Dispersive Transport Equations and Multiscale Models

ISBN-13: 9781461264736 / Angielski / Miękka / 2012 / 295 str.

Ben Abdallah Naoufel; Anton Arnold; Pierre Degond

Opis

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 wdie 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.

Spis treści

On the derivation of nonlinear Schrödinger and Vlasov equations.- Taking on the multiscale challenge.- Nonresonant smoothing for coupled wave + transport equations and the Vlasov-Maxwell system.- Integrated multiscale process simulation in microelectronics.- Constitutive relations for viscoleastic fluid models derived from kinetic theory.- Dispersive/hyperbolic hydrodynamic models for quantum transport (in semiconductor devices).- A review on small debye length and quasi-neutral limits in macroscopic models for charged fluids.- Global solution of the Cauchy problem for the relativistic Vlasov-Poisson equation with cylindrically symmetric data.- Mesoscopic scale modeling for chemical vapor deposition in semiconductor manufacturing.- Asymptotic limits in macroscopic plasma models.- A Landau-Zener formula for two-scaled Wigner measures.- Mesoscopic modeling of surface processes.- Homogenous and heterogeneous models for silicon oxidation.- Feature-scale to wafer-scale modeling and simulation of physical vapor deposition.- WKB analysis in the semiclassical limit of a discrete NLS system.- Bifurcation analysis of cylindrical Couette flow with evaporation and condensation by the Boltzmann equation.- Magnetic instability in a collisionless plasma.- Combined list of workshops participants for IMA volumes 135: transport in transition regimes and 136: dispersive transport equations and multiscale models.

O autorze

IMA Volumes 135 and 136 focus on mathematical and computational issues
involved in modeling processes that contain a wide range of length
scales over different spatio-temporal regimes.
The papers in these two volumes address applications such as
semiconductors, plasmas, fluids, chemically reactive gases, etc.