Transport Phenomena and Kinetic Theory (Birkhauser 2007)

Carlo Cercignani, Ester Gabetta9780817644895, 9780817645540, 081764489X

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 many applications 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.

The overall presentation covers not only modeling aspects and qualitative analysis of mathematical problems, but also inverse problems, which lead to a detailed assessment of models in connection with their applications, and to computational problems, which lead to an effective link of models to the analysis of real-world systems. The book is divided into three parts: Part I presents fundamental aspects of the Boltzmann equation; Part II deals with the modeling of semiconductor devices as well as related applications and computational topics; Part III covers a variety of applications in physics and the natural sciences, offering a range of very different conceivable developments of mathematical kinetic theory.

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.

 

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Table of contents :
Cover……Page 1
Contents……Page 10
Part I. Analytic Aspects of the Boltzmann Equation
……Page 15
1. Rigorous results for conservation equations and trend to equilibrium in space-inhomogeneous kine tic theo
ry……Page 16
2. Results on optimal rate of convergence to equilibrium for spatially homogeneous Maxwellian gases
……Page 31
3. Nonresonant velocity averaging and the Vlasov-Maxwell system
……Page 50
Part II. Modeling Applications, Inverse and Computational Problems in Quantum Kinetic
Theory
……Page 64
4. Multiband quantum transport models for semiconductor devices
……Page 65
5. Optimization models for semiconductor dopant profiling
……Page 100
6. Inverse problems for semiconductors: models and methods
……Page 125
7. Deterministic kinetic solvers for charged particle transport in semiconductor devices
……Page 158
Part III. Miscellaneous Applications in Physics and Natural Sciences
……Page 179
8. Methods and tools of mathematical kinetic theory towards modelling complex biological systems
……Page 180
9. Kinetic modelling of late stages of phase separation
……Page 199
10. Ground states and dynamics of rotating Bose–Einstein condensates
……Page 219
11. Two inverse problems in photon transport theory: evaluation of a time-dependent source and of a time-dependent cross section
……Page 260