Transport in Transition Regimes (The IMA Volumes in Mathematics and its Applications, 135)

**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. Front Matter....Pages i-x BGK-Burnett Equations: A New Set of Second-Order Hydrodynamic Equations for Flows in Continuum-Transition Regime....Pages 1-35 Steady States for Streater’s Energy-Transport Models of Self-Gravitating Particles....Pages 37-56 Towards a Hybrid Monte Carlo Method for Rarefied Gas Dynamics....Pages 57-73 Comparison of Monte Carlo and Deterministic Simulations of a Silicon Diode....Pages 75-84 Discrete-Velocity Models for Numerical Simulations in Transitional Regime for Rarefied Flows and Radiative Transfer....Pages 85-101 Some Recent Results on the Kinetic Theory of Phase Transitions....Pages 103-120 Fluids with Multivalued Internal Energy: The Anisotropic Case....Pages 121-136 A Note on the Energy-Transport Limit of the Semiconductor Boltzmann Equation....Pages 137-153 Generalized Hydrodynamics and Irreversible Thermodynamics....Pages 155-176 A Steady-State Capturing Method for Hyperbolic Systems with Geometrical Source Terms....Pages 177-183 Maximum Entropy Moment Problems and Extended Euler Equations....Pages 189-198 Numerical Methods for Radiative Heat Transfer in Diffusive Regimes and Applications to Glass Manufacturing....Pages 199-212 Hydrodynamic Limits of the Boltzmann Equation....Pages 217-230 Sobolev Norm and Carrier Transport in Semiconductors....Pages 231-237 The Evolution of a Gas in a Radiation Field from a Kinetic Point of View....Pages 241-248 Hybrid Particle-Based Approach for the Simulation Of Semiconductor Devices: The Full-Band Cellular Automaton/Monte Carlo Method....Pages 249-264 Some Remarks on the Equations of Burnett and Grad....Pages 265-276 Boundary Conditions and Boundary Layers for a Class of Linear Relaxation Systems in a Quarter Plane....Pages 279-292 Back Matter....Pages 293-301 From the 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. This volume focuses on modeling processes for which transport is one of the most complicated components, requiring different transport models in each region. The authors apply questions to a wide variety of application areas, such as semiconductors, plasmas, fluids, chemically reactive gases, etc.