects that were observed during the process or influenced it. Thirdly, we briefly inform about investigation based on 3D thermo-elastic modelling. Fourthly, we introduce simplied 2D models representing a cross-section of the pillar. The models geometry and loading path correspond with the previous 3D thermo-elastic modelling. We consider three preliminary continual approaches elastic, perfect elastoplastic and a combination of perfect elastoplasticity and continuum damage mechanics. We discuss advantages and disadvantages of the approaches from mathematical and experimental points of view. We also introduce a simple coupling of the models with thermal loading. Fifthly, we mention few comments to implementation of the problems. Sixthly, we perform few numerical experiments to investigate stability of the models or to describe which of the investigated effects can be described by the models or not.
 21.5.2012
15:40
 Doc. Dr. rer. nat. Ing. Jan Valdman (VSB-TU Ostrava): Multi-surface elastoplastic continuum - modeling and computations Abstract: The quasi-static evolution of an elastoplastic body with a multi-surface constitutive law of linear kinematic hardening type allows the modeling of curved stress-strain relations. It generalizes classical small-strain elastoplasticity from one to various plastic phases. We presents the mathematical model, existence and uniqueness of the solution of the corresponding initial-boundary value problem and numerical computation using finite elements. The talk is based on PhD thesis of Jan Valdman from 2002 and later joint journal publications with M. Brokate, C. Carstensen and A. Hofinger.
 28.5.2012
15:40
 Privatdozent Dr. Dirk Pauly (Universitat Duisburg-Essen, Fakultat fur Mathematik): Poincare meets Korn via Maxwell: Extending Korn s First Inequality to Incompatible Tensor Fields
 27.9.2012
10:00
Prof. Zdeňek Bažant
(Northwestern University, Evanston, Illinois, USA):
Energy Conservation Errors of Objective Stress Rates in ABAQUS, ANSYS, LS-DYNA and Other FE Codes: Their Magnitude and How to Correct Them
Abstract: PDF file

## Please notice different date and place: on Thursday, September 27, in Ústav termomechaniky (lecture room B), Dolejškova 5, Praha 8.

 1.10.2012
15:40
 Prof. Alexander Gelfgat (School of Mechanical Engineering, Tel Aviv University, Israel): Numerical modeling of instabilities of confined flows: concepts, achievements, benchmarks and comparison with experiment Abstract: This is a review lecture describing recent achievements in computational modelling of three-dimensional instabilities of flows in closed containers. The study is motivated by melt instabilities in bulk crystal growth processes and requires consideration of rather complicated domains, as well as accounting for different non-linear phenomena, e.g., phase change and radiation. This makes it impossible to apply spectral or pseudo-spectral methods, which were traditionally used for solution of model stability problems. Lower-order methods, which are more flexible but converge slower, become the choice. We discuss how a numerical process containing a direct solver for calculation of a developed steady flow and an eigenvalue solver needed for the stability analysis should be treated. The first question addressed in this study is how fine should be a finite volume grid to yield converged critical parameters corresponding to the primary instability of a developed flow. For this purpose we consider a series of model problems which includes also some well-known benchmarks. The second issue is the comparison of numerical results with the existing experimental data, which yields the most important validation of a numerical code. We discuss also results of parametric stability studies for some model configurations and describe effects of stabilization and destabilization of flows by different combinations of heating and rotation.
 8.10.2012
15:40
 Dr. Sebastian Heinz (Weierstrass Institute, Berlin): On the structure of the quasiconvex hull in planar elasticity Abstract: We study quasiconvexity in the calculus of variations, in particular, quasiconvexity for sets of matrices. Let K and L be compact sets of real 2x2 matrices with positive determinant. Suppose that both sets are frame invariant, meaning invariant under the left action of the special orthogonal group. Then we give an algebraic condition for K and L to be incompatible for microstructures. This result permits a simplified characterization of the quasiconvex hull and the rank-one convex hull in planar elasticity. At the beginning of the talk, there will be a short motivation and an introduction to quasiconvexity.
 15.10.2012
15:40
 Ing. Vaclav Klika, Ph.D. and Prof. Frantisek Marsik (KM, FJFI CVUT and Institute of Thermomechanics, AV CR): Nonequilibrium thermodynamics and bone tissue remodelling Abstract: Motivated by biological applications and a great debate in literature (e.g. in bone tissue development and regeneration) about the significance of mechano-chemical coupling and the nature of these quantities, we try to pursue this problem from thermodynamical point of view. First, we shall discuss the use of non-equilibrium thermodynamics, classical irreversible thermodynamics, for extensions of Law of Mass Action that is frequently used in chemical kinetics. Such extensions enable to study the effects and nature of mechano-chemical coupling. Further, within GENERIC framework we propose a thermodynamically consistent way (or ways) of capturing a non-linear coupling between scalar quantities, namely affinities and scalar mechanical quantities. A modified version of the law of mass action is obtained which reflects the coupling effects by modification of reaction constants. The results from nonlinear coupling shall be discussed with CIT predictions. Also a means of comparison of the effects of different types of already recognised mechanical stimulation shall be given.As an illustrative example we shall apply the theoretical findings to model bone remodelling process.
 22.10.2012
15:40
 prof. RNDr. Miloslav Feistauer, DrSc., Dr.h.c. (KNM, MFF UK): Numerical simulation of interaction of compressible flow with elastic structures
 29.10.2012
15:40
 RNDr. Jiri Kroc, Ph.D. Introduction To Dynamic Recrystallization And Structural Design Based On Complex Systems: Building Vocabulary Abstract: Complex systems (CSs) represent a vital, productive, fast growing theory with applications in all scientific fields. Today, we briefly encounter development of CSs accompanied by carefully selected applications explaining their power. CSs are often called as post-Newtonian scientific approach because they do not work with the concept of equations. Instead of equations, CSs employ a vast number of identical copies of units (just of several generic types), representing the bottom-level of the system, which are mutually interacting on this bottom-level. The top-level behavior resulting from mutual interactions of the bottom-level units is not encoded, as e.g. in ant colony created through interactions of ants. The theory of cellular automata, which are firmly sitting within the core of modeling of CSs, is reviewed. The concept of self-organization and emergence and ideas behind it are briefly demonstrated. The main attention of this talk is focused to presentation of novel CSs approaches employed in models of dynamic recrystallization (DRX) and structural design. In DRX, experimental observations are reviewed and followed by historical development of models of DRX which is demonstrated on two presented models (discrete and continuous). In structural design, models based on cellular automata formulation of elastic or plastic deformations of constructions subjected to static or dynamic load are reviewed. The case of truss bridge is shown in detail. This enables us to optimize shape, weight, internal structure, etc., against desired properties of the final product. Such computationally supported design of not only mechanical components and constructions c an leads to a substantial increase of their performance.
 5.11.2012
15:40
 prof. Didier Henrion (LAAS-CNRS Univ. Toulouse and FEL-CVUT Prague): Continuity equations on measures and semidefinite programming for polynomial control systems Abstract: Following original ideas of Liouville (1838), Poincare (1899), Carleman (1932), Kryloff-Bogoliouboff (1937) and L. C. Young (1969), many nonconvex nonlinear infinite-dimensional optimization problems can be reformulated into convex linear programming (LP) problems in a Banach space of measures. Recent developments in functional analysis and real algebraic geometry can be exploited to solve numerically these measure LPs with the help of semidefinite programming (SDP), via a converging hierarchy of finite-dimensional LPs in the cone of positive semidefinite matrices. In this talk we apply these techniques to solve the problem of estimating the region of attraction of controlled ODEs with polynomial vector field and semialgebraic state and control constraints. We first reformulate this problem as an conic Banach LP involving the Liouville continuity (advection) PDE on occupation measures. Then we apply our hierarchy of SDP problems to generate nested semialgebraic outer approximations converging almost uniformly to the region of attraction.
 12.11.2012
15:40
 Prof. K.R. Rajagopal, DrHC (Mechanical Engineering, Texas A&M University, College Station): Modeling fracture in brittle solids
 19.11.2012
15:40
 Petr Filip, CSc. (Institute of Hydrodynamics, ASCR): Similar and quasi-similar solutions for flows of Newtonian and non-Newtonian fluids Abstract: A similarity solution of the swirling radial jet is derived including an interpretation of circumference-point-source. The solution is applied to a description of velocity field in so-called rotor region in a mixing vessel when a Rushton-type impeller is used. The parameters obtained during the similarity procedure are matched with the parameters describing mixing conditions. Helical steady state, laminar, isothermal flow of incompressible power-law fluids through a concentric annulus is analysed for a stationary outer cylinder with the inner pipe rotating with constant torque. Pressure is applied in an axial direction. Using dimensionless analysis, a quasisimilarity solution is derived for a sufficiently broad region of rheological, geometrical and dynamical parameters. This solution provides functional dependence of flow rate on an aspect ratio of the inner-to-outer cylinders, parameters in the power-law rheological model, and torque.
 26.11.2012
15:40
 Mgr. Petra Pustejovska, Ph.D. (Institute of Computational Mathematics, TU Graz): Modeling of blood flow in real geometry aneurysm
 3.12.2012
15:40
 Dr. Giuseppe Tomassetti (Dipt. Ingegneria Civile, Universita di Roma Tor Vergata): Modeling hydrogen transport and phase transformation in metallic solids Abstract: A continuum theory coupling diffusion, phase transformation, and deformation in solids under large strains will be presented, and possible applications to the modeling of hydrogen storage in metallic compounds will be discussed and mathematical analysis will briefly be outlined, too.
 10.12.2012
15:40
 * * * Jindrich NECAS MEMORIAL SEMINAR * * * * * *
15:45
 doc. RNDr. Oldrich John, CSc. (Dept. of Math. Anal., Math.-Phys. Faculty, Charles Univ.): Jindrich Necas a regularita - nekolik vzpominek
16:00
 RNDr. Miroslav Bulicek, Ph.D. (Math. Inst., Charles Univ.): On recent progress in the regularity theory for minimizers of variational integrals Abstract: The 19th Hilbert problem asks whether minimizers of a regular variational problem are analytic. In 60s, E.DeGiorgi and J.Nash proved that this hypothesis is true in the scalar case. On the other hand, in the vectorial case the hypothesis is not true, as was shown by J.Necas (1975), who found a variational problem whose minimizer is Lipschitz continuous but not better. Moreover, it was shown by V.Sverak and X.Yan (2000), that some minimizers can even be discontinuous and unbounded. Therefore, it is of a real interest to identify a nontrivial class of vectorial variational problems that admit smooth or at least Holder continuous minimizers. First such result is due to the Uhlenbeck (1977) who found a very special class for which the minimizer is smooth. In last decades, a lot of extensions of the Uhlenbeck result was proved for various types of variational problems but only under the very restrictive assumptions which are, in fact, not far from the Uhlenbeck setting. In this talk, a new, much more general class of variational problems for which it is possible to prove the Holder continuity of the minimizer will be presented. Moreover, it will be seen that the convexity of the potential in fact does not play any role, and revealed much more importance of a structural condition, which in our case can read as a splitting condition.
 17.12.2012
15:40
 Mgr. J. Stebel, Ph.D. jointly with Prof.RNDr. J.Haslinger, DrSc. (Math. Institute of the ASCR & Dept. of Numer. Math., Charles Univ.): Shape optimization in Stokes problems with threshold slip boundary conditions Abstract: We study the Stokes problems in a bounded planar domain Omega with a friction-type boundary condition that switches between a slip and no-slip stage. Our main goal is to determine under which conditions concerning smoothness of Omega, solutions to the Stokes system with the slip boundary conditions depend continuously on variations of Omega. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero.
 7.1.2013
15:40
 prof. Ing. Tomas Roubicek, DrSc. (Charles Univ. & Acad. Sci.): Adhesive contact of visco-elastic bodies and defect measures arising by vanishing viscosity Abstract: An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional. The asymptotics for the viscosity or for external loading speed approaching zero is proved in some special cases, in particular when inertia is neglected or when delamination is in Mode II (pure shear). The solutions thus obtained involve certain defect-like measures recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity. Very typically (and perhaps surprisingly), these measures show to be nontrivial. Reflecting also the conventional engineering concept, the delamination is thus driven rather by stress than energy. An explicit example leading to a nontrivial defect measure is given. Computation simulations based on algorithm based on a semi-implicit discretisation in time (launched by C.G.Panagiotopoulos) evaluating numerically such measures in 2-dimensional situations will be presented, too.
 18.2.2013
15:40
 RNDr. Petr Salac, CSc. (TU Liberec): Optimalizace chlazeni razniku pri lisovani skla Abstract: Prednaska je venovana vyuziti tvarove optimalizace pri reseni technologickych problemu pri lisovani velke sklenene produkce. Pro dosazeni vysoke kvality povrchu vylisku je potreba, aby v okamziku separace lisovaciho nastroje a vylisku byla povrchova teplota nastroje konstantni predem zvolene hodnoty. Regulace teploty razniku je provadena vnitrnim chlazenim proudici vodou v dutine razniku. Nejprve je provadena optimalizace zmenou tvaru chladici dutiny a nasledne regulaci rychlosti proudici vody uzitim tzv. regulacniho proudoveho telesa. Za stavovou ulohu bereme variacni formulaci rovnice energie s uvazovanym potencialnim proudenim chladici vody. Ucelovy funkcional je definovan ve tvaru druhe mocniny Lr2 normy z rozdilu mezi predepsanou konstantou a teplotou na vnejsim povrchu razniku. Je dokazana existence a jednoznacnost reseni stavove ulohy a existence reseni obou uloh optimalniho navrhu. Rovnez budou prezentovany pomerne uspokojive vysledky laboratornich experimentu.
 25.2.2013
15:40
 Lu Yong (Universite Paris Diderot - Paris 7): High-frequency limit of the Maxwell-Landau-Lifshitz system in the diffractive optics regime: the application of normal form method Abstract: We study semilinear Maxwell-Landau-Lifshitz systems in one space dimension. For highly oscillatory and prepared initial data, we construct WKB approximate solutions over long times O(1/epsilon). The leading terms of the WKB solutions solve cubic Schrodinger equations. We show that the nonlinear normal form method of Joly, Metivier and Rauch applies to this context. This implies that the Schrodinger approximation stays close to the exact solution of Maxwell-Landau-Lifshitz over diffractive times.
 4.3.2013
15:40
 Dr. Jurgen Fuhrmann (Weierstrass Institut fur angewandte Analysis und Stochastik, Berlin): Mathematical and numerical modeling of coupled processes in electrochemical devices Abstract: Electrochemical devices have manifold applications in technical systems. In particular, the growing share of fluctuating renewable sources in the supply of energy calls for the ability to store electrical energy in significantly larger quantities as before. In this context, electrochemical storage methods based on secondary batteries, fuel cells, redox flow cells and electrolysis cells are in the focus of significant new research efforts, which include modeling from the molecular scale up to the system scale. At the macroscale of a single electrochemical cell, coupled nonlinear systems of PDEs describe tightly coupled flow, transport, reactions and electric field. In the talk, we review elements of mathematical models of this kind, and discuss mathematical and numerical challenges connected with their investigation. In this context, we discuss the advantages and challenges of the implicit Euler, Voronoi box based finite volume method which allows to derive a framework for the numerical implementation of mathematical models based on reaction-diffusion-convection systems. Particular advantages of the method are unconditional stability, positivity, discrete maximum principle, local and global mass conservation, and efficient ways to solve stationary and time dependent cases. It relies on the ability to create Delaunay meshes conforming to interior and exterior boundaries. We mention challenges in connection with the resolution of boundary layers and handling of anisotropies. We present results of cooperation with electrochemical groups concerning the modeling of direct methanol fuel cells and thin layer flow cells.
 11.3.2013
15:40
 Petr Puncochar (AON Benfield): Mathematical Modeling inside Catastrophe Models Abstract: Serious number of fatalities and financial losses caused by natural disasters in recent decades affected significantly the insurance/reinsurance industry and led to rapid development of models that quantify financial loss occurring on insured portfolios. Impact Forecasting is Aon Benfield (market leading re-insurance broker) catastrophe (CAT) model development center whose primary aim is to develop these tools. Apart of exposure and vulnerability component, the very complex CAT models contain hazard part that covers the modeling of extreme behavior of natural phenomena, such as wind storm, flood or earthquake. The flood model development with a particular focus on hydrodynamic flood extent modeling using numerical models will be described in detail as well as probabilistic modeling that helps to determine the correct probability of various synthetic events. Finally the loss estimation and other CAT model components are shown to see all components in context.
 18.3.2013
15:40
 Prof. Ing. Miloslav Pekar, CSc. (Centrum materialoveho vyzkumu, Fak. chemicka, VUT Brno): Thermodynamics and kinetics of chemical reactions Abstract: In chemistry, thermodynamics and kinetics are traditionally considered to be independent disciplines. Thermodynamics is said to give criteria on direction or feasibility of a reaction and to give no information on its rate; this is the domain of chemical kinetics. However, they meet in equilibrium of chemical reactions, at least. Different thermodynamic and kinetic descriptions of -common- equilibrium have been combined to find some thermodynamic restrictions on kinetics. Validity and correctness of these results, which are in fact derived on the basis of equilibrium thermodynamics, are limited to ideal systems. Nonequilibrium thermodynamics points to closer contacts between chemical thermodynamics and kinetics and even enables to formulate a framework for design of chemical rate equations and rate networks which are thus consistent with thermodynamics. Then also (thermodynamic) restrictions on rate constants (coefficients, better speaking), well known to chemists, follow. Further, the role of dependent reactions, which are also sometimes looked for and discussed in chemical kinetics, in description of reaction rates is naturally clarified. The thermodynamic methodology will be illustrated on simple example of reacting mixture of three isomers.
 25.3.2013
15:40
 Prof.Dr. Anja Schloemerkemper (Univ. Wuerzburg): Non-Laminate Microstructures in Two Kinds of Monoclinic-I Martensite Abstract: The most common shape memory alloys are monoclinic-I martensite. We study their zero energy states and have two surprising results: First, there is a five-dimensional continuum in which the energy minimising microstructures are T3s, i.e. in finite-rank laminates. To our knowledge, this is the first real material in which T3s occur. We discuss some of the consequences of this discovery. Second, there are in fact two types of monoclinic-I martensite, which di ffer by their convex polytope structure but not by their symmetry properties. It happens that all known materials belong to one of the two types. We explore whether materials belonging to the other type would have superior properties since they have different zero-energy states. Our analysis uses algebraic methods, in particular the theory of convex polytopes. This is joint work with I.V. Chenchiah.
 8.4.2013
15:40
 Doc. RNDr. Josef Voldrich, CSc. (New technologies research center, Univ. of West Bohemia): Thermal Analysis of Brakes and Frictionally Excited Thermoelastic Instability Abstract: V prispevku bude ukazan inzenyrsky pristup k problematice brzd z hlediska matematickeho modelovani a vypoctu. Pozornost bude venovana nekterym aktualnim problemum ohrevu brzd, predevsim vsak jejich nachylnosti ke vzniku termoelasticke nestability vyvolane trenim.
 15.4.2013
15:40
 Piotr Minakowski (University of Warsaw, Inst. of Appl. Math. & Mech. + Charles Univ., Math. Inst.): An introduction to finite strain gradient crystal plasticity Abstract: The aim is to briefly present finite strain gradient crystal plasticity. We derive the kinematic equations form the Kroner decomposition and give basic thermodynamic description of the evolution of the Kirchhoff stress. In the second part of the talk we present an approach such that material is treated as a highly viscous, incompressible, anisotropic fluid which flows through an adjustable crystal lattice. Moreover implicit constitutive relation between slip rate and resolved shear stress is covered. As a motivation of our numerical experiments we consider the Equal Channel Angular Extrusion. The experiment, in which a specimen under presence of a high pressure together with large shear strains, exhibits significant changes in the internal structure. The results of simulations by mixed finite element, are presented. This is joint work with Jan Kratochvil, Josef Malek, Martin Kruzik and Jaroslav Hron.
 22.4.2013
15:40
 C.Bertoglio, R.Chabiniok, J.Tintera (Technical University of Munich, Germany; King s College London, UK; Inst. Clinical & Experimental Medicine, CR): Biophysical modeling of cardiovascular system in clinical setup Abstract: Biophysical modeling coupled with clinical data has the potential to extract some additional metrics which is not directly visible in the data and could be used for more accurate diagnosis and understanding of disease progress. This data-model coupling relies on a good balance between the types of data, model complexity and data assimilation techniques. During this seminar, we are going to address all these three aspects and we will demonstrate them with an example of modeling of various parts of the cardiovascular system.
 29.4.2013
15:40
 The seminar is exceptionally RESCHEDULED for Thursday May 2, between 2pm and 5pm. On Thursday May 2, 2pm-5pm, at Refectory at Mala Strana, there will be the Necas Center Inauguration and Colloquium talk of Endre Suli (University of Oxford). Abstract: The event organized by the dean of the faculty and vicedean for mathematics will take place at Refectory at Mala Strana faculty building.
 6.5.2013
15:40
 Petr Paus (Katedra aplikovane matematiky FJFI CVUT): Numerical analysis of the critical cross-slip annihilation distance and the cyclic saturation stress in copper and nickel single crystals Abstract: An interpretation of the experimentally determined critical distance of the screw dislocation annihilation in persistent slip bands [1] is still an open question. We attempt to analyze this problem using discrete dislocation dynamics simulations. Glide dislocations are represented by parametrically described curves. The model is based on the numerical solution of the dislocation motion law belonging to the class of curvature driven curve dynamics. We focus on the simulation of the cross-slip of two dislocation curves of the opposite signs where each evolves in a different primary slip plane in a channel of a persistent slip band. The dislocations move under their mutual interaction, the line tension and an applied stress forming a screw dislocation dipole. A cross-slip leads to annihilation of the dipolar parts. In the changed topology each dislocation evolves in two slip planes and the plane where cross-slip occurred. The goal of our work is to determine the conditions under which the cross-slip occurs and the saturation stress required. The simulation of the dislocation evolution and merging is performed by improved parametric approach and numerical stability is enhanced by the tangential redistribution of the discretization points. The critical annihilation distance and the saturation stress determined by the simulations are close to the experimental values.
 13.5.2013
15:40
 Prof. Eduardo Casas (Universidad de Cantabria, Santander, Spain): Elliptic Control Problems in Measure Spaces with Sparse Solutions Abstract: In the control of distributed parameter systems, those formulated by partial differential equations, usually we cannot put control devices at every point of the domain. Actually, we are allowed to use small regions to put the controllers. Then, the big issue is which region is the most convenient to localize them. Of course, we have to determine the power of the controllers as well. These controls are called sparse because they are not zero only in a small region of the domain. In the last few years, some researchers have focused their investigation in this direction. First, it was observed that the use of the L1 norm of the control in the cost functional leads to the sparsity of the solution. Of course, this introduces some mathematical difficulties in the problem due to the lack of differentiability of this functional. However, despite this difficulty, a lot of progress has been done and the numerical computations show the interest and applicability of this Taking a further step in this direction, we find that many times it is even desirable to put the controllers only in a zero Lebesgue measure set (along a line or on a surface). These controllers cannot be identified with functions, they are measures. This is the starting point of a new type of control problems where the controls are Borel measures. Adding the norm of the measure to the cost functional, we obtain optimal controls having the desired sparsity property. This talk deals with the analysis of optimal control problems in measure spaces, which are known to promote sparse solutions. The semilinear elliptic case is considered. First and second order optimality conditions are derived and some of the structural properties of their solutions, in particular sparsity, are discussed. Some numerical results are also presented.
 20.5.2013
15:40
 Prof.RNDr.Josef Malek, DSc and Mgr. Josef Zabensky (MUUK): On Darcy, Forchheimer, and Brinkman models for flows through porous media and their generalizations Abstract: We introduce several models connected with the classical models of Darcy, Forchheimer, and Brinkman and present two results concerning the existence of weak solutions and their properties.
 27.5.2013
15:40
 Dr. Vladimir Lyakhovsky (Geological Survey of Israel, Jerusalem): Continuum Damage Mechanics for Brittle Rocks and Geophysical Applications Abstract: We present a basic concept of the continuum damage rheology model based on thermodynamic principles and fundamental observations of rock deformation. Fundamental nonlinear aspects of rock deformation, such as microcrack and flaw nucleation, development of process zones at rupture tips, and branching from the main rupture plane are of crucial importance for evolutionary self-organization of faults at various spatio-temporal domains. 3-D numerical simulations reproduce the main features of a quasi-static fault evolution at various scales from laboratory sample testing to processes associated with hydraulic borehole stimulation and regional lithospheric models. A recently developed theoretical model for continuum damage-breakage mechanics allows detailed description of the dynamic rupture process. This new approach combines and extends previous results of a continuum damage model that accounts for distributed cracks using a scalar damage parameter, and a continuum breakage model that measures the relative distance of a given grain size distribution of a granular phase to the ultimate distribution with a breakage parameter. Several features of the model including development of wide damage zones and its localization into a narrow slip zone with transition from slow to rapid dynamic slip are illustrated using numerical simulations.
 5.6.2013
10:00
 PLACE EXCEPTIONALLY AT MATH. INST. Zitna 25, P-2. ____ Dr. Radek Erban (University of Oxford): Hybrid Modelling of Reaction, Diffusion and Taxis Processes in Biology Abstract: I will discuss methods for spatio-temporal modelling in cellular and molecular biology. Three classes of models will be considered: (i) microscopic (molecular-based, individual-based) models which are based on the simulation of trajectories of individual molecules and their localized interactions (for example, reactions); (ii) mesoscopic (lattice-based) models which divide the computational domain into a finite number of compartments and simulate the time evolution of the numbers of molecules in each compartment; and (iii) macroscopic (deterministic) models which are written in terms of reaction-diffusion-advection partial differential equations (PDEs) for spatially varying concentrations. In the first part of my talk, I will discuss connections between the modelling frameworks (i)-(iii). I will consider chemical reactions both at a surface and in the bulk. In the second part of my talk, I will present hybrid (multiscale) algorithms which use models with a different level of detail in different parts of the computational domain. The main goal of this multiscale methodology is to use a detailed modelling approach in localized regions of particular interest (in which accuracy and microscopic detail is important) and a less detailed model in other regions in which accuracy may be traded for simulation efficiency. I will also discuss hybrid modelling of chemotaxis where an individual-based model of cells is coupled with PDEs for extracellular chemical signals.
 10.6.2013
15:40
 prof. RNDr. Ales Pultr, DrSc. (KAM MFF UK): Bezbodovy pristup k pojmu prostoru
 7.10.2013
15:40
 Prof.RNDr.Josef Malek, DSc (Necas Center for Mathematical Modeling and Mathematical Institute of the Charles University): On implicitly constituted fluids and implicitly constituted interactions of a fluid with a solid boundary Abstract: In the analysis of weak solutions relevant to evolutionary flows of incompressible fluids with non-constant viscosity or with non-linear constitutive equation, it is in general an open question whether a globally integrable pressure exists if the flows are subject to no-slip boundary conditions. Here we overcome this deficiency by considering threshold boundary conditions stating that the fluid adheres to the boundary until certain critical value for the wall shear stress is reached. Once the wall shear stress exceeds this critical value, the fluid slips. The main ingredient in our approach is to look at this type of activated, stick-slip, boundary condition as an implicit constitutive equation on the boundary. We present key steps in the proof of the long-time and large-data existence of weak solutions, with integrable pressure, to unsteady internal three-dimensional flows of the Bingham (and Navier-Stokes) fluids subject to such threshold slip boundary conditions. This is a joint work with Miroslav Bulicek. We also mention several essential generalizations. This particular result will be put in a general scope linking modeling in continuum physics with computer simulations via the PDE analysis of initial and boundary value problems and numerical analysis of finite-dimensional solution algorithms.
 14.10.2013
15:40
 Dr. Giordano Tierra (MFF UK): Numerical approximations for the Cahn-Hilliard equation and some related models Abstract: The diffuse interface theory, which was originally developed as methodology for modeling and approximating solid-liquid phase transitions in which the effects of surface tension and non-equilibrium thermodynamic behavior may be important at the surface. The diffuse interface model describes the interface by a mixing energy represented as a layer of small thickness. This idea can be traced to van der Waals , and is the foundation for the phase-field theory for phase transition and critical phenomena. Thus, the structure of the interface is determined by molecular forces; the tendencies for mixing and de-mixing are balanced through the non-local mixing energy. The method uses an auxiliary function (so-called phase-field function) to localize the phases, assuming distinct values in the bulk phases (for instance 1 in a phase and -1 in the other one) away from the interfacial regions over which the phase function varies smoothly. The Cahn-Hilliard model describes the complicated phase separation and coarsening phenomena in the mixture of different fluids, solid or gas where only two different concentration phases can exist stably. During the seminar, different numerical schemes to approximate the Cahn-Hilliard model will be presented, showing the advantage and disadvantages of each scheme. In particular, the focus will be on the study of the constraints on the physical and discrete parameters that can appear to assure the energy-stability, unique solvability and, in the case of nonlinear schemes, the convergence of Newton s method to the nonlinear schemes. Moreover, an adaptive time stepping algorithm will be presented. This algorithm is based on the numerical dissipation introduced in the discrete energy law in each time step. The behavior of the schemes and the effectiveness of the adapt-time algorithm will be compared through several computational experiments. In the second part of the seminar, several physically motivated models such as liquid crystals, vesicle membranes, two-phase fluids (with same and different densities) and mechanical behavior of biofilms will be introduced. The key point is to try to extend the ideas presented for the Cahn-Hilliard equation to preserve the properties of the original models while the numerical schemes are efficient in time. Finally, some numerical simulations for these models will be presented to show the effectiveness of the proposed numerical schemes.
 21.10.2013
15:40
 Dr. Iryna Rybak (Institut fur Angewandte Analysis und Numerische Simulation, Universitat Stuttgart): Coupling porous medium and free flow systems: Mathematical modeling. Abstract: Fluid flows and species transport in coupled porous medium and free flow systems appear in a wide spectrum of environmental settings (evaporation from the soil influenced by the wind, overland flow interactions with groundwater aquifers, groundwater pollution), industrial applications (filtration, insulation, drying, fuel cells) and biological processes (flows in blood vessels and biological tissues, transport of drugs and nutrients). The governing equations of these two systems have been widely investigated (the free flow is usually modeled by the Stokes or Navier-Stokes equations and the porous medium is typically assumed to satisfy a variation of the Darcy law), but a challenge arises in describing the transition between the free flow and porous medium flow regimes. Modeling the coupling of the free flow and porous medium systems can be done through the sharp interface approach by imposing the appropriate set of interface conditions at the boundary between the flow domains or by considering a transition zone between two flow regions and developing a transition region model. The lecture is focused on modeling strategies for the coupled systems. We consider mathematical models for the free flow and porous medium domains and different sets of interface conditions at the fluid-porous interface. We start with the single-fluid-phase stationary problem, consider different coupling techniques and gradually complicate the problem by considering nonstationary flows, adding a second fluid phase to the porous medium and taking into account species and energy transport.
 28.10.2013
15:40
 . Seminar se nekona - statni svatek
 4.11.2013
15:40
 prof. RNDr. Eduard Feireisl, DrSc. (Institute of Mathematics AS CR): Maximal dissipation and well posedness for models of inviscid fluids Abstract: We discuss the principle of maximal dissipation introduced in 1974 by C.M.Dafermos in the light of recent results obtained by the method of convex integration for the compressible Euler system. We show examples of non-uniqueness in the class of admissible entropy solutions and inspecting the method of construction we infer that all violate the principle of maximal dissipation. We therefore conjecture that the latter should be retained as a criterion of well posedness, at least for certain problems in fluid mechanics.
 11.11.2013
15:40
 Viktor Vialov, Ph.D. (MU UK): On the boundary regularity of the weak solutions to the magneto hydrodynamics system Abstract: Magneto hydrodynamics system describe the motion of a charged fluid in the magnetic field. We investigate a sufficient conditions of local regularity of suitable weak solutions to this system near the smooth boundary. Our goal is to generalize the known Caffarelli-Kohn-Nirenberg theorem.
 18.11.2013
15:40
 Prof. Gabriel N. Gatica (Dept. de Ing. Matem., Universidad de Concepcion, Chile): ATTENTION: Location, date and time change! 19.11. at 14:15 at the Institute of Computer Science A finite element method for a three-dimensional fluid-solid interaction problem Abstract: We introduce and analyze a new finite element method for a three-dimensional fluid-solid interaction problem. The media are governed by the acoustic and elastodynamic equations in time-harmonic regime, and the transmission conditions are given by the equilibrium of forces and the equality of the corresponding normal displacements. We employ a dual-mixed variational formulation in the solid, in which the Cauchy stress tensor and the rotation are the only unknowns, and maintain the usual primal formulation in the fluid. The main novelty of our method, with respect to previous approaches for a 2D version of this problem, consists of the introduction of the first transmission condition as part of the definition of the space to which the stress of the solid and the pressure of the fluid belong. As a consequence, and since the second transmission condition becomes natural, no Lagrange multipliers on the coupling boundary are needed, which certainly leads to a much simpler variational formulation. We show that a suitable decomposition of the space of stresses and pressures allows the application of the Babuska-Brezzi theory and the Fredholm alternative for concluding the solvability of the whole coupled problem. The unknowns of the fluid and the solid are then approximated, respectively, by Lagrange and Arnold-Falk-Winther finite element subspaces of order 1, which yields a conforming Galerkin scheme. In this way, the stability and convergence of the discrete method relies on a stable decomposition of the finite element space used to approximate the stress and the pressure variables, and also on a classical result on projection methods for Fredholm operators of index zero. The lecture of Professor Gabriel Gatica, originally scheduled on November 18, 2013 is due to speakers late arrival to Prague rescheduled to November 19 at 14:15. The lecture will be organized as a joint event of the Seminar of Computational Methods and the Necas Seminar on Continuum Mechanics.
 25.11.2013
15:40
 (click here for details) The seminar is cancelled because of the workshop of the MORE project at Chateau Liblice.
 2.12.2013
15:40
 Ing. Jakub Sistek, PhD. (MU AV CR): Efficient solution methods for modelling of flows around insect wings. Abstract: We deal with a pressure-correction method for solving unsteady incompressible flows. In this approach, five subsequent equations are solved within each time step. These correspond to three scalar convection-diffusion problems, one for each component of velocity, a pure Neumann problem for the correction of pressure, and a problem of the L2 projection for pressure update. We present a comparative study of several parallel preconditioners and Krylov subspace methods from the PETSc library and investigate their suitability for solving the arising linear systems after discretizing by the finite element method. The target application are large-scale simulations of flows around wings of insects. This is a joint work with Fehmi Cirak.
 9.12.2013
15:40
 Prof. Thomas Richter (Institut f. Angew. Mathematik, Univ. Heidelberg): A Fully Eulerian Formulation for Fluid-Structure Interactions Abstract: This presentation is about a monolithic variational formulation for fluid-structure interaction problems. Instead of the standard approach - where the fluid-problem is transformed into an artificial coordinate system - the Arbitrary Lagrangian Eulerian coordinates - we state both sub-problems, fluid and solid in the Eulerian coordinate system. By this approach, we avoid the introduction of artificial coordinates, that usually give rise to problems, when very large deformation, motion or contact of the structure takes place. As a Eulerian approach our method involves some specific difficulties: First, it is a fixed-mesh interface-capturing scheme, where the interface between solid and fluid is freely moving and must be captured by the discretization. Here, we introduce the Initial Point Set technique as an alternative to Level-Sets. Second, as the type of equation changes within the domain from fluid to solid, the Eulerian approach is an interface problem with a solution, that lacks regularity across the interface. To deal with this weak discontinuities, we introduce a locally modified finite element approach. Numerical results will demonstrate the potential of the new Fully Eulerian approach to deal with problems involving large deformation, motion and contact.
 16.12.2013
15:40
 Prof. Paul J. Tackley (Department of Earth Sciences, ETH Zurich Institute fuer Geophysik): The dynamics and evolution of terrestrial planets in our solar system and beyond Abstract: Convection of the rocky mantle is the key process that drives the interior evolution and surface tectonics of terrestrial planets Earth, Venus, Mars and Mercury, yet these planets are quite different. Mantle convection in Earth causes plate tectonics, controls heat loss from the metallic core (which generates the magnetic field) and drives long-term volatile cycling between the atmosphere/ocean and interior. Plate tectonics is thus a key process, yet exactly how plate tectonics arises is still quite uncertain; other terrestrial planets like Venus and Mars instead have a stagnant lithosphere- like a single plate covering the entire planet. Here, numerical modelling of the interior dynamics and thermo-chemical evolution of Venus, Mars and Earth is presented, to develop a unified framework that can be applied to predicting the dynamics and possible habitability of terrestrial planets around other stars (super-Earths as well as smaller planets), of which astronomers have so far found ~10s.
 6.1.2014
15:40
 Dr. Ondrej Sramek (University of Maryland, Department of Geology): Modeling Mars early internal dynamics Abstract: The hemispheric dichotomy and Tharsis volcanic province are dominant planetary scale features on Mars. The formation mechanism of the dichotomy remains unclear and arguments have been made for both exogenic (i.e., giant impacts) and endogenic (i.e., related to internal dynamics) origin. I will present a model of thermochemical convection in a global spherical shell, representing the silicate mantle of Mars, where we investigate the plausibility of the endogenic hypothesis for the dichotomy and Tharsis formation and their early evolution. In particular, we focus on the effect of viscosity structure on the dominant wavelength of convective flow, the evolution of lithospheric thickness as a result of partial melting, and the dynamics of the mantle-lithosphere system. I will spend some time discussing the numerical tool we use: CitcomS, a finite element convection code, which is widely used in the geophysical community.
 20.1.2014
15:40
 Prof. Dr. Helmut Abels (University of Regensburg): Well-posedness of a fully-coupled Navier-Stokes/Q-tensor system with inhomogeneous boundary data
 17.2.2014
15:40
 Prof. Dr. Christian Kreuzer (Faculty of Mathematics, Ruhr-Universitat Bochum): Instance optimality of an AFEM with maximum marking strategy Abstract: Adaptive finite element methods (AFEMs) with Dorflers marking strategy are known to converge with optimal asymptotical rate. Practical experiences show that AFEMs with maximum marking strategy produces optimal results thereby being less sensitive to choices of the marking parameter. In this talk, we prove that an AFEM with a modified maximum strategy is even instance optimal for the total error, i.e., for the sum of the error and the oscillation. This is a non-asymptotical optimality result. Our approach uses new techniques based on the minimisation of the Dirichlet energy and a newly developed tree structure of the nodes of admissible triangulations.
 24.2.2014
15:40
 Priv.-Doz.RNDr. Martin Kruzik, PhD. (UTIA AV CR + FSv CVUT + MFF UK): Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment Abstract: An adhesive unilateral contact between visco-elastic bodies at small strains and in a Kelvin-Voigt rheology is scrutinized, neglecting inertia. The flow-rule for debonding the adhesive is considered rate independent, unidirectional, and nonassociative due to dependence on the mixity of modes of delamination, namely Mode I (opening) needs (= dissipates) less energy than Mode II (shearing). Such mode-mixity dependence of delamination is a very pronounced (and experimentally confirmed) phenomenon typically considered in engineering models. An efficient semi-implicit-in-time FEM discretization leading to recursive quadratic mathematical programs is devised. Its convergence and thus the existence of weak solutions is proved. Computational experiments implemented by BEM illustrate the modeling aspects and the numerical efficiency of the discretization. This is a joint work with T. Roubicek and C. Panagiotopoulos .
 3.3.2014
15:40
 doc.Ing. Jan Zeman, PhD. (Katedra mechaniky, FSv CVUT): An FFT-based Galerkin method for homogenization of periodic media Abstract: In 1994, Moulinec and Suquet introduced an efficient technique for the numerical resolution of the cell problem arising in homogenization of periodic media. The scheme is based on a fixed-point iterative solution to an integral equation of the Lippmann-Schwinger type, with action of its kernel efficiently evaluated by the Fast Fourier Transform techniques. The aim of this work is to demonstrate that the Moulinec-Suquet setting is actually equivalent to a Galerkin discretization of the cell problem, based on approximation spaces spanned by trigonometric polynomials and a suitable numerical integration scheme. For the latter framework and scalar elliptic setting, we prove convergence of the approximate solution to the weak solution, including a-priori estimates for the rate of convergence for sufficiently regular data and the effects of numerical integration. Moreover, we also show that the variational structure implies that the resulting non-symmetric system of linear equations can be solved by the conjugate gradient method. Apart from providing a theoretical support to Fast Fourier Transform-based methods for numerical homogenization, these findings significantly improve on the performance of the original solver and pave the way to similar developments for its many generalizations proposed in the literature. This is a joint work with Jaroslav Vondrejc (UWB in Pilsen) and Ivo Marek (CTU in Prague).
 10.3.2014
15:40
 Dr. Jan Heyda (Inst. Soft Matter and Functional Materials, Helmholtz Zentrum Berlin): Molecular dynamics: Route to dynamics, kinetics, and thermodynamics Abstract: Apparatus of theoretical chemistry and polymer physics successfully handle challenges of soft matter and complex systems. The increasing computational power allows to routinely perform all-atom resolved molecular dynamics simulations in explicit solvent at ambient conditions on long timescales and obtain kinetic and thermodynamic properties of the investigated system. First, I will introduce the simulation methods, basic assumptions, and the way, how the macroscopic properties (activity, stability, solubility, mobility, etc.) are obtained from simulation data. Subsequently, few case studies will be chosen for demonstration of these techniques. In first example, I will document, how the insight into protein denaturation can be gained, and build a 2-state model that maintain the essence, i.e. to quantify the denaturation and stabilization energy. Another example will describe the electrophoretic mobilization of neutral particles in water. The connection to the solution structure in its vicinity will be provided as well as the direct comparison with experimental data. I will conclude my talk with a description of a model for thermoresponsive polymer, which shrinks above and swells below its critical temperature. Furthermore this temperature is very sensitive and specifically respond to addition of salts to the solution, thus resembles behavior of biopolymers and proteins.
 17.3.2014
15:40
 Dr. Barbora Benesova (Dept. of Mathematics I, RWTH Aachen University): Quasiconvexity conditions when minimizing over homeomorphisms in the plane Abstract: In this talk we characterize necessary and sufficient conditions on the stored energy density in order to assure weak* lower semicontinuity on the set of bi-Lipschitz functions in the plane. This problem is motivated by variational problems in nonlinear elasticity where the orientation preservation and injectivity of the admissible deformations are key requirements. Generally speaking, the main difficulty in finding such conditions is that the set of bi-Lipschitz functions is non-convex. Thus, standard cut-off techniques that modify the generating sequence to have the same boundary conditions as the limit generally fail; however, the standard proofs of in calculus of variations rely on such methods. We obtain this cut-off by following a strategy inspired by Daneri&Pratelli, i.e. we modify the generating sequence (on a set of gradually vanishing measure near the boundary) first on a one dimensional grid and then rely on bi-Lipschitz extension theorems. We also present method of modifying the sequence on the grid that could be extended to more general classes of mappings. This is joint work with Martin Kruzik (Prague) and Malte Kampschulte (Aachen).
 24.3.2014
15:40
 Mgr. Michal Pavelka (MU UK Praha + CNT ZCU Plzen): Consistent theory of mixtures on different levels of description Abstract: Theory of mixtures is a theory which provides evolution equations describing non-equilibrium behavior of mixtures, and this lecture is about a new theory of mixtures of fluids. Although there have been many theories of mixtures developed so far, many question remain unanswered. For example, should kinetic energy of diffusion be considered a part of internal energy or not? And what about potential energy? How can one define partial pressures for non-ideal mixtures? All those questions will be clarified in the lecture. The new theory will be then compared with earlier theories of mixtures developed within classical irreversible thermodynamics, rational (extended) thermodynamics, extended irreversible thermodynamics and GENERIC. To do so it will be shown how different evolution equations emerge on different levels of description (or detail) and how to distinguish reversible evolution from irreversible using time-reversal parity.
 31.3.2014
15:40
 Prof. Zdeněk P. Bažant, DrHC mult. (Northwestern University, Evanston, Illinois, USA): Comminution of solids due to kinetic energy of high-rate shear: Turbulence analogy, impact, shock and shale fracturing Abstract: Fragmentation, crushing and pulverization of solids, briefly called comminution, has long been a problem of interest for mining, tunneling, explosions, meteorite impact, missile impact, groundshock, defence against terrorist attack, and various kinds of industrial processes. Recently interest surged in the comminution of gas or oil shale, which can raise permeability by orders of magnitude. Particularly intriguing is an environmentally friendlier alternative to hydraulic fracturing, in which comminution of the shale would be achieved by shock waves generated by explosions or electro-hydraulic pulsed arc in the pipe of a horizontal borehole. In all these problems, the size of particles or their surface-volume ratio, which controls energy dissipation as well as permeability enhancement, is the key parameter to predict. Whereas the comminution in the so-called Mescall zones of impacted or shocked solids has theoretically been explained by branching of dynamically propagating cracks, no viable, theoretically well founded, comminution model appears to be available for macroscopic dynamic analysis of structures conducted, e.g., by finite elements. Comminution ignored, simulations of missile penetration through concrete walls grossly overestimate the exit velocities. This paper presents a model inspired by noting that the local kinetic energy of shear strain rate plays a role analogous to the local kinetic energy of eddies in turbulent flow. In contrast to static fracture, in which the driving force is the release of strain energy, the high-rate comminution under compression is considered to be driven by the release of the local kinetic energy of shear strain rate, whose density is shown to exceed (at strain rates > 1000/s) the maximum possible strain energy density by several orders of magnitude. The new theory predicts the particle size or crack spacing to be proportional to the -2/3 power of the shear strain rate. A dimensionless indicator of the comminution intensity is formulated. The comminution process is shown to be macroscopically equivalent to an apparent shear viscosity proportional to the -1/3 power of the shear strain rate. This viscosity is combined with the latest version M7 of the microplane model for concrete and is shown to lead to correct predictions of missile penetration. Applications to shock loading of gas shale suggest a tantalizing potential of gas extraction with a negligible release of contaminated water to the surface (see Proc. Nat. Academy of Sciences 110, 2013, 19291-19294.)
 7.4.2014
15:40
 doc.Ing. Jaroslav Kruis, CSc. (Katedra mechaniky FSv CVUT): Damage mechanics in civil engineering: models, numerical implementation and applications Abstract: In civil engineering, damage mechanics is connected with analysis of concrete and rock materials which behave in tension and compression differently. Therefore, application of simple isotropic damage models with a single damage parameter is limited to special problems. Models with two damage parameters or orthotropic damage models are used for general loading paths. All damage models have to be equipped with regularization because of softening and possible non-physical energy dissipation. Integral non-local formulation and its implementation will be discussed. Application of damage models in two real-world problems will be shown. One example is analysis of a containment in nuclear power plant and the second example is devoted to the analysis of water-tightness of a foundation slab. This is a joint work with T. Koudelka and T. Krejci.
 14.4.2014
15:45
 Opening Ceremonial Seminar on the occasion of the 80th anniversary of physicist Professor Jan Kratochvil
15:55
 Prof. RNDr. Jan Kratochvil, DrSc. (Dept. of Physics, Faculty of Civil Engineering, CTU, and Matematical Institute, CU): Model of ultra-strength materials produced by severe plastic deformation
16:30
 prof. Dr.Ing. Michal Benes (Faculty of Phys. & Nuclear Engr., Czech Technical University): Discrete Dislocation Dynamics
17:00
 Ing. Zdenek Prevorovsky, CSc. (Institute of Thermomechanics, ASCR): Civil structures health monitoring
 28.4.2014
15:40
 Dr. Sebastian Schwarzacher (Mathematisches Institut, Ludwig-Maxmillians-Universitat Munchen): Solenoidal Lipschitz truncation and its application to existence theory for fluids Abstract: We consider functions u from Linfty(L2) and Lp(W1,p), p bigger than 1, on a time space domain. Solutions to non-linear evolutionary PDE s typically belong to these spaces. Many applications require a Lipschitz approximation of u which coincides with u on a large set. For existence theory in fluid mechanics one needs to work with solenoidal (divergence-free) functions. Thus, we present a Lipschitz approximation, which is also solenoidal. We will show how this can be applied to existence proofs for certain non-Newtonian fluids.
 5.5.2014
15:40
 Prof.RNDr. Pavel Jungwirth, PhD. (Institute of Organic Chemistry and Biochemistry, ASCR): Pocitacove modelovani vnitrniho ucha Abstract: Elektromechanicka excitace vlaskovych bunk v Cortiho organu v kochlee je slozity fyziologicky proces, ktery nam dovoluje vnimat zvuk. Nasim cilem je vytvorit flexibilni a presny pocitacovy model vnitrniho ucha, zalozeny na teorii ekvivalentnich linearnich elektrickych obvodu. Takovy model nam nejen pomuze detailne pochopit zakladni mechanismy procesu slyseni, ale i pochopit efekty genetickych mutaci, zpusobujicich sluchove vady. Ve spolupraci s vyvojari v rakouske firme Medel se take pokousime vytvorit model poskozeneho vnitrniho ucha s vlozenym kochlearnim implantatem.
 12.5.2014
15:40
 Prof.Dr. Dieter Bothe (Center of Smart Interfaces, TU Darmstadt, Germany): Continuum thermodynamics of chemically reacting fluid mixtures Abstract: We consider viscous and heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, a closed system of partial mass and partial momentum balances plus a common balance of internal energy is derived by means of an extended form of the entropy principle. The interaction forces split into a thermo-mechanical and a chemical part, where the former is symmetric if binary interactions are assumed, while the chemical interaction force is non-symmetric, unless chemical equilibrium is attained. Introducing cross-effects already before closure as entropy invariant couplings between principal dissipative mechanisms, the Onsager symmetry relations are a strict consequence of the entropy principle. A new classification of the factors forming the binary products in the entropy production according to their parity-instead of the classical distinction between so-called fluxes and driving forces-explains the apparent anti-symmetry of certain couplings. If the diffusion velocities are small compared to the speed of sound, the well-known Maxwell-Stefan equations together with the so-called generalized thermodynamic driving forces follow in the special case without chemical reactions, thereby neglecting wave phenomena in the diffusive motion. In the reactive case, this approximation via a scale separation argument is no longer possible. We therefore develop the concept of entropy invariant model reduction, which yields an additional contribution to the transport coefficients due to the chemical interactions. This extends the Maxwell-Stefan equations to chemically reactive mixtures. (The talk is based on a joint work with Wolfgang Dreyer, WIAS, Berlin.)
 19.5.2014
15:40
 Ing. Michal Malinsky, PhD. (Inst. of Particle & Nuclear Phys., MFF UK): Higgs boson in the mosaic of the quantum world Abstract: The talk will review in brief the birth of what is nowadays called The Standard Theory of particle interactions and the key role played by the so called Higgs field in its construction, as well as the long experimental search and the ultimate 2012 discovery of the associated particle, the Higgs boson.
 9.6.2014
15:40
 Prof.Dr. Barbara Wolhmuth (Zentrum Math., TU Muenchen): Duality and hierarchy in modern finite element analysis Abstract: Duality principles play an important role in the textbook analysis for finite elements. Beyond this, exploiting the duality of spaces, problems or meshes and the structure of hierarchical fine scales in the design of numerical schemes can highly improve the algorithmic performance. We use this abstract concept in several illustrating examples. Standard mortar finite elements on non-matching meshes are quite often used in multi-physics applications due to their flexibility. For that case biorthogonal basis functions can be locally constructed while preserving reproduction properties. This results in sparse local and not in dense global coupling operators. Graded meshes or singular component enrichment are popular strategies to compensate a lack of regularity in finite element approaches. Interior regularity results allow us to use weighted dual pairings and to design a pollution free algorithmic modification of the energy. Optimal order convergence rates for eigenvalues, traces and fluxes are then recovered even for cases where no full elliptic regularity is granted. Widely used equal order schemes for flow problems are well-known for their superconvergence on structured meshes. This numerical observation can be theoretically analyzed by interface estimates in combination with local consistency and global stability considerations. Local post-processes on dual meshes can guarantee element-wise mass conservation for Stokes systems as well as facilitate the design of equilibrated a posteriori error estimators. The application relevance is illustrated by systematic numerical studies.
16:40
 Prof.Dr. Ulrich Rude (Dept. Informatik, Uni. Erlangen-Nurnberg): Is 2.44 trillion unknowns the largest finite element system that can be solved today? Abstract: Supercomputers have progressed beyond the Peta-Scale, i.e. they are capable to perform in excess of 10^(15) operations per second. I will present parallel multigrid based solvers for FE problems with beyond a trillion unknowns. This is e.g. enough to discretize the whole volume of planet with a global resolution of about 1 km. Since the compute times are around 1 minute for computing a single solution, they can still be used reasonably within an implicit time stepping procedure or a nonlinear iteration.
 16.6.2014
15:40
 Prof. Miroslav Grmela (Ecole Polytechnique de Montreal, Montreal, Canada): Entropy Abstract: I will discuss in particular the role that this non-mechanical concept plays in the multiscale mesoscopic time evolution of macroscopic systems. I will show that there is as many entropies as there is pairs of mutually compatible levels of description. The entropy is essentially a potential generating approach of a level 1 to a level 2 (that is more macroscopic than and compatible with the level 1 ). The framework provided by contact geometry is used to unify the gradient and the symplectic dynamics that both combine to form the (GENERIC) mesoscopic dynamics. References: Entropy, 15, 5003 (2013); Entropy, 16, 1625 (2014)
 7.7.2014
15:40
 Dr. Jessika Camano (Universidad Catolica de la Santisima Concepcion, Chile): An adaptive strategy to solve the inverse problem of electroencephalography Abstract: Electroencephalography is a non-invasive technique for detecting brain activity from the measurement of the electric potential on the head surface. In mathematical terms, it reduces to an inverse problem in which the goal is to determine the source that has generated the electric field from measurements of boundary values of the electric potential. Since for reasonable models the time-variation of the electric and magnetic fields can be disregarded, the mathematical modeling of the corresponding forward problem leads to an electrostatics problem with a current dipole source. This is a singular problem, since the current dipole model involves first-order derivatives of a Dirac delta measure. Its solution lies in $L^p$ for $1 le p<3/2$ in three dimensional domains and $1 le p <2$ in the two dimensional case. We consider the numerical approximation of the forward problem by means of standard piecewise linear continuous finite elements. We prove a priori error estimates in $L^p$ norm. Then, we propose a residual-type a posteriori error estimator. We prove that it is reliable and efficient; namely, it yields global upper and local lower bounds for the corresponding norms of the error. We solve the electrostatic problem by means of an adaptive process based on the a posteriori error estimator, which allows creating meshes appropriately refined around the singularity. We compare this method with the so called subtraction approach. The latter is based on subtracting a fundamental solution, which has the same singular character of the actual solution, and solving computationally the resulting non-singular problem. A set of experimental tests for both, the forward and the inverse problems, are reported. The main conclusion of these tests is that the approach based on the adaptive processis preferable when the localization of the dipole is close to an interface between brain tissues with different conductivities.
16:30
 Dr. Ricardo Oyarzua (Universidad del Bio Bio, Concepcion, Chile): Analysis of new fully-mixed finite element methods for the Stokes-Darcy coupled problem Abstract: In this paper we introduce and analyze two new fully-mixed variational formulations for the coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy equations, respectively, and the corresponding transmission conditions are given by mass conservation, balance of normal forces, and the Beavers-Joseph-Saffman law. We first extend recent related results involving a pseudostress/velocity-based formulation in the fluid, and consider a fully-mixed formulation in which the main unknowns are given now by the stress, the vorticity, and the velocity, all them in the fluid, together with the velocity and the pressure in the porous medium. The aforementioned formulation is then partially augmented by introducing the Galerkin least-squares type terms arising from the constitutive and equilibrium equations of the Stokes equation, and from the relation defining the vorticity in terms of the free fluid velocity. These three terms are multiplied by stabilization parameters that are chosen in such a way that the resulting continuous formulation becomes well-posed. The classical Babuska-Brezzi theory is applied to provide sufficient conditions for the well-posedness of the continuous and discrete formulations of both approaches. Next, we derive a reliable and efficient residual-based a posteriorierror estimator for the augmented mixed finite element scheme. The proof of reliability makes use ofthe global inf-sup condition, Helmholtz decomposition, and local approximation propertiesof the Clement interpolant and Raviart-Thomas operator. In turn, inverse inequalities, the localization technique basedon element-bubble and edge-bubble functions, and known results from previous works, arethe main tools to prove the efficiency of the estimator. This work is based on joint work with Jessika Camano, Gabriel N. Gatica, Ricardo Ruiz and Pablo Venegas.
 21.7.2014
15:40
 Prof.Dr. Christof Melcher (Dept. for mathematics I, RWTH Aachen University): Topological solitons in chiral magnetism Abstract: Magnets without inversion symmetry are a prime example of a solid state system featuring topological solitons on the nanoscale, and a promising candidate for novel spintronic applications. We prove existence of isolated chiral skyrmions minimizing a ferromagnetic energy in a non-trivial homotopy class. In contrast to the classical Skyrme mechanism from nuclear physics, the stabilization is due to a Dzyaloshinskii-Moriya interaction term of linear gradient dependence, which breaks the chiral symmetry.
 6.10.2014
15:40
 Prof. Dr. Ing. Eduard Rohan, DSc. (Zapadoceska Univerzita v Plzni, Fak. aplikovanych ved): Homogenization of perfused porous media with applications in biomechanics. Computational aspects. Abstract: Porous media still belongs to very challenging areas of mathematical modelling namely because of the need of solving coupled problems of multi-physical interactions at several scales. This talk will focus on modelling fluid saturated deformable porous media under quasi-static loading. A special type of porous media is presented by perfused tissues which have a character of double-porous media where the pores are hierarchically organised, taking the form of perfusion trees. Different approaches will be presented, some of them can be combined to provide multiscale computationally tractable models of such complex structures. A direct approach consists in decomposing the perfusion trees into so-called compartments, so that each of them is associated with a pressure field. Structure of such a model can be derived using homogenization of a double porous medium of the Biot type with large contrasts in permeability, which presents another modelling approach. As a consequence of upscaling, the fading memory effects are represented by the time convolutions involved in the homogenized medium model. Its extension for large deforming media can be considered in the framework of the incremental formulation in the moving frame. Local microscopic configurations must be updated with integration in time which leads to the the FEM-square complexity of the numerical implementation. To treat cases of moderate deformations, a weakly nonlinear model of the Biot medium has been proposed which captures some important effects of deformation-dependent homogenized coefficients. The basic ingredient of this model is presented by linear expansions of all involved homogenized coefficients with respect to macroscopic strains and pressures. These expansions are provided by the sensitivity analysis of the homogenized coefficients with respect to deforming microstructures. Due to this treatment, the computational complexity remains in the order of linear problems. Numerical illustrations will be presented and perspectives related to the problem of material data identification using the multi-scale approach will be discussed.
 13.10.2014
15:40
 Prof. Dr. Maria Lukacova-Medvidova (Johannes Gutenberg-Universitat Mainz, Institut fur Mathematik): Mathematical and numerical analysis of some fluid-structure interaction problems Abstract: Fluid-structure interaction problems appear in many areas. In the present lecture we will concentrate on specific problems arising in hemodynamics. The aim will be to study the resulting strongly nonlinear coupled system from analytical as well as numerical point of view. We address theoretical questions of well-posedness and present an efficient and robust numerical scheme in order to simulate blood flow in compliant vessels. With respect to the numerical simulations we will in particular discuss the questions of the added mass effect, stability and convergence order. We will present results of numerical simulations and demonstrate the efficiency of new kinematic splitting scheme.
 20.10.2014
15:40
 RNDr. Tomas Barta, Ph.D. (MFF UK, KMA): Heat conduction problem of an evaporating liquid wedge: from physics to function spaces Abstract: We consider stationary heat transfer near contact line of an evaporating liquid wedge surrounded by the atmosphere of its pure vapor. In a simplified setting, the problem reduces to the Laplace equation in a half circle, subject to a non-homogeneous and singular boundary condition. By the means of classical tools (conformal mapping, the Green function), we re-formulate the problem as an integral equation for the unknown Neumann boundary condition in the setting of appropriate fractional Sobolev and weighted space. The unique solvability is then obtained by means of the Fredholm theorem.
 3.11.2014
15:40
 Prof.RNDr. Jan Kratochvil, DrSc. (FSv CVUT + MU UK): Modeling of a mechanism of a ultra-fine subsbstructure formation in metals exposed to severe plastic deformation Abstract: The formation of deformation bands with the typically alternating sign of the misorientation across their boundaries prevails the deformation substructure observed in severally deformed metals. The bands are interpreted as a spontaneous deformation instability caused by an anisotropy of hardening. To analyze the nature of the fragmentation a model of a rigid-plastic crystal domain deformed by symmetric double slip in a plane strain compression is considered. The simple version of the model reflects the basic reason of the deformation band existence: a local decrease of number of active slip systems in the bands is energetically less costly than a homogeneous deformation by multislip. However, the predicted bands have an extreme orientation and their width tends to zero. A modified hardening rule of a more realistic version of the model incorporates a hardening caused by a buildup of the band boundaries and a dislocation bowing (Orowan) stress. The enriched model provides an explanation of the observed orientation of the bands, their width, the dislocation content of their boundaries, the lattice misorientation across them and the band reorientation occurring at large strains.
 10.11.2014
15:40
 Prof. Giuseppe Tomassetti (Dip. Ingegneria Civile e Ing. Inform., Univ. Roma II Tor Vergata): Assessing energetic and dissipative effects in strain-gradient plasticity Abstract: Metallic components undergoing inhomogeneous plastic flow display size-dependent behavior in the size range below 100μm, with smaller components being harder and having higher relative strength. This behavior is captured by strain-gradient plasticity theories, whose free energy and dissipation incorporate material length scales through a dependence on the gradient of plastic strain. In previous work [M. Chiricotto, L. Giacomelli, G.T., SIAM J. Appl. Math., 72 (2012), 1169-1191] we have considered the rate-independent case of a theory of strain-gradient plasticity devised in [M. Gurtin, L. Anand J. Mech. Phys. Solids 53 (2005) 1624-1649] in the setting of small strains and we have quantified the influence of the energetic scale on hardening by a careful analysis of the solutions of a quasistatic evolution problem that mimics torsion experiments. Our ongoing research is now focusing on the dissipative scale, which is known to affect size-dependent strengthening: the smaller the sample, the higher the critical load which triggers plastic flow. In order to quantify the effect of the dissipative scale on strengthening, we consider a rate-independent evolution problem that describes simple shear of an infinite strip [L. Anand et al, J. Mech. Phys. Solids 53 (2005) 1789-1826]. For this problem we can rigorously prove that smaller samples are stronger and we can determine the dependence of the critical load on the dissipative scale.
 24.11.2014
15:40
 Dr. Ewelina Zatorska (Inst. of Mathematics, Polish Acad. Sci., Warszaw): Two-velocity Hydrodynamics in Fluid Mechanics: Well Posedness for Zero Mach Number Systems Abstract: This talk is devoted to the the low Mach number limit system obtained from the full compressible Navier-Stokes system. Relaxing a certain algebraic constraint between the viscosity and the conductivity introduced by D.~Bresch, E.H. Essoufi, and M. Sy, (J. Math. Fluid Mech., 2007) gives a more complete answer to an open question about existence of global in time weak solutions. A new mathematical entropy shows clearly the existence of two-velocity hydrodynamics with a fixed mixture ratio. The concept of two velocities is also used in construction of the approximate solutions, where we first consider the augmented regularized system of parabolic type. This is a joint result with Didier Bresch (Universite de Savoie) and Vincent Giovangigli (Ecole Polytechnique).
 1.12.2014
15:40
 Dr. Martin Weiser (Zuse-Institute Berlin): Adaptive spectral deferred correction methods for cardiac simulation Abstract: A quantitative understanding of human heart function is necessary for understanding disease mechanisms and for individual therapy planning, but is hampered by the significant computational effort needed for numerical simulation. The electrical excitation is described by a reaction-diffusion equation coupled to pointwise ODEs and exhibits a wide range of temporal and spatial scales. One way to address the challenge is to devise efficient adaptive algorithms exploiting the locality of solutions in space and time. In this talk we will investigate the use of spectral deferred correction (SDC) methods for time integration, and their interplay with different forms of adaptivity. SDC methods are fixed point solvers for collocation systems. Their iterative nature allows to interleave the SDC convergence with mesh refinement, operator splitting, and inexact linear solvers, and thus provides many possibilities for adapting the overall algorithm to the problem at hand. We will look at some of those options and work out corresponding adaptive algorithms, illustrating their efficiency at numerical examples.
 8.12.2014
15:40
 * * * Jindrich NECAS MEMORIAL SEMINAR * * * * * *
15:45
 Prof. Gerhard Wanner (Universite de Geneve, Section de mathematiques): On the discovery of Lagrange multipliers and Lagrange mechanics Abstract: The talk explains how -- a thick book on statics (Varignon 1725), -- a letter by Johann Bernoulli to Varignon (1715), -- the Euler Methodus (1744, on variational calculus), and -- d Alembert Dynamique from 1743 led to the famous Mecanique analytique (1788, 1811) by Lagrange, in which, in the first part, the advantage of the methods of multipliers is demonstrated at many examples and, in the second part, the equations of Lagrange dynamics are derived from the principle of least action. In the last part of the talk we show the connection of the ideas of Euler and Lagrange with problems of optimal control (Caratheodory, Pontryagin).
 15.12.2014
15:40
 Dr. Patrick Dondl (Dept. of Math. Sciences, Durham University): A phase field model for the optimization of the Willmore energy in the class of connected surfaces Abstract: We consider the problem of minimizing the Willmore energy on confined and connected surfaces with prescribed surface area. To this end, we approximate the surface by a level set function u admitting the value +1 on the inside of the surface and -1 on its outside. The confinement of the surface is now simply given by the domain of definition of u. A diffuse interface approximation for the area functional, as well as for the Willmore energy are well known. We address the main difficulty, namely the topological constraint of connectedness by a nested minimization of two phase fields, the second one being used to identify connected components of the surface. We provide a proof of Gamma-convergence of our model to the sharp interface limit. This is joint work with Matthias Roger (TU Dortmund) and Luca Mugnai (MPI Leipzig).
 5.1.2015
15:40
 prof. RNDr. J. Malek, CSc., DSc. (Mathematical Inst., Charles Univ.): Large data analysis for the Kolmogorov two-equation model of turbulence Abstract: A.N.Kolmogorov seems to be the first who recognized that a two equation model of turbulence might be used as the basis of turbulent flow prediction. Although his model has so far been almost unnoticed it exhibits interesting features. First of all, its structure is similar to the Navier-Stokes(-Fourier) equations for incompressible fluid, the only difference is that the viscosity is not constant but depends on the fraction of the two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velovity fluctuations and the measure related to the length scales of turbulence. The dependence is such that the material coefficients such as viscosity and turbulent diffusivities may degenerate, and thus the apriori control of the derivatives of the involved quantities is unclear. Furthermore, the system includes the dissipation of the energy, which is merely an $L^1$ quantity, standing at the right-hand side of the equation for turbulent kinetic energy. We establish large data existence of suitable weak solution to such a system completed by the initial and generalized Navier s slip and stick-slip boundary conditions.
 19.1.2015
15:40
 Prof. Susanne Ditlevsen (University of Copenhagen, Denmark): Partially observed stochastic models in neuroscience Abstract: When constructing a mathematical model for a given system under study, decisions about characteristics and levels of detail of the model have to be taken. Which choices are appropriate depend on the questions, one wants to answer. It should also depend on available data, such that the model can exploit the information that can be extracted and not suffer too much by what cannot. I will present some examples where a simple model extracted from more biophysical based models can answer specific questions of interest, as long as the simple model is interpreted and used in a suitable way. This is 12th Colloquium Lecture, School of Mathematics Faculty of Mathematics and Physics - [Official anouncement]
 9.2.2015
15:40
 Dr. Roland Tomasi (Ludwig-Maximilians-Universitat Munchen, Math. Inst.): Smoothed Particle Hydrodynamics (SPH) Abstract: Smoothed Particle Hydrodynamics is a mesh-free Lagrangian method for the simulation of fluids. In this talk I will present the basic theory behind SPH, applied to a simple case of the compressible Navier-Stokes Equation. Furthermore I will talk about practical and programming considerations that are relevant in order to efficiently implement an SPH simulation. Finally I will present a working implementation of an interactive (real-time) simulation of a fluid. The aim of the talk is not to present new results: I seek contact to people that are willing to help me to improve my understanding of fluid dynamics. The talk should be accessible to anyone with a mathematics or physics background.
 23.2.2015
15:40
(University of Florence, Dept. of Mathematics and Appl.):
Eigenfunctions of the Laplace-Beltrami operator and geometric inequalities
Abstract:

## A joint event as a 13th Colloquium Lecture of the School of Mathematics

Some methods of geometric nature in the study of qualitative and quantitative aspects of eigenvalue problems for the Laplace operator, and of its analogue on Riemannian manifolds will be discussed. Two questions will be especially focused. On the one hand, information on the spectrum of the Laplacian, and, in particular, on its discreteness, will be provided. On the other hand, criteria for the regularity of eigenfunctions, and specifically their integrability and boundedness, will be illustrated. The results to be presented are the fruits of a collaboration with V. G. Maz ya.
 2.3.2015
15:40
 Prof. Gabriel N. Gatica (Universidad de Concepcion, Chile): A mixed-primal finite element method for the stationary Boussinesq problem Abstract: In this talk we propose and analyze a new mixed variational formulation for the stationary Boussinesq problem. Our method, which employs a technique previously applied to the Navier-Stokes equations, is based first on the introduction of a modified pseudostress tensor depending nonlinearly on the velocity through the respective convective term. Next, the pressure is eliminated, and an augmented approach for the fluid flow, which incorporates Galerkin type terms arising from the constitutive and equilibrium equations, and from the Dirichlet boundary condition, is coupled with a primal-mixed scheme for the main equation modeling the temperature. In this way, the only unknowns of the resulting formulation are given by the aforementined nonlinear pseudostress, the velocity, the temperature, and the normal derivative of the latter on the boundary. An equivalent fixed-point setting is then introduced and the corresponding classical Banach Theorem, combined with the Lax-Milgram Theorem and the Babuv ska-Brezzi theory, are applied to prove the unique solvability of the continuous problem. In turn, the Brouwer and the Banach fixed point theorems are utilized to establish existence and uniqueness of solution, respectively, of the associated Galerkin scheme. In particular, Raviart-Thomas spaces of order $k$ for the pseudostress, continuous piecewise polynomials of degree $le k +1$ for the velocity and the temperature, and piecewise polynomials of degree $le k$ for the boundary unknown become feasible choices. Finally, we derive optimal a priori error estimates, and provide several numerical results illustrating the good performance of the augmented mixed-primal finite element method and confirming the theoretical rates of convergence.
 9.3.2015
15:40
 Prof. Dr. Lisa Beck (Universitaet Augsburg, Inst. f. Mathematik): Duality, regularity and uniqueness for BV-minimizers Abstract: For a smooth function $u colon Omega omathds R$ the $n$-dimensional area of its graph over a bounded domain $Omega subset mathds R^n$ is given by $$int_Omega sqrt 1+|Du|2,dx,.$$ A natural question is whether or not minimizers of this functional exist among all functions taking prescribed boundary values. It turns out that solutions of the least area problem exist only in a suitably generalized sense. This formulation is based on an extension of the original functional to the space of functions of bounded variation via relaxation, where attainment of the prescribed boundary values is not mandatory, but non-attainment is penalized. Consequently, such generalized minimizers do not need to be unique. In my talk I will discuss similar convex variational integrals under a linear growth condition. After a short introduction to the dual problem in the sense of convex analysis I will explain the duality relations between generalized minimizers and the dual solution. The duality relations can be interpreted as mutual respresentation formulas, and in particular they allow to deduce statements on uniqueness and regularity for generalized minimizers. The results presented in this talk are based on a joined project with Thomas Schmidt (Erlangen).
 16.3.2015
15:40
 Prof.Dr. Christian Rohde (Univ. Stuttgart, Inst. f. angewandte Analysis u. numerische Simulation): Multiphase and Phase Transition Flows Abstract: 1st part will present Diffuse-Interface and Phase Field Models. (2nd part, focused on Sharp-Interface Models, will be presented on 19 March 2013 at 14:00 in K3.)
 23.3.2015
15:40
 prof. Ing. Frantisek Pochyly, CSc. (Fakulta strojinho inzenyrstvi, VUB): Studium vlastnosti hydrofobnich povrchu Abstract: V ramci seminare budou ucastnici seznameni s obsahovou naplni a vysledky vyzkumu proudeni kapalin po hydrofobnich povrsich. Obsahova cast: - definice hydrofobniho povrchu - definice povrchove energie - stekani vrstvy tekutiny po hydrofobnim povrchu - stekani kapky po hydrofobnim povrchu - definice adhesniho soucinitele - okrajova podminka interakce tekutiny s hydrofobnim povrchem - vliv hydrofobniho povrchu na vznik kavitace - souvislost Lorentzovy sily a hydrofobniho povrchu - prakticke ukazky ruznych druhu hydrofobnich povrchu
 30.3.2015
15:40
 Dr. Karel Tuma (Institute of Fundamental Technological Research, Polish Academy of Sciences): Phase Field Model of Formation and Evolution of Martensitic Microstructures Abstract: We develop a micromechanical phase field model that describes the phase transformation between the austenite and twinned martensites. It improves the model by Hildebrand and Miehe (2012) that described two variants of martensite only. Furthermore, the new model constrains the volume fractions of both parent and internally twinned phases such that they remain in the physical range. As an application, we study the twinned martensite and austenitemartensite interfaces in the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and estimate the elastic part of the interfacial energy. Several problems are simulated using Finite element method.
 13.4.2015
15:40
 Prof. RNDr. Miloslav Feistauer, DrSc., Dr.h.c. (KNM MFF UK): On vibrations of an airfoil with 3 degrees of freedom induced by turbulent flow Abstract: The subject of the lecture is the numerical simulation of the interaction of two-dimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. The airfoil with three degrees of freedom performs rotation around an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the stabilized finite element solution of the Reynolds averaged Navier-Stokes equations combined with Spalart-Allmaras or k-omega turbulence models, coupled with a system of nonlinear ordinary differential equations describing the airfoil motion with consideration of large amplitudes. The time-dependent computational domain and approximation on a moving grid are treated by the Arbitrary Lagrangian-Eulerian formulation of the flow equations.
 20.4.2015
15:40
 Dr. Christophe Prange (Dept. of Mathematics, University of Chicago): Improved Regularity in Bumpy Lipschitz Domains Abstract: In this talk we will explain how to get Lipschitz regularity up to the microscale for elliptic systems over a bumpy boundary. The analysis relies on a compactness scheme and on an estimate in a space of non localized energy for a boundary layer corrector in the half-space. This is joint work with Carlos Kenig.
 4.5.2015
15:40
 Prof. RNDr. Antonin Novotny (IMATH et Dept. Mathematiques, Universite du Sud Toulon-Var): Error estimates for the compressible Navier-Stokes equations Abstract: Inspired by the notion and properties of dissipative solutions investigated in the theory of compressible Navier-Stokes equations, we shall derive an unconditional error estimate with respect to a weak solution with bounded density for a mixed finite volume / finite element numerical scheme for the compressible Navier-Stokes equations.
 11.5.2015
15:40
 Prof. Tomáš Roubíček, DrSc. (Mathematical Inst., Charles Univ.): Damage with plasticity at small strains - an overview of various models Abstract: Coupling of plasticity with damage allows for modelling many complex processes occurring in solid continuum mechanics and physics, in contrast to mere plasticity or mere damage. First, a quasistatic model of linearized plasticity with hardening at small strains combined with gradient damage will be presented in its basic scenario with unidirectional damage and in the fully rate-independent setting. Various concepts of weak solutions will be discussed, ranging from the concept of energetic (i.e., in particular, energy conserving) solutions to stress-driven local solutions. Some modifications of this model will then be presented. In particular a rate-dependent damage allowing possibly also healing, and plasticity possibly without hardening and with damageable yield stress. This variant seems to need the concept of 2nd-grade non-simple materials and allows e.g. for modelling of thin shearbands surrounded by a wider damage zone. An opposite variant is rate-dependent plasticity but damage again rate independent and unidirectional, which allows for energy conservation and in particular for extension towards anisothermal processes. Also combination of this model with a concept of large plastic strains or some other rate-dependent processes like diffusion of some fluidic medium with wide applications covering e.g. heat/moisture transport in concrete or rocks, or a metal/hybrid transformation under diffusion of hydrogen will be discussed.
 18.5.2015
15:40
 Prof. Ronald E. Miller (Dept. of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Canada): The Cauchystat : accurate control of the true stress in molecular dynamics simulations of martensitic phase transformations. Abstract: After a brief introduction to the use of molecular dynamics (MD) simulations in materials science, I will discuss the specifics of stress-controlled MD, and describe how many stress-controlled simulations are incorrectly interpreted due to misunderstandings about what stress measure is being used (Cauchy stress or Engineering stress). I will then present a new MD algorithm that correctly controls the true Cauchy stress applied to the system. This Cauchystat is based on the constant stress ensemble presented by Tadmor and Miller (Modeling Materials: Continuum, Atomistic and Multiscale Techniques, Cambridge University Press, 2011), but with modified equations of motion that update the system boundary conditions in response to the resulting deformation of the simulation cell. As a clear example of the methods usefulness, we show that the correct stress control is important in the case of martensitic phase transformations, where the predicted martensitic start temperature and austenitic finish temperature are significantly altered as compared to the result using other stress-control algorithms. We also examine the effects of shear stress on the mechanism of the phase transformation.
 24.9.2015
9:00
 Prof. Dr. Joerg Liesen (Inst. f. Mathematik, Technische Univ. Berlin): Rational harmonic functions and their applications in gravitational lensing Abstract: This talk will discuss recent results on the zeros of rational harmonic functions f(z)=r(z)-conj{z}, which have fascinating applications ranging from numerical linear algebra to astrophysics. A particular focus will be on extremal functions, where r(z) is of degree n>=2 and f(z) has the maximal possible number of 5n-5 zeros. Examples of such functions will be visualized using phase portraits, and the implication of our theoretical results in the theory of graviational lensing will be discussed. This special seminar is organized jointly with Computational Mathematics Seminar (Institute of Computer of Science) as an activity of the Necas Center for mathematical modeling
 12.10.2015
15:40
 Prof. dr hab. Piotr Gwiazda (Institute of Mathematics, Polish Academy of Science): From structured populations models to polymeric flows
 19.10.2015
15:40
 Prof. RNDr. Josef Malek, DSc. (Charles University in Prague, Faculty of Mathematics and Physics, Mathematical institute, Czech Rep.)): Implicitly constituted materials: from modeling towards PDE-analysis of relevant initial and boundary value problems Abstract: We investigate strengths of implicit constitutive equations, paying a particular attention to their impact on PDE-analysis of relevant initial and boundary value problems. We view the role of (PDE) analysis in defining an object suitable for numerical approximation. Using several problems, we will present the achieved results and emphasize the novelties that the implicit constitutive theory brings, while skipping the details of the proofs that can be found in the given references. We will concentrate on the problems in the following areas: (i) implicitly constituted incompressible fluids, (ii) nonlinear models for solids with the bounded linearized strain, (iii) threshold slip boundary conditions stated in the form of implicit constitutive equations, (iv) flows through porous media with pressure dependent porosity, (v) compressible fluids with bounded divergence of the velocity field.
 26.10.2015
15:40
 Ing. Miroslav Soóš, PhD. (Dept. of Chemical Engineering, Univ. Chemistry & Technology Prague): Modeling of multiphase flows Abstract: In many unit operations used in chemical industry is typical existence of several phases. Common examples are extraction, aerobic fermentation of cells of various kind, polymerization, emulsification, crystallization etc. System behavior or final product properties are almost always dependent on the interaction of involved phases. It is therefore of a key importance to better understand the mechanisms occurring locally between involved phases as well as their impact on the macroscopic properties of the system. This lecture would cover three examples of multiphase flow, i.e. L-L (suspension polymerization), G-L (flow of air bubbles in the stirred bioreactor) and S-L (gel formation during the mixing of stream containing polymeric nanoparticle with stream containing an electrolyte), where will be introduced concept of modeling of dispersed phase using population balances as well as their connection with the fluid dynamic model of 2-phases (Euler-Euler RANS, pseudo-single phase approach). Since turbulence is commonly essential for these unit operations it will be shown also the case when local conditions could lead to the substantial increase of viscosity and thus change of the flow type. Since presented simulations are based on several model assumptions validity of the used approach will be discussed when comparing the obtained results with the experimental data obtained in the same unit.
 2.11.2015
15:40
 Prof. RNDr. Josef Malek, DSc. (Mathematical Inst., Charles Univ.): Limiting strain models in elasticity theory and variational integrals with linear growth Abstract: Starting from implicit constitutive models for elastic solids we introduce its subclass consisting of elastic solids with limiting small strain. The main goal is to present the results concerning the existence of weak solution to boundary value problems in bounded domains. The lecture is based on joint papers with Lisa Beck, Miroslav Bulicek, Endre Suli and K.R. Rajagopal.
 9.11.2015
15:40
 Dr. Jan Giesselmann (University of Stuttgart, Institute of Applied Analysis and Numerical Simulations): Relative Energy for Euler-Korteweg and Related Hamiltonian Flows Abstract: We consider the Euler equations containing the generator of the variational derivative of an energy functional. Attention is paid to the analysis of the Euler-Korteweg system with a special, in general nonconvex, potential energy functional. Note: A continuation under the title Discontinuous Galerkin Schemes for Compressible Multi-Phase Dynamics, will be delivered on Tuesday 12 November 2015 at the Seminar on Numerical Mathematics, lecture hall K3 at 14:00.
 23.11.2015
15:40
 Prof. Ing. Vaclav Uruba, CSc (Institute of Thermomechanics, Czech Acad. Sci.): SMStability of laminar shear flows and transition to turbulence Abstract: Laminar shear flow of a real fluid is subjected to instability under certain conditions and its character is changed to the final turbulent state. The turbulence is considered to be the last unsolved problem of classical physics. Even the process of transition from laminar to turbulent state is still not fully understood. However the process of birth could provide key information related to turbulence itself. That is why the suggested presentation is focused on this phenomenon. The following particular problems will be addressed: * Flow of real fluids * Shear flow instability concepts * Laminar and turbulent structure * Typical cases of instable flows * Possible scenarios of the transition process * Some of known issues of the stability theories
 30.11.2015
15:40
 Mgr. Vit Prusa, PhD. (Math. Institute, Charles Univ.): Towards mathematical description of creep and stress relaxation tests in the mechanics of nonlinear viscoelastic materials Abstract: The response of physical systems governed by linear ordinary differential equations to a step input is traditionally investigated using the classical theory of distributions. The response of nonlinear systems is however beyond the reach of the classical theory. The reason is that the simplest nonlinear operation---multiplication---is not defined for the distributions. Yet the response of nonlinear systems is of interest in many applications, most notable example is the analysis of the creep and stress relaxation tests in mechanics of viscoelastic materials. Consequently, a mathematical framework capable of handling such problems is needed. We argue that a suitable framework is provided by the so-called Colombeau algebra that gives one the possibility to overcome the limits of the classical theory of distributions, namely the possibility to simultaneously handle discontinuity, differentiation and nonlinearity. Our thesis is documented by means of studying the response of two systems governed by nonlinear ordinary differential equations to a step input. In particular, we show that using the rules of calculus in Colombeau algebra it is possible to obtain an explicit and practically relevant characterisation of the behaviour of the considered systems at the point of the jump discontinuity.
 7.12.2015
15:40
 Prof.Ing. Tomas Roubicek, DrSc. (MU UK): Energy-conserving time discretisation for dynamical problems in solids involving inelastic processes Abstract: Second-order evolution variational inequalities governed by quadratic or separately quadratic energies with set constraints and possibly nonsmooth and degree-1 homogeneous dissipated energies are discretised by implicit formulas in such a way that the energy of the discrete scheme is conserved. Applications in continuum mechanics of solids at small strains includes e.g. dynamic Signorini contacts or linearized plasticity possibly combined with damage etc. This allows efficient implementation transient problems without artificial numerical attenuation within vibrations. Illustrative numerical simulations by C.G.Panagiotopolos will be presented, too.
 14.12.2015
15:40
 *** Jindřich NECAS MEMORIAL SEMINAR *** doc.RNDr. Milan Pokorný, PhD.: Presentation of the book Selected works of Jindřich Nečas (Eds. M.Pokorný, S.Nečasová, V.Sverák), Birkhauser, Basel, 2015 . Abstract: The book collects the most significant contributions of the outstanding Czech mathematician Jindřich Nečas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with J.Nečas brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career.
16:10
 doc. RNDr. Sarka Nečasová, PhD. (Mathematical Institute CAS): The motion of incompressible viscous fluid around a moving rigid body Abstract: The dynamics of fluids, i.e. liquids and gases, is an important part of the continuum mechanics. This lecture is devoted to the qualitative analysis of mathematical models of motion of a viscous incompressible fluid around a compact body B, translating and rotating in the fluid with given time-independent translational and angular velocities u and omega. The translation can be considered, without the loss of generality, to be parallel to the x3 axis. We shall study - the time-periodic Stokes system, Oseen system in the whole space, in an exterior domain and we will investigate the strong solution of the problem in Lq setting with corresponding weight describing the behavior in the large distance. Moreover, we shall discuss the fundamental solution of the Oseen rotating system and the asymptotic decay for the Oseen case and also for nonlinear case.
 21.12.2015
15:40
 Dr. Giuseppe Tomassetti (Univ. Roma II Tor Vergata): Accretion of an actin layer on a spherical bead: the treadmilling regime. Abstract: Inspired by experiments on actin growh on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere. One of the peculiar characters of our model is that accretion does not take place on the external surface of the body, but rather on the surface that separates it from its support. This mechanism of growth is responsible for stress accumulation within the body because when a new layer of material is deposited on the support it pushes outwards the pre-existing layers. Eventually, stress buildup inhibits accretion at the internal surface and promotes ablation at the external surface of the body, insofar as a stationary regime called treadmilling sets in, characterized by internal accretion being balanced by external ablation. The relevant ingredients of our model are: a law that governs accretion and ablation accounting for both chemistry and mechanics; a far-from-standard choice of the reference configuration, which eases our task of coping with the continuously evolving material structure and with the lack of a conventional stress-free reference configuration.
 4.1.2016
15:40
 Doc.RNDr. Martin Kružík, PhD. (UTIA AV CR + FSv CVUT Praha): Boundary effects and weak lower semicontinuity for signed integral functionals on BV Abstract: We characterize lower semicontinuity of integral functionals with respect to weak convergence in BV, including integrands whose negative part has linear growth. In addition, we allow for sequences without a fixed trace at the boundary. In this case, both the integrand and the shape of the boundary play a key role. This is made precise in our newly found condition, a quasi-sublinear growth from below at points of the boundary, which compensates for possible concentration effects generated by the sequence. Some applications to relaxation of variational problems with linear growth will be outlined. It is a joint work with B. Benesová (Wurzburg) and S. Kromer (Cologne).
 11.1.2016
15:40
 Ing. Miroslav Kolář (KM, FJFI CVUT Praha): Modeling of moving curves by curvature driven flow and its application in discrete dislocation dynamics Abstract: We investigate the numerical solution of the evolution law for the mean curvature flow of open or closed non-self-intersecting curves in a plane. The model schematically reads as normal velocity = (mean) curvature + force. We treat the motion law by means of the parametric method, resulting into a system of degenerate parabolic partial differential equations for the curve parametrization. Unlike other interface-capturing methods, such as level-set method or phase-field method, the parametric approach allows us to treat the dynamics of open curves comfortably. The parametric equations are spatially discretized by means of the flowing finite volume method. To improve the quality of the numerical solution, we discuss the effect of artificial designed tangential terms redistributing the discretization points. In the second part of the lecture, we present the application of the curvature driven flow to a microscale modeling of basic mechanisms in discrete dislocation dynamics.
 22.2.2016
15:40
 Prof. Victor A. Kovtunenko (Inst. for Math. and Sci. Comp., Univ. of Graz, Austria, and Lavrent ev Inst. of Hydrodynamics, Novosibirsk, Russia): On generalized Poisson-Nernst-Planck equations Abstract: A strongly nonlinear system of Poisson-Nernst-Planck equations is considered. The diffusion laws are coupled with the Landau grand potential for entropy variables. The model describes electro-kinetic phenomena on multiphase medium in physical, chemical, and biological sciences. The generalized model is supplemented by the mass balance, positivity and volume constraints, quasi-Fermi statistics depending on the pressure, and inhomogeneous Robin boundary conditions representing interfacial reactions . In our research we aim at proper variational modelling, wellposedness properties and dynamic stability, as well as homogenization of the problem supported by rigorous estimate of the energy and entropy types.
 29.2.2016
15:40
 Dr. Koya Sakakibara (University of Tokyo): Structure-preserving numerical scheme for the one-phase Hele-Shaw problems by the method of fundamental solutions combined with the uniform distribution method Abstract: In this talk, the one-phase Hele-Shaw problems and their numerical scheme are considered. The one-phase interior Hele-Shaw problem has curve-shortening (CS), area-preserving (AP), and barycenter-fixed (BF) properties. We construct numerical scheme which satisfies the above properties in a discrete sense. As a result, computing the normal velocities by the method of fundamental solutions and the tangential velocities by the uniform distribution method, a discrete version of CS-, AP-, and BF-properties are satisfied. The one-phase exterior Hele-Shaw problem and one-phase interior Hele-Shaw problem with sink/source points can also be treated. We also show some numerical results which exemplify the effectiveness of our scheme.
 7.3.2016
15:40
 Dr. Miroslav Frost (Inst. of Thermomechanics, Czech Acad. Sci.): Constitutive model of NiTi SMA polycrystals: from experiments to simulations Abstract: Mechanical response of polycrystals of NiTi shape memory alloys (SMA) exhibits several interesting features, e.g. strong dependence on temperature, loading mode or loading history. These effects result from interplay of deformation mechanisms of various origin with the dominant influence of martensitic phase transformation. In the talk, I will introduce a constitutive model of textured NiTi SMA which allows for a realistic description of the mechanical response under various loading conditions. Particular attention has been paid to the description of martensite reorientation, occurrence of intermediate phase and the localization effect. Simulations demonstrating capabilities of the model both at the macro- and meso- scale will be presented and compared to experimental data.
 14.3.2016
15:40
 Prof.Dr. Patrick Dondl (Abt. f. angew. Math., Albert-Ludwigs-Universitat Freiburg): Energy estimates, relaxation, and existence for strain gradient plasticity with cross hardening Abstract: We consider a variational formulation of gradient elasto-plasticity subject to a class of single-slip side conditions. Such side conditions typically render the associated boundary-value problems non-convex. We first show that, for a large class of plastic deformations, a given single-slip condition (specification of Burgers vectors and slip planes) can be relaxed by introducing a microstructure through a two-stage process of mollification and lamination. This yields a relaxed side condition which only prescribes slip planes and allows for arbitrary slip directions. This relaxed model can be thought of as an aid to simulating macroscopic plastic behavior without the need to resolve arbitrarily fine spatial scales. We then discuss issues of existence of solutions for the relaxed model. Finally, we apply this relaxed model to a specific system, in order to be able to compare the analytical results with experiments. A rectangular shear sample is clamped at each end, and is subjected to a prescribed horizontal, modelled by an appropriate Dirichlet condition. We ask: how much energy is required to impose such a shear, and how does the energy depend on the aspect ratio of the sample? Assuming that just two slip systems are active, we show that there is a critical aspect ratio, above which the energy is strictly positive, and below which it is zero. Furthermore, in the respective regimes determined by the aspect ratio, we prove energy scaling bounds, expressed in terms of the amount of prescribed shear.
 21.3.2016
15:40
 Dr. Paolo Piovano (Faculty of Mathematics, University of Vienna, Austria): Wulff Shape Emergence in Graphene Abstract: In this talk the problem of understanding why particles self-assemble in macroscopic clusters with overall polyhedral shape is investigated. At low temperature ground states for a general finite number n of particles of suitable phenomenological energies possibly accounting for two- and three-body atomic interactions are shown to be connected subsets of regular lattices L, such as the triangular and the hexagonal lattice. The hexagonal lattice well represents the arrangement of carbon atoms in the graphene layers. By means of a characterization of minimal configurations via a discrete isoperimetric inequality, ground states will be seen to converge to the hexagonal Wulff shape as the number n of particles tends to infinity. Furthermore, ground states are shown to be given by hexagonal configurations with some extra particles at their boundary, and the n3/4 scaling law for the deviation of ground states from their corresponding hexagonal configurations is shown to hold. Precisely, the number of extra particles is carefully estimated to be at most KL n3/4 + o(n3/4 ), where both the rate n3/4 and the explicitly determined constant KL are proven to be sharp. The new designed method allows to sharpen previous results [1, 5] for the triangular setting [2] and allows to provide a first analytical evidence of the zigzag-edge selectivity and the emergence of the asymptotic Wulff shape for the hexagonal setting [3] in accor- dance with what is experimentally observed in the growth of graphene flakes [4]. Results presented are in collaboration with Elisa Davoli and Ulisse Stefanelli (Vienna). References [1] Y. Au Yeung, G. Friesecke, and B. Schmidt, Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff-shape, Calc. Var. Partial Differential Equations 44 (2012), 81-100. [2] E. Davoli, P. Piovano, and U. Stefanelli, Sharp n3/4 law for the minimizers of the edge-isoperimetric problem on the triangular lattice, Submitted (2015). [3] E. Davoli, P. Piovano, U. Stefanelli, Wulff shape emergence in graphene, Submitted (2015). [4] Z. Luo, S. Kim, N. Kawamoto, A.M. Rappe, and A.T. Charlie Johnson, Growth mechanism of hexagonal-shape graphene flakes with zigzag edges, ACSNano 11 (2011), 1954-1960. [5] B. Schmidt, Ground states of the 2D sticky disc model: fine properties and N 3/4 law for the deviation from the asymptotic Wulff-shape, J. Stat. Phys. 153 (2013), 727-738.
 4.4.2016
15:40
 Dr. Diego Grandi (University of Vienna): Modeling shape memory alloys at finite strains: solvability and linearization Abstract: We discuss the macroscale modeling of shape memory alloys according to a finite strain-version of the Souza-Auricchio model. Assuming the isotropy of the hyperelastic stored energy functional, a convenient formulation in terms of the Green-St-Venant transformation strain tensor can be established. For the chosen rate-independent constitutive relation, coupled to a quasi-static elastic response and with an additional regularizing interface-energy contribution, the global existence of energetic solutions to the boundary value problem (i.e. variational evolution) is proven. A similar finite-strain approach is applied to provide a model for the magneto-elastic evolution in magnetic shape-memory materials. The possibility of a rigorous linearization limit of the models at small strain is addressed within the framework of the evolutive variational convergence for rate independent processes.
 11.4.2016
15:40
 prof. Endre Suli (University of Oxford): Finite element approximation of non-divergence form PDEs Abstract: Non-divergence form partial differential equations with discontinuous coefficients do not generally possess a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. Such equations arise in many applications from areas such as probability and stochastic processes. These equations also arise as linearizations to fully nonlinear PDEs, as obtained for instance from the use of iterative solution algorithms. In such cases, it can rarely be expected that the coefficients of the operator be smooth or even continuous. For example, in applications to Hamilton-Jacobi-Bellman equations, the coefficients will usually be merely essentially bounded. In contrast to the study of divergence form equations, it is usually not possible to define a notion of weak solution when the coefficients are non-smooth. In the case of continuous but possibly non-differentiable coefficients, the Calderon-Zygmund theory of strong solutions establishes the well-posedness of the problem in sufficiently smooth domains. However, without additional hypotheses, well-posedness is generally lost in the case of discontinuous coefficients. The aim of the lecture is to survey recent developments concerning the numerical approximation of such problems by finite element methods. The lecture is based on joint work with Iain Smears (INRIA Paris).
 18.4.2016
15:40
 prof. Endre Suli (University of Oxford): Numerical analysis of nonlocal Cahn-Hilliard equations Abstract: We discuss the numerical approximation of a class of nonlinear evolution problems that arise as L2 and H-1 gradient flows for the Modica-Mortola regularization of a certain functional on BV involving the interfacial energy per unit length or unit area, the flat torus in Rd , and a nonnegative Fourier multiplier, that is continuous and symmetric, and which decays to zero at infinity. Such functionals feature in mathematical models of pattern-formation in micromagnetics and models of diblock copolymers. The resulting evolution equation is discretized by a Fourier spectral method with respect to the spatial variables and a Crank-Nicolson or an implicit midpoint scheme with respect to the temporal variable. We investigate the stability and convergence properties of the proposed numerical schemes and illustrate the theoretical results by numerical simulations. The lecture is based on joint work with Christof Melcher (RWTH Aachen), Barbora Benesova (University of Wurzburg) and Nicolas Condette (Humboldt University, Berlin).
 25.4.2016
15:40
 Prof. Dr. Fredi Tröltzsch (Inst. f. Mathematik, Technische Univ. Berlin): Optimal control of some reaction-diffusion equations Abstract: Results on the optimal control of the Nagumo equation and the FitzHugh-Nagumo system are surveyed. Special emphasis is laid on first- and second-order optimality conditions for sparse optimal controls. The second-order analysis is applied to explain observed numerical stability with respect to certain perturbations. The theory is illustrated by various numerical examples.
16:50
 Dr. Barbora Benešová (Inst. f. Mathematik, Univ. Würzburg): Existence of weak solutions for a model of magnetoelasticity Abstract: In the talk, we will present a model for particles in micromagnetic fluids. Such fluids have many technological applications. They can not only be found in medical applications, but also in loud speakers and shock absorbers. We investigate micromagnetic material in the framework of complex fluids. The system of PDEs to model the flow of the material is derived in a continuum mechanical setting. We outline the process of modeling. Moreover, we highlight the coupling between the elastic and the magnetic properties of the material. Restricting our scope to the two dimensional setting, we then prove existence of solutions under the assumption of small initial data. This is joint work with Carlos García-Cervera (Mathematics Department, University of California, Santa Barbara, USA), Johannes Forster, Anja Schlömerkemper (Institute for Mathematics, University of Würzburg, Germany), and Chun Liu (Department of Mathematics, Penn State University, University Park, USA).
 2.5.2016
15:40
 Ing. Vaclav Klika, PhD. (Katedra matematiky, FJFI CVUT): On modelling self-organisation in real systems Abstract: Self-organisation in nature is widely recognised and is extensively modelled. In some systems (e.g. Drosophila embryo) the spatial pattern is not self-orchestrated. On the other hand, Turing model of pattern formation is capable of breaking symmetry without pre-existing positional information. This mechanism has driven numerous experimental studies even in the context of developmental systems which suggest that Turing-like morphogen interactions and patterns can occur in such scenarios. However, a direct verification has remained elusive. We start by introduction to the classical Turing instability. As the aim is to reveal mechanism behind the observed pattern in nature, robustness is required not only with respect to parameter sensitivity or the choice of initial or boundary conditions but also with respect to the model formulation itself. Only then are these models subjected to a detailed mathematical analysis. We illustrate the essence of these ideas on the reaction-diffusion-advection system, where we indicate that such a system should be preferred from both physical and mathematical viewpoint for self-organisation modelling. Particularly, we shall use the mixture theory within extended irreversible thermodynamics to reveal what evolution equations are relevant in real physical systems and can be considered as small perturbations of reaction-diffusion equations and mathematically analyse the possibility of the emergence of pattern in RDA systems. Note that it is required to identify plausible extensions of the Turing concept of self-organisation into more general cases. Such extensions are not unambiguous but their discussion is beneficial even for understanding the standart Turing model of spatial self-organisation.
 9.5.2016
15:40
 Dr. Jan Haskovec (King Abdullah Univ. of Sci. and Technology): PDE-based modelling of biological network formation Abstract: Motivated by recent papers describing rules for natural network formation in discrete settings, we propose an elliptic-parabolic system of partial differential equations. The model describes the pressure field due to a Darcy-type equation and the dynamics of the conductance network under pressure force effects with a diffusion rate representing randomness in the material structure. We prove the existence of global weak solutions and of local mild solutions and study their long term behavior. Moreover, we study the structure and stability properties of steady states that play a central role to understand the pattern capacity of the system. We show that patterns (network structures) occur in the regime of small material randomness. Moreover, we present results of systematic numerical simulations of the system that provide further insights into the properties of the network-type solutions.
 16.5.2016
15:40
 Mgr. Michal Pavelka, PhD. (VSCHT, Praha): A hierarchy of Poisson brackets Abstract: Reversible part of evolution equations is often governed by a Poisson bracket and energy. For example, Hamilton canonical equations are given by the canonical Poisson bracket on cotangent bundle of classical mechanics and by energy (a Hamiltonian). Similarly, Liouville equation is given by an induced Liouville Poisson bracket. Reversible parts of more macroscopic evolution equations, for example Boltzmann equation, Navier-Stokes equation, equations for polymeric fluids or turbulent flows, are also generated by Poisson brackets. The goal of this talk is to show how the more macroscopic Poisson brackets are derived from the Liouville Poisson bracket in a systematic way.
 23.5.2016
15:40
 Dr. Stanislav Parez (VSCHT, Praha): Flow of granular materials: What can we say about landslides? Abstract: Large landslides exhibit surprisingly long runout distances compared to a rigid body sliding from the same slope, and the mechanism of this phenomena has been studied for decades. Here we propose a scenario in which the observed long runouts are explained via a granular flow, including its spreading, but not including frictional weakening that has traditionally been suggested to cause long runouts. Kinematics of the granular flow is divided into center of mass motion and spreading due to flattening of the flowing mass. We solve the center of mass motion analytically based on a frictional law valid for granular flows, and find that the center of mass runout is similar to that of a rigid body. Based on the shape of deposits observed in experiments with collapsing granular columns and numerical simulations of landslides, we estimate the effect of spreading and derive a characteristic spreading length R_f ~ V^{1/3}. Spreading is shown to be an important, often dominating, contribution to the total runout distance. The combination of the predicted center of mass runout and the spreading length gives the runout distance in a very good match to natural landslides.
 27.6.2016
15:40
 Prof. Miroslav Grmela (Lecole Polytechnique Montreal): Modeling of flows of complex fluids by modeling their internal structure Abstract: Fluids with internal structure that evolves in time on a scale that is comparable with the scale on which the macroscopic flow evolves exhibit a complex flow behavior and are therefore called complex fluids. The internal structure can be flow-induced (e.g. the structure emerging in turbulent flows) or it can also be a mesoscopic or microscopic structure of the fluids at rest (e.g. structure of macromolecules in polymeric fluids or suspended particles in suspensions). I investigate consequences of the requirement that the time evolution of complex fluids is compatible with mechanics (i.e. it is a Hamiltonian time evolution) and compatible with thermodynamics (it obeys the second law of thermodynamics).
16:50
 Dr. J. Murali Krishnan (Dept. of Civil Engr., IIT Madras): Experimental Investigations on Asphalt Binders - What are the challenges? Abstract: 90% of the highways and runways throughout the world use asphalt binders for road construction. Such materials are by-products of oil refinery. They are a complicated mixture of thousands of hydrocarbons and show diverse range of behavior as the temperature is varied. These material exhibit transitory behavior from a viscoelastic fluid to viscoelastic solid during service. In this talk, I present novel experimental techniques designed to elicit the rich behavior of these materials. These include large amplitude oscillatory shear, stress relaxation and creep and recovery. I also show some interesting observations related to manifestation of normal force and its relaxation. Such experimental data pose challenge while modeling as most of the existing models cannot describe such behavior.
 10.10.2016
15:40
 Prof.RNDr. Miloslav Feistauer, DrSc., Dr.h.c. (KNM MFF UK): On a robust DG method for the solution of compressible Euler and Navier-Stokes equations Abstract: The lecture presents numerical method for the numerical solution of compressible flow, which is robust with respect to the Mach number and Reynolds numbers. It is based on the application of the discontinuous Galerkin method and allows the numerical simulation of compressible flow with low Mach numbers up to an incompressible limit and high speed flow, in general in time-dependent domains. The method is used for the solution of fluid-structure interaction problems.
 17.10.2016
15:40
 Dr. Elisa Davoli (Faculty of Math., Univ. Vienna): Dynamic perfect plasticity as convex minimization Abstract: We present a novel approximation of solutions to the equations of dynamic linearized perfect plasticity, based on a global variational formulation of the problem by means of the Weighted-Inertia- Dissipation-Energy (WIDE) approach. Solutions to the system of dynamic Prandtl-Reuss perfect plasticity are identified as limit of minimizers of parameter-dependent energy functionals evaluated on trajectories (the WIDE functionals). Compactness is achieved by means of time- discretization, uniform energy estimate on minimizers of discretized WIDE-functionals, and passage to the limit in a parameter-dependent energy inequality. This is a joint work with Ulisse Stefanelli.
 24.10.2016
15:40
 RNDr. Michal Pavelka, PhD. (Math. Inst., Charles Uni.): Minicourse of Non-Equilibrium Thermodynamics. Part I. Abstract: Non-equilibrium thermodynamics is the theory within which we should be able to derive evolution equations of any macroscopic or mesoscopic physical system. Although such a task is very important in modern physics and applied mathematics, it seems to be still far away from current state of the art. The theory is still under construction. The goal of this minicourse is to review some fundamental concepts and results of non-equilibrium thermodynamics, which we can use in mathematical modeling, and to open discussion so that we find the most important open problems. In the fist part, we will discuss the concepts of equilibrium, non-equilibrium, levels of description, geometrization of thermodynamics, reversibility and irreversibility.
 31.10.2016
15:40
 RNDr. Michal Pavelka, PhD. (Math. Inst., Charles Uni.): Minicourse of Non-Equilibrium Thermodynamics. Part II. Abstract: In the second part we will discuss mainly the reversible part of evolution equations. We will start with Liouville equation in the Hamiltonian form and we will pass to lower levels of description as kinetic theory or fluid mechanics. Perhaps we will have time to start talking about the irreversible evolution.
 7.11.2016
15:40
 Prof. Yannis F. Dafalias (Univ. of California, Davis, & National Technical University of Athens): Anisotropic Critical State Theory: Challenging a Paradigm in Granular Mechanics Abstract: Consider the following thought experiment: load a granular specimen in triaxial compression till Critical State (CS) is reached, where shear deformation continues under fixed stress and zero volume change. At CS impose a rotation of stress Principal Axes (PA) keeping the stress principal values fixed. Will the sample continue being at CS or not? The answer to this seemingly simple and of academic interest question can challenge the paradigm of Critical State Theory (CST) that defines failure and mechanical response of granular media in soil mechanics for more than half a century. The recently developed Anisotropic Critical State Theory (ACST) will be presented as a paradigm replacement for the classical CST. The main novel ingredient entering the new formulation is fabric, expressed in terms of a properly defined fabric tensor that evolves towards a unique norm CS value. The presentation will be narrative providing stages of development and problems encountered and solved or still pending a solution. In the process constitutive models of soil plasticity will be presented within the framework of ACST, and the use of numerical/experimental techniques such as Discrete Element Method (DEM) and X-Ray tomography will be outlined.
 14.11.2016
15:40
 RNDr. Michal Pavelka, PhD. (Math. Inst., Charles Uni.): Minicourse of Non-Equilibrium Thermodynamics. Part III. Abstract: We will derive the Poisson bracket of one-particle kinetic theory, classical hydrodynamics and a theory of mixtures. We will then start discussing entropy. It will be introduced as the Shannon entropy at the Liouville level of description. Entropy of ideal gas at the levels of kinetic theory, classical hydrodynamics and thermodynamic equilibrium will be derived by the principle of maximum entropy (MaxEnt).
 21.11.2016
15:40
 Prof.Dr. Hans Knupfer (Univ. Heidelberg, Inst. of Mathematik): Self-similar lifting and persistent touch-down point solutions in the thin-film equation Abstract: In the talk I discuss the appearance of self-similar blow-up solutions for thin-film equations with different mobility exponents. This is related to non-uniqueness phenomena for weak solution of the same equation. The proof is based on dynamical systems arguments.
 28.11.2016
15:40
 RNDr. Michal Pavelka, PhD. (Math. Inst., Charles Uni.): Minicourse of Non-Equilibrium Thermodynamics. Part IV. Abstract: After having introduced energy, entropy and Poisson brackets on different levels of description, we will discuss various forms of irreversible evolution, in particular gradient dynamics (generated by dissipation potentials). We will show connection to the method of entropy production maximization and implicit constitutive relations. All so far brought up topics will be summarized in the formulation of the GENERIC framework, particular realizations and applications (solid mechanics, plasticity, chemical reactions, electrochemistry, diffusion, nonlocal phenomena) of which will dominate the following seminars.
 5.12.2016
15:40
 Mgr. Jan Stebel, PhD. (T. U. Liberec): Shape optimization for Stokes problem with stick-slip boundary conditions Abstract: We consider the problem of finding an optimal shape of a domain occupied by a viscous fluid. A part of the boundary represents a solid wall to which the fluid may or need not adhere depending on the magnitude of the shear stress. Such model describes e.g. hydrophobic or microscale surfaces. The existence of an optimal shape is proved. Moreover, a regularized-penalized problem is formulated and it is proved that its solutions converge to the solution of the original shape optimization problem. Finally we present an approximation of the problem and numerical results. This is a joint work with J. Haslinger and R.A.E. M{ a}kinen.
 12.12.2016
15:40
 * * * Jindrich NECAS MEMORIAL SEMINAR * * * ____________________________
15:45
 prof. RNDr. Alois Kufner, DrSc. (MU AV CR + ZCU Plzen): My life with J.N. Abstract: The talk will deal with a rather private description of the long lasting collaboration with my teacher, colleague and friend, professor Jindrich Necas, and will mention some facts about common events (like seminars and workshops), about some of his students and about his results.
 19.12.2016
15:40
 doc. dr. Giuseppe Tomassetti (Universita di Roma Tor Vergata): A nonsmooth variant of the nonlinear diffusion equation
 9.1.2017
15:40

## 50th ANNIVERSARY OF SEMINAR ON CONTINUUM MECHANICS (now Necas seminar on cont. mech.)

### An interview with one of the founders of this seminar, Ing. IVAN HLAVACEK, DrSc. (in Czech)

16:15
 Prof. Ing. Tomas Roubicek, DrSc. (Math. Inst. of the Charles Univ. & Czech Academy of Sci.): Open mathematical problems in the continuum mechanics of solids Abstract: An attempt of a short overview on the occasion of 50 years of seminar from continuum mechanics. In particular static and evolution problems at large strains will be discussed.
16:35
 Prof. RNDr. Eduard Feireisl, DrSc. (Math. Inst., Czech Academy of Sci.): Open problems in mathematics of fluids Abstract: Most of the great open problems are related to the pioneering work of Jean Leray. We give a short list of them that have remained open up to these days. We briefly mention the contribution of the Prague school of fluid mechanics to solving some of them.
16:55
 Prof. RNDr. Miloslav Feistauer, DrSc. DrHC. (Dept. of Numerical Math., Math.-Phys.Fac., Charles Univ.): Progress and open problems in CFD Abstract: Originally the Seminar on Continuum Mechanics was oriented to problems of solid mechanics, i.e., elasticity, plasticity and similar subjects. This was changed since the year 1984, when I started cooperating with Prof. J. Necas on the problem of potential transonic flow. We obtained interesting results on entropy compactification of transonic flow. They were applied with success in the finite element solution of this problem, but our main goal, the proof of the existence of a solution, is still open. Another open problem in Computational Fluid Dynamics (CFD) is the theoretical analysis of numerical methods for the solution of compressible Euler or Navier-Stokes equations. In our department we contributed strongly to the development of efficient, accurate and robust methods for the solution of compressible flow using the discontinuous Galerkin method. However, the convergence of these techniques is still open. Something similar is true for flows in time-dependent domains and fluid-structure interaction.
 20.2.2017
15:40
 Dr. Mathias Schaeffner (Inst. f. Wissensch. Rechnen, Tech. Univ. Dresden): Quantitative homogenization in non-linear elasticity Abstract: In this talk, I consider periodic homogenization of non-convex integral functionals that are motivated by non-linear elasticity. It is well kown that, due to the non-convexity, the effective integrand is determined by an asymptotic multi-cell formula. From this formula it is difficult to deduce qualitative or quantitative properties of the effective energy. Under suitable assumptions, in particular that the integrand has a single, non-degenerate, energy well at the set of rotations, I show that the multi-cell formula reduces to a much simpler single-cell formula in a neighbourhood of the rotations. This allows for a more refined, corrector based, analysis. In particular, for small data, I establish an estimate on the homogenization error. This is joint work with Stefan Neukamm (Dresden).
 27.2.2017
15:40
 RNDr. Karel Tuma, PhD. (IPPT PAN, Warszawa): Phase-field model for martensitic transformation Abstract: The shape memory effect or pseudoelasticity observed in shape memory alloys is associated with martensitic phase transformation. A recently developed finite-strain phase-field model for martensitic transformation in shape memory alloys is modified. The standard double-well potential that is present in the interfacial part of the free energy is replaced by more advanced double-obstacle potential. For implementation of such model it is crucial to hold the order parameters in a physical range. This is done by employing the augmented Lagrangian method. Furthermore, the classical purely rate-dependent dissipation potential is replaced by the rate-independent one which causes that the material starts to transform after some critical driving force is achieved which is observed in experiments. The proposed model is then used to study several problems in CuAlNi shape memory alloy. For example a size-dependent morphology of austenite-twinned martensite interface is studied, or the compression of 3D nano-pilar is simulated and compared with the experimental data.
 6.3.2017
15:40
 RNDr. Michal Pavelka, PhD. (MFF UK Praha): Minicourse of Non-Equilibrium Thermodynamics. Part V. Abstract: At last, some applications of the GENERIC framework will be covered. In particular, we will start with Navier-Stokes-Fourier equations, which can be easily generalized to Korteweg fluids. Mixtures will be covered in the form of Maxwell-Stefan diffusion, and the dissipation potential leading to the law of mass action in chemical kinetics will be shown. Finally, a speculative theory describing fluids and solids within a single framework will be suggested.
 13.3.2017
15:40
 Priv.-Doz.Dr. Stefan Kromer (UTIA AV CR): Heterogeneous thin films: local and nonlocal effects Abstract: I will discuss a variational model for heterogeneous thin films (membranes) including so-called Cosserat vectors (directors). As it turns out, although the corresponding finite-scale model is a perfectly local integral functional, nonlocal effects can appear in the homogenized thin film limit in some cases. On the other hand, this phenomenon can be ruled out for sufficiently fine heterogeneities. This is joint work with Carolin Kreisbeck (Utrecht).
 20.3.2017
15:40
 there is no seminar
 27.3.2017
15:40
 Doc.RNDr. Milan Pokorny, PhD. (MU UK): Incompressible Fluid Model of Electrically Charged Chemically Reacting and Heat Conducting Mixtures Abstract: We consider a model of a mixture of fluids which is modeled by an incompressible non-Newtonian (power-law) fluid. We allow that the constituents may undergo chemical reactions and the fluid in total can transfer heat and is generally electrically charged. We show existence of a weak solution to this system of partial differential equations which exists globally in time and without any restriction on the size of the data. In dependence of the power-law exponent $r$ we consider different weak formulations of the system which are all equivalent on the level of strong solutions, but not necessarily on the level of weak solutions. This is a results achieved together with Miroslav Bulicek and Nicola Zamponi.
 3.4.2017
15:40
 prof.Ing. Frantisek Pochyly, CSc. (VUT Brno): Studium hydrofobie na zaklade experimentu Abstract: Uvod bude venovan popisu jednotlivych experimentu: - stekani kapky po naklonene rovine a metodika stanoveni kontaktniho uhlu a soucinitele adheze; - vyuziti hydrofobie pro aeraci; - rychlostni profily na hydrofobnim povrchu v zavislosti na Reynoldsove cisle; tlakova diference pri proudeni vody v trubce s hydrofobnim povrchem; - proudeni vody v trubce s hydrofobnim povrchem s otevrenou hladinou. Jednotlive vysledky, zejmena neocekavane, budou komentovany na zaklade Navier-Stokesovych rovnic a modelu turbulence.
 10.4.2017
15:40
 doc. PaedDr. Karel Jelen, CSc. (Fac. Physical Educ. & Sports, Charles Univ.): MOZNOSTI lab BEZ v oblasti kinematickych a dynamickych analyz
 17.4.2017
15:40
 there is no seminar (Easter Monday)
 24.4.2017
15:40
 Dr. Josef Zabensky (Inst. f. Math., Univ. Wuerzburg): A Navier-Stokes-Fourier-like system capturing transitions between viscous and inviscid fluid regimes and between no-slip and perfect-slip boundary conditions Abstract: We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is continuously parametrized by the temperature. As such, the considered fluid may go through transitions between three of the following regimes: it can flow as a Bingham fluid for a specific value of the temperature, while it can behave as the Navier-Stokes fluid for another value of the temperature or, for yet another temperature, it can respond as the Euler fluid until a certain activation initiates the response of the Navier-Stokes fluid. At the same time, we regard a generalized threshold slip on the boundary that also may go through various regimes continuously with the temperature. All material coefficients like the dynamic viscosity, friction or activation coefficients are assumed to be temperature-dependent. We establish the large-data and long-time existence of weak solutions.
 15.5.2017
15:40
 MSc. Piotr Minakowski, PhD. (Interdisciplinary Center for Sci. Comput., Heidelberg University): On the Euler system with variable congestion Abstract: I will talk about the fluid equations used to model pedestrian motion and traffic, namely the compressible-incompressible two phase Euler system describing the flow in the free and in the congested regimes, respectively. The congested regime appears when the density in the uncongested regime reaches a threshold value that describes the comfort zone of individuals. This quantity is prescribed initially and transported along with the flow. That system can be approximated by the compressible Euler equations with singular pressure for the fixed barrier densities. I will review recent analytical developments for the barrier densities varying in the space and time. Main focus is directed to the numerical simulations of the Euler system with variable congestion encoded by a singular pressure. An asymptotic preserving finite volume scheme based on a conservative formulation of the system in terms of density, momentum and density fraction, is given. A second order accuracy version of the scheme is also presented. The scheme is validated on one-dimensional test-cases by the comparison with the Riemann problem. Finally, two dimensional numerical simulations that exhibit typical crowd dynamics are being shown. This is joint work with: Pierre Degond, Laurent Navoret and Ewelina Zatorska.
 22.5.2017
15:40
 Prof. Ing. Tomas Roubicek, DrSc. (Math. Inst. of the Charles Univ. & Czech Academy of Sci.): Thermodynamics of magneto- and poro-elastic materials at large strains Abstract: The theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick s and Fourier s laws in the deformed (Eulerian) configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn-Hilliard equations are used. The formulation of the problem uses Lagrangian (reference) configuration while the transport processes are pulled back. Except the static (or quasistatic) problems, the demagnetising field is ignored and only local non-selfpenetration is considered. The analysis as far as existence of weak solutions of the (thermo)dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetalics under diffusion of hydrogen accompanied possibly by magnetic effects (and in particular ferro-to-antiferromagnetic phase transformation), all in the full thermodynamical context under large strains. The talk is in large parts based on a joint paper with Giuseppe Tomassetti.
 9.10.2017
15:45
 Prof. Dr. Ulisse Stefanelli (University of Vienna): Three ways around intermediate configurations in finite plasticity Abstract: More than half a century after its first appearance, the theory of finite plastic deformations still features a number of controversial points. Issues as basic the composition of elastic and plastic effects and the nature of plastic flow are still lively debated. A prominent controversial point is the role of the so called intermediate configuration, which is assumed to store the memory of all previous plastic deformations. The intermediate configurations is immaterial, for it is not the image of a plastic deformation in general. Still, its tangent space is instrumental to define the classic multiplicative strain decomposition. I have recently found myself going around this point in three different ways. At first, in collaboration with A. Mielke I have derived a rigorous linearization result based on Gamma-convergence. Secondly, together with D. Grandi I have advanced a theory based on the so called plastic-metric tensor. Eventually, I have considered the special case of compatible plastic deformations. In all of these cases, the issue of the intermediate configuration is quite naturally settled.

 Po semináři se podává opět čaj a káva. Všichni zájemci jsou srdečně zváni.