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IRTG Modern Inverse Problems (MIP)
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EU Regional School with Prof. Irene Gamba, Ph.D.

25. März 2021 @ 15:00 - 18:30

Prof. Irene Gamba, Ph.D. – Non-linear Boltzmann type models in Collisional Theory

 

Department of Mathematics and Oden Institute of Computational Engineering and Sciences (ICES)
The University of Texas in Austin

 

Abstract:

These introductory lectures will focus on a unified approach to analyze the main properties of particle interactions of binary nature and their connections to statistical physics and thermodynamics.

We will focus on the model structure and common features, whether they corresponds to the classical elastic or inelastic monoatomic gases, or the more complex dynamics of polyatomic gases as well as gas mixtures with disparate masses.

We focus in the framework that naturally arises when modeling particle density functions subject to gain and loss rates when such particle interact in a binary law  as well as the transition probability rates (or scattering mechanisms) as a natural stabilization mechanism that enable us to construct solutions, to study their uniqueness properties and their long time behavior in suitable functional (Banach) spaces associated to the description of the evolution of  particle probability densities, to the shape of the probability density tails referred by polynomial or exponential moments and Fourier transform structure.

Of special significance is the understanding of the role of scattering mechanisms in the analytical properties of such solutions to be able to raise from the  Banach space  structure into the Sobolev (or Hilbert) structures. This observation plays a fundamental role in their approximations by finitely generated functions supported in bounded domains, the numerical approximations as well as error estimates.  Towards the end, we will focus of the special task to understand the grazing collision limit that gives raise to the Landau model.

The lecture will be supported by recent numerical implementation by  the presentation of hybrid computational solvers of two kinds: conservative spectral based and Finite Element Method (FEM) based for the Boltzmann equation binary interactions.

The functional analysis tools enable  proofs of consistency schemes,  construction of error estimates and convergence to statistical equilibrium results, both, in the  conservative spectral method as well as  on  Petrov-Galerkin FEM approach.

Details

Datum:
25. März 2021
Zeit:
15:00 - 18:30

Veranstaltungsort

a link for the Zoom meeting room will be send in the newsletter one week before the seminar starts. If you want to participate, please send an email to office@aices.rwth-aachen.de to get the zoom link.

Veranstalter

IRTG-2379 MIP