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Tuesday, 17.10.2017, 15.00 Uhr (WIAS-ESH)
Seminar Modern Methods in Applied Stochastics and Nonparametric Statistics
Dr. A. Suvorikova, WIAS Berlin:
Two-sample test based on 2-Wasserstein distance
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin
Tuesday, 17.10.2017, 15.15 Uhr (FU-140)
Oberseminar Nonlinear Dynamics
Dr. J. Sieber, University of Exeter, UK:
Smooth center manifolds for delay-differential equations
more ... Location
Freie Universität Berlin, Arnimallee 7, 14195 Berlin, Hinterhaus, Raum: 140

Abstract
Delay-differential equations (DDEs) with state-dependent delays are, as far as is known, at best continuously differentiable once as dynamical systems. That is, the time-t map does not depend on its argument with a higher degree of smoothness than 1. However, as I will show, center manifolds near equilibria are still as smooth as expected from the spectral gap and from the smoothness of coefficients. In particular, I will review what precisely ßmoothness of coefficients" means.

Host
Freie Universität Berlin
WIAS Berlin
Wednesday, 18.10.2017, 10.00 Uhr (WIAS-ESH)
Forschungsseminar Mathematische Statistik
Prof. Dr. V. Spokoiny, WIAS Berlin:
Big ball probability with applications in statistical inference
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We derive the bounds on the Kolmogorov distance between probabilities of two Gaussian elements to hit a ball in a Hilbert space. The key property of these bounds is that they are dimensional-free and depend on the nuclear (Schatten-one) norm of the difference between the covariance operators of the elements. We are also interested in the anticoncentration bound for a squared norm of a non-centered Gaussian element in a Hilbert space. All bounds are sharp and cannot be improved in general. We provide a list of motivation examples and applications in statistical inference for the derived results as well. (joint with Götze, Naumov and Ulyanov)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Universität Potsdam
Thursday, 19.10.2017, 14.00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. L. Rebholz, Clemson University, USA:
On conservation laws of Navier--Stokes Galerkin discretizations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We study conservation properties of Galerkin methods for the incompressible Navier-Stokes equations, without the divergence constraint strongly enforced. In typical discretizations such as the mixed finite element method, the conservation of mass is enforced only weakly, and this leads to discrete solutions which may not conserve energy, momentum, angular momentum, helicity, or vorticity, even though the physics of the Navier-Stokes equations dictate that they should. We aim in this work to construct discrete formulations that conserve as many physical laws as possible without utilizing a strong enforcement of the divergence constraint, and doing so leads us to a new formulation that conserves each of energy, momentum, angular momentum, enstrophy in 2D, helicity and vorticity (for reference, the usual convective formulation does not conserve most of these quantities). Several numerical experiments are performed, which verify the theory and test the new formulation.

Host
WIAS Berlin
Tuesday, 24.10.2017, 13.45 Uhr (WIAS-406)
Seminar Materialmodellierung
A. Zubkova, Karl-Franzens-Universität Graz, Österreich:
Homogenization of the generalized Poisson--Nernst--Planck system with nonlinear interface conditions
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstract
We consider the generalized system of nonlinear Poisson-Nernst-Planck equations, which describes concentrations of multiple charged particles with the overall electrostatic potential. It is modeled in terms of the Fickian multiphase diffusion law coupled with thermodynamic principles. The generalized model is supplied by volume and positivity constraints and quasi-Fermi electrochemical potentials depending on the pressure. The model describes a plenty of electrokinetic phenomena in physical and biological sciences. We examine nonlinear inhomogeneous transmission conditions describing electro-chemical reactions on the interface in a periodic two-phase medium. We aim at a proper variational modeling, well-posedness, and asymptotic analysis as well as homogenization of the model.

Host
WIAS Berlin
Wednesday, 25.10.2017, 15.15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. J. Rehberg, WIAS Berlin:
Explicit and uniform resolvent estimates for second order divergence operators on Lp spaces
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Monday, 30.10.2017, 14.00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Prof. Dr. L. Berlyand, Pennsylvania State University, USA:
Hierarchy of PDE Models of Cell Motility
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
We consider mathematical PDE models of motility of eukaryotic cells on a substrate and discuss them in a broader context of active materials. Our goal is to capture mathematically the key biological phenomena such as steady motion with no external stimuli and spontaneous breaking of symmetry. We first describe the hierarchy of PDE models of cell motility and then focus on two specific models: the phase-field model and the free boundary problem model. The phase-field model consists of the Allen-Cahn equation for the scalar phase field function coupled with a vectorial parabolic equation for the orientation of the actin filament network. The key mathematical properties of this system are (i) the presence of gradients in the coupling terms and (ii) the mass (volume) preservation constraints. These properties lead to mathematical challenges that are specific to active (out of equilibrium) systems, e.g., the fact that variational principles do not apply. Therefore, standard techniques based on maximum principle and Gamma-convergence cannot be used, and one has to develop alternative asymptotic techniques. The free boundary problem model consists of an elliptic equation describing the flow of the cytoskeleton gel coupled with a convection-diffusion PDE for the density of myosin motors. This PDE system is of Keller-Segel type but in a free boundary setting with nonlocal condition that involves boundary curvature. Analysis of this system allows for a reduction to a Liouville type equation which arises in various applications ranging from geometry to chemotaxis. This equation contains an additional term that presents an additional challenge in analysis. In the analysis of the above models our focus is on establishing the traveling wave solutions that are the signature of the cell motility. We also study breaking of symmetry by proving existence of non-radial steady states. Bifurcation of traveling waves from steady states is established via the Schauder's fixed point theorem for the phase field model and the Leray-Schauder degree theory for the free boundary problem model. These results are obtained in collaboration with Jan Fuhrmann, M. Potomkin, and V. Rybalko.

Host
WIAS Berlin
Wednesday, 01.11.2017, 15.15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. T. Roubíček, Czech Academy of Sciences, Tschechische Republik:
Seismic waves and earthquakes in a global monolithic model
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Further Informations
Berliner Oberseminar “Nichtlineare Partielle Differentialgleichungen” (Langenbach Seminar)

Host
WIAS Berlin
Humboldt-Universität zu Berlin
Tuesday, 07.11.2017, 13.30 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Prof. J. Novo, Universidad Autónoma de Madrid, Spanien:
Quasi-optimal methods to approximate the incompressible Navier--Stokes squations
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstract
In this talk we will consider different methods to approximate the incompressible Navier--Stokes squations. Our main concern is to get error bounds with constants independent on inverse powers of the viscosity parameter. We will consider inf-sup stable methods with grad-div stabilization, non inf-sup stable methods with local projection stabilization and fully discrete schemes based on projection methods in time plus grad-div stabilization in space. Some numerical experiments will be shown to check the optimality of the theoretical rates of convergence of the methods.

Host
WIAS Berlin
Wednesday, 22.11.2017, 14.00 Uhr (WIAS-406)
FG Stochastische Systeme mit Wechselwirkung
Dr. S. Simonella, Technische Universität München:
Correlations in the mean field dynamics: a random walk expansion
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Host
WIAS Berlin
Monday, 27.11.2017, 14.00 Uhr (WIAS-ESH)

Dr. A. Höner, Forschungsverbund Berlin e.V.:
Funding opportunities for WIAS Researchers within the European Framework Programme Horizon 2020
more ... Location
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Host
WIAS Berlin