Propagation of Waves in Reaction-diffusion Systems: Applications to Biology and Chemistry PDF Download
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Author: J. H. Merkin
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: J. H. Merkin
Publisher:
ISBN:
Category :
Languages : en
Pages : 84
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Book Description
Author: Arnaud Ducrot
Publisher: Editions Publibook
ISBN: 2748346319
Category : Differential operators
Languages : en
Pages : 119
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Book Description
Author: Bartosz A. Grzybowski
Publisher: John Wiley & Sons
ISBN: 9780470741634
Category : Technology & Engineering
Languages : en
Pages : 302
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Book Description
Change and motion define and constantly reshape the world around us, on scales from the molecular to the global. In particular, the subtle interplay between chemical reactions and molecular transport gives rise to an astounding richness of natural phenomena, and often manifests itself in the emergence of intricate spatial or temporal patterns. The underlying theme of this book is that by “setting chemistry in motion” in a proper way, it is not only possible to discover a variety of new phenomena, in which chemical reactions are coupled with diffusion, but also to build micro-/nanoarchitectures and systems of practical importance. Although reaction and diffusion (RD) processes are essential for the functioning of biological systems, there have been only a few examples of their application in modern micro- and nanotechnology. Part of the problem has been that RD phenomena are hard to bring under experimental control, especially when the system’s dimensions are small. Ultimately this book will guide the reader through all the aspects of these systems – from understanding the basics to practical hints and then to applications and interpretation of results. Topics covered include: An overview and outlook of both biological and man-made reaction-diffusion systems. The fundamentals and mathematics of diffusion and chemical reactions. Reaction-diffusion equations and the methods of solving them. Spatial control of reaction-diffusion at small scales. Micro- and nanofabrication by reaction-diffusion. Chemical clocks and periodic precipitation structures. Reaction-diffusion in soft materials and at solid interfaces. Microstructuring of solids using RD. Reaction-diffusion for chemical amplification and sensing. RD in three dimensions and at the nanoscale, including nanosynthesis. This book is aimed at all those who are interested in chemical processes at small scales, especially physical chemists, chemical engineers, and material scientists. The book can also be used for one-semester, graduate elective courses in chemical engineering, materials science, or chemistry classes.
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: University of Minnesota. Institute for Mathematics and Its Applications
Publisher:
ISBN:
Category :
Languages : en
Pages : 43
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Author: John Rinzel
Publisher:
ISBN:
Category :
Languages : en
Pages : 63
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Book Description
Consideration is given to a system of reaction diffusion equations which have qualitative significance for several applications including nerve conduction and distributed chemical/biochemical systems. These equations are of the FitzHugh-Nagumo type and contain three parameters. For certain ranges of the parameters the system exhibits two stable singular points. A singular perturbation construction is given to illustrate that there may exist both pulse type and transition type traveling waves. A complete, rigorous, description of which of these waves exist for a given set of parameters and how the velocities of the waves vary with the parameters is given for the case when the system has a piecewise linear nonlinearity. Numerical results of solutions to these equations are also presented. These calculations illustrate how waves are generated from initial data, how they interact during collisions, and how they are influenced by local disturbances and boundary conditions.
Author: Peter Grindrod
Publisher:
ISBN:
Category : Reaction-diffusion equations
Languages : en
Pages : 275
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Book Description
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: Franz Rothe
Publisher: Springer
ISBN: 9783662207000
Category : Science
Languages : en
Pages : 218
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Book Description
Author: V.A. Vasiliev
Publisher: Springer Science & Business Media
ISBN: 9400937512
Category : Mathematics
Languages : en
Pages : 265
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Book Description
Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).
