Information Theory And Stochastics For Multiscale Nonlinear Systems

Author : Andrew Majda,Rafail V. Abramov,Marcus J. Grote
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 45,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9780821838433

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Information Theory and Stochastics for Multiscale Nonlinear Systems by Andrew Majda,Rafail V. Abramov,Marcus J. Grote Pdf

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.

Author : Andrew Majda,Rafail V. Abramov,Marcus J. Grote
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 54,8 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 0821869868

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Information Theory and Stochastics for Multiscale Nonlinear Systems by Andrew Majda,Rafail V. Abramov,Marcus J. Grote Pdf

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.

Author : G A Pavliotis,Andrew Stuart
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 45,5 Mb
Release : 2008-02-19
Category : Mathematics
ISBN : 9780387738284

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Multiscale Methods by G A Pavliotis,Andrew Stuart Pdf

This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.

Author : Stefan Heinz,Hakima Bessaih
Publisher : Springer
Page : 192 pages
File Size : 46,6 Mb
Release : 2015-05-06
Category : Mathematics
ISBN : 9783319182063

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Stochastic Equations for Complex Systems by Stefan Heinz,Hakima Bessaih Pdf

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.

Author : Andrew J. Majda
Publisher : Springer
Page : 91 pages
File Size : 48,7 Mb
Release : 2016-09-14
Category : Mathematics
ISBN : 9783319322179

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Introduction to Turbulent Dynamical Systems in Complex Systems by Andrew J. Majda Pdf

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.

Author : Philippe G. Ciarlet,Tatsien Li,Yvon Maday
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 42,5 Mb
Release : 2013-11-29
Category : Mathematics
ISBN : 9783642414015

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Partial Differential Equations: Theory, Control and Approximation by Philippe G. Ciarlet,Tatsien Li,Yvon Maday Pdf

This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

Author : Sai Ravela,Adrian Sandu
Publisher : Springer
Page : 360 pages
File Size : 48,5 Mb
Release : 2015-11-26
Category : Computers
ISBN : 9783319251387

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Dynamic Data-Driven Environmental Systems Science by Sai Ravela,Adrian Sandu Pdf

This book constitutes the refereed proceedings of the First International Conference on Dynamic Data-Driven Environmental Systems Science, DyDESS 2014, held in Cambridge, MA, USA, in November 2014.The 24 revised full papers and 7 short papers were carefully reviewed and selected from 62 submissions and cover topics on sensing, imaging and retrieval for the oceans, atmosphere, space, land, earth and planets that is informed by the environmental context; algorithms for modeling and simulation, downscaling, model reduction, data assimilation, uncertainty quantification and statistical learning; methodologies for planning and control, sampling and adaptive observation, and efficient coupling of these algorithms into information-gathering and observing system designs; and applications of methodology to environmental estimation, analysis and prediction including climate, natural hazards, oceans, cryosphere, atmosphere, land, space, earth and planets.

Author : Gui-Qiang Chen
Publisher : World Scientific
Page : 401 pages
File Size : 42,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814273275

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Nonlinear Conservation Laws, Fluid Systems and Related Topics by Gui-Qiang Chen Pdf

This book is a collection of lecture notes on Nonlinear Conservation Laws, Fluid Systems and Related Topics delivered at 2007 Shanghai Mathematics Summer School held at Fudan University, China, by world's leading experts in the field. The volume comprises ªve chapters that cover a range of topics from mathematical theory and numerical approximation of both incompressible and compressible ªuid ªows, kinetic theory and conservation laws, to statistical theories for ªuid systems. Researchers and graduate students who want to work in this field will benefit from this essential reference as each chapter leads readers from the basics to the frontiers of the current research in these areas.

Author : Shih-Yu (Simon) Wang,Robert Gillies
Publisher : BoD – Books on Demand
Page : 402 pages
File Size : 43,8 Mb
Release : 2012-03-09
Category : Science
ISBN : 9789535100959

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Modern Climatology by Shih-Yu (Simon) Wang,Robert Gillies Pdf

Climatology, the study of climate, is no longer regarded as a single discipline that treats climate as something that fluctuates only within the unchanging boundaries described by historical statistics. The field has recognized that climate is something that changes continually under the influence of physical and biological forces and so, cannot be understood in isolation but rather, is one that includes diverse scientific disciplines that play their role in understanding a highly complex coupled "whole system" that is the earth's climate. The modern era of climatology is echoed in this book. On the one hand it offers a broad synoptic perspective but also considers the regional standpoint, as it is this that affects what people need from climatology. Aspects on the topic of climate change - what is often considered a contradiction in terms - is also addressed. It is all too evident these days that what recent work in climatology has revealed carries profound implications for economic and social policy; it is with these in mind that the final chapters consider acumens as to the application of what has been learned to date.

Author : Nan Chen
Publisher : Springer Nature
Page : 208 pages
File Size : 45,7 Mb
Release : 2023-03-13
Category : Mathematics
ISBN : 9783031222498

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Stochastic Methods for Modeling and Predicting Complex Dynamical Systems by Nan Chen Pdf

This book enables readers to understand, model, and predict complex dynamical systems using new methods with stochastic tools. The author presents a unique combination of qualitative and quantitative modeling skills, novel efficient computational methods, rigorous mathematical theory, as well as physical intuitions and thinking. An emphasis is placed on the balance between computational efficiency and modeling accuracy, providing readers with ideas to build useful models in practice. Successful modeling of complex systems requires a comprehensive use of qualitative and quantitative modeling approaches, novel efficient computational methods, physical intuitions and thinking, as well as rigorous mathematical theories. As such, mathematical tools for understanding, modeling, and predicting complex dynamical systems using various suitable stochastic tools are presented. Both theoretical and numerical approaches are included, allowing readers to choose suitable methods in different practical situations. The author provides practical examples and motivations when introducing various mathematical and stochastic tools and merges mathematics, statistics, information theory, computational science, and data science. In addition, the author discusses how to choose and apply suitable mathematical tools to several disciplines including pure and applied mathematics, physics, engineering, neural science, material science, climate and atmosphere, ocean science, and many others. Readers will not only learn detailed techniques for stochastic modeling and prediction, but will develop their intuition as well. Important topics in modeling and prediction including extreme events, high-dimensional systems, and multiscale features are discussed.

Author : Chih-Pei Chang,Michael Ghil,Mojib Latif,John M Wallace
Publisher : World Scientific
Page : 388 pages
File Size : 44,7 Mb
Release : 2015-08-06
Category : Science
ISBN : 9789814579940

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Climate Change: Multidecadal and Beyond by Chih-Pei Chang,Michael Ghil,Mojib Latif,John M Wallace Pdf

This book focuses on two major challenges in the climate sciences: 1) to describe the decadal-to-centennial variations in instrumental and proxy records; and 2) to distinguish between anthropogenic variations and natural variability. The National Taiwan University invited some of the world's leading experts across the areas of observational analysis, mathematical theory, and modeling to discuss these two issues. The outcome of the meeting is the 23 chapters in this book that review the state of the art in theoretical, observational and modeling research on internal, unforced and externally forced climate variability. The main conclusion of this research is that internal climate variability on decadal and longer time scales is so large that sidestepping it may lead to false estimates of the climate's sensitivity to anthropogenic forcing. Contents:Attribution of Climate Change in the Presence of Internal Variability (John M Wallace, Clara Deser, Brian V Smoliak, and Adam S Phillips)A Mathematical Theory of Climate Sensitivity or, How to Deal With Both Anthropogenic Forcing and Natural Variability? (Michael Ghil)Fluctuation-dissipation Theorem with Application to Climate Change Studies with Seasonal Impact (Xiaoming Wang)Parametrization of Cross-scale Interaction in Multiscale Systems (Jeroen Wouters and Valerio Lucarini)Dynamics of Nonlinear Error Growth and the "Spring Predictability Barrier" for El Niño Predictions (Wansuo Duan and Mu Mu)An Adaptive Approach for Nonlinear and Nonstationary Data Analysis (Norden E Huang)Internal Southern Ocean Centennial Variability: Dynamics, Impacts and Implications for Global Warming (Mojib Latif, Torge Martin, Wonsun Park, and Mohammad H Bordbar)Atlantic Meridional Overturning Circulation and Climate (Rong Zhang)North Atlantic Multi-Decadal Variability — Mechanisms and Predictability (Noel S Keenlyside, Jin Ba, Jennifer Mecking, Nour-Eddine Omrani, Mojib Latif, Rong Zhang, and Rym Msadek)A Review of the Dynamics of Pacific Interdecadal Climate Variability (Zhengyu Liu)Global-Scale Decadal Hyper Modes (Dietmar Dommenget)Evidence for a Recurrent Multi-Decadal Oscillation in Global Temperature and Possible Impacts on 21st Century Climate Projections (Ka-Kit Tung and Jiansong Zhou)Variability of Sea Ice Extent Over Decadal and Longer Timescales (John E Walsh and William L Chapman)Multi-year Prediction and Predictability (Timothy DelSole, Michael K Tippett, and Liwei Jia)Decadal Hydroclimate Variability Across the Americas (Richard Seager)The Interhemispheric Pattern and Long-Term Variations in the Tropical Climate over the 20th and 21st Centuries (John C H Chiang)Climate of China in the Holocene (Wang Shaowu, Wen Xinyu, and Huang Jianbin)North Atlantic Hurricane Activity: Past, Present and Future (Rym Msadek, Gabriel A Vecchi, and Thomas R Knutson)Observed Variations of Western North Pacific Tropical Cyclone Activity on Decadal Time Scales and Longer (Johnny C L Chan)Record-Breaking Increase of Tropical Cyclone Heavy Rainfall in Taiwan in the First Decade of 21st Century (Chih-Pei Chang, Hung-Chi Kuo, and Chung-Hsiung Sui)Multi-Decadal Variability in Indian Summer Monsoon Rainfall Using Proxy Data (Bhupendra N Goswami, Ramesh H Kripalani, Hemant P Borgaonkar, and Bhaskar Preethi)The South-Flood North-Drought Pattern Over Eastern China and the Drying of the Gangetic Plain (Sumant Nigam, Yongjing Zhao, Alfredo Ruiz-Barradas, and Tianjun Zhou)Impacts of Aerosols on the Asian Monsoon — An Interim Assessment (William K M Lau and Kyu-Myong Kim) Readership: Graduate students, academics and researchers in atmospheric sciences, oceanography, mathematics, and climate change. Keywords:Climate Change;Multidecadal Variability;Climate Variability Asia-Pacific Weather

Author : Wang Wei,Chen Xiaopeng,Lv Yan
Publisher : World Scientific
Page : 240 pages
File Size : 54,9 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9789811200366

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Stochastic Pdes And Modelling Of Multiscale Complex System by Wang Wei,Chen Xiaopeng,Lv Yan Pdf

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 44,5 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Author : Alex Amenta,Pascal Auscher
Publisher : American Mathematical Soc.
Page : 152 pages
File Size : 41,9 Mb
Release : 2018-04-03
Category : Boundary value problems
ISBN : 9781470442507

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Elliptic Boundary Value Problems with Fractional Regularity Data: The First Order Approach by Alex Amenta,Pascal Auscher Pdf

A co-publication of the AMS and Centre de Recherches Mathématiques In this monograph the authors study the well-posedness of boundary value problems of Dirichlet and Neumann type for elliptic systems on the upper half-space with coefficients independent of the transversal variable and with boundary data in fractional Hardy–Sobolev and Besov spaces. The authors use the so-called “first order approach” which uses minimal assumptions on the coefficients and thus allows for complex coefficients and for systems of equations. This self-contained exposition of the first order approach offers new results with detailed proofs in a clear and accessible way and will become a valuable reference for graduate students and researchers working in partial differential equations and harmonic analysis.

Author : Joseph H. Silverman
Publisher : American Mathematical Soc.
Page : 151 pages
File Size : 46,9 Mb
Release : 2024-07-02
Category : Mathematics
ISBN : 9780821885031

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Moduli Spaces and Arithmetic Dynamics by Joseph H. Silverman Pdf