Author: Paul C. Fife
Publisher:
ISBN:
Category : Differential equations, Partial
Languages : en
Pages : 24
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Book Description
A class of models for target patterns (concentric circular waves emanating from a point called the leading center) is constructed in the context of singularly perturbed reaction-diffusion systems of partial differential equations. First, the theory of wave fronts is detailed for scalar equations and systems of equations. A scaling method reduces complex waves to the consideration of a group of simple wave phenomena. It is shown that expanding wave fronts can be generated spontaneously at a point. This process, together with the laws of their subsequent motion, reduces the problem to an ordinary differential initial value problem, whose solution is required to have certain properties. A discussion is given of the connection between these results and experimental observations. (Author).
Author: Raymond Kapral
Publisher: Springer Science & Business Media
ISBN: 9401111561
Category : Science
Languages : en
Pages : 641
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Book Description
The concept of macroscopic waves and patterns developing from chemical reaction coupling with diffusion was presented, apparently for the first time, at the Main Meeting of the Deutsche Bunsengesellschaft fur Angewandte Physikalische Chemie, held in Dresden, Germany from May 21 to 24, 1906. Robert Luther, Director of the Physical Chemistry Laboratory in Leipzig, read his paper on the discovery and analysis of propagating reaction-diffusion fronts in autocatalytic chemical reactions [1, 2]. He presented an equation for the velocity of these new waves, V = a(KDC)1/2, and asserted that they might have features in common with propagating action potentials in nerve cell axons. During the discussion period, a skeptic in the audience voiced his objections to this notion. It was none other than the great physical chemist Walther Nernst, who believed that nerve impulse propagation was far too rapid to be akin to the propagating fronts. He was also not willing to accept Luther's wave velocity equation without a derivation. Luther stood his ground, saying his equation was "a simple consequence of the corresponding differential equation. " He described several different autocatalytic reactions that exhibit propagating fronts (recommending gelling the solution to prevent convection) and even presented a demonstration: the autocatalytic permanganate oxidation of oxalate was carried out in a test tube with the image of the front projected onto a screen for the audience.
Author: H. Haken
Publisher: Springer Science & Business Media
ISBN: 3642675921
Category : Science
Languages : en
Pages : 272
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Book Description
This book contains the invited papers of an international symposium on Synergetics which was held at ZIF (Center for interdisciplinary research) at Bielefeld. Fed. Rep. of Germany. Sept. 24. -29 . • 1979. In keeping with our previous meetings. this one was truly interdisciplinary. Synergetic systems are those that can produce macroscopic spatial. temporal or functional structures in a self-organized way. I think that these proceedings draw a rather coherent picture of the present status of Synergetics, emphasizing this time theoretical aspects, although the proceedings contain also important con tributions from the experimental side. Synergetics has ties to many quite different disciplines as is clearly mirrored by the following articles. Out of the many ties I pick here only one example which is alluded to in the title of this book. Indeed, there is an important branch of mathematics called dynamic systems theory for which the problems of Synergetics might become an eldorado. While, undoubtedly, a good deal of dynamic systems had been motivated by mechanics, such as celestial and fluid dynamics, theory Synergetics provides us with a wealth of related problems of quite different fields, e. g. , lasers or chemical reaction processes. In order to become adequately applicable, in quite a number of realistic cases dynamic systems theory must be developed further. This is equally true for a number of other approaches.
Author: O. Axelsson
Publisher: Elsevier
ISBN: 0080871585
Category : Mathematics
Languages : en
Pages : 399
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Book Description
Analytical and Numerical Approaches to Asymptotic Problems in Analysis
Author: C. Vidal
Publisher: Springer Science & Business Media
ISBN: 3642701965
Category : Science
Languages : en
Pages : 260
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Book Description
Markedly apart from elementary particle physics, another current has been building up and cont i nuous ly growi ng within contemporary phys i cs for severa 1 decades, and even expanding into many other disciplines, especially chemistry, biology and, quite recently, economics. Several reasons account for this: presumably the most impor tant one lies in the fact that, whatever the specific problem, model or material concerned, the same basic mathematical features are always involved. In this way, a general phenomenology has emerged which, unlike thermodynamics, is no longer depen dent upon the details or specifics: what largely prevails is the nonlinear charac ter of the underlying dynamics. Perhaps we are witnessing the emergence of a "non linear physics"--In a way similar to the birth of "quantum physics" in the twen ties - a physics which deals with the general behaviour of systems, whatever they are or may be. Over the past fifteen years, chemical systems evolving sufficiently far from equilibrium have proved to be particularly well fitted to experimental research on nonlinear behaviour: oscillation, multistability, birhythmicity, chaotic evolution, spatial self-organization and hysteresis are displayed by chemical reactions whose number is growing each year. In this volume are collected the lectures, communica tions and posters (abstracts) presented at an international meeting entitled: "Non-Equilibrium Dynamics in Chemical Systems", held in Bordeaux (France), Septem ber 3 rd-lth, 1984.
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 744
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Book Description
Author: Jun Miyazaki
Publisher: Elsevier Inc. Chapters
ISBN: 012806157X
Category : Medical
Languages : en
Pages : 34
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Book Description
In this chapter, temporal and spatial patterns observed in the Belousov–Zhabotinsky (BZ) reaction are described, which is a typical nonlinear chemical reaction system that exhibits oscillation and wave propagation. Some related phenomena in biological systems are presented. The underlying mechanism and modeling of oscillation based on chemical equations are then introduced. Reaction diffusion equations are derived and numerical simulations are performed based on the model to explain how the dynamical pattern appears. Finally, synchronous phenomena observed in the BZ reaction are described with an analytical method based on the phase model.
Author: Hermann Haken
Publisher: Springer Science & Business Media
ISBN: 364268808X
Category : Mathematics
Languages : en
Pages : 294
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Book Description
These proceedings contain the invited lectures presented at the International Sym posium on Synergetics at Schloss Elmau in April, 1982. This symposium marked the th 10 anniversary of symposia on synergetics, the first of which was held at Schloss Elmau in 1972. As is now weIl known, these symposia are devoted to the study of the formation of structures in physical systems far from thermal equilibrium, as weIl as in nonphysical systems such as those in biology and sociology. While the first proceedings were published by Teubner Publishing Company in 1973 and the second by North Holland Publishing Company in 1974, the subsequent proceed ings have been published in the Springer Series in Synergetics. I believe that these proceedings give a quite faithful picture of the developments in this new interdisciplinary field over the past decade. As H.J. Queisser recently noted, the prefix "non", which is used quite frequent ly in modern scientific literature in words such as "nonequilibrium", "nonlinear", etc., indicates a new development in scientific thinking. Indeed, this new develop ment was anticipated and given a framework in the introduction of "synergetics" more than a decade ago.
Author: Nicolas Giuseppone
Publisher: John Wiley & Sons
ISBN: 3527346155
Category : Science
Languages : en
Pages : 450
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Book Description
Out-of-Equilibrium (Supra)molecular Systems and Materials A must-have resource that covers everything from out-of-equilibrium chemical systems to active materials Out-of-Equilibrium (Supra)molecular Systems and Materials presents a comprehensive overview of the synthetic approaches that use molecular and supramolecular bonds in various out-of-equilibrium situations. With contributions from noted experts on the topic, the text contains information on the design of dissipative chemical systems that adapt their structures in space and time when fueled by an external source of energy. The contributors also examine molecules, nanoscale objects and materials that can produce mechanical work based on molecular machines. Additionally, the book explores living supramolecular polymers that can be trapped in kinetically stable states, as well as out-of-equilibrium chemical networks and oscillators that are important to understand the emergence of complex behaviors and, in particular, the origin of life. This important book: Offers comprehensive coverage of fields from design of out-of-equilibrium self-assemblies to molecular machines and active materials Presents information on a highly emerging and interdisciplinary topic Includes contributions from internationally renowned scientists Written for chemists, physical chemists, biochemists, material scientists, Out-of-Equilibrium (Supra)molecular Systems and Materials is an indispensable resource written by top scientists in the field.
Author: S Kai
Publisher: World Scientific
ISBN: 9814555339
Category :
Languages : en
Pages : 596
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Book Description
In this volume, the problems of pattern formation in physics, chemistry and other related fields in complex and nonlinear dissipative systems are studied. Main subjects discussed are formation mechanisms, properties, statistics, characterization and dynamics of periodic and nonperiodic patterns in the electrohydrodynamics in liquid crystals, Rayleigh-Benard convection, crystallization, viscous fingering and Belouzov-Zhabotinsky chemical reaction. Recent developments in topological and defect-mediated chaos, chaos in systems with large degrees of freedom and turbulence-turbulence transitions are also discussed.
