Department Colloquium

The colloquium at the Department of Mathematics takes place in a loose sequence, with two lectures each:

from 14:30 - 15:30 and 16:00 - 17:00 in lecture hall 3 (MI 00.06.011).

During the break we offer you drinks and pretzels in the Magistrale.

 

Lectures in Winter Semester 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

14th November, 14:30 - 15:30

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

14th November, 16:00 - 17:00

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

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.

Earlier colloquia

Lectures in summer semester 2018
Lectures in winter semester 2017/18