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

16:15  (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  (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  (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 NavierStokes 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 timedependent domains and fluidstructure interaction. 



15:40  (Inst. f. Wissensch. Rechnen, Tech. Univ. Dresden):  Quantitative homogenization in nonlinear elasticity  Abstract: In this talk, I consider periodic homogenization of nonconvex integral functionals that are motivated by nonlinear elasticity. It is well kown that, due to the nonconvexity, the effective integrand is determined by an asymptotic multicell 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, nondegenerate, energy well at the set of rotations, I show that the multicell formula reduces to a much simpler singlecell 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). 



15:40  (IPPT PAN, Warszawa):  Phasefield 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 finitestrain
phasefield model for martensitic transformation in shape
memory alloys is modified. The standard doublewell
potential that is present in the interfacial part of the
free energy is replaced by more advanced doubleobstacle
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 ratedependent
dissipation potential is replaced by the rateindependent
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
sizedependent morphology of austenitetwinned martensite
interface is studied, or the compression of 3D nanopilar
is simulated and compared with the experimental data. 



15:40  (MFF UK Praha):  Minicourse of NonEquilibrium Thermodynamics. Part V.  Abstract: At last, some applications of the GENERIC framework will be covered. In particular, we will start with NavierStokesFourier equations, which can be easily generalized to Korteweg fluids. Mixtures will be covered in the form of MaxwellStefan 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. 



15:40  (UTIA AV CR):  Heterogeneous thin films: local and nonlocal effects  Abstract: I will discuss a variational model for heterogeneous thin films (membranes)
including socalled Cosserat vectors (directors). As it turns out, although
the corresponding finitescale 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). 



15:40  (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 nonNewtonian (powerlaw) 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 powerlaw 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. 



15:40  (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 NavierStokesovych rovnic a modelu turbulence. 



15:40  (Fac. Physical Educ. & Sports, Charles Univ.):  MOZNOSTI lab BEZ v oblasti kinematickych a dynamickych analyz  



15:40  there is no seminar (Easter Monday)   



15:40  (Inst. f. Math., Univ. Wuerzburg):  A NavierStokesFourierlike system capturing transitions between viscous and inviscid fluid regimes and between noslip and perfectslip boundary conditions  Abstract: We study a generalization of the NavierStokesFourier 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 2graph 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 NavierStokes 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 NavierStokes 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 temperaturedependent. We establish the largedata and longtime existence of weak solutions. 



15:40  (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 compressibleincompressible 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 onedimensional testcases 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. 



15:40  (Math. Inst. of the Charles Univ. & Czech Academy of Sci.):  Thermodynamics of magneto and poroelastic 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 CahnHilliard 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 nonselfpenetration
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 ferrotoparamagnetic transformation
in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied
by magnetic effects (magnetic gels), or metalhydride phase transformation
in some intermetalics under diffusion of hydrogen accompanied possibly
by magnetic effects (and in particular ferrotoantiferromagnetic 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. 


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