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Author: Lui Lam
Publisher: Springer Science & Business Media
ISBN: 9780387406145
Category : Science
Languages : en
Pages : 436
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Book Description
This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.
Author: Lui Lam
Publisher: Springer Science & Business Media
ISBN: 9780387406145
Category : Science
Languages : en
Pages : 436
Get Book
Book Description
This textbook provides an introduction to the new science of nonlinear physics for advanced undergraduates, beginning graduate students, and researchers entering the field. The chapters, by pioneers and experts in the field, share a unified perspective. Nonlinear science developed out of the increasing ability to investigate and analyze systems for which effects are not simply linear functions of their causes; it is associated with such well-known code words as chaos, fractals, pattern formation, solitons, cellular automata, and complex systems. Nonlinear phenomena are important in many fields, including dynamical systems, fluid dynamics, materials science, statistical physics, and paritcel physics. The general principles developed in this text are applicable in a wide variety of fields in the natural and social sciences. The book will thus be of interest not only to physicists, but also to engineers, chemists, geologists, biologists, economists, and others interested in nonlinear phenomena. Examples and exercises complement the text, and extensive references provide a guide to research in the field.
Author: H D I Abarbanel
Publisher: World Scientific
ISBN: 9814504122
Category : Science
Languages : en
Pages : 168
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Book Description
This series of lectures aims to address three main questions that anyone interested in the study of nonlinear dynamics should ask and ponder over. What is nonlinear dynamics and how does it differ from linear dynamics which permeates all familiar textbooks? Why should the physicist study nonlinear systems and leave the comfortable territory of linearity? How can one progress in the study of nonlinear systems both in the analysis of these systems and in learning about new systems from observing their experimental behavior? While it is impossible to answer these questions in the finest detail, this series of lectures nonetheless successfully points the way for the interested reader. Other useful problems have also been incorporated as a study guide. By presenting both substantial qualitative information about phenomena in nonlinear systems and at the same time sufficient quantitative material, the author hopes that readers would learn how to progress on their own in the study of such similar material hereon. Contents:IntroductionNonlinear Oscillator without DissipationEquilibrium States of a Nonlinear Oscillator with DissipationOscillations in Systems with Nonlinear Dissipation-GeneratorsThe Van der Pol GeneratorThe Poincaré MapSlow and Fast Motions in Systems with One Degree of FreedomForced Nonlinear Oscillators: Linear and Nonlinear ResonancesForced Generator: SynchronizationCompetition of ModesPoincaré Indices and Bifurcations of Equilibrium StatesResonance Interactions between OscillatorsSolitonsSteady Propagation of Shock WavesFormation of Shock WavesSolitons. Shock Waves. Wave Interaction. The Spectral ApproachWeak Turbulence. Random Phase ApproximationRegular Patterns in Dissipative MediaDeterministic Chaos. Qualitative DescriptionDescription of a Circuit with Chaos. Chaos in MapsBifurcations of Periodic Motions. Period DoublingControlled Nonlinear Oscillator. IntermittencyScenarios of the Onset of Chaos. Chaos through Quasi-PeriodicityCharacteristics of Chaos. Experimental Observation of ChaosMultidimensional Chaos. Discrete Ginzburg-Landau ModelProblems to Accompany the Lectures Readership: Physicists. keywords: “These lecture notes briefly introduce the reader to new ideas, so would be a useful addition to a library or a source of ideas for lectures or projects; a good student may also find this text useful as a quick introduction to many new ideas.” Contemporary Physics “Introduction to Nonlinear Dynamics for Physicists … is a compact and fairly terse high-level set of 24 lectures.” New Scientist
Author: G. Nicolis
Publisher: Cambridge University Press
ISBN: 9780521467827
Category : Mathematics
Languages : en
Pages : 274
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Book Description
The aim of this book is to develop a unified approach to nonlinear science, which does justice to its multiple facets and to the diversity and richness of the concepts and tools developed in this field over the years. Nonlinear science emerged in its present form following a series of closely related and decisive analytic, numerical and experimental developments that took place over the past three decades. It appeals to an extremely large variety of subject areas, but, at the same time, introduces into science a new way of thinking based on a subtle interplay between qualitative and quantitative techniques, topological and metric considerations and deterministic and statistical views. Special effort has been made throughout the book to illustrate both the development of the subject and the mathematical techniques, by reference to simple models. Each chapter concludes with a set of problems. This book will be of great value to graduate students in physics, applied mathematics, chemistry, engineering and biology taking courses in nonlinear science and its applications.
Author: Steven H. Strogatz
Publisher: CRC Press
ISBN: 0429961111
Category : Mathematics
Languages : en
Pages : 532
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Book Description
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Author: George Datseris
Publisher: Springer Nature
ISBN: 3030910326
Category : Science
Languages : en
Pages : 243
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Book Description
This concise and up-to-date textbook provides an accessible introduction to the core concepts of nonlinear dynamics as well as its existing and potential applications. The book is aimed at students and researchers in all the diverse fields in which nonlinear phenomena are important. Since most tasks in nonlinear dynamics cannot be treated analytically, skills in using numerical simulations are crucial for analyzing these phenomena. The text therefore addresses in detail appropriate computational methods as well as identifying the pitfalls of numerical simulations. It includes numerous executable code snippets referring to open source Julia software packages. Each chapter includes a selection of exercises with which students can test and deepen their skills.
Author: Richard H. Enns
Publisher: Springer Science & Business Media
ISBN: 1461202116
Category : Mathematics
Languages : en
Pages : 706
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Book Description
Nonlinear physics continues to be an area of dynamic modern research, with applications to physics, engineering, chemistry, mathematics, computer science, biology, medicine and economics. In this text extensive use is made of the Mathematica computer algebra system. No prior knowledge of Mathematica or programming is assumed. This book includes 33 experimental activities that are designed to deepen and broaden the reader's understanding of nonlinear physics. These activities are correlated with Part I, the theoretical framework of the text.
Author: Irving R. Epstein
Publisher: Oxford University Press
ISBN: 0198025661
Category : Science
Languages : en
Pages : 407
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Book Description
Just a few decades ago, chemical oscillations were thought to be exotic reactions of only theoretical interest. Now known to govern an array of physical and biological processes, including the regulation of the heart, these oscillations are being studied by a diverse group across the sciences. This book is the first introduction to nonlinear chemical dynamics written specifically for chemists. It covers oscillating reactions, chaos, and chemical pattern formation, and includes numerous practical suggestions on reactor design, data analysis, and computer simulations. Assuming only an undergraduate knowledge of chemistry, the book is an ideal starting point for research in the field. The book begins with a brief history of nonlinear chemical dynamics and a review of the basic mathematics and chemistry. The authors then provide an extensive overview of nonlinear dynamics, starting with the flow reactor and moving on to a detailed discussion of chemical oscillators. Throughout the authors emphasize the chemical mechanistic basis for self-organization. The overview is followed by a series of chapters on more advanced topics, including complex oscillations, biological systems, polymers, interactions between fields and waves, and Turing patterns. Underscoring the hands-on nature of the material, the book concludes with a series of classroom-tested demonstrations and experiments appropriate for an undergraduate laboratory.
Author: Daniel Kaplan
Publisher: Springer Science & Business Media
ISBN: 1461208238
Category : Mathematics
Languages : en
Pages : 438
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Book Description
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 well as the classical techniques of applied mathematics. This renewal of interest, both in 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 level 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 Sciences (AMS) series, which will focus on advanced textbooks and research level monographs. About the Authors Daniel Kaplan specializes in the analysis of data using techniques motivated by nonlinear dynamics. His primary interest is in the interpretation of irregular physiological rhythms, but the methods he has developed have been used in geo physics, economics, marine ecology, and other fields. He joined McGill in 1991, after receiving his Ph.D from Harvard University and working at MIT. His un dergraduate studies were completed at Swarthmore College. He has worked with several instrumentation companies to develop novel types of medical monitors.
Author: Lam
Publisher:
ISBN: 9788181286659
Category :
Languages : en
Pages : 417
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Book Description
Author: Minoru Fujimoto
Publisher: Morgan & Claypool Publishers
ISBN: 1627052771
Category : Science
Languages : en
Pages : 217
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Book Description
Nonlinear physics is a well-established discipline in physics today, and this book offers a comprehensive account of the basic soliton theory and its applications. Although primarily mathematical, the theory for nonlinear phenomena in practical environment
