Veranstaltungen

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Mittwoch, 13.11.2019, 10:00 Uhr (WIAS-405-406)
Forschungsseminar Mathematische Statistik
Merle Behr, University of California, Berkeley:
Learning compositional structures
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Raum: 405/406

Veranstalter
Humboldt-Universität zu Berlin
Universität Potsdam
WIAS Berlin
Mittwoch, 13.11.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Dr. Michael Kniely, Institute of Science and Technology Austria (IST Austria) , Österreich:
On the large-time behavior of a class of semiconductor equations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
This talk will be concerned with the exponential convergence to equilibrium of solutions to some semiconductor models arising from different modeling perspectives. The resulting PDE systems typically include drift-diffusion terms for electrons and holes as well as reaction terms describing the underlying electron-hole recombination mechanism. Including also the self-consistent electrostatic potential is often desired from a physical point of view. The main goal of the talk is the derivation of functional entropy-entropy dissipation inequalities in a constructive way for a set of semiconductor equations with and without potential and including different reaction processes. To this end, we will revisit nowadays classical calculations for prototype systems, and we shall also investigate more elaborate strategies necessary to deal with more complex models. Some parts of the talk are based on joint work with Klemens Fellner.

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Berliner Oberseminar Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Dienstag, 19.11.2019, 15:15 Uhr (FU Berlin)
Oberseminar Nonlinear Dynamics
Ralf Toenjes, University of Potsdam:
The constructive role of noise in the dynamics on network hubs for network synchronization
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Freie Universität Berlin, Arnimallee 3, 14195 Berlin, Hinterhaus, Raum 130

Abstrakt
We describe and analyze a coherence resonance phenomenon for synchronization in bipartite networks of well connected hubs and followers when the hubs are subjected to noise. Using the Ott-Antonsen ansatz for globally coupled phase oscillators the dynamics of the mean fields is described by a low-dimensional system of Langevin equations. Averaging over the fast stochastic dynamics of the hubs yields ordinary differential equations which predict the coherence resonance reasonably well.

Veranstalter
Freie Universität Berlin
WIAS Berlin
Mittwoch, 20.11.2019, 11:30 Uhr (WIAS-HVP-3.13)
Seminar Interacting Random Systems
D. R. Michiel Renger:
Dynamical Phase Transitions on Finite Graphs
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Weierstraß-Institut, Hausvogteiplatz 11A, 10117 Berlin, 3. Etage, Raum: 3.13

Abstrakt
We consider systems where particles jump through edges of a finite graph with nonlinear intensities, and study time-averaged particle fluxes as both the number of particles and the end time go to infinity. The corresponding large-deviation rate functional involve a minimisation over trajectories with a given time-averaged flux. The minimisation can often be restricted to constant paths, resulting in a very simple expression for the rate functional. However, for specific models and specific regimes of the average flux, such expression overshoot the large-deviation rate functional, which typically happens if small oscillations in the trajectories are more profitable. In that case we say that a dynamical phase transition occurs. The literature on dynamical phase transition is almost exclusively restricted to models where the graph becomes continuous in the limit, yielding quadratic rate functionals. In our work we focus on graphs that remain discrete in the limit, which leads to entropic rate functionals. We present conditions that rule out dynamical phase transition, and for zero-range processes on a discrete ring, we give sufficient conditions under which a dynamical phase transition can be constructed. (Joint work with Davide Gabrielli, l'Aquila)

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Mittwoch, 20.11.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Antonius Frederik Maria ter Elst, The University of Auckland, Neuseeland:
The Dirichlet-to-Neumann operator on C 1+κ -domains
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
We present some recent results on kernel bounds for the semigroup generated by the Dirichlet-to-Neumann operator when the underlying operator has Hölder continuous coefficients and the domain has a C 1+κ-boundary. The proof depends on Gaussian bounds for derivatives of the semigroup kernel of an elliptic operator with Dirichlet boundary conditions. As a consequence the Dirichlet-to-Neumann semigroup is holomorphic on the right half-plane on L¹. Moreover, it is also strongly continuous on the space of continuous functions on the boundary and holomorphic on the right half-plane.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Donnerstag, 21.11.2019, 11:00 Uhr (WIAS-ESH)
Joint Research Seminar on Nonsmooth Variational Problems and Operator Equations / Mathematical Optimization
Jo Brüggemann, WIAS:
On the existence of solutions and solution methods for elliptic obstacle-type quasi-variational inequalities with volume constraints
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
In this talk, an elliptic obstacle-type quasi-variational inequality (QVI) with volume constraints is studied. This type of QVI is motivated by the reformulation of a compliant obstacle problem, where two elastic membranes are subject to external forces while enclosing a constant volume. The existence of solutions to this QVI is established building on fixed-point arguments and partly on the concept of Mosco-convergence. Since Mosco-convergence of the considered feasible sets usually requires complete continuity or compactness properties of the obstacle map, a two-fold approach is explored towards generalising the available existence results for the considered QVI. Based on the analytical findings, the solution of the QVI is approached by solving a sequence of variational inequalities (VIs). Each of these VIs is tackled in function space via a path-following semismooth Newton method. An a posteriori error estimator is derived towards enhancement of the algorithm's numerical performance by using adaptive finite element methods.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 27.11.2019, 14:00 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Johannes Zimmer, University of Bath, GB:
Regularisation and analysis of Dean--Kawasaki-type equations
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
The Dean--Kawasaki-model consists of a nonlinear stochastic partial differential equation describing the evolution of the density function for a system of finitely many particles governed by Langevin dynamics. This equation is formally obtained, in a Schwartz distribution setting, on the hydrodynamic scale. As motivation for the study of this class of equations, we will show that the fluctuations they describe can, in the purely diffusive case, be linked to macroscopic diffusion operators of Wasserstein type. We then derive and analyse a suitably regularised Dean--Kawasaki-model for noninteracting particles obeying a second order Langevin equation, in one space dimension. We prove a high-probability result for the existence and uniqueness of mild solutions to this regularised Dean--Kawasaki-model. Extensions to the case of weakly interacting particles will also be described. This is joint work with Federico Cornalba and Tony Shardlow.

Veranstalter
Humboldt-Universität zu Berlin
WIAS Berlin
Mittwoch, 27.11.2019, 15:15 Uhr (WIAS-ESH)
Berliner Oberseminar „Nichtlineare partielle Differentialgleichungen” (Langenbach-Seminar)
Prof. Dr. Tomáš Roubíček, Charles University Prague, Tschechische Republik:
Fully convective models of some processes in the Earth
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Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Devised towards geophysical applications for modeling of the solid Earth, a model of poro-elastodynamics with inelastic strains and with convection/diffusion of water will be formulated fully in the Eulerian setting. There, concepts of gradient of the total strain rate as well as the additive splitting of the total strain rate are used, eliminating the displacement from the formulation. It relies on that the elastic strain is small while the inelastic and the total strains can be large. The energetics behind this model is derived and used for analysis as far as the existence of global weak energy-conserving solutions concerns. In some aspects, it improves a model of V. Lyakhovsky at al. to make it thermodynamically consistent and amenable for analysis. Coupling with the fluidic parts of the Earth is also possible while using the concept of elastic (so-called semi-compressible) fluids. Also magnetic phenomena will be discussed both in the solid and the fluidic parts, i.e. paleomagnetism and Earth dynamo, respectively. The talk reflects a collaboration with Giuseppe Tomassetti (Univ. Roma Tre).

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Berliner Oberseminar Nichtlineare partielle Differentialgleichungen (Langenbach-Seminar)

Veranstalter
WIAS Berlin
Humboldt-Universität zu Berlin
Montag, 09.12.2019, 14:00 Uhr (WIAS-ESH)
INSTITUTSKOLLOQUIUM
Dr. Katharina Schratz, Heriot-Watt University Edinburgh, UK:
Nonlinear Fourier integrators for dispersive equations and beyond
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
Partial differential equations (PDEs) play a central role in mathematics, allowing us to describe physical phenomena ranging from ultra-cold atoms (Bose-Einstein condensation) up to ultra-hot matter (nuclear fusion), from learning algorithms to fluids in the human brain. To understand nature we have to understand their qualitative behavior: existence and long time behavior of solutions, their geometric and dynamical properties - as well as to compute reliably their numerical solution. While linear problems and smooth solutions are nowadays well understood, a reliable description of 'non-smooth' phenomena remains one of the most challenging open problems in computational mathematics since the underlying PDEs have very complicated solutions exhibiting high oscillations and loss of regularity. This leads to huge errors, massive computational costs and ultimately provokes the failure of classical schemes. Nevertheless, 'non-smooth phenomena' play a fundamental role in modern physical modeling (e.g., blow-up phenomena, turbulences, high frequencies, low dispersion limits, etc.) which makes it an essential task to develop suitable numerical schemes. In this talk I present a new class of nonlinear Fourier integrators. The key idea is to tackle and hardwire the underlying structure of resonances into the numerical discretization. This new approach offers strong geometric structure at low regularity and high oscillations - linking the finite dimensional discretization to powerful existence results for nonlinear PDEs at very low regularity.

Veranstalter
WIAS Berlin
Mittwoch, 11.12.2019, 11:30 Uhr (WIAS-406)
Seminar Interacting Random Systems
Benjamin Lees, University of Bristol:
The phase transition for random loop models on trees
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, 4. Etage, Weierstraß-Hörsaal (Raum: 406)

Abstrakt
We show the existence of a sharp phase transition from non-existence to existence of infinite loops for a random loop model on d-regular trees, for all dimensions d ≥ 3. The loop model is built up by randomly placed 'crosses' and 'bars' whose relative intensity is controlled by a parameter u. We give a recursive scheme to obtain an expansion of the critical parameter in powers of 1/d, which in principle is explicit but whose combinatorial complexity grows very quickly. We were able to explicitly obtain the first 6 terms (the first two were previously found by Ueltschi and Bjornberg for the limit d → ∞), and observed that (as functions of u) they seem to have a very interesting structure. This is a joint work with Volker Betz and Johannes Ehlert.

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Seminar Interacting Random Systems

Veranstalter
WIAS Berlin
Donnerstag, 12.12.2019, 10:00 Uhr (WIAS-ESH)
Seminar Numerische Mathematik
Dr. Nancy Hitschfeld Kahler, Universdad de Chile, Santiago:
GPU computing and meshing
mehr ... Veranstaltungsort
Weierstraß-Institut, Mohrenstr. 39, 10117 Berlin, Erdgeschoss, Erhard-Schmidt-Hörsaal

Abstrakt
GPUs are an efficient and low cost alternative to CPU clusters for solving problems that are data-parallel or close to data parallel, but there are some restrictions in the current GPU hardware that must be taken into account in order to get efficient solutions. In this talk, fundamental concepts of GPU computing will be first introduced along with relevant techniques to make optimal use of GPU hardware, such as thread branching, coalesced memory, effective use of shared memory, thread mappings onto a triangular mesh, dynamic memory allocation, thread-safe exclusion mechanisms for neighboring triangles, and indeterminate decisions and traversals over the discrete graph structure of unstructured meshes. Then, an algorithm to transform any triangulation into a Delaunay triangulation and an implementation of a particle tracking algorithm that uses previous algorithm will be discussed. Finally, other relevant aspects to take into account such as gpu-mapping techniques and the ongoing work will be mentioned.

Veranstalter
WIAS Berlin