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  • © 2007

Vorticity, Statistical Mechanics, and Monte Carlo Simulation

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  • Will be a unique addition to the literature

  • Offers fresh insights into an important field

Part of the book series: Springer Monographs in Mathematics (SMM)

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  • ISBN: 978-0-387-49431-9
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Softcover Book
USD 159.99
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Table of contents (13 chapters)

  1. Front Matter

    Pages i-xiv
  2. Introduction

    Pages 1-8
  3. Probability

    Pages 9-27
  4. Statistical Mechanics

    Pages 29-49
  5. Spectral Methods

    Pages 67-78
  6. Spin-Lattice Models

    Pages 115-132
  7. Mesh Generation

    Pages 187-211
  8. Back Matter

    Pages 263-290

About this book

This book is drawn from across many active fields of mathematics and physics, and has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors f this book explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them. In reading this book, the reader will learn how to research a topic and how to understand statistical mechanics treatments of fluid dynamics. Of particular interest should be the application of Monte Carlo methods to problems like dispersal of points on the sphere, the phase transitions of in viscid fluid flows in models that increasingly approach the conditions of actual planetary atmospheres, and the treatment of negative absolute temperatures and the effects these extremely high-energy states have on fluid flows. Special attention is given to spherical models as well.

This book is intended for the upper-level undergraduate or the beginning graduate level courses of mathematics and physics. It will also be of interest to readers interested in statistical mechanics methods applied to fluid mechanics problems. Readers will gain an understanding of how to synthesize new mathematics by applying familiar tools in new ways, and develop new tools to fit particular applications.

Keywords

  • Boundary value problem
  • Monte Carlo method
  • fluid dynamics
  • fluid mechanics
  • optimization
  • fluid- and aerodynamics

Reviews

From the reviews:

"The textbook for advanced undergraduate students is written to provide an overview of many aspects encountered in classical and quantum statistical mechanics. … This volume is a convincing invitation to modern mathematical concepts and new techniques. It will prove useful and attractive to graduate students and teachers in this active field." (Vicentin D. Radulescu, Zentralblatt MATH, Vol. 1145, 2008)

Editors and Affiliations

  • Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, USA

    Chjan Lim

  • Department of Mathematics, National University of Singapore, Singapore

    Joseph Nebus

Bibliographic Information

Buying options

eBook
USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-0-387-49431-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 159.99
Price excludes VAT (USA)
Hardcover Book
USD 159.99
Price excludes VAT (USA)