Books in Mathematical methods in physics

41-50 of 74 results in All results

Singularity and Dynamics on Discontinuous Vector Fields

• 1st Edition
• Volume 3
• July 7, 2006
• Albert C.J. Luo
• English
• eBook 978-0-08-048093-0

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This book discussed fundamental problems in dynamics, which extensively exist in engineering, natural and social sciences. The book presented a basic theory for the interactions among many dynamical systems and for a system whose motions are constrained naturally or artificially. The methodology and techniques presented in this book are applicable to discontinuous dynamical systems in physics, engineering and control. In addition, they may provide useful tools to solve non-traditional dynamics in biology, stock market and internet network et al, which cannot be easily solved by the traditional Newton mechanics. The new ideas and concepts will stimulate ones’ thought and creativities in corresponding subjects. The author also used the simple, mathematical language to write this book. Therefore, this book is very readable, which can be either a textbook for senior undergraduate and graduate students or a reference book for researches in dynamics.

Bifurcation and Chaos in Complex Systems

• 1st Edition
• Volume 1
• June 30, 2006
• Jian-Qiao Sun + 1 more
• English
• Hardback 978-0-444-52229-0

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• eBook 978-0-08-046266-0

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The book presents the recent achievements on bifurcation studies of nonlinear dynamical systems. The contributing authors of the book are all distinguished researchers in this interesting subject area. The first two chapters deal with the fundamental theoretical issues of bifurcation analysis in smooth and non-smooth dynamical systems. The cell mapping methods are presented for global bifurcations in stochastic and deterministic, nonlinear dynamical systems in the third chapter. The fourth chapter studies bifurcations and chaos in time-varying, parametrically excited nonlinear dynamical systems. The fifth chapter presents bifurcation analyses of modal interactions in distributed, nonlinear, dynamical systems of circular thin von Karman plates. The theories, methods and results presented in this book are of great interest to scientists and engineers in a wide range of disciplines. This book can be adopted as references for mathematicians, scientists, engineers and graduate students conducting research in nonlinear dynamical systems.

Mathematical Statistical Physics

• 1st Edition
• Volume 83
• June 27, 2006
• Anton Bovier + 4 more
• English
• Hardback 978-0-444-52813-1

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• eBook 978-0-08-047923-1

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The proceedings of the 2005 les Houches summer school on Mathematical Statistical Physics give and broad and clear overview on this fast developing area of interest to both physicists and mathematicians.

Fractal Dimensions for Poincare Recurrences

• 1st Edition
• Volume 2
• June 21, 2006
• Valentin Afraimovich + 2 more
• English
• Hardback 978-0-444-52189-7

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• eBook 978-0-08-046239-4

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This book is devoted to an important branch of the dynamical systems theory : the study of the fine (fractal) structure of Poincare recurrences -instants of time when the system almost repeats its initial state. The authors were able to write an entirely self-contained text including many insights and examples, as well as providing complete details of proofs. The only prerequisites are a basic knowledge of analysis and topology. Thus this book can serve as a graduate text or self-study guide for courses in applied mathematics or nonlinear dynamics (in the natural sciences). Moreover, the book can be used by specialists in applied nonlinear dynamics following the way in the book. The authors applied the mathematical theory developed in the book to two important problems: distribution of Poincare recurrences for nonpurely chaotic Hamiltonian systems and indication of synchronization regimes in coupled chaotic individual systems.

Uncertain Input Data Problems and the Worst Scenario Method

• 1st Edition
• Volume 46
• December 9, 2004
• Ivan Hlavacek + 2 more
• Jan Achenbach
• English
• eBook 978-0-08-054337-6

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This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is presented, and then applied to various state problems modeled by differential equations or variational inequalities: nonlinear heat flow, Timoshenko beam vibration and buckling, plate buckling, contact problems in elasticity and thermoelasticity with and without friction, and various models of plastic deformation, to list some of the topics. Dozens of examples, figures, and tables are included.Although the book concentrates on the mathematical aspects of the subject, a substantial part is written in an accessible style and is devoted to various facets of uncertainty in modeling and to the state of the art techniques proposed to deal with uncertain input data.A chapter on sensitivity analysis and on functional and convex analysis is included for the reader's convenience.

Unstable Singularities and Randomness

• 1st Edition
• June 18, 2004
• Joseph P. Zbilut
• English
• eBook 978-0-08-047469-4

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Traditionally, randomness and determinism have been viewed as being diametrically opposed, based on the idea that causality and determinism is complicated by “noise.” Although recent research has suggested that noise can have a productive role, it still views noise as a separate entity. This work suggests that this not need to be so. In an informal presentation, instead, the problem is traced to traditional assumptions regarding dynamical equations and their need for unique solutions. If this requirement is relaxed, the equations admit for instability and stochasticity evolving from the dynamics itself. This allows for a decoupling from the “burden” of the past and provides insights into concepts such as predictability, irreversibility, adaptability, creativity and multi-choice behaviour. This reformulation is especially relevant for biological and social sciences whose need for flexibility a propos of environmental demands is important to understand: this suggests that many system models are based on randomness and nondeterminism complicated with a little bit of determinism to ultimately achieve concurrent flexibility and stability. As a result, the statistical perception of reality is seen as being a more productive tool than classical determinism. The book addresses scientists of all disciplines, with special emphasis at making the ideas more accessible to scientists and students not traditionally involved in the formal mathematics of the physical sciences. The implications may be of interest also to specialists in the philosophy of science.

Encyclopedia of Mathematical Physics

• 1st Edition
• February 28, 2004
• Jean-Pierre Françoise + 2 more
• English
• eBook 978-0-12-512666-3

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The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher’s own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, FranceGregory L. Naber, Drexel University, Philadelphia, PA, USATsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) – featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy. For more information, pricing options and availability visit www.info.sciencedirect.com.

Essential Mathematical Methods for Physicists, ISE

• 1st Edition
• August 8, 2003
• Hans J. Weber + 1 more
• English
• Hardback 978-0-12-059877-9

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• eBook 978-0-08-046985-0

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This new adaptation of Arfken and Weber's bestselling Mathematical Methods for Physicists, Fifth Edition, is the most comprehensive, modern, and accessible reference for using mathematics to solve physics problems. REVIEWERS SAY: "Examples are excellent. They cover a wide range of physics problems." --Bing Zhou, University of Michigan "The ideas are communicated very well and it is easy to understand...It has a more modern treatment than most, has a very complete range of topics and each is treated in sufficient detail....I'm not aware of another better book at this level..." --Gary Wysin, Kansas State University

Handbook of Mathematical Fluid Dynamics

• 1st Edition
• March 27, 2003
• S. Friedlander + 1 more
• English
• eBook 978-0-08-053354-4

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The Handbook of Mathematical Fluid Dynamics is a compendium of essays that provides a survey of the major topics in the subject. Each article traces developments, surveys the results of the past decade, discusses the current state of knowledge and presents major future directions and open problems. Extensive bibliographic material is provided. The book is intended to be useful both to experts in the field and to mathematicians and other scientists who wish to learn about or begin research in mathematical fluid dynamics. The Handbook illuminates an exciting subject that involves rigorous mathematical theory applied to an important physical problem, namely the motion of fluids.

Mathematical Methods for Mathematicians, Physical Scientists and Engineers

• 1st Edition
• March 1, 2003
• Jeremy Dunning-Davies
• English
• eBook 978-0-85709-956-3

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This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced as solutions. The book will serve for postgraduate reference worldwide, with variation for USA.