Fakultätskolloquium

Das Kolloquium an der Fakultät für Mathematik findet in loser Folge mittwochs statt, mit Vorträgen von 14:30 - 15:30 Uhr bzw. 16:00 - 17:00 Uhr im Hörsaal 3 (MI 00.06.011).

In der Pause sorgen wir mit Getränken und Brezen in der Magistrale für Ihr leibliches Wohl.

 

Termine im Wintersemester 2018/19

  • 17. Oktober 2018: Claudia Redenbach
  • 14. November 2018: Michael Dumbser (14:30), Holger Dullin (16:00)
  • 09. Januar 2019: George Karniadakis & Vlad Vicol
  • 06. Februar 2019: Thomas Strohmer & Clotilde Fermanian Kammerer
Prof. George Karniadakis

9. Januar

Prof. George Karniadakis, Brown University & MIT:

Physics-Informed Learning Machines for Physical Systems

In this talk, we will present a new approach to develop a data-driven, learning-based framework for predicting outcomes of physical systems and for discovering hidden physics from noisy data.

A key concept is the seamless fusion and integration of data of variable fidelity into the predictive models. First, we will present a Bayesian approach using Gaussian Process Regression (GPR), and subsequently a deep learning approach based on neural networks (NNs) and generative adversarial networks (GANs). Unlike other approaches that rely on big data, here we “learn” from small data by exploiting the information provided by the physical conservation laws, which are used to obtain informative priors or regularize the neural networks. We will also make connections between GPR and NNs and discuss the new powerful concept of meta-learning.

Prof. Vlad Vicol

9. Januar

Prof. Vlad Vicol, Courant Institute NYU: 

Wild solutions to the Navier-Stokes equation

We consider the uniqueness question for weak solutions of the 3D Navier-Stokes equation. We prove that solutions are not unique within the class of weak solutions with finite kinetic energy. Moreover, we prove that any continuous weak solutions of the 3D Euler equations may be obtained as a strong vanishing viscosity limit.

14. November, 14:30 - 15:30 Uhr

Prof. Michael Dumbser, ​​​University of Trento:

New mathematical models and numerical algorithms for Newtonian and general relativistic continuum physics

In the first part of the talk we present a family of arbitrary high order accurate (ADER) finite volume and discontinous Galerkin finite element schemes for the numerical solution of a new unified first oder symmetric hyperbolic and thermodynamically compatible (SHTC) formulation of Newtonian continuum physics, including a general description of fluid and solid mechanics as well as electro-magnetic fields in one single system of governing partial differential equations (PDE). The model is based on previous work of Godunov, Peshkov and Romenski (so-called GPR model) on symmetric hyperbolic and thermodynamically compatible systems.

 

In the second part of the talk, we show a successful extension of the GPR model to general relativity, leading to a novel and unified first order hyperbolic formulation of general relativistic continuum mechanics. The model is able to describe nonlinear elasto-plastic solids, as well as ideal and non-ideal (viscous) fluids in full general relativity. Formal asymptotic expansion of the governing PDE reveals the structure of the viscous stress tensor in the asymptotic relaxation limit. The key features of the new model are its symmetric hyperbolicity and thermodynamical compatibility. The proposed PDE system is causal, covariant and has bounded signal speeds for all involved processes, including disspative ones. Since the new model also contains elastic solids as a special case, it should be understood as an alternative to existing models for vicous relativistic fluids that are usually derived from kinetic theory and extended irreversible thermodynamics. We present numerical results obtained with high oder ADER schemes for inviscid and viscous relativistic flows obtained in the stiff relaxation limit of the system, as well as results for solid mechanics.

 

In the last part of the talk we introduce a new, provably strongly hyperbolic first order reduction of the CCZ4 formalism of the Einstein field equations of general relativity and its solution with high order ADER discontinuous Galerkin finite element schemes.

Prof. Holger Dullin

14. November, 16:00 - 17:00 Uhr

Prof. Holger Dullin, University of Sydney:

The three body problem in four dimensions

The Newtonian three body problem has undergone a Renaissance in recent years. I will present an overview of old and new results on periodic solutions, symbolic dynamics, and chaos in this problem. Then I will describe new results about the symplectic symmetry reduction and dynamics of relative equilibria when the spatial dimension is at least four. In particular we will show that there are families of relative equilibria that are minima of the reduced Hamiltonian, and hence are Lyapunov stable. This establishes the first proof of Lyapunov stable periodic orbits in the three body problem, albeit in dimension four.

Prof. Claudia Redenbach

17. Oktober, 16:00 - 17:00 Uhr

Prof. Claudia Redenbach, Universität Kaiserslautern​​​​:

Anisotropy analysis of spatial point patterns

This talk will give an overview of techniques for detecting anisotropy in spatial point patterns. As an example of application, we will analyse the pore system in polar ice. In a depth below approx. 100 m, the ice contains isolated air bubbles which can be studied by using tomographic images of ice core samples. Interpreting the system of bubble centres as a realisation of a regular point process subject to geometric anisotropy, preferred directions and strength of compression can be estimated.

Frühere Fakultätskolloquien

Vorträge im Sommersemester 2018
Vorträge im Wintersemester 2017/18