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Short presentation of the team I3

Sites of I3 Pavia CNR.IAN + Pavia (Uni.), Milano (Politec.), Catania
URL http://www.imati.cnr.it/~pietra/hyke/I3_team.html
Team Organizer P. Pietra

The team has a consolidate experience of research concerned with both theoretical and numerical methods for many particle systems. Most of the team members have a well established collaboration and they interact regularly via joint research, meetings and seminars.

The research groups at the University of Pavia and Politecnico of Milan have a consolidate expertise in kinetic theory of rarefied gases. Existence theorems for Boltzmann equation, discrete velocity models, model kernels for gas-surface interaction (task 7 ) are topics of investigation, in collaboration with E2 and S1. Recently, the main activity of this group includes the modeling of granular gas particles, in which the main characteristic is the intrinsic inelasticity of the collisions between grains; astrophysical application of granular flows (task 10); entropy production methods for nonlinear diffusion with potential confinement; study of the intermediate asymptotics of diffusion processes in industry (task 3 ). A continuative intense collaboration with E2,F4,A1,D1 on these topics is well established. For the previous applications, an important part will be reserved to numerical simulation. Numerical simulation of kinetic equation for granular gases has been started in collaboration with I2. Further studies concern numerical relaxation approximation to higher order diffusion processes with I2,E2 (task 1 ), large eddy simulations of turbulent flows, turbulent reactive flows, tokamak non-linear instabilities (task 16 ).

The research groups at the University of Catania and at IAN Pavia have a decade long expertise in kinetic theory and mathematical physics, and in numerical methods for conservation laws, kinetic equations and quantum systems. In particular, for charge transport in semiconductors, the group developed hydro-dynamical models, based on Extended Thermodynamics and Maximum Entropy principle (task 4 ), numerical schemes for the Energy--Transport model based on mixed finite elements (task 16 ), reduced kinetic models for the Boltzmann equation (task 9 ). All the models have been validated by state of the art Monte Carlo simulation. Collaboration on these topics have been established with D1,F3,I2. Other active fields of research are numerical methods for conservation and balance laws (also applied to device simulation) (task 15 and 16 , involving collaboration with A1,D2,E1,E2,I1,I2), numerical methods for the Boltzmann equation and for the Fokker-Planck-Landau equation (task 7 , in collaboration with F1,I2), numerical schemes for quantum systems (quantum--hydrodynamic model, Wigner equation) based on adaptive multi--level schemes (task 9 , in collaboration with A1,D1).

The group has a long time experience in cooperation with industries and non academic research institutions. The Catania group developed several models and algorithms for semiconductor simulation in collaboration with the TCAD Center of the ST-Micro-electronics (Catania Plant). The group in Milan is involved in two projects with ENEA (Italian Energy Agency) and ASI (Italian Space Agency).

The key scientific staff consists of the following members:

- P. Pietra (TO) (IAN-CNR Pavia, 25%);  - G. Toscani (SAB) (Univ. Pavia, 20%);  - E. Gabetta (Univ.Pavia, 20%);  - A. Pulvirenti (SAB) (Univ. Pavia, 20%);  - C. Cercignani (Politecnico Milan, 20%);  - A. Frezzotti (Politecnico Milan, 20%);  - M. Lampis (Politecnico Milan, 20%);  - A. Abba (Politecnico Milan, 20%);  - M. Anile (IAB) (Univ. Catania, 20) ;  - A. Majorana (Univ. Catania, 20%);  - G. Russo (Univ. Catania, 20%);  - R. Pidatella (Univ. Catania, 20%).

The two most significant publication for the IHP project are the following

[1] A.M. Anile, V. Romano, G. Russo, Extended Hydrodynamical Model of Carrier Transport in Semiconductors , SIAM J. Appl. Math. 61 (1) (2000), 74-101.

[2] A. Arnold(D1), P.A. Markowich(A1), G. Toscani(I3), A. Unterreiter(A1), On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for Fokker-Planck type equations , to appear in Comm. PDE (2001), 85 pages.

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HYperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis - HYKE