An Introduction To Nonlinear Chemical Dynamics

Author : Irving R. Epstein,John A. Pojman
Publisher : Oxford University Press
Page : 407 pages
File Size : 45,6 Mb
Release : 1998-10-22
Category : Science
ISBN : 9780198025665

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An Introduction to Nonlinear Chemical Dynamics by Irving R. Epstein,John A. Pojman Pdf

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 : Steven H. Strogatz
Publisher : CRC Press
Page : 532 pages
File Size : 41,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9780429961113

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Nonlinear Dynamics and Chaos by Steven H. Strogatz Pdf

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 : Marc R Roussel
Publisher : Morgan & Claypool Publishers
Page : 190 pages
File Size : 50,8 Mb
Release : 2019-05-01
Category : Science
ISBN : 9781643274645

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Nonlinear Dynamics by Marc R Roussel Pdf

This book uses a hands-on approach to nonlinear dynamics using commonly available software, including the free dynamical systems software Xppaut, Matlab (or its free cousin, Octave) and the Maple symbolic algebra system. Detailed instructions for various common procedures, including bifurcation analysis using the version of AUTO embedded in Xppaut, are provided. This book also provides a survey that can be taught in a single academic term covering a greater variety of dynamical systems (discrete versus continuous time, finite versus infinite-dimensional, dissipative versus conservative) than is normally seen in introductory texts. Numerical computation and linear stability analysis are used as unifying themes throughout the book. Despite the emphasis on computer calculations, theory is not neglected, and fundamental concepts from the field of nonlinear dynamics such as solution maps and invariant manifolds are presented.

Author : Daniel Kaplan,Leon Glass
Publisher : Springer Science & Business Media
Page : 438 pages
File Size : 52,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461208235

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Understanding Nonlinear Dynamics by Daniel Kaplan,Leon Glass Pdf

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 : Peter Gray,Stephen K. Scott
Publisher : Oxford University Press
Page : 453 pages
File Size : 47,7 Mb
Release : 1990
Category : Science
ISBN : 0198556462

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Chemical Oscillations and Instabilities by Peter Gray,Stephen K. Scott Pdf

Today, scientists in many fields are expressing considerable interest in non-linearity and the ideas of oscillations and chaos. Chemical reactions provide perfect examples of these phenomena. This book is an excellent introduction to the area of nonlinear phenomena in chemical kinetics that involve chemical feedback such as chain branching, autocatalysis, and self-heating. The emphasis is on physical and pictorial representation, and on identifying those gross features which are essential. The experimental conditions under which such behavior will occur can be predicted using simple mathematical recipes, and these are also included. Readers will find full discussions of long-lived oscillations for autocatalytic or exothermic reactions in closed vessels and stationary states, bistability, and oscillations in continuous flow reactors and diffusion cells. Other topics considered include chemical wave propagation, pattern selection and formation, heterogeneous reactions, complex oscillations, quasiperiodicity, and chemical chaos, both forced and spontaneous. The second part of the book describes actual experimental systems, such as the Belousov-Zhabotinskii reaction, and include discussion of the behavior of important gas-phase reactions. This volume is an ideal sourcebook of applied problems for graduate courses in dynamical systems, advanced chemical kinetics, and chemical reactor engineering, as well as for research workers in physical chemistry, and mathematicians, biologists, physicists, and physiologists.

Author : Christian Vidal,Adolphe Pacault
Publisher : Springer
Page : 304 pages
File Size : 45,6 Mb
Release : 1981
Category : Science
ISBN : UOM:39015016006614

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Nonlinear Phenomena in Chemical Dynamics by Christian Vidal,Adolphe Pacault Pdf

Author : H. D. I. Abarbanel,M. I. Rabinovich,Mikhael M. Sushchik
Publisher : World Scientific Publishing Company Incorporated
Page : 158 pages
File Size : 43,6 Mb
Release : 1993
Category : Science
ISBN : 981021409X

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Introduction to Nonlinear Dynamics for Physicists by H. D. I. Abarbanel,M. I. Rabinovich,Mikhael M. Sushchik Pdf

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.

Author : G. Nicolis
Publisher : Cambridge University Press
Page : 274 pages
File Size : 55,8 Mb
Release : 1995-06-22
Category : Mathematics
ISBN : 0521467829

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Introduction to Nonlinear Science by G. Nicolis Pdf

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 : Sandro Wimberger
Publisher : Unknown
Page : 0 pages
File Size : 44,9 Mb
Release : 2022
Category : Electronic
ISBN : 303101250X

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Nonlinear Dynamics and Quantum Chaos by Sandro Wimberger Pdf

This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.

Author : Robert C. Hilborn
Publisher : Unknown
Page : 676 pages
File Size : 42,8 Mb
Release : 2000
Category : Mathematics
ISBN : 0198507232

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Chaos and Nonlinear Dynamics by Robert C. Hilborn Pdf

This book introduces readers to the full range of current and background activity in the rapidly growing field of nonlinear dynamics. It uses a step-by-step introduction to dynamics and geometry in state space to help in understanding nonlinear dynamics and includes a thorough treatment of both differential equation models and iterated map models as well as a derivation of the famous Feigenbaum numbers. It is the only introductory book available that includes the important field of pattern formation and a survey of the controversial questions of quantum chaos. This second edition has been restructured for easier use and the extensive annotated references are updated through January 2000 and include many web sites for a number of the major nonlinear dynamics research centers. With over 200 figures and diagrams, analytic and computer exercises this book is a necessity for both the classroom and the lab.

Author : Misha Meyer Pesenson
Publisher : John Wiley & Sons
Page : 307 pages
File Size : 42,7 Mb
Release : 2013-09-13
Category : Science
ISBN : 9783527671656

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Multiscale Analysis and Nonlinear Dynamics by Misha Meyer Pesenson Pdf

Since modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinary task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience, computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscale analysis is the major integrating theme of the book, its subtitle does not call for bridging the scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts referred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.

Author : Alwyn Scott
Publisher : Routledge
Page : 1107 pages
File Size : 40,7 Mb
Release : 2006-05-17
Category : Reference
ISBN : 9781135455583

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Encyclopedia of Nonlinear Science by Alwyn Scott Pdf

In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Author : Bruce E. Hobbs,Alison Ord
Publisher : Elsevier
Page : 680 pages
File Size : 42,5 Mb
Release : 2014-11-21
Category : Science
ISBN : 9780124079335

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Structural Geology by Bruce E. Hobbs,Alison Ord Pdf

Structural Geology is a groundbreaking reference that introduces you to the concepts of nonlinear solid mechanics and non-equilibrium thermodynamics in metamorphic geology, offering a fresh perspective on rock structure and its potential for new interpretations of geological evolution. This book stands alone in unifying deformation and metamorphism and the development of the mineralogical fabrics and the structures that we see in the field. This reflects the thermodynamics of systems not at equilibrium within the framework of modern nonlinear solid mechanics. The thermodynamic approach enables the various mechanical, thermal, hydrological and chemical processes to be rigorously coupled through the second law of thermodynamics, invariably leading to nonlinear behavior. The book also differs from others in emphasizing the implications of this nonlinear behavior with respect to the development of the diverse, complex, even fractal, range of structures in deformed metamorphic rocks. Building on the fundamentals of structural geology by discussing the nonlinear processes that operate during the deformation and metamorphism of rocks in the Earth's crust, the book's concepts help geoscientists and graduate-level students understand how these processes control or influence the structures and metamorphic fabrics—providing applications in hydrocarbon exploration, ore mineral exploration, and architectural engineering. Authored by two of the world's foremost experts in structural geology, representing more than 70 years of experience in research and instruction Nearly 300 figures, illustrations, working examples, and photographs reinforce key concepts and underscore major advances in structural geology

Author : Satoshi Nakata,Véronique Pimienta,István Lagzi,Hiroyuki Kitahata,Nobuhiko J Suematsu
Publisher : Royal Society of Chemistry
Page : 388 pages
File Size : 53,7 Mb
Release : 2018-11-01
Category : Science
ISBN : 9781788015431

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Self-organized Motion by Satoshi Nakata,Véronique Pimienta,István Lagzi,Hiroyuki Kitahata,Nobuhiko J Suematsu Pdf

Self-propelled objects (particles, droplets) are autonomous agents that can convert energy from the environment into motion. These motions include nonlinear behaviour such as oscillations, synchronization, bifurcation, and pattern formation. In recent years, there has been much interest in self-propelled objects for their potential role in mass transport or their use as carriers in confined spaces. An improved understanding of self-organized motion has even allowed researchers to design objects for specific motion. This book gives an overview of the principles of self-propelled motion in chemical objects (particles, droplets) far from their thermodynamic equilibrium, at various spatial scales. Theoretical aspects, the characteristics of the motion and the design procedures of such systems are discussed from the viewpoint of nonlinear dynamics and examples of applications for these nonlinear systems are provided. This book is suitable for researchers and graduate students interested in physical and theoretical chemistry as well as soft matter.

Author : B.K Shivamoggi
Publisher : Springer Science & Business Media
Page : 415 pages
File Size : 54,9 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401724425

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Nonlinear Dynamics and Chaotic Phenomena by B.K Shivamoggi Pdf

FolJowing the formulation of the laws of mechanics by Newton, Lagrange sought to clarify and emphasize their geometrical character. Poincare and Liapunov successfuIJy developed analytical mechanics further along these lines. In this approach, one represents the evolution of all possible states (positions and momenta) by the flow in phase space, or more efficiently, by mappings on manifolds with a symplectic geometry, and tries to understand qualitative features of this problem, rather than solving it explicitly. One important outcome of this line of inquiry is the discovery that vastly different physical systems can actually be abstracted to a few universal forms, like Mandelbrot's fractal and Smale's horse-shoe map, even though the underlying processes are not completely understood. This, of course, implies that much of the observed diversity is only apparent and arises from different ways of looking at the same system. Thus, modern nonlinear dynamics 1 is very much akin to classical thermodynamics in that the ideas and results appear to be applicable to vastly different physical systems. Chaos theory, which occupies a central place in modem nonlinear dynamics, refers to a deterministic development with chaotic outcome. Computers have contributed considerably to progress in chaos theory via impressive complex graphics. However, this approach lacks organization and therefore does not afford complete insight into the underlying complex dynamical behavior. This dynamical behavior mandates concepts and methods from such areas of mathematics and physics as nonlinear differential equations, bifurcation theory, Hamiltonian dynamics, number theory, topology, fractals, and others.