Asymptotics, Numerics, Analysis 
of the network 


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 gassurface interaction (taskÂ 7Â ) 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 (taskÂ 10); entropy production methods for nonlinear diffusion with potential confinement; study of the intermediate asymptotics of diffusion processes in industry (taskÂ 3Â ). 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 (taskÂ 1Â ), large eddy simulations of turbulent flows, turbulent reactive flows, tokamak nonlinear instabilities (taskÂ 16Â ).
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 hydrodynamical models, based on Extended Thermodynamics and Maximum Entropy principle (taskÂ 4Â ), numerical schemes for the EnergyTransport model based on mixed finite elements (taskÂ 16Â ), reduced kinetic models for the Boltzmann equation (taskÂ 9Â ). 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) (taskÂ 15Â andÂ 16Â , involving collaboration with A1,D2,E1,E2,I1,I2), numerical methods for the Boltzmann equation and for the FokkerPlanckLandau equation (taskÂ 7Â , in collaboration with F1,I2), numerical schemes for quantum systems (quantumhydrodynamic model, Wigner equation) based on adaptive multilevel schemes (taskÂ 9Â , 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 STMicroelectronics (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) (IANCNR 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,Â Extended Hydrodynamical Model of Carrier Transport in SemiconductorsÂ , SIAM J. Appl. Math.Â 61Â (1) (2000), 74101.
[2] A. Arnold(D1), P.A. Markowich(A1), G. Toscani(I3), A. Unterreiter(A1),Â On logarithmic Sobolev inequalities and the rate of convergence to equilibrium for FokkerPlanck type equationsÂ , to appear in Comm. PDE (2001), 85 pages.