NEČAS SEMINAR ON CONTINUUM MECHANICS
organized by the Mathematical Institute of the Charles University
each Monday at 15:40
in the MFF UK building,
Sokolovská 83, lecture room K1, 2^{nd}
floor,
proceeds with the following presentations:

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  icesheets  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 icesheets on sufficiently long time and spatial scales may be viewed as a thermomechanically coupled freesurface flow of a nonNewtonian 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 singlecomponent 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, noslip (frozen bed) Dirichlet boundary condition is applied, while in regions where basal temperature exceeds the local pressuremelting point, a rapid sliding occurs, governed by a Newtontype sliding law. As shown in recent numerical studies, such a type of thermallyconditioned boundary conditions may become a trigger of largescale intrinsic instabilities of the whole icesheet, 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 finiteelements. 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 KellerSegel model in 2D  Abstract: We construct an approximation to the measure valued, global in time solutions to the KellerSegel 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 (blowups). 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 KellerSegel system when the number of particles tends to infinity. The proof is based on the BBGKYapproach 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 KellerSegel 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). 



15:40  Doc. RNDr. Eduard Feireisl, DrSc. (Institute of Mathematics AS CR):  Suitable weak solutions to the compressible NavierStokes system  Abstract: We introduce a class of suitable weak solutions to the NavierStokes
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 weakstrong 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 NavierStokesFourier system for the iceflow problem.
The simplest possible (still physically relevant) setting is considered. Ice is described as a singlecomponent continuum and described by a model of a heatconducting nonNewtonian powerlaw fluid. The icesheet geometry is described by two smooth boundaries, the first one representing the upper free surface with a prescribed massproduction rate and surface temperature, the bottom representing the glacier base, where the heat flux is prescribed and the sliding law is specified by a Newtontype
boundary condition. Apriori scaling is introduced into the stresstensor 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 NavierStokesFourier system as a leadingorder limit of the perturbation expansion for the flatness parameter and the Froude number approaching zero. 



15:40  Prof. Lorenzo Freddi (Dipartimento di Matematica e Informatica, Universita di Udine):  From 3D nonlinear elasticity to 1D elastic models for thinwalled beams  Abstract: Geometrically, a thinwalled beam is a slender structural element whose
length is much larger than the diameter of the crosssection 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 thinwalled 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 threedimensional nonlinear elasticity, we rigorously
derive a hierarchy of onedimensional models for a thinwalled 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 thinwalled beam. Finally, in the third regime we deduce one dimensional linear/quasilinear models for thinwalled beams. 

17:20  Dr. Chiara Zanini (Dipartimento di Matematica e Informatica, Universita di Udine):  Quasistatic delamination models for KirchhoffLove plates  Abstract: The talk will address a quasistatic rateindependent brittle delamination
problem and also an adhesive unilateral contact problem
on a cylinder with a prescribed normallypositioned
surface inside. By letting the height of the cylinder
go to zero, we obtain two quasistatic rateindependent crack models
with prescribed path for KirchhoffLove plates.
(This is essentially based on a joint work with L.Freddi, R.Paroni,
and T.Roubicek.) 



15:40  Prof. Dr. Christian Grossmann (TU Dresden, Institute of Numerical Mathematics):  Convergence of InteriorExterior Penalty Methods in Optimal Control  



15:40  Dr. Agnieszka SwierczewskaGwiazda (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 powerlaw type fluids, stress powerlaw fluids, Bingham and HerschelBulkley fluids, etc.
We are interested in the development of (largedata) existence theory for internal flows subject to noslip
boundary conditions. We study first Stokeslike 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. 



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. 



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 matrixvalued 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 nonlinearelasticity 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. 



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. 



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 timediscretization scheme, based on the Minimizing Movement approach by Ennio De Giorgi. We present some applications. 



15:40  (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 twophase 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 twophase flow and deformation in a twophase medium. The model offers a selfconsistent 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. 



15:40  Easter Monday  seminar canceled   



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 JohnsonSegalman model is proposed to be solved. 



15:40  Dr. Giuseppe Tomassetti (Dipt. Ingegneria Civile, Univ. di Roma II  Tor Vergata):  Energetic solution of the torsion problem in straingradient plasticity  Abstract: We consider elastoplastic torsion in a thin wire in the framework
of the straingradient 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 rateindependent
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. 



15:40  Dr. Jan Valdman (University of Iceland, Reykjavik, Iceland and MaxPlanck Institute Leipzig):  Computations and a posteriori error estimates in elastoplasticity  Abstract: download abstract 



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, twoscale convergence and periodic unfolding. As an outlook
we will also look at the homogenization methods for stochastic geometries. 



15:40  Prof. E. FernandezCara (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 FursikovImanuvilov s approach. In the linear case, according to this strategy, the (original) controllability problems can be reduced to the solution of appropriate higherorder 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. 



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




15:40  Prof. E. FernandezCara (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, L1OptimalControl.pdf, L2HeatandWaves, 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. 



15:40  Prof. E. FernandezCara (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, L1OptimalControl.pdf, L2HeatandWaves, 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 NavierStokes systems, stochastic controllability, etc. 

17:20  Prof. E. FernandezCara (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, L1OptimalControl.pdf, L2HeatandWaves, 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, viscoelastic fluids, etc. 



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  



15:40  Prof Vlastimil Krivan (Biology center, Ceske Budejovice):  The LotkaVolterra predatorprey 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 LotkaVolterra predatorprey 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 LotkaVolterra 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  



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. 



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, 610640.
S. Repin and S. Sauter. Estimates of the modeling error for the KirchhoffLove plate model. C. R. Math. Acad. Sci. Paris 348 (2010), no. 1718, 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 nonconforming discretizations  Abstract: The solution of Boundary Value Problems of linear elasticity using a Domain Decomposition approach (DDBVPs) with nonoverlapping 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 nonconforming meshes along interfaces between subdomains if required. Finally, some numerical results are presented incuding the cases with nonconforming 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. 



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 pseudoelastic 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, rankone convexity or quasiconvexity 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 rateindependent dissipation, one can minimize the total incremental energy supplied quasistatically 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 secondorder terms can yield an exact solution in the firstorder rates, provided an appropriate symmetry restriction is imposed on the constitutive law. Loss of quasiconvexity by the ratepotential 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 atomicscale energy of phase boundaries (taken from the materials science literature) and the elastic microstrain 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.
Sizedependent 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 lengthscale parameters. 



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. 



15:40  Dr. Adrian Hirn (IWR, Heidelberg University):  Stabilized finite elements for fluids with shearrate and pressuredependent viscosity  Abstract: NonNewtonian fluid motions are frequently modeled by a powerlaw 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 infsup stability condition or dominating
convection in case of high Reynolds numbers, we propose a stabilization
method that is based on the wellknown 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. 



15:40  prof. E. Feireisl (Institute of Mathematics, Academy of Sciences of the Czech Republic):  Weak solutions and weak strong uniqueness for the NavierStokesFourier system  Abstract: We introduce a concept of weak solution based on Second law of thermodynamics for the full Navier StokesFourier system describing the motion of a general viscous, compressible, and heatconducting 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. 


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