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Slow Rarefied Flows

Theory and Application to Micro-Electro-Mechanical Systems

  • Book
  • © 2006

Overview

Authors:
  1. Carlo Cercignani

    1. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

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  • Provides an understanding of the essential mathematical tools required to deal with slow rarefied flows
  • Material can be used for a one-semester course or seminar
  • Gives the background for studies of the original literature
  • It is devised in such a way that certain parts can be skipped by readers interested in mathematical aspects and others by readers interested in applications.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Progress in Mathematical Physics (PMP, volume 41)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xi
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  2. The Boltzmann Equation

    Pages 1-28

  3. Validity and Existence

    Pages 29-39

  4. Perturbations of Equilibria

    Pages 41-67

  5. Boundary Value Problems

    Pages 69-102

  6. Slow Flows in a Slab

    Pages 103-129

  7. Flows in More Than One Dimension

    Pages 131-144

  8. Rarefied Lubrication in Mems

    Pages 145-163

  9. Back Matter

    Pages 165-168
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About this book

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.

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)

Authors and Affiliations

  • Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Carlo Cercignani

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