Asymptotics, Numerics, Analysis 
of the network 


Sites of D1  Saarbru¼cken + TU Berlin, Darmstadt, Kaiserslautern, Hamburg, Ilmenau, Konstanz, Mu¼nster, TU Mu¼nchen 
URL  http://wwwmath.unimuenster.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 Saarbru¼cken, 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 "quantumkinetic equations (Wigner equations)", "(quantum) hydrodynamic models", "energytransport models for semiconductors and relations to nonequilibrium thermodynamics", and "quantum mechanical multiscale models (separation of fast and slow degrees of freedom)". In this direction (topicsÂ 6Â ,Â 9Â ,Â 16Â of the work programme) there exists intense collaboration with the teams A1, E2, I3, F3.
A further topic is the "largetime behavior of parabolic and kinetic equations (via the entropy method and logarithmic Sobolev inequalities)" (taskÂ 3Â ) where fruitful collaborations with the teams A1, I3, E2 exist.Â
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 longtime 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 (taskÂ 12Â ,Â 14Â ,Â 16Â ). 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 (taskÂ 10Â ), glass manufacturing, semiconductors, etc.).
In connection with the "Institute for Industrial Mathematics", the University of Kaiserslautern has numerous industrial contacts: In cooperation withÂ Engineering Systems InternationalÂ (ESIGroup, Paris) the process of airbag inflation is simulated which involves computational complex flows (tasksÂ 4Â ,Â 14Â ,Â 16Â ). Together with the German companyÂ MVT Bernhard Platon GmbHÂ the behavior of granular material in mixbeds is analyzed (taskÂ 10Â ), and a project in cooperation with the Norwegian research instituteÂ SINTEFÂ deals with flood predictions and channel flows using shallow water equations and other modifications of the NavierStokes system (tasksÂ 14Â ,Â 16Â ).
Concerning relaxation methods for fluid dynamical equations (taskÂ 1Â ) 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) (Saarbru¼cken, 30%)  S. Rjasanow (Saarbru¼cken, 20%)  A. Zisowsky (Saarbru¼cken, 25%)  A. Ju¼ngel (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) (TUMu¼nchen, 20%)
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The two most significant publications for the IHP project are:
[1] Herbert Spohn,Â Semiclassical limit of the Dirac equation and spin precessionÂ , Ann. PhysicsÂ 282Â (2000), no. 2, 420431.
[2] Ansgar Ju¼ngel:QuasiHydrodynamic Semiconductor EquationsÂ , Birkhu¤user; 2001.