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  (Mathematical Inst., Charles Univ.):  Large data analysis for the Kolmogorov twoequation model of turbulence  Abstract: A.N.Kolmogorov seems to be the first who recognized that a two
equation model of turbulence might be used as the basis of turbulent flow prediction. Although his model has so far been almost unnoticed it exhibits interesting features. First of all, its structure is similar to the NavierStokes(Fourier) equations for incompressible fluid, the only difference is that the viscosity is not constant but depends on the fraction of the two scalar quantities that measure the effect of turbulence: the average of the kinetic energy of velovity fluctuations and the measure related to the length scales of turbulence. The dependence is such that the material coefficients such as viscosity and turbulent diffusivities may degenerate, and thus the apriori control of the
derivatives of the involved quantities is unclear. Furthermore, the system
includes the dissipation of the energy, which is merely an $L^1$ quantity, standing at the righthand side of the equation for turbulent kinetic energy. We establish large data existence of suitable weak solution to such a system completed by the initial and generalized Navier s slip and stickslip boundary conditions. 



15:40  Prof. Susanne Ditlevsen (University of Copenhagen, Denmark):  Partially observed stochastic models in neuroscience  Abstract: When constructing a mathematical model for a given system under study, decisions about characteristics and levels of detail of the model have to be taken. Which choices are appropriate depend on the questions, one wants to answer. It should also depend on available data, such that the model can exploit the information that can be extracted and not suffer too much by what cannot. I will present some examples where a simple model extracted from more biophysical based models can answer specific questions of interest, as long as the simple model is interpreted and used in a suitable way.
This is 12th Colloquium Lecture, School of Mathematics Faculty of Mathematics and Physics  [Official anouncement] 



15:40  (LudwigMaximiliansUniversitat Munchen, Math. Inst.):  Smoothed Particle Hydrodynamics (SPH)  Abstract: Smoothed Particle Hydrodynamics is a meshfree Lagrangian method for the
simulation of fluids. In this talk I will present the basic theory
behind SPH, applied to a simple case of the compressible NavierStokes
Equation.
Furthermore I will talk about practical and programming considerations
that are relevant in order to efficiently implement an SPH simulation.
Finally I will present a working implementation of an interactive
(realtime) simulation of a fluid. The aim of the talk is not to present new results: I seek contact to people that are willing to help me to improve my understanding of fluid dynamics. The talk should be accessible to anyone with a mathematics or physics background. 



15:40  (University of Florence, Dept. of Mathematics and Appl.):  Eigenfunctions of the LaplaceBeltrami operator and geometric inequalities  Abstract: A joint event as a 13th Colloquium Lecture of the School of Mathematics
Some methods of geometric nature in the study of qualitative and quantitative aspects of eigenvalue problems for the Laplace operator, and of its analogue on Riemannian manifolds will be discussed. Two questions will be especially focused. On the one hand, information on the spectrum of the Laplacian,
and, in particular, on its discreteness, will be provided. On the other hand, criteria for the regularity of
eigenfunctions, and specifically their integrability and boundedness, will be illustrated. The results to
be presented are the fruits of a collaboration with V. G. Maz ya. 



15:40  (Universidad de Concepcion, Chile):  A mixedprimal finite element method for the stationary Boussinesq problem  Abstract: In this talk we propose and analyze a new mixed variational formulation
for the stationary Boussinesq problem. Our method, which employs a
technique previously applied to the NavierStokes equations, is based
first on the introduction of a modified pseudostress tensor depending
nonlinearly on the velocity through the respective convective term.
Next, the pressure is eliminated, and an augmented approach for the
fluid flow, which incorporates Galerkin type terms arising from the
constitutive and equilibrium equations, and from the Dirichlet boundary
condition, is coupled with a primalmixed scheme for the main equation
modeling the temperature. In this way, the only unknowns of the
resulting formulation are given by the aforementined nonlinear
pseudostress, the velocity, the temperature,
and the normal derivative of the latter on the boundary. An equivalent
fixedpoint setting is then introduced and the corresponding classical
Banach Theorem, combined with the LaxMilgram Theorem and the Babuv
skaBrezzi theory, are applied to prove the unique solvability of the
continuous problem. In turn, the Brouwer and the Banach fixed point
theorems are utilized to establish existence and uniqueness of solution,
respectively, of the associated Galerkin scheme. In particular,
RaviartThomas spaces of order $k$ for the pseudostress, continuous
piecewise polynomials of degree $le k +1$ for the velocity and the
temperature, and piecewise polynomials of degree $le k$ for the
boundary unknown become feasible choices. Finally, we derive optimal a
priori error estimates, and provide several numerical results
illustrating the good performance of the augmented mixedprimal finite
element method and confirming the theoretical rates of convergence. 



15:40  (Universitaet Augsburg, Inst. f. Mathematik):  Duality, regularity and uniqueness for BVminimizers  Abstract: For a smooth function $u colon Omega omathds R$ the $n$dimensional area of its graph over a bounded domain $Omega subset mathds R^n$ is given by
$$int_Omega sqrt 1+Du2,dx,.$$
A natural question is whether or not minimizers of this functional exist among all functions taking prescribed boundary values. It turns out that solutions of the least area problem exist only in a suitably generalized sense. This formulation is based on an extension of the original functional to the space of functions of bounded variation via relaxation, where attainment of the prescribed boundary values is not mandatory, but nonattainment is penalized. Consequently, such generalized minimizers do not need to be unique.
In my talk I will discuss similar convex variational integrals under a linear growth condition. After a short introduction to the dual problem in the sense of convex analysis I will explain the duality relations between generalized minimizers and the dual solution. The duality relations can be interpreted as mutual respresentation formulas, and in particular they allow to deduce statements on uniqueness and regularity for generalized minimizers. The results presented in this talk are based on a joined project with Thomas Schmidt (Erlangen). 



15:40  (Univ. Stuttgart, Inst. f. angewandte Analysis u. numerische Simulation):  Multiphase and Phase Transition Flows  Abstract: 1st part will present DiffuseInterface and Phase
Field Models. (2nd part, focused on SharpInterface Models, will be presented on 19 March 2013 at 14:00 in K3.) 



15:40  (Fakulta strojinho inzenyrstvi, VUB):  Studium vlastnosti hydrofobnich povrchu  Abstract: V ramci seminare budou ucastnici seznameni s obsahovou naplni a vysledky vyzkumu proudeni kapalin po hydrofobnich povrsich.
Obsahova cast:
 definice hydrofobniho povrchu
 definice povrchove energie
 stekani vrstvy tekutiny po hydrofobnim povrchu
 stekani kapky po hydrofobnim povrchu
 definice adhesniho soucinitele
 okrajova podminka interakce tekutiny s hydrofobnim povrchem
 vliv hydrofobniho povrchu na vznik kavitace
 souvislost Lorentzovy sily a hydrofobniho povrchu
 prakticke ukazky ruznych druhu hydrofobnich povrchu 



15:40  (Institute of Fundamental Technological Research, Polish Academy of Sciences):  Phase Field Model of Formation and Evolution of Martensitic Microstructures  Abstract: We develop a micromechanical phase field model that describes the
phase transformation between the austenite and twinned martensites. It
improves the model by Hildebrand and Miehe (2012) that described two
variants of martensite only. Furthermore, the new model constrains the
volume fractions of both parent and internally twinned phases such that they
remain in the physical range. As an application, we study the twinned
martensite and austenitemartensite interfaces in the cubictoorthorhombic
transformation in a CuAlNi shape memory alloy and estimate the elastic part
of the interfacial energy. Several problems are simulated using Finite
element method. 



15:40  (KNM MFF UK):  On vibrations of an airfoil with 3 degrees of freedom induced by turbulent flow  Abstract: The subject of the lecture is the numerical simulation of the interaction of twodimensional incompressible viscous flow and a vibrating airfoil with large amplitudes. The airfoil with three degrees of freedom performs rotation around
an elastic axis, oscillations in the vertical direction and rotation of a flap. The numerical simulation consists of the stabilized finite element solution of the
Reynolds averaged NavierStokes equations combined with
SpalartAllmaras or komega turbulence models, coupled with a system of nonlinear ordinary
differential equations describing the airfoil motion with consideration of large amplitudes. The timedependent computational domain and approximation on a moving grid are treated by the Arbitrary LagrangianEulerian formulation of the flow equations. 



15:40  (Dept. of Mathematics, University of Chicago):  Improved Regularity in Bumpy Lipschitz Domains  Abstract: In this talk we will explain how to get Lipschitz regularity up to the microscale for elliptic systems over a bumpy boundary. The analysis relies on a compactness scheme and on an estimate in a space of non localized energy for a boundary layer corrector in the halfspace. This is joint work with Carlos Kenig. 



15:40  (IMATH et Dept. Mathematiques, Universite du Sud ToulonVar):  Error estimates for the compressible NavierStokes equations  Abstract: Inspired by the notion and properties of dissipative solutions investigated in the theory of compressible NavierStokes equations, we shall derive an unconditional error estimate with respect to a weak solution with bounded density for a mixed finite volume / finite element numerical scheme for the compressible NavierStokes equations. 



15:40  (Mathematical Inst., Charles Univ.):  Damage with plasticity at small strains  an overview of various models  Abstract: Coupling of plasticity with damage allows for modelling many complex processes
occurring in solid continuum mechanics and physics, in contrast to mere
plasticity or mere damage. First, a quasistatic model of linearized plasticity
with hardening at small strains combined with gradient damage will be
presented in its basic scenario with unidirectional damage and in the fully
rateindependent setting. Various concepts of weak solutions will be discussed, ranging from the concept of energetic (i.e., in particular, energy conserving)
solutions to stressdriven local solutions. Some modifications of this
model will then be presented. In particular a ratedependent damage
allowing possibly also healing, and plasticity possibly without hardening
and with damageable yield stress. This variant seems to need the concept of
2ndgrade nonsimple materials and allows e.g. for modelling of thin
shearbands surrounded by a wider damage zone. An opposite variant is
ratedependent plasticity but damage again rate independent and
unidirectional, which allows for energy conservation and in particular
for extension towards anisothermal processes. Also combination of this model
with a concept of large plastic strains or some other ratedependent processes
like diffusion of some fluidic medium with wide applications covering
e.g. heat/moisture transport in concrete or rocks, or a metal/hybrid
transformation under diffusion of hydrogen will be discussed. 



15:40  (Dept. of Mechanical and Aerospace Engineering, Carleton University, Ottawa, Canada):  The ``Cauchystat`` : accurate control of the true stress in molecular dynamics simulations of martensitic phase transformations.  Abstract: After a brief introduction to the use of molecular dynamics (MD) simulations in materials science, I will discuss the specifics of stresscontrolled MD, and describe how many stresscontrolled simulations are incorrectly interpreted due to misunderstandings about what stress measure is being used (Cauchy stress or ``Engineering`` stress). I will then present a new MD algorithm that correctly controls the true Cauchy stress applied to the system. This ``Cauchystat`` is based on the constant stress ensemble presented by Tadmor and Miller (``Modeling Materials: Continuum, Atomistic and Multiscale Techniques``, Cambridge University Press, 2011), but with modified equations of motion that update the system boundary conditions in response to the resulting deformation of the simulation cell. As a clear example of the method`s usefulness, we show that the correct stress control is important in the case of martensitic phase transformations, where the predicted martensitic start temperature and austenitic finish temperature are significantly altered as compared to the result using other stresscontrol algorithms. We also examine the effects of shear stress on the mechanism of the phase transformation. 



9:00  (Inst. f. Mathematik, Technische Univ. Berlin):  Rational harmonic functions and their applications in gravitational lensing  Abstract: This talk will discuss recent results on the zeros of rational harmonic functions f(z)=r(z)conj{z}, which have fascinating applications ranging from numerical linear algebra to astrophysics. A particular focus will be on extremal functions, where r(z) is of degree n>=2 and f(z) has the maximal possible number of 5n5 zeros. Examples of such functions will be visualized using phase portraits, and the implication of our theoretical results in the theory of graviational lensing will be discussed.
This special seminar is organized jointly with
Computational Mathematics Seminar (Institute of Computer of Science) as an activity of the Necas Center for mathematical modeling 



15:40  (Institute of Mathematics, Polish Academy of Science):  From structured populations models to polymeric flows  



15:40  (Charles University in Prague, Faculty of Mathematics and Physics, Mathematical institute, Czech Rep.)):  Implicitly constituted materials: from modeling towards PDEanalysis of relevant initial and boundary value problems  Abstract: We investigate strengths of implicit constitutive equations,
paying a particular attention to their impact on PDEanalysis of relevant initial and boundary value problems. We view the role of (PDE) analysis in defining an object suitable for numerical approximation. Using several problems, we will present the achieved results and emphasize the novelties that the implicit constitutive theory brings, while skipping the details of the proofs that can be found in the given references. We will concentrate on the problems in the following areas:
(i) implicitly constituted incompressible fluids,
(ii) nonlinear models for solids with the bounded linearized strain,
(iii) threshold slip boundary conditions stated in the form of implicit
constitutive equations,
(iv) flows through porous media with pressure dependent porosity,
(v) compressible fluids with bounded divergence of the velocity field. 



15:40  (Dept. of Chemical Engineering, Univ. Chemistry & Technology Prague):  Modeling of multiphase flows  Abstract: In many unit operations used in chemical industry is typical existence of several phases. Common examples are extraction, aerobic fermentation of cells of various kind, polymerization,
emulsification, crystallization etc. System behavior or final product properties are almost always
dependent on the interaction of involved phases. It is therefore of a key importance to better
understand the mechanisms occurring locally between involved phases as well as their impact
on the macroscopic properties of the system. This lecture would cover three examples of
multiphase flow, i.e. LL (suspension polymerization), GL (flow of air bubbles in the stirred
bioreactor) and SL (gel formation during the mixing of stream containing polymeric nanoparticle
with stream containing an electrolyte), where will be introduced concept of modeling of
dispersed phase using population balances as well as their connection with the fluid dynamic
model of 2phases (EulerEuler RANS, pseudosingle phase approach). Since turbulence is
commonly essential for these unit operations it will be shown also the case when local conditions
could lead to the substantial increase of viscosity and thus change of the flow type. Since
presented simulations are based on several model assumptions validity of the used approach will
be discussed when comparing the obtained results with the experimental data obtained in the same unit. 



15:40  (Mathematical Inst., Charles Univ.):  Limiting strain models in elasticity theory and variational integrals with linear growth  Abstract: Starting from implicit constitutive models for elastic solids we introduce
its subclass consisting of elastic solids with limiting small strain. The main goal is
to present the results concerning the existence of weak solution
to boundary value problems in bounded domains. The lecture is based
on joint papers with Lisa Beck, Miroslav Bulicek, Endre Suli and K.R. Rajagopal. 



15:40  (University of Stuttgart, Institute of Applied Analysis and Numerical Simulations):  Relative Energy for EulerKorteweg and Related Hamiltonian Flows  Abstract: We consider the Euler equations containing the generator of the variational
derivative of an energy functional. Attention is paid to the analysis of the
EulerKorteweg system with a special, in general nonconvex, potential energy
functional.
Note: A continuation under the title ``Discontinuous Galerkin Schemes for Compressible MultiPhase Dynamics``, will be delivered on Tuesday 12 November 2015 at the Seminar on Numerical Mathematics, lecture hall K3 at 14:00. 



15:40  (Institute of Thermomechanics, Czech Acad. Sci.):  SMStability of laminar shear flows and transition to turbulence  Abstract: Laminar shear flow of a real fluid is subjected to instability under certain conditions and its character is changed to the final turbulent state. The turbulence is considered to be the last unsolved problem of classical physics. Even the process of transition from laminar to turbulent state is still not fully understood. However the process of birth could provide key information related to turbulence itself.
That is why the suggested presentation is focused on this phenomenon. The following particular problems will be addressed:
* Flow of real fluids
* Shear flow instability concepts
* Laminar and turbulent structure
* Typical cases of instable flows
* Possible scenarios of the transition process
* Some of known issues of the stability theories 



15:40  (Math. Institute, Charles Univ.):  Towards mathematical description of creep and stress relaxation tests in the mechanics of nonlinear viscoelastic materials  Abstract: The response of physical systems governed by linear ordinary
differential equations to a step input is traditionally investigated
using the classical theory of distributions. The response of nonlinear
systems is however beyond the reach of the classical theory. The
reason is that the simplest nonlinear operationmultiplicationis
not defined for the distributions. Yet the response of nonlinear
systems is of interest in many applications, most notable example is
the analysis of the creep and stress relaxation tests in mechanics of
viscoelastic materials. Consequently, a mathematical framework capable
of handling such problems is needed.
We argue that a suitable framework is provided by the socalled
Colombeau algebra that gives one the possibility to overcome the
limits of the classical theory of distributions, namely the
possibility to simultaneously handle discontinuity, differentiation
and nonlinearity. Our thesis is documented by means of studying the
response of two systems governed by nonlinear ordinary differential
equations to a step input. In particular, we show that using the rules
of calculus in Colombeau algebra it is possible to obtain an explicit
and practically relevant characterisation of the behaviour of the
considered systems at the point of the jump discontinuity. 



15:40  (MU UK):  Energyconserving time discretisation for dynamical problems in solids involving inelastic processes  Abstract: Secondorder evolution variational inequalities governed by
quadratic or separately quadratic energies with set constraints
and possibly nonsmooth and degree1 homogeneous dissipated energies
are discretised by implicit formulas in such a way that the
energy of the discrete scheme is conserved. Applications in
continuum mechanics of solids at small strains includes
e.g. dynamic Signorini contacts or linearized plasticity possibly
combined with damage etc. This allows efficient implementation
transient problems without artificial numerical attenuation
within vibrations. Illustrative numerical simulations
by C.G.Panagiotopolos will be presented, too. 



15:40   doc.RNDr. Milan Pokorný, PhD.: Presentation of the book Selected works of Jindřich Nečas (Eds. M.Pokorný, S.Nečasová, V.Sverák), Birkhauser, Basel, 2015 .  Abstract: The book collects the most significant contributions of the outstanding Czech mathematician Jindřich Nečas, who was honoured with the Order of Merit of the Czech Republic by President Václav Havel. Starting with J.Nečas brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. 

16:10  (Mathematical Institute CAS):  The motion of incompressible viscous fluid around a moving rigid body  Abstract: The dynamics of fluids, i.e. liquids and gases, is an important part of the continuum mechanics. This lecture is devoted to the qualitative analysis of mathematical models of motion of a viscous incompressible fluid around a compact body B, translating and rotating in the fluid with given timeindependent translational and angular velocities u and omega. The translation can be considered, without the loss of
generality, to be parallel to the x3 axis. We shall study  the timeperiodic Stokes system, Oseen system in the whole space, in an exterior domain and we will investigate the strong solution of the problem in Lq setting with corresponding weight describing the behavior in the large distance. Moreover, we shall discuss the fundamental solution of the Oseen rotating system and the asymptotic decay for the Oseen case and also for nonlinear case. 



15:40  (Univ. Roma II `Tor Vergata):  Accretion of an actin layer on a spherical bead: the treadmilling regime.  Abstract: Inspired by experiments on actin growh on spherical beads, we formulate and
solve a model problem describing the accretion of an incompressible elastic
solid on a rigid sphere.
One of the peculiar characters of our model is that accretion does not take
place on the external surface of the body, but rather on the surface that
separates it from its support. This mechanism of growth is responsible for
stress accumulation within the body because when a new layer of material is
deposited on the support it pushes outwards the preexisting layers.
Eventually, stress buildup inhibits accretion at the internal surface and
promotes ablation at the external surface of the body, insofar as a
stationary regime called treadmilling sets in, characterized by internal
accretion being balanced by external ablation.
The relevant ingredients of our model are: a law that governs accretion and
ablation accounting for both chemistry and mechanics; a farfromstandard
choice of the reference configuration, which eases our task of coping with
the continuously evolving material structure and with the lack of a
conventional stressfree reference configuration. 


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Všichni zájemci jsou srdečně zváni. 
