Synopses & Reviews
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.
Review
From the reviews: "In this collection of articles by experts in the field the reader is given a rather comprehensive overview of many of the mathematical aspects and applications of the Boltzmann equation ... . intended for scientists and engineers in the applied sciences, my own feeling is that investigators whose acquaintance with mathematics is at an advanced level are likely to be the main beneficiaries of this book. The presentation of the material is excellent, very well organized, and highly recommended to this audience." (L.S. García-Colín, Journal of Statistical Physics, Vol. 132, 2008)
Synopsis
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.
Table of Contents
Preface List of Contributors Part I. Analytic Aspects of the Boltzmann Equation Rigorous Results for Conservation Equations and Trend to Equilibrium in Space-Inhomogeneous Kinetic Theory / Carlo Cercignani Results on Optimal Rate of Convergence to Equilibrium for Spatially Homogeneous Maxwellian Gases / Ester Gabetta Nonresonant Velocity Averaging and the Vlasov-Maxwell System / François Golse Part II. Modeling Applications, Inverse and Computational Problems in Quantum Kinetic Theory Multiband Quantum Transport Models for Semiconductor Devices / Luigi Barletti, Lucio Demeio, Giovanni Frosali Optimization Models for Semiconductor Dopant Profiling / Martin Burger, Michael Hinze, Rene Pinnau Inverse Problems for Semiconductors: Models and Methods / A. Leitão, P.A. Markowich, and J.P. Zubelli Deterministic Kinetic Solvers for Charged Particle Transport in Semiconductor Devices / M.J. Cáceres, J.A. Carrillo, I.M. Gamba, A. Majorana, and C.-W. Shu Part III. Miscellaneous Applications in Physics and Natural Sciences Methods and Tools of Mathematical Kinetic Theory Towards Modelling Complex Biological Systems / Nicola Bellomo, Abdelghani Bellouquid, and Marcello Delitala Kinetic Modelling of Late Stages of Phase Separation / Guido Manzi and Rossana Marra Ground States and Dynamics of Rotating Bose-Einstein Condensates / Weizhu Bao Two Inverse Problems in Photon Transport Theory: Evaluation of a Time-Dependent Source and of a Time-Dependent Cross-Section / Aldo Belleni-Morante