5.1.2015
15:40
 prof. RNDr. J. Malek, CSc., DSc. (Mathematical Inst., Charles Univ.): Large data analysis for the Kolmogorov two-equation 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 Navier-Stokes(-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 right-hand 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 stick-slip boundary conditions.
 19.1.2015
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]
 9.2.2015
15:40
 Dr. Roland Tomasi (Ludwig-Maximilians-Universitat Munchen, Math. Inst.): Smoothed Particle Hydrodynamics (SPH) Abstract: Smoothed Particle Hydrodynamics is a mesh-free 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 Navier-Stokes 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 (real-time) 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.
 23.2.2015
15:40
(University of Florence, Dept. of Mathematics and Appl.):
Eigenfunctions of the Laplace-Beltrami 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.
 2.3.2015
15:40
 Prof. Gabriel N. Gatica (Universidad de Concepcion, Chile): A mixed-primal 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 Navier-Stokes 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 primal-mixed 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 fixed-point setting is then introduced and the corresponding classical Banach Theorem, combined with the Lax-Milgram Theorem and the Babuv ska-Brezzi 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, Raviart-Thomas 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 mixed-primal finite element method and confirming the theoretical rates of convergence.
 9.3.2015
15:40
 Prof. Dr. Lisa Beck (Universitaet Augsburg, Inst. f. Mathematik): Duality, regularity and uniqueness for BV-minimizers 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 $$int_Omega sqrt 1+|Du|2,dx,.$$ 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 non-attainment 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).
 16.3.2015
15:40
 Prof.Dr. Christian Rohde (Univ. Stuttgart, Inst. f. angewandte Analysis u. numerische Simulation): Multiphase and Phase Transition Flows Abstract: 1st part will present Diffuse-Interface and Phase Field Models. (2nd part, focused on Sharp-Interface Models, will be presented on 19 March 2013 at 14:00 in K3.)
 23.3.2015
15:40
 prof. Ing. Frantisek Pochyly, CSc. (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
 30.3.2015
15:40
 Dr. Karel Tuma (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 cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and estimate the elastic part of the interfacial energy. Several problems are simulated using Finite element method.
 13.4.2015
15:40
 Prof. RNDr. Miloslav Feistauer, DrSc., Dr.h.c. (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 two-dimensional 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 Navier-Stokes equations combined with Spalart-Allmaras or k-omega turbulence models, coupled with a system of nonlinear ordinary differential equations describing the airfoil motion with consideration of large amplitudes. The time-dependent computational domain and approximation on a moving grid are treated by the Arbitrary Lagrangian-Eulerian formulation of the flow equations.
 20.4.2015
15:40
 Dr. Christophe Prange (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 half-space. This is joint work with Carlos Kenig.
 4.5.2015
15:40
 Prof. RNDr. Antonin Novotny (IMATH et Dept. Mathematiques, Universite du Sud Toulon-Var): Error estimates for the compressible Navier-Stokes equations Abstract: Inspired by the notion and properties of dissipative solutions investigated in the theory of compressible Navier-Stokes 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 Navier-Stokes equations.
 11.5.2015
15:40
 Prof. Tomáš Roubíček, DrSc. (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 rate-independent setting. Various concepts of weak solutions will be discussed, ranging from the concept of energetic (i.e., in particular, energy conserving) solutions to stress-driven local solutions. Some modifications of this model will then be presented. In particular a rate-dependent damage allowing possibly also healing, and plasticity possibly without hardening and with damageable yield stress. This variant seems to need the concept of 2nd-grade non-simple materials and allows e.g. for modelling of thin shearbands surrounded by a wider damage zone. An opposite variant is rate-dependent 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 rate-dependent 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.
 18.5.2015
15:40
 Prof. Ronald E. Miller (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 stress-controlled MD, and describe how many stress-controlled 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 methods 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 stress-control algorithms. We also examine the effects of shear stress on the mechanism of the phase transformation.
 24.9.2015
9:00
 Prof. Dr. Joerg Liesen (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 5n-5 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
 12.10.2015
15:40
 Prof. dr hab. Piotr Gwiazda (Institute of Mathematics, Polish Academy of Science): From structured populations models to polymeric flows
 19.10.2015
15:40
 Prof. RNDr. Josef Malek, DSc. (Charles University in Prague, Faculty of Mathematics and Physics, Mathematical institute, Czech Rep.)): Implicitly constituted materials: from modeling towards PDE-analysis of relevant initial and boundary value problems Abstract: We investigate strengths of implicit constitutive equations, paying a particular attention to their impact on PDE-analysis 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.
 26.10.2015
15:40
 Ing. Miroslav Soóš, PhD. (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. L-L (suspension polymerization), G-L (flow of air bubbles in the stirred bioreactor) and S-L (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 2-phases (Euler-Euler RANS, pseudo-single 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.
 2.11.2015
15:40
 Prof. RNDr. Josef Malek, DSc. (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.
 9.11.2015
15:40
 Dr. Jan Giesselmann (University of Stuttgart, Institute of Applied Analysis and Numerical Simulations): Relative Energy for Euler-Korteweg 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 Euler-Korteweg system with a special, in general nonconvex, potential energy functional. Note: A continuation under the title Discontinuous Galerkin Schemes for Compressible Multi-Phase Dynamics, will be delivered on Tuesday 12 November 2015 at the Seminar on Numerical Mathematics, lecture hall K3 at 14:00.
 23.11.2015
15:40
 Prof. Ing. Vaclav Uruba, CSc (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
 30.11.2015
15:40
 Mgr. Vit Prusa, PhD. (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 operation---multiplication---is 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 so-called 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.
 7.12.2015
15:40
 Prof.Ing. Tomas Roubicek, DrSc. (MU UK): Energy-conserving time discretisation for dynamical problems in solids involving inelastic processes Abstract: Second-order evolution variational inequalities governed by quadratic or separately quadratic energies with set constraints and possibly nonsmooth and degree-1 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.
 14.12.2015
15:40
 *** Jindřich NECAS MEMORIAL SEMINAR *** 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
 doc. RNDr. Sarka Nečasová, PhD. (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 time-independent 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 time-periodic 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.
 21.12.2015
15:40
 Dr. Giuseppe Tomassetti (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 pre-existing 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 far-from-standard choice of the reference configuration, which eases our task of coping with the continuously evolving material structure and with the lack of a conventional stress-free reference configuration.

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