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"Stochastic Tools in Mathematics and Science" covers basic
stochastic tools used in physics, chemistry, engineering and the
life sciences. The topics covered include conditional expectations,
stochastic processes, Brownian motion and its relation to partial
differential equations, Langevin equations, the Liouville and
Fokker-Planck equations, as well as Markov chain Monte Carlo
algorithms, renormalization, basic statistical mechanics, and
generalized Langevin equations and the Mori-Zwanzig formalism. The
applications include sampling algorithms, data assimilation,
prediction from partial data, spectral analysis, and turbulence.
The book is based on lecture notes from a class that has attracted
graduate and advanced undergraduate students from mathematics and
from many other science departments at the University of
California, Berkeley. Each chapter is followed by exercises. The
book will be useful for scientists and engineers working in a wide
range of fields and applications. For this new edition the material
has been thoroughly reorganized and updated, and new sections on
scaling, sampling, filtering and data assimilation, based on recent
research, have been added. There are additional figures and
exercises. Review of earlier edition: "This is an excellent concise
textbook which can be used for self-study by graduate and advanced
undergraduate students and as a recommended textbook for an
introductory course on probabilistic tools in science."
Mathematical Reviews, 2006
This book provides an introduction to turbulence in vortex systems,
and to turbulence theory for incompressible flow described in terms
of the vorticity field. It is the author's hope that by the end of
the book the reader will believe that these subjects are identical,
and constitute a special case of fairly standard statistical
mechanics, with both equilibrium and non-equilibrium aspects. The
author's main goal is to relate turbulence to statistical
mechanics. The book is organized as follows: the first three
chapters constitute a fairly standard introduction to homogeneous
turbulence in incompressible flow; a quick review of fluid
mechanics; a summary of the appropriate Fourier theory; a summary
of Kolmogorov's theory of the inertial range. The next four
chapters present the statistical theory of vortex notion, and the
vortex dynamics of turbulence. The book ends with the major
conclusion that turbulence can no longer be viewed as
incomprehensible. This book will be appropriate for professionals
in the fields of applied mathematics, mechanical engineering, or
physics, as well as graduate students in these noted areas.
A presentation of some of the basic ideas of fluid mechanics in a mathematically attractive manner. The text illustrates the physical background and motivation for some constructions used in recent mathematical and numerical work on the Navier- Stokes equations and on hyperbolic systems, so as to interest students in this at once beautiful and difficult subject. This third edition incorporates a number of updates and revisions, while retaining the spirit and scope of the original book.
"Stochastic Tools in Mathematics and Science" covers basic
stochastic tools used in physics, chemistry, engineering and the
life sciences. The topics covered include conditional expectations,
stochastic processes, Brownian motion and its relation to partial
differential equations, Langevin equations, the Liouville and
Fokker-Planck equations, as well as Markov chain Monte Carlo
algorithms, renormalization, basic statistical mechanics, and
generalized Langevin equations and the Mori-Zwanzig formalism. The
applications include sampling algorithms, data assimilation,
prediction from partial data, spectral analysis, and turbulence.
The book is based on lecture notes from a class that has attracted
graduate and advanced undergraduate students from mathematics and
from many other science departments at the University of
California, Berkeley. Each chapter is followed by exercises. The
book will be useful for scientists and engineers working in a wide
range of fields and applications. For this new edition the material
has been thoroughly reorganized and updated, and new sections on
scaling, sampling, filtering and data assimilation, based on recent
research, have been added. There are additional figures and
exercises. Review of earlier edition: "This is an excellent concise
textbook which can be used for self-study by graduate and advanced
undergraduate students and as a recommended textbook for an
introductory course on probabilistic tools in science."
Mathematical Reviews, 2006
This book provides an introduction to the theory of turbulence in
fluids based on the representation of the flow by means of its
vorticity field. It has long been understood that, at least in the
case of incompressible flow, the vorticity representation is
natural and physically transparent, yet the development of a theory
of turbulence in this representation has been slow. The pioneering
work of Onsager and of Joyce and Montgomery on the statistical
mechanics of two-dimensional vortex systems has only recently been
put on a firm mathematical footing, and the three-dimensional
theory remains in parts speculative and even controversial. The
first three chapters of the book contain a reasonably standard
intro duction to homogeneous turbulence (the simplest case); a
quick review of fluid mechanics is followed by a summary of the
appropriate Fourier theory (more detailed than is customary in
fluid mechanics) and by a summary of Kolmogorov's theory of the
inertial range, slanted so as to dovetail with later vortex-based
arguments. The possibility that the inertial spectrum is an
equilibrium spectrum is raised."
The 60th birthday of Peter Lax was celebrated at Berkeley by a
conference entitled Wave Motion: theory, application and
computation held at the mathematical Sciences Research Institute,
June 9-12, 1986. Peter Lax has made profound and essential
contributions to the topics described by the title of the
conference, and has also contributed in important ways to many
other mathematical subjects, and as a result this conference volume
dedicated to him includes research work on a variety of topics, not
all clearly related to its title.
Mathematics is playing an ever more important role in the physical
and biological sciences, provoking a blurring of boundaries between
scientific disciplines and a resurgence of interest in the modern
as weil as the clas sical techniques of applied mathematics. This
renewal of interest, bothin research and teaching, has led to the
establishment of the series: Texts in Applied Mathematics (TAM).
The development of new courses is a natural consequence of a high
Ievel of excitement on the research frontier as newer techniques,
such as numerical and symbolic computer systems, dynamical systems,
and chaos, mix with and reinforce the traditional methods of
applied mathematics. Thus, the purpose of this textbook series is
to meet the current and future needs of these advances and
encourage the teaching of new courses. TAM will publish textbooks
suitable for use in advanced undergraduate and beginning graduate
courses, and will complement the Applied Mathematical Seiences
(AMS) series, which will focus on advanced textbooks and research
Ievel monographs. Preface This book is based on a one-term coursein
fluid mechanics originally taught in the Department of Mathematics
of the U niversity of California, Berkeley, during the spring of
1978. The goal of the course was not to provide an exhaustive
account of fluid mechanics, nor to assess the engineering value of
various approximation procedures."
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