Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photons, and Biological Systems

ISBN-13: 9780817644895 / Angielski / Twarda / 2006 / 271 str.

Carlo Cercignani; Ester Gabetta

Opis

This volume aims to provide an overview of some recent developments of mathematical kinetic theory focused on its application in modelling complex systems in various ?elds of applied sciences. Mathematical kinetic theory is essentially based on the Boltzmann eq- tion, which describes the evolution, possibly far from equilibrium, of a class of particles modelled as point masses. The equation de?nes the evolution in time and space of the distribution function over the possible microscopic states of the test particle, classically position and velocity. The test particle is subject to pair collisions with the ?eld particles. The interested reader can ?nd in the book, Theory and Application of the Boltzmann Equation, by C. Cercignani, R. Illner, and M. Pulvirenti, Springer, Heidelberg, 1993, all necessary knowledge of the physics and mathematical topics related to this celebrated model of non-equilibrium statistical mech- ics. Another important model of mathematical kinetic theory is the Vlasov equation, where interactions between particles are not speci?cally collisions, but mean ?eld actions of the ?eld particles over the test particle. The model de?nes again an evolution equation for the one-particle distribution function over the microscopic state of the test particle. The two models brie?y mentioned above can be regarded as the fun- mental models of mathematical kinetic theory and the essential background o?ered from the kinetic theory for classical particles towards the modelling of large systems of several particles undergoing non classical interactions.

Recenzje

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)

Spis treści

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

O autorze

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.

Blurb

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.