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

(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.
(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.
(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.
(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).
(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.
(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.
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).
there is no seminar
(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.
(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.
(Fac. Physical Educ. & Sports, Charles Univ.):
MOZNOSTI lab BEZ v oblasti kinematickych a dynamickych analyz
there is no seminar (Easter Monday)
(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.
(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.
(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.

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