IMA Volumes 135: Transport in Transition Regimes and 136: Dispersive Transport Equations and Multiscale Models, focus on the modeling of processes for which transport is one of the most complicated components. This includes processes that involve a wide range of length scales over different spatio-temporal regions of the problem, ranging from the order of mean-free paths to many times this scale. Consequently, effective modeling techniques require different transport models in each region.

The first issue is that of finding efficient simulations techniques, since a fully resolved kinetic simulation is often impractical. One therefore develops homogenization, stochastic, or moment based subgrid models.

Another issue is to quantify the discrepancy between macroscopic models and the underlying kinetic description, especially when dispersive effects become macroscopic, for example due to quantum effects in semiconductors and superfluids.

These two volumes address these questions in relation to a wide variety of application areas, such as semiconductors, plasmas, fluids, chemically reactive gases, etc.

Contributors : About 40 authors

Contents

• BGK-Burnett equations: A new set of second-order hydrodynamic equations for flows in continuum-transition regime
• Steady states for Streater's energy-transport models of self-gravitating particles
• Towards a hybrid Monte-Carlo method for rarefied gas dynamics
• Comparison of Monte Carlo and deterministic simulations of a silicon diode
• Discrete-velocity models for numerical simulations in transitional regime for rarefied flows and radiative transfer
• Some recent results on the kinetic theory of phase transitions
• Fluids with multivalued internal energy: The anisotropic case
• A note on the energy-transport limit of the semiconductor Boltzmann equation
• Generalized hydrodynamics and irreversible thermodynamics
• A steady- state capturing method for hyperbolic systems with geometrical source terms
• Maximum entropy moment problems and extended Euler equations
• Numerical methods for radiative heat transfer in diffusive regimes and applications to glass manufacturing
• Hydrodynamic limits of the Boltzmann equation
• Sobolev norm and carrier transport in semiconductors
• The evolution of a gas in a radiation field from a kinetic point of view
• Hybrid particle-based approach for the simulation of semiconductor devices : The full-band cellular automaton / Monte Carlo method
• Some remarks on the equations of Burnett and Grad
• Boundary conditions and boundary layers for a class of linear relaxations systems in a quarter plane
• Combined list of workshops participants for IMA volumes 135 and 136