NEČAS SEMINAR ON CONTINUUM MECHANICS
organized by the Mathematical Institute of the Charles University
each Monday at 15:45
in the MFF UK building,
Sokolovská 83, lecture room K3, 2^{nd}
floor,
proceeds with the following presentations:

15:40  (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 mantlelithosphere 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. 



15:40  Prof. Dr. Helmut Abels (University of Regensburg):  Wellposedness of a fullycoupled NavierStokes/Qtensor system with inhomogeneous boundary data  



15:40  (Faculty of Mathematics, RuhrUniversitat 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 nonasymptotical 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. 



15:40  (UTIA AV CR + FSv CVUT + MFF UK):  Quasistatic adhesive contact delaminating in mixed mode and its numerical treatment  Abstract: An adhesive unilateral contact between viscoelastic bodies at small strains
and in a KelvinVoigt rheology is scrutinized,
neglecting inertia. The flowrule 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 modemixity dependence
of delamination is a very pronounced (and experimentally confirmed)
phenomenon typically considered in engineering models. An efficient
semiimplicitintime 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 . 



15:40  (Katedra mechaniky, FSv CVUT):  An FFTbased 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 fixedpoint iterative solution to
an integral equation of the LippmannSchwinger type, with action of its
kernel efficiently evaluated by the Fast Fourier Transform techniques. The
aim of this work is to demonstrate that the MoulinecSuquet 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 apriori 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 nonsymmetric system of linear equations can be solved by the conjugate gradient method. Apart from providing a theoretical support to Fast Fourier Transformbased 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). 



15:40  (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
allatom 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 2state 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. 



15:40  (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 biLipschitz 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 biLipschitz functions is nonconvex. Thus,
standard cutoff 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
cutoff 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 biLipschitz
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). 



15:40  (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 nonequilibrium 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 nonideal 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 timereversal parity. 



15:40  (Northwestern University, Evanston, Illinois, USA):  Comminution of solids due to kinetic energy of highrate 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 electrohydraulic pulsed arc in the pipe of a horizontal borehole. In all these problems, the size of particles or their surfacevolume ratio, which controls energy dissipation as well as permeability enhancement, is the key parameter to predict. Whereas the comminution in the socalled `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 highrate 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, 1929119294.) 



15:40  (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 nonphysical energy dissipation. Integral nonlocal
formulation and its implementation will be discussed. Application of damage models in two realworld 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 watertightness of a foundation slab. This is a joint work with T. Koudelka and T. Krejci. 



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 ultrastrength materials produced by severe plastic deformation  

16:30  (Faculty of Phys. & Nuclear Engr., Czech Technical University):  Discrete Dislocation Dynamics  

17:00  (Institute of Thermomechanics, ASCR):  Civil structures health monitoring  



15:40  (Mathematisches Institut, LudwigMaxmilliansUniversitat 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 nonlinear 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 (divergencefree) functions. Thus, we present a Lipschitz approximation, which is also solenoidal. We will show how this can be applied to existence proofs for certain nonNewtonian fluids. 



15:40  (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. 



15:40  (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 thermomechanical and a chemical part, where the former is symmetric if binary interactions
are assumed, while the chemical interaction force is nonsymmetric, unless chemical equilibrium is attained. Introducing crosseffects 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 parityinstead of the classical distinction between socalled fluxes and driving forcesexplains the apparent antisymmetry of certain couplings. If the diffusion velocities are small compared to the speed of sound, the wellknown MaxwellStefan equations together with the socalled 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 MaxwellStefan equations to chemically reactive mixtures. (The talk is based on a joint work with Wolfgang Dreyer, WIAS, Berlin.) 



15:40  (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. 



15:40  (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 nonmatching meshes are
quite often used in multiphysics 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 wellknown 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 postprocesses on dual meshes can guarantee elementwise 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  (Dept. Informatik, Uni. ErlangenNurnberg):  Is 2.44 trillion unknowns the largest finite element system that can be solved today?  Abstract: Supercomputers have progressed beyond the PetaScale, 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. 



15:40  (Ecole Polytechnique de Montreal, Montreal, Canada):  Entropy  Abstract: I will discuss in particular the role that this nonmechanical 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) 



15:40  (Universidad Catolica de la Santisima Concepcion, Chile):  An adaptive strategy to solve the inverse problem of electroencephalography  Abstract: Electroencephalography is a noninvasive 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 timevariation 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 firstorder 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 residualtype 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 nonsingular 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  (Universidad del Bio Bio, Concepcion, Chile):  Analysis of new fullymixed finite element methods for the StokesDarcy coupled problem  Abstract: In this paper we introduce and analyze two new fullymixed 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 BeaversJosephSaffman law. We first extend
recent related results involving a pseudostress/velocitybased formulation in the fluid, and consider a fullymixed
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 leastsquares 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
wellposed. The classical BabuskaBrezzi theory is applied to provide sufficient conditions for the wellposedness of
the continuous and discrete formulations of both approaches. Next, we derive a reliable and efficient residualbased a posteriorierror estimator for the augmented mixed finite element scheme. The proof of reliability makes use ofthe global
infsup condition, Helmholtz decomposition, and local approximation propertiesof the Clement interpolant and
RaviartThomas operator. In turn, inverse inequalities, the localization technique basedon elementbubble and edgebubble
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. 



15:40  (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
nontrivial homotopy class. In contrast to the classical Skyrme mechanism from nuclear physics, the stabilization is due to a DzyaloshinskiiMoriya interaction term of linear gradient dependence, which breaks the chiral symmetry. 



15:40  (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
multiphysical interactions at several scales. This talk will focus on modelling fluid saturated deformable porous media under quasistatic loading.
A special type of porous media is presented by perfused tissues which have a
character of doubleporous 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 socalled
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 FEMsquare 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 deformationdependent 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 multiscale approach will
be discussed. 



15:40  (Johannes GutenbergUniversitat Mainz, Institut fur Mathematik):  Mathematical and numerical analysis of some fluidstructure interaction problems  Abstract: Fluidstructure 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
wellposedness 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. 



15:40  (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 nonhomogeneous and singular boundary condition. By the means of classical tools (conformal mapping, the Green function), we reformulate 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. 



15:40  Prof.RNDr. Jan Kratochvil, DrSc. (FSv CVUT + MU UK):  Modeling of a mechanism of a ultrafine 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 rigidplastic 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. 



15:40  (Dip. Ingegneria Civile e Ing. Inform., Univ. Roma II `Tor Vergata`):  Assessing energetic and dissipative effects in straingradient plasticity  Abstract: Metallic components undergoing inhomogeneous plastic flow display
sizedependent behavior in the size range below 100μm, with smaller
components being harder and having higher relative strength. This behavior is captured by straingradient 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), 11691191] we have considered the rateindependent case of a theory of straingradient plasticity devised in [M. Gurtin, L. Anand J. Mech. Phys. Solids 53 (2005) 16241649] 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 sizedependent 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 rateindependent evolution problem that describes simple shear of an infinite strip [L. Anand et al, J. Mech. Phys. Solids 53 (2005) 17891826]. 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. 



15:40  (Inst. of Mathematics, Polish Acad. Sci., Warszaw):  Twovelocity 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 NavierStokes 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
twovelocity 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). 



15:40  (ZuseInstitute 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 reactiondiffusion 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. 



15:40  
15:45  (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). 



15:40  (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 Gammaconvergence of our model to the sharp interface limit. This is joint work with Matthias Roger (TU Dortmund) and Luca Mugnai (MPI Leipzig). 


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Všichni zájemci jsou srdečně zváni. 
