Andrew J. Majda's Books

Information Theory and Stochastics for Multiscale Nonlinear Systems

By: Andrew Majda,Rafail V. Abramov,Marcus J. Grote

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Information Theory and Stochastics for Multiscale Nonlinear Systems

By: Andrew Majda,Rafail V. Abramov,Marcus J. Grote

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.

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Page Count

145

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821838431

ISBN 13

9780821838433

Filtering Complex Turbulent Systems

By: Andrew J. Majda,John Harlim

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Filtering Complex Turbulent Systems

By: Andrew J. Majda,John Harlim

The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required.

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368

Publisher

Cambridge University Press

Published Date

ISBN 10

1107016665

ISBN 13

9781107016668

Tropical Intraseasonal Variability and the Stochastic Skeleton Method

By: Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual

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Tropical Intraseasonal Variability and the Stochastic Skeleton Method

By: Andrew J. Majda,Samuel N. Stechmann,Shengqian Chen,H. Reed Ogrosky,Sulian Thual

In this text, modern applied mathematics and physical insight are used to construct the simplest and first nonlinear dynamical model for the Madden-Julian oscillation (MJO), i.e. the stochastic skeleton model. This model captures the fundamental features of the MJO and offers a theoretical prediction of its structure, leading to new detailed methods to identify it in observational data. The text contributes to understanding and predicting intraseasonal variability, which remains a challenging task in contemporary climate, atmospheric, and oceanic science. In the tropics, the Madden-Julian oscillation (MJO) is the dominant component of intraseasonal variability. One of the strengths of this text is demonstrating how a blend of modern applied mathematical tools, including linear and nonlinear partial differential equations (PDEs), simple stochastic modeling, and numerical algorithms, have been used in conjunction with physical insight to create the model. These tools are also applied in developing several extensions of the model in order to capture additional features of the MJO, including its refined vertical structure and its interactions with the extratropics. This book is of interest to graduate students, postdocs, and senior researchers in pure and applied mathematics, physics, engineering, and climate, atmospheric, and oceanic science interested in turbulent dynamical systems as well as other complex systems.

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Page Count

131

Publisher

Springer Nature

Published Date

ISBN 10

3030222470

ISBN 13

9783030222475

Vorticity and Incompressible Flow

By: Andrew J. Majda,Andrea L. Bertozzi

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Vorticity and Incompressible Flow

By: Andrew J. Majda,Andrea L. Bertozzi

This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.

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562

Publisher

Cambridge University Press

Published Date

ISBN 10

0521639484

ISBN 13

9780521639484

Introduction to Turbulent Dynamical Systems in Complex Systems

By: Andrew J. Majda

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Introduction to Turbulent Dynamical Systems in Complex Systems

By: Andrew J. Majda

This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.

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Springer

Published Date

ISBN 10

3319322176

ISBN 13

9783319322179

Filtering Complex Turbulent Systems

By: Andrew J. Majda,John Harlim

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Filtering Complex Turbulent Systems

By: Andrew J. Majda,John Harlim

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Page Count

368

Publisher

Cambridge University Press

Published Date

ISBN 10

1107016665

ISBN 13

9781107016668

Book's by Andrew J. Majda

Information Theory and Stochastics for Multiscale Nonlinear Systems

Information Theory and Stochastics for Multiscale Nonlinear Systems

Filtering Complex Turbulent Systems

Filtering Complex Turbulent Systems

Tropical Intraseasonal Variability and the Stochastic Skeleton Method

Tropical Intraseasonal Variability and the Stochastic Skeleton Method

Vorticity and Incompressible Flow

Vorticity and Incompressible Flow

Introduction to Turbulent Dynamical Systems in Complex Systems

Introduction to Turbulent Dynamical Systems in Complex Systems

Filtering Complex Turbulent Systems

Filtering Complex Turbulent Systems

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