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:

15:45  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?
 



15:40  Prof. A. Novotny (Universite du Sud ToulonVar (France)):  Low Mach number limits to the complete NavierStokesFourier system  



15:40  Prof. Dr. AnnaMargaret Saendig (IANS, Univeritaet Stuttgart, Germany):  Variational methods for nonlinear boundary value problems in elasticity
 

17:20  Prof. Antonín Novotný (Universite du Sud ToulonVar, France):  Low Mach number limits to the complete NavierStokesFourier system
 



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 NavierStokes System  Abstract: The three lectures deal with the theory of very weak solutions to the stationary and instationary Stokes and NavierStokes 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 NavierStokes equations in the sense of LerayHopf and to prove local or even global in time regularity beyond Serrin s condition.




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
 



15:40  Dr. C. Schwarz (TU Muenchen, Germany):  Continuum dislocationbased plasticity: numerical implementation and shortrange interactions  Abstract: In this talk, the latest advances on the continuum dislocationbased 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 sizedependent 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 NavierStokes equations  Abstract: The talk is concerned with the study of optimal distributed control problems for the nonstationary NavierStokes equations. The control $u$ in our problem is vectorvalued. Thus, boxconstraints 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 setvalued mapping with convex and closed images. We present necessary as well as sufficient optimality conditions for that general type of constraint. The firstorder necessary conditions imply a representation of locally optimal controls by projections, a fact which leads to new regularity results. In the presence of boxconstraints 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 SQPmethod for our optimal control problem. The talk closes with an outlook on open questions, which are connected to regularity issues of the NavierStokes system. 



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, CahnHilliard problem, LandauGinzburg 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 NavierStokesKorteweg equations which consists of the classical Navier_Stokes equations and additional higher order derivatives of the density on the righthand 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.




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. 




Seminář se nekoná  Velikonoce  



15:40  Prof P. PodioGuidugli (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 wellknown 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.




15:40  Dr. A. Timofte (Institute of Mathematics, Romanian Academy, Bucharest):  Twoscale homogenization for evolutionary variational inequalities  Abstract: This topic (subject of a joint work with Alexander Mielke) is
devoted to the twoscale homogenization for a class of
rateindependent 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  




15:40  No program for this date.   



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 minicourse 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. 



15:40  Prof. Dr. Torsten Linss (TU Dresden, Germany):  Parameter robust methods for systems of singularly perturbed problems  

17:20  Dr. Soeren Bartels (HumboldtUniversitaet 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
nonsmooth potential are adressed. Preliminary illustrative numerical
experiments will be shown. This is joint work with Tomas Roubicek. 



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 minicourse 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"




15:40  Lecture room K1 Doc. RNDr. Josef Malek, CSc. (Mathematical Institut, Charles University, Prague):  Blood as an example of nonNewtonean material  Abstract: The aim of this talk is to recall basic facts concerning nonNewtonean 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 cellbased view. Then, the ODEmodel 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. 



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




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):  Gammaconvergence 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 wavefocusing 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 



15:40  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 fluidstructure 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)  



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)  



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) 



15:40  (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  (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart):  Boundary Integral Equations and Pseudodifferential Operators (lecture 2 of 6)  



15:40  (Mathematical Institute, Charles University, Prague):  Rate independent processes in viscous solids and their thermodynamics  Abstract: Socalled generalized standard solids (of HalphenNguen type)
involving also activated typically rateindependent processes such
as
plasticity, damage, or phase transformations, will be described as
a
system of a forceequilibrium equation and variational inequality
for internal parametr variable. Various definitions of weak
solutions will be examined, especially from the viewpoint of
ability to combine rateindependent processes and other
ratedependent phenomena, as viscosity or inertia. If those
ratedependent phenomena are suppressed, then the system becomes
fully rateindependent and then the concept of the
socalled 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 ratedependent) heat transfer will be scrutinized, too. 



15:40  Ing. Miroslav Sedlacek, CSc. (Stavebni fakulta, CVUT):  Zakladni parametry odvalovaciho principu  Abstract: This lecture will be presented in Czech language. 

17:20  (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart):  Boundary Integral Equations and Pseudodifferential Operators (lecture 5 of 6)  



15:40  (Mathematical Institute of Charles University, Prague):  On unsteady flows of Fluids with Pressure, Shearrate and Temperature Dependent Material Moduli, that slip at solid boundaries  Abstract: We rigorously investigate the mathematical properties of
unsteady threedimensional internal flows of incompressible fluids
with pressure, shearrate 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 longtime existence of a
(suitable) weak solution when the data are large. This result
includes the classical NavierStokesFourier 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  (Institut fuer Angewandte Analysis und numerische Simulation , Lehrstuhl fuer Angewandte Mathematik, Uni Stuttgart):  Boundary Integral Equations and Pseudodifferential Operators (lecture 6 of 6)  



15:40  (CSIRO Mathematical and Information Sciences, Canberra):  The Double Clumping Model of WheatFlour Dough Extension  Abstract: The response of a wheatflour dough to the flow and deformation performed on it during mixing is a sequence of hysteretic extensionrupturerecoilrelax 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 stressstrain 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 rulesofthumb correlations between the global structure of extensograms and the baking performance of good breads and cakes. In many ways, the rulesofthumb simply reduce to being indirect measurements of the protein content of wheatfours. From the baker?s perspective, extensograph testing, in conjunction with the rulesofthumb, 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 wheatflours 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. 



15:40  Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institut, Charles University, Prague):  On existence of solution to incompressible NavierStokesFourier 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 NSF 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 socalled 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 socalled method of Lipschitz
approximation, that perfectly works if flux has some $r1$ 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
pointwise convergence of temperature gradient. 



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. !!! 


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