HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
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Short presentation of the team D1

Sites of D1 Saarbruľcken + TU Berlin, Darmstadt, Kaiserslautern, Hamburg, Ilmenau, Konstanz, Muľnster, TU Muľnchen
URL http://wwwmath.uni-muenster.de/u/arnold/projekt_teamD1.html
Team Organizer A. Arnold

This team has a more than one decade long expertise in the field of applied kinetic equations and mathematical physics. While several of its members are now located at different German universities, most of the team members come `originally' from either the "University of Kaiserslautern" or the "Technical University Berlin". Therefore the individual "satellites" of this team are in continuous contact, e.g. via regular joint seminars and the exchange of common students.

The research groups in Saarbruľcken, Konstanz and Munich have an extensive experience in the analysis and modeling of quantum systems with applications to semiconductor device simulations and mathematical physics. The current fields of activity of these groups focus on "quantum-kinetic equations (Wigner equations)", "(quantum) hydrodynamic models", "energy-transport models for semiconductors and relations to non-equilibrium thermodynamics", and "quantum mechanical multiscale models (separation of fast and slow degrees of freedom)". In this direction (topics¬†6¬†,¬†9¬†,¬†16¬†of the work programme) there exists intense collaboration with the teams A1, E2, I3, F3.
A further topic is the "large-time behavior of parabolic and kinetic equations (via the entropy method and logarithmic Sobolev inequalities)" (task 3 ) where fruitful collaborations with the teams A1, I3, E2 exist. 
The main competence of these research groups lies in the modeling aspect, i.e. the derivation of physically meaningful macroscopic models from kinetic equations, and its mathematical analysis.

The research groups in Kaiserslautern, Darmstadt, Hamburg, and Ilmenau have a long-time experience on numerical methods for fluid dynamics and the development of simulation codes. Specifically, particle methods for kinetic equations in rarefied gas dynamics and kinetic boundary layers have been extensively studied (task 12 , 14 , 16 ). Research results have been transferred in a large number of current industrial projects with industry in the field of transport processes (traffic (task~{*bf~7 ) and granular flow (task 10 ), glass manufacturing, semiconductors, etc.).
In connection with the "Institute for Industrial Mathematics", the University of Kaiserslautern has numerous industrial contacts: In cooperation with Engineering Systems International (ESI-Group, Paris) the process of airbag inflation is simulated which involves computational complex flows (tasks 4 , 14 , 16 ). Together with the German company MVT Bernhard Platon GmbH the behavior of granular material in mix-beds is analyzed (task 10 ), and a project in cooperation with the Norwegian research institute SINTEF deals with flood predictions and channel flows using shallow water equations and other modifications of the Navier-Stokes system (tasks 14 , 16 ).

Concerning relaxation methods for fluid dynamical equations (task 1 ) these researchers collaborate with the teams I2, F3; on traffic and granular flow problems with the teams F3, S1 and, respectively, with E2.

The key scientific staff consists of the following members (with project involvement percentages):

- H. Neunzert (Uni Kaiserslautern, 20%);  - A. Arnold (TO) (Saarbruľcken, 30%)  - S. Rjasanow (Saarbruľcken, 20%)  - A. Zisowsky (Saarbruľcken, 25%)  - A. Juľngel (co - TO) (Konstanz, 25%);  - H. Neunzert (IAB) (Uni Kaiserslautern, 20%)  - S. Tang (Konstanz, 25%)  - W. Du∂rfler (Uni Kaiserslautern, 20%)  - R. Wegener (Uni Kaiserslautern, 20%);  - A. Klar (Darmstadt, 25%)  - J. Struckmeier (Uni Hamburg, 20%)  - H. Babovsky (Ilmenau, 20%);  - H. Spohn (SAB) (TU-Muľnchen, 20%)


The two most significant publications for the IHP project are:

[1] Herbert Spohn, Semiclassical limit of the Dirac equation and spin precession , Ann. Physics 282 (2000), no. 2, 420--431.

[2] Ansgar Juľngel:Quasi-Hydrodynamic Semiconductor Equations¬†, Birkhu§user; 2001.

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