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Progress in Mathematical Physics

Theory and Application to Micro-Electro-Mechanical Systems

By: Carlo Cercignani

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Hardcover | 19 April 2006

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Hardcover
184 Pages

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22.86 x 15.88 x 1.91

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This volume is intended to coverthe presentstatus of the mathematicaltools used to deal with problems related to slow rare?ed ?ows. The meaning and usefulness of the subject, and the extent to which it is covered in the book, are discussed in some detail in the introduction. In short, I tried to present the basic concepts and the techniques used in probing mathematical questions and problems which arise when studying slow rare?ed ?ows in environmental sciences and micromachines. For the book to be up-to-date without being excessively large, it was necessary to omit some topics, which are treated elsewhere, as indicated in the introd- tion and, whenever the need arises, in the various chapters of this volume. Their omission does not alter the aim of the book, to provide an understanding of the essential mathematical tools required to deal with slow rare?ed ?ows and give the background for a study of the original literature. Although I have tried to give a rather complete bibliographical coverage,the choice of the topics and of the references certainly re?ects a personal bias and I apologize in advance for any omission. I wish to thank Lorenzo Valdettaro, Antonella Abb` a, Silva Lorenzani and Paolo Barbante for their help with pictures and especially Professor Ching Shen for his permission to reproduce his pictures on microchannel ?ows.

Industry Reviews

From the reviews: "The main topic of the book is rarefied gas dynamics which can be defined as the study of gas flows in which the distance between two subsequent collisions of a molecule ... is not negligible in comparison with the length typical for the surrounding structure. ... The book will be useful to specialists in the mathematical theory of fluids. It can serve also those who are beginners in this area provided they have some erudition in mathematics on graduate level." (Ivan Straskraba, Applications of Mathematics, Vol. 54 (4), 2009)

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You Can Find This Book In

Non-Fiction Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Fluids Science Physics Classical Mathematics Fluid Mechanics Atomic & Molecular Physics Mathematics Calculus & Mathematical Analysis

Differential Calculus & Equations Electronics & Communications Engineering Electronics Engineering Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

Preface	p. vii
Introduction	p. ix
The Boltzmann Equation	p. 1
Historical Introduction	p. 1
The Boltzmann Equation	p. 4
Molecules Different from Hard Spheres	p. 11
Collision Invariants	p. 12
The Boltzmann Inequality and the Maxwell Distributions	p. 15
The Macroscopic Balance Equations	p. 16
The H-theorem	p. 20
Equilibrium States and Maxwellian Distributions	p. 22
The Boltzmann Equation in General Coordinates	p. 24
Mean Free Path	p. 25
References	p. 26
Validity and Existence	p. 29
Introductory Remarks	p. 29
Lanford's Theorem	p. 30
Existence and Uniqueness Results	p. 36
Remarks on the Mathematical Theory of the Boltzmann Equation	p. 39
References	p. 39
Perturbations of Equilibria	p. 41
The Linearized Collision Operator	p. 41
The Basic Properties of the Linearized Collision Operator	p. 43
Some Spectral Properties	p. 50
Asymptotic Behavior	p. 60
The Global Existence Theorem for the Nonlinear Equation	p. 63
The Periodic Case and Problems in One and Two Dimensions	p. 65
References	p. 66
Boundary Value Problems	p. 69
Boundary Conditions	p. 69
Initial-Boundary and Boundary Value Problems	p. 74
Properties of the Free-streaming Operator	p. 81
Existence in a Vessel with an Isothermal Boundary	p. 84
The Results of Arkeryd and Maslova	p. 85
Rigorous Proof of the Approach to Equilibrium	p. 88
Perturbations of Equilibria	p. 90
A Steady Flow Problem	p. 91
Stability of the Steady Flow Past an Obstacle	p. 97
Concluding Remarks	p. 99
References	p. 100
Slow Flows in a Slab	p. 103
Solving the Linearized Boltzmann Equation in a Slab	p. 103
Model Equations	p. 109
Linearized Collision Models	p. 111
Transformation of Models into Pure Integral Equations	p. 113
Variational Methods	p. 115
Poiseuille Flow	p. 123
References	p. 128
Flows in More Than One Dimension	p. 131
Introduction	p. 131
Linearized Steady Problems	p. 131
Linearized Solutions of Internal Problems	p. 136
External Problems	p. 139
The Stokes Paradox in Kinetic Theory	p. 140
References	p. 143
Rarefied Lubrication in Mems	p. 145
Introductory Remarks	p. 145
The Modified Reynolds Equation	p. 146
The Reynolds Equation and the Flow in a Microchannel	p. 149
The Poiseuille-Couette Problem	p. 151
The Generalized Reynolds Equation for Unequal Walls	p. 156
Concluding remarks	p. 160
References	p. 161
Index	p. 165
Table of Contents provided by Publisher. All Rights Reserved.

Progress in Mathematical Physics

Theory and Application to Micro-Electro-Mechanical Systems

At a Glance

Hardcover

Industry Reviews

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Defective items

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