Ebook: Dispersive Transport Equations and Multiscale Models

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.

---

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.

---

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.
Content:
Front Matter....Pages i-x
On the Derivation of Nonlinear Schr?dinger and Vlasov Equations....Pages 1-23
Taking on the Multiscale Challenge....Pages 25-35
Nonresonant Smoothing for Coupled Wave + Transport Equations and the Vlasov-Maxwell System....Pages 37-50
Integrated Multiscale Process Simulation in Microelectronics....Pages 51-76
Constitutive Relations for Viscoleastic Fluid Models Derived from Kinetic Theory....Pages 77-89
Dispersive/Hyperbolic Hydrodynamic Models for Quantum Transport (In Semiconductor Devices)....Pages 91-106
A Review on Small Debye Length and Quasi-Neutral Limits in Macroscopic Models for Charged Fluids....Pages 107-119
Global Solution of the Cauchy Problem for the Relativistic Vlasov-Poisson Equation with Cylindrically Symmetric Data....Pages 121-132
Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing....Pages 133-149
Asymptotic Limits in Macroscopic Plasma Models....Pages 151-166
A Landau-Zener Formula for Two-Scaled Wigner Measures....Pages 167-177
Mesoscopic Modeling of Surface Processes....Pages 179-198
Homogenous and Heterogeneous Models for Silicon Oxidation....Pages 199-217
Feature-Scale to Wafer-Scale Modeling and Simulation of Physical Vapor Deposition....Pages 219-236
WKB Analysis in the Semiclassical Limit of a Discrete NLS System....Pages 237-258
Bifurcation Analysis of Cylindrical Couette Flow with Evaporation and Condensation by the Boltzmann Equation....Pages 259-279
Magnetic Instability in a Collisionless Plasma....Pages 281-286
Back Matter....Pages 287-295

---

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.
Content:
Front Matter....Pages i-x
On the Derivation of Nonlinear Schr?dinger and Vlasov Equations....Pages 1-23
Taking on the Multiscale Challenge....Pages 25-35
Nonresonant Smoothing for Coupled Wave + Transport Equations and the Vlasov-Maxwell System....Pages 37-50
Integrated Multiscale Process Simulation in Microelectronics....Pages 51-76
Constitutive Relations for Viscoleastic Fluid Models Derived from Kinetic Theory....Pages 77-89
Dispersive/Hyperbolic Hydrodynamic Models for Quantum Transport (In Semiconductor Devices)....Pages 91-106
A Review on Small Debye Length and Quasi-Neutral Limits in Macroscopic Models for Charged Fluids....Pages 107-119
Global Solution of the Cauchy Problem for the Relativistic Vlasov-Poisson Equation with Cylindrically Symmetric Data....Pages 121-132
Mesoscopic Scale Modeling for Chemical Vapor Deposition in Semiconductor Manufacturing....Pages 133-149
Asymptotic Limits in Macroscopic Plasma Models....Pages 151-166
A Landau-Zener Formula for Two-Scaled Wigner Measures....Pages 167-177
Mesoscopic Modeling of Surface Processes....Pages 179-198
Homogenous and Heterogeneous Models for Silicon Oxidation....Pages 199-217
Feature-Scale to Wafer-Scale Modeling and Simulation of Physical Vapor Deposition....Pages 219-236
WKB Analysis in the Semiclassical Limit of a Discrete NLS System....Pages 237-258
Bifurcation Analysis of Cylindrical Couette Flow with Evaporation and Condensation by the Boltzmann Equation....Pages 259-279
Magnetic Instability in a Collisionless Plasma....Pages 281-286
Back Matter....Pages 287-295
....