Transport Phenomena and Kinetic Theory

The study of kinetic equations related to gases, semiconductors, photons, traffic flow, and other systems has developed rapidly in recent years because of its role as a mathematical tool in areas such as engineering, meteorology, biology, chemistry, materials science, nanotechnology, and pharmacy. Written by leading specialists in their respective fields, this book presents an overview of recent developments in the field of mathematical kinetic theory with a focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning.

Transport Phenomena and Kinetic Theory is an excellent self-study reference for graduate students, researchers, and practitioners working in pure and applied mathematics, mathematical physics, and engineering. The work may be used in courses or seminars on selected topics in transport phenomena or applications of the Boltzmann equation.

Focus on modeling complex systems, emphasizing both mathematical properties and their physical meaning Written by leading specialists in their respective fields Presentation covers not only modeling aspects and qualitative analysis of mathematical problems, but also inverse and computational problems, which lead to detailed model assessment and analysis of real-world systems For a broad audience of graduate students, researchers, and professionals working in pure and applied mathematics, mathematical physics, and engineering May be used in a course or seminar on selected topics in transport phenomena or applications of the Boltzmann equation to many-particle transport

Inhalt
Analytic Aspects of the Boltzmann Equation.- Rigorous results for conservation equations and trend to equilibrium in space-inhomogeneous kinetic theory.- Results on optimal rate of convergence to equilibrium for spatially homogeneous Maxwellian gases.- Nonresonant velocity averaging and the Vlasov-Maxwell system.- Modeling Applications, Inverse and Computational Problems in Quantum Kinetic Theory.- Multiband quantum transport models for semiconductor devices.- Optimization models for semiconductor dopant profiling.- Inverse problems for semiconductors: models and methods.- Deterministic kinetic solvers for charged particle transport in semiconductor devices.- Miscellaneous Applications in Physics and Natural Sciences.- Methods and tools of mathematical kinetic theory towards modelling complex biological systems.- Kinetic modelling of late stages of phase separation.- Ground states and dynamics of rotating Bose-Einstein condensates.- Two inverse problems in photon transport theory: evaluation of a time-dependent source and of a time-dependent cross section.