There are several fundamental applications involving kinetic theory and computations. They range from semiconductor modeling involving kinetic and quantum charged transport, radiative transfer in cosmology, conservative and dissipative phenomena in rarefied gas dynamics in mixtures, and grain and polymer flows.

Issues to be addressed involve the derivation and multi-scale modeling due to different scales of effective constants, spatial heterogeneities and strength of boundary conditions. Because the basic drift-diffusion, hydrodynamic and quantum models may interact through interfaces, a basic understanding of boundary conditions as well as phase transitions are critical. An example of such modeling problem appears naturally in semiconductors devices where the electron and holes density flows through a highly heterogeneous crystal lattice.

It is well established that drift-diffusion models are currently inadequate for the simulations of submicron devices where effective fields become very strong. As a consequence, kinetic transport modeling and even quantum modeling corrections are necessary to accurately model the current flow through devices. Mathematically it is critical to address the analytical and approximating properties of hydrodynamic and kinetic models of Euler and Boltzmann type coupled to Poisson's equation, as well as the Schrödinger and quantum Boltzmann equations that become relevant in different scaling regimes.

Recently, there have been new applications to biological systems, chain supply dynamics and quantitative finance, where statistical methods for multi-agent systems have given raised to of extension of Boltzmann equation to models for particle swarms, networks or the dynamics of information. This is a mathematical area that is not as well developed as its semiconductor counterpart. Our program will pay special attention to these new developments in an attempt to set basic benchmarks of terms of analytical as well as numerical modeling.