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, 2nd
floor,
proceeds with the following presentations:
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15:40 | Prof. A. Novotny (Universite du Sud Toulon-Var (France)): | Low Mach number limits to the complete Navier-Stokes-Fourier system | |
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17:20 | Prof. Dr. R. Farwig (TU Darmstadt, Germany): | From the Theory of Very Weak Solutions to Regularity of Weak Solutions of the Instationary Navier-Stokes System | Abstract: The three lectures deal with the theory of very weak solutions to the
stationary and instationary Stokes and Navier-Stokes 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 Navier-Stokes equations in the sense of Leray-Hopf and to prove local or even global in
time regularity beyond Serrin s condition. |
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15:40 | Doc. RNDr. L. Pick, DrSc. (KMA MFF UK): | Optimal Sobolev Embeddings and Interpolation | |
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17:20 | Dr. J. Schneider (NCMM, Prague): | Function Spaces of Varying Smoothness | |
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17:20 | Dr. D. Wachsmuth (Institute of Mathematics, TU Berlin, Germany): | Optimal control of the unsteady Navier-Stokes equations | Abstract: The talk is concerned with the study of optimal distributed control problems for the non-stationary Navier-Stokes equations. The control $u$ in our problem is vector-valued. Thus, box-constraints 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 set-valued mapping with convex and closed images. We present necessary as well as sufficient optimality conditions for that general type of constraint. The first-order necessary conditions imply a representation of locally optimal controls by projections, a fact which leads to new regularity results. In the presence of box-constraints 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 SQP-method for our optimal control problem. The talk closes with an outlook on open questions, which are connected to regularity issues of the Navier-Stokes system. |
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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, Cahn-Hilliard problem,
Landau-Ginzburg 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 Navier-Stokes-Korteweg equations which consists of the
classical Navier_Stokes equations and additional higher order
derivatives of the density on the right-hand 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. |
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15:40 | Prof P. Podio-Guidugli (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 well-known 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. |
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15:40 | Dr. A. Timofte (Institute of Mathematics, Romanian Academy, Bucharest): | Two-scale homogenization for evolutionary variational inequalities | Abstract: This topic (subject of a joint work with Alexander Mielke) is
devoted to the two-scale homogenization for a class of
rate-independent 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. |
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17:20 | Dr. Jonathan Healey (Department of Mathematics, Keele University, Keele, United Kingdom): | Destabilizing fluid flows by confinement | |
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15:40 | No program for this date. | | |
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17:20 | Prof. Jan Sokolowski (Laboratoire de Mathématiques, 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. |
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15:40 | Prof. Dr. Torsten Linss (TU Dresden, Germany): | Parameter robust methods for systems of singularly perturbed problems | |
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17:20 | Dr. Soeren Bartels (Humboldt-Universitaet 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
non-smooth potential are adressed. Preliminary illustrative numerical
experiments will be shown. This is joint work with Tomas Roubicek. |
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15:40 | Lecture room K1 Doc. RNDr. Josef Malek, CSc. (Mathematical Institut, Charles University, Prague): | Blood as an example of non-Newtonean material | Abstract: The aim of this talk is to recall basic facts concerning non-Newtonean fluid mechanics, and to illustrate why the blood when considered as a single continuum can be modeled as a viscoelastic shear thinning incompressible fluid. |
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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 cell-based view. Then, the ODE-model 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. |
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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. |
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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 |
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17:00 | Doc. RNDr. Martin Kruzik, PhD. (Institute of Information Theory and Automation, AS CR): | Gamma-convergence methods and applications | Abstract: Part of workshop Analysis of Multiphase Problems
place: UTIA, CAS, Pod Vodrenskou vezi 4, Praha |
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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 wave-focusing 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 |
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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 fluid-structure 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. |
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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) | |
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15:40 | Prof. Bodo Werner (Fachbereich Mathematik, Uni Hamburg, Germany): | Microscopic Car Following Traffic models - Road works and macroscopic observations | Abstract: here |
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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) | |
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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) |
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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) | |
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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) | |
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15:40 | (Mathematical Institute, Charles University, Prague): | Rate independent processes in viscous solids and their thermodynamics | Abstract: So-called generalized standard solids (of Halphen-Nguen type)
involving also activated typically rate-independent processes such
as
plasticity, damage, or phase transformations, will be described as
a
system of a force-equilibrium equation and variational inequality
for internal parametr variable. Various definitions of weak
solutions will be examined, especially from the viewpoint of
ability to combine rate-independent processes and other
rate-dependent phenomena, as viscosity or inertia. If those
rate-dependent phenomena are suppressed, then the system becomes
fully rate-independent and then the concept of the
so-called 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 rate-dependent) heat transfer will be scrutinized, too. |
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15:40 | Ing. Miroslav Sedlacek, CSc. (Stavebni fakulta, CVUT): | Zakladni parametry odvalovaciho principu | Abstract: This lecture will be presented in Czech language. |
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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) | |
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15:40 | (Mathematical Institute of Charles University, Prague): | On unsteady flows of Fluids with Pressure, Shear-rate and Temperature Dependent Material Moduli, that slip at solid boundaries | Abstract: We rigorously investigate the mathematical properties of
unsteady three-dimensional internal flows of incompressible fluids
with pressure, shear-rate 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 long-time existence of a
(suitable) weak solution when the data are large. This result
includes the classical Navier-Stokes-Fourier 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. |
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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) | |
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15:40 | (CSIRO Mathematical and Information Sciences, Canberra): | The Double Clumping Model of Wheat-Flour Dough Extension | Abstract: The response of a wheat-flour dough to the flow and deformation performed on it during mixing is a sequence of hysteretic extension-rupture-recoil-relax 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 stress-strain 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 rules-of-thumb correlations between the global structure of extensograms and the baking performance of good breads and cakes. In many ways, the rules-of-thumb simply reduce to being indirect measurements of the protein content of wheat-fours. From the baker?s perspective, extensograph testing, in conjunction with the rules-of-thumb, 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 wheat-flours 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. |
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15:40 | Mgr. Miroslav Bulicek, Ph.D. (Mathematical Institut, Charles University, Prague): | On existence of solution to incompressible Navier-Stokes-Fourier 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 N-S-F system whenever the weak formulation
makes a good sense. |
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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 so-called 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 so-called method of Lipschitz
approximation, that perfectly works if flux has some $r-1$ 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
point-wise convergence of temperature gradient. |
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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. !!! |
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Po semináři se podává opět čaj a káva.
Všichni zájemci jsou srdečně zváni. |
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