Bibliographic Details

Slow rarefied flows : theory and application to micro-electro-mechanical systems / Carlo Cercignani.

Author / Creator Cercignani, Carlo.
Imprint Basel ; Boston : Birkhäuser, c2006.
Description xi, 166 p. : ill. ; 24 cm.
Language English
Series Progress in mathematical physics ; v. 41
Subject Kinetic theory of gases.
Rarefied gas dynamics.
Statistical mechanics.
Kinetic theory of gases.
Rarefied gas dynamics.
Statistical mechanics.
Format Print, Book
URL for this record http://pi.lib.uchicago.edu/1001/cat/bib/6019127
ISBN 3764375345 (alk. paper)
376437537X (e-ISBN)
Notes Includes bibliographical references and index.
Standard no. 9783764375348
Table of Contents:
  • Preface
  • Introduction
  • 1. The Boltzmann Equation
  • 1.1. Historical Introduction
  • 1.2. The Boltzmann Equation
  • 1.3. Molecules Different from Hard Spheres
  • 1.4. Collision Invariants
  • 1.5. The Boltzmann Inequality and the Maxwell Distributions
  • 1.6. The Macroscopic Balance Equations
  • 1.7. The H-theorem
  • 1.8. Equilibrium States and Maxwellian Distributions
  • 1.9. The Boltzmann Equation in General Coordinates
  • 1.10. Mean Free Path
  • References
  • 2. Validity and Existence
  • 2.1. Introductory Remarks
  • 2.2. Lanford's Theorem
  • 2.3. Existence and Uniqueness Results
  • 2.4. Remarks on the Mathematical Theory of the Boltzmann Equation
  • References
  • 3. Perturbations of Equilibria
  • 3.1. The Linearized Collision Operator
  • 3.2. The Basic Properties of the Linearized Collision Operator
  • 3.3. Some Spectral Properties
  • 3.4. Asymptotic Behavior
  • 3.5. The Global Existence Theorem for the Nonlinear Equation
  • 3.6. The Periodic Case and Problems in One and Two Dimensions
  • References
  • 4. Boundary Value Problems
  • 4.1. Boundary Conditions
  • 4.2. Initial-Boundary and Boundary Value Problems
  • 4.3. Properties of the Free-streaming Operator
  • 4.4. Existence in a Vessel with an Isothermal Boundary
  • 4.5. The Results of Arkeryd and Maslova
  • 4.6. Rigorous Proof of the Approach to Equilibrium
  • 4.7. Perturbations of Equilibria
  • 4.8. A Steady Flow Problem
  • 4.9. Stability of the Steady Flow Past an Obstacle
  • 4.10. Concluding Remarks
  • References
  • 5. Slow Flows in a Slab
  • 5.1. Solving the Linearized Boltzmann Equation in a Slab
  • 5.2. Model Equations
  • 5.3. Linearized Collision Models
  • 5.4. Transformation of Models into Pure Integral Equations
  • 5.5. Variational Methods
  • 5.6. Poiseuille Flow
  • References
  • 6. Flows in More Than One Dimension
  • 6.1. Introduction
  • 6.2. Linearized Steady Problems
  • 6.3. Linearized Solutions of Internal Problems
  • 6.4. External Problems
  • 6.5. The Stokes Paradox in Kinetic Theory
  • References
  • 7. Rarefied Lubrication in Mems
  • 7.1. Introductory Remarks
  • 7.2. The Modified Reynolds Equation
  • 7.3. The Reynolds Equation and the Flow in a Microchannel
  • 7.4. The Poiseuille-Couette Problem
  • 7.5. The Generalized Reynolds Equation for Unequal Walls
  • 7.6. Concluding remarks
  • References
  • Index