基本信息出版社：Springer
页码：290 页
出版日期：2006年11月
ISBN：0387350756
International Standard Book Number：0387350756
条形码：9780387350752
EAN：9780387350752
版本：1
装帧：精装
正文语种：英语
丛书名：Springer Monographs in Mathematics

内容简介 在线阅读本书

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.

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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)

目录
Introduction.- Probability.- Statistical Mechanics.- The Monte Carlo Approach.- Spectral Methods.- Discrete Models in Fluids.- Spin-Lattice Models.- Monte Carlo Simulations.- Polyhedra and Ground States.- Mesh Generation.- Statistical Mechanics for a Vortex Gas.- Two-layer Quasi-geostrophic Models.- Barotropic Vorticity Dynamics.- Mean Field Theory.
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