**CRM Monograph Series**

Volume: 25;
2005;
133 pp;
Hardcover

MSC: Primary 60;
Secondary 62; 76; 82; 86; 94

Print ISBN: 978-0-8218-3843-3

Product Code: CRMM/25

List Price: $46.00

Individual Member Price: $36.80

**Electronic ISBN: 978-1-4704-3869-2
Product Code: CRMM/25.E**

List Price: $46.00

Individual Member Price: $36.80

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#### Supplemental Materials

# Information Theory and Stochastics for Multiscale Nonlinear Systems

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*Andrew J. Majda; Rafail V. Abramov; Marcus J. Grote*

A co-publication of the AMS and Centre de Recherches Mathématiques

This book introduces mathematicians to the fascinating
mathematical interplay between ideas from stochastics and information
theory and practical issues in studying complex multiscale nonlinear
systems. It emphasizes the serendipity between modern applied
mathematics and applications where rigorous analysis, the development
of qualitative and/or asymptotic models, and numerical modeling all
interact to explain complex phenomena.

After a brief introduction to the emerging issues in multiscale
modeling, the book has three main chapters. The first chapter is an
introduction to information theory with novel applications to
statistical mechanics, predictability, and Jupiter's Red Spot for
geophysical flows. The second chapter discusses new mathematical
issues regarding fluctuation-dissipation theorems for complex
nonlinear systems including information flow, various approximations,
and illustrates applications to various mathematical models. The third
chapter discusses stochastic modeling of complex nonlinear
systems. After a general discussion, a new elementary model, motivated
by issues in climate dynamics, is utilized to develop a self-contained
example of stochastic mode reduction.

Based on A. Majda's Aisenstadt lectures at the University of Montreal,
the book is appropriate for both pure and applied mathematics graduate
students, postdocs and faculty, as well as interested researchers in
other scientific disciplines. No background in geophysical flows is
required.

About the authors: Andrew Majda is a member of the
National Academy of Sciences and has received numerous honors and
awards, including the National Academy of Science Prize in Applied
Mathematics, the John von Neumann Prize of the Society of Industrial
and Applied Mathematics, the Gibbs Prize of the American Mathematical
Society, and the Medal of the College de France. In the past several
years at the Courant Institute, Majda and a multi-disciplinary faculty
have created the Center for Atmosphere Ocean Science to promote
cross-disciplinary research with modern applied mathematics in climate
modeling and prediction. R.V. Abramov is a young researcher; he
received his PhD in 2002. M. J. Grote received his Ph.D. under Joseph
B. Keller at Stanford University in 1995.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## Information Theory and Stochastics for Multiscale Nonlinear Systems

- Cover Cover11
- Title page i2
- Contents iii4
- Overview on multiscale modeling in complex nonlinear systems v6
- Information theory, predictability, Jupiter’s great red spot, and equilibrium statistical mechanics 110
- The fluctuation-dissipation theorem for complex nonlinear systems 2534
- Mathematical strategies for stochastic mode reduction in climate 105114
- Back Cover Back Cover1145

#### Readership

Graduate students and research mathematicians interested in multiscale modeling, information theory, and geophysical flows.