Progress in Mathematical Physics

Slow Rarefied Flows

Theory and Application to Micro-Electro-Mechanical Systems

Authors: Cercignani, Carlo

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About this book

The book presents the mathematical tools used to deal with problems related to slow rarefied flows, with particular attention to basic concepts and problems which arise in the study of micro- and nanomachines. The mathematical theory of slow flows is presented in a practically complete fashion and provides a rigorous justification for the use of the linearized Boltzmann equation, which avoids costly simulations based on Monte Carlo methods. The book surveys the theorems on validity and existence, with particular concern for flows close to equilibria, and discusses recent applications of rarefied lubrication theory to micro-electro-mechanical systems (MEMS). It gives a general acquaintance of modern developments of rarefied gas dynamics in various regimes with particular attention to low speed microscale gas dynamics.

Senior students and graduates in applied mathematics, aerospace engineering, and mechanical mathematical physics will be provided with a basis for the study of molecular gas dynamics. The book will also be useful for scientific and technical researchers engaged in the research on gas flow in MEMS.

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 Straškraba, Applications of Mathematics, Vol. 54 (4), 2009)

Table of contents (7 chapters)

  • The Boltzmann Equation

    Pages 1-28

  • Validity and Existence

    Pages 29-39

  • Perturbations of Equilibria

    Pages 41-67

  • Boundary Value Problems

    Pages 69-102

  • Slow Flows in a Slab

    Pages 103-129

Buy this book

eBook 91,62 €
price for India (gross)
  • ISBN 978-3-7643-7537-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 109,99 €
price for India (gross)
  • ISBN 978-3-7643-7534-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Slow Rarefied Flows
Book Subtitle
Theory and Application to Micro-Electro-Mechanical Systems
Authors
Series Title
Progress in Mathematical Physics
Series Volume
41
Copyright
2006
Publisher
Birkhäuser Basel
Copyright Holder
Birkhäuser Basel
eBook ISBN
978-3-7643-7537-9
DOI
10.1007/3-7643-7537-X
Hardcover ISBN
978-3-7643-7534-8
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XI, 166
Topics