Reaction Diffusion Systems
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Global Solutions Of Reaction Diffusion Systems
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Author : Franz Rothe
language : en
Publisher: Springer
Release Date : 2006-12-08
Global Solutions Of Reaction Diffusion Systems written by Franz Rothe and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Science categories.
Chemistry In Motion
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Author : Bartosz A. Grzybowski
language : en
Publisher: John Wiley & Sons
Release Date : 2009-04-03
Chemistry In Motion written by Bartosz A. Grzybowski and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Technology & Engineering categories.
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.
A Closer Look Of Nonlinear Reaction Diffusion Equations
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Author : L. Rajendran
language : en
Publisher: Nova Science Publishers
Release Date : 2020-08-26
A Closer Look Of Nonlinear Reaction Diffusion Equations written by L. Rajendran and has been published by Nova Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Reaction-diffusion equations categories.
By using mathematical models to describe the physical, biological or chemical phenomena, one of the most common results is either a differential equation or a system of differential equations, together with the correct boundary and initial conditions. The determination and interpretation of their solution are at the base of applied mathematics. Hence the analytical and numerical study of the differential equation is very much essential for all theoretical and experimental researchers, and this book helps to develop skills in this area.Recently non-linear differential equations were widely used to model many of the interesting and relevant phenomena found in many fields of science and technology on a mathematical basis. This problem is to inspire them in various fields such as economics, medical biology, plasma physics, particle physics, differential geometry, engineering, signal processing, electrochemistry and materials science.This book contains seven chapters and practical applications to the problems of the real world. The first chapter is specifically for those with limited mathematical background. Chapter one presents the introduction of non-linear reaction-diffusion systems, various boundary conditions and examples. Real-life application of non-linear reaction-diffusion in different fields with some important non-linear equations is also discussed. In Chapter 2, mathematical preliminaries and various advanced methods of solving non-linear differential equations such as Homotopy perturbation method, variational iteration method, exponential function method etc. are described with examples.Steady and non-steady state reaction-diffusion equations in the plane sheet (chapter 3), cylinder (chapter 4) and spherical (chapter 5) are analyzed. The analytical results published by various researchers in referred journals during 2007-2020 have been addressed in these chapters 4 to 6, and this leads to conclusions and recommendations on what approaches to use on non-linear reaction-diffusion equations.Convection-diffusion problems arise very often in applied sciences and engineering. Non-linear convection-diffusion equations and corresponding analytical solutions in various fields of chemical sciences are discussed in chapter6. Numerical methods are used to provide approximate results for the non-linear problems, and their importance is felt when it is impossible or difficult to solve a given problem analytically. Chapter 7 identifies some of the numerical methods for finding solutions to non-linear differential equations.
Shock Waves And Reaction Diffusion Equations
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Author : Joel Smoller
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shock Waves And Reaction Diffusion Equations written by Joel Smoller and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For this edition, a number of typographical errors and minor slip-ups have been corrected. In addition, following the persistent encouragement of Olga Oleinik, I have added a new chapter, Chapter 25, which I titled "Recent Results." This chapter is divided into four sections, and in these I have discussed what I consider to be some of the important developments which have come about since the writing of the first edition. Section I deals with reaction-diffusion equations, and in it are described both the work of C. Jones, on the stability of the travelling wave for the Fitz-Hugh-Nagumo equations, and symmetry-breaking bifurcations. Section II deals with some recent results in shock-wave theory. The main topics considered are L. Tartar's notion of compensated compactness, together with its application to pairs of conservation laws, and T.-P. Liu's work on the stability of viscous profiles for shock waves. In the next section, Conley's connection index and connection matrix are described; these general notions are useful in con structing travelling waves for systems of nonlinear equations. The final sec tion, Section IV, is devoted to the very recent results of C. Jones and R. Gardner, whereby they construct a general theory enabling them to locate the point spectrum of a wide class of linear operators which arise in stability problems for travelling waves. Their theory is general enough to be applica ble to many interesting reaction-diffusion systems.
Reaction Diffusion Systems
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Author : Gabriela Caristi
language : en
Publisher: CRC Press
Release Date : 1997-09-19
Reaction Diffusion Systems written by Gabriela Caristi and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-19 with Mathematics categories.
"Based on the proceedings of the International Conference on Reaction Diffusion Systems held recently at the University of Trieste, Italy. Presents new research papers and state-of-the-art surveys on the theory of elliptic, parabolic, and hyperbolic problems, and their related applications. Furnishes incisive contribution by over 40 mathematicians representing renowned institutions in North and South America, Europe, and the Middle East."
Reaction Diffusion And Solid State Chemical Kinetics
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Author : V.I. Dybkov
language : en
Publisher: Trans Tech Publications Ltd
Release Date : 2010-03-18
Reaction Diffusion And Solid State Chemical Kinetics written by V.I. Dybkov and has been published by Trans Tech Publications Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-03-18 with Technology & Engineering categories.
Volume is indexed by Thomson Reuters BCI (WoS). This monograph deals with a physico-chemical approach to the problem of the solid-state growth of chemical compound layers and reaction-diffusion in binary heterogeneous systems formed by two solids; as well as a solid with a liquid or a gas. It is explained why the number of compound layers growing at the interface between the original phases is usually much lower than the number of chemical compounds in the phase diagram of a given binary system. For example, of the eight intermetallic compounds which exist in the aluminium-zirconium binary system, only ZrAl3 was found to grow as a separate layer at the Al–Zr interface under isothermal conditions. The physico-chemical approach predicts that, in most cases, the number of compound layers should not exceed two; with the main factor, resulting in the appearance of additional layers, being crack formation due to thermal expansion and volume effects.
Nonlinear Reaction Diffusion Systems
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Author : Roman Cherniha
language : en
Publisher: Springer
Release Date : 2017-09-18
Nonlinear Reaction Diffusion Systems written by Roman Cherniha and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-18 with Mathematics categories.
This book presents several fundamental results in solving nonlinear reaction-diffusion equations and systems using symmetry-based methods. Reaction-diffusion systems are fundamental modeling tools for mathematical biology with applications to ecology, population dynamics, pattern formation, morphogenesis, enzymatic reactions and chemotaxis. The book discusses the properties of nonlinear reaction-diffusion systems, which are relevant for biological applications, from the symmetry point of view, providing rigorous definitions and constructive algorithms to search for conditional symmetry (a nontrivial generalization of the well-known Lie symmetry) of nonlinear reaction-diffusion systems. In order to present applications to population dynamics, it focuses mainly on two- and three-component diffusive Lotka-Volterra systems. While it is primarily a valuable guide for researchers working with reaction-diffusion systems and those developing the theoretical aspects of conditional symmetry conception, parts of the book can also be used in master’s level mathematical biology courses.
Reaction Diffusion Equations And Their Applications To Biology
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Author : N. F. Britton
language : en
Publisher:
Release Date : 1986
Reaction Diffusion Equations And Their Applications To Biology written by N. F. Britton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Science categories.
Although the book is largely self-contained, some knowledge of the mathematics of differential equations is necessary. Thus the book is intended for mathematicians who are interested in the application of their subject to the biological sciences and for biologists with some mathematical training. It is also suitable for postgraduate mathematics students and for undergraduate mathematicians taking a course in mathematical biology. Increasing use of mathematics in developmental biology, ecology, physiology, and many other areas in the biological sciences has produced a need for a complete, mathematical reference for laboratory practice. In this volume, biological scientists will find a rich resource of interesting applications and illustrations of various mathematical techniques that can be used to analyze reaction-diffusion systems. Concepts covered here include:**systems of ordinary differential equations**conservative systems**the scalar reaction-diffusion equation**analytic techniques for systems of parabolic partial differential equations**bifurcation theory**asymptotic methods for oscillatory systems**singular perturbations**macromolecular carriers -- asymptotic techniques.
Spatial Ecology
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Author : Stephen Cantrell
language : en
Publisher: CRC Press
Release Date : 2009-08-05
Spatial Ecology written by Stephen Cantrell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-05 with Mathematics categories.
Exploring the relationship between mathematics and ecology, Spatial Ecology focuses on some important emerging challenges in the field. These challenges consist of understanding the impact of space on community structure, incorporating the scale and structure of landscapes into mathematical models, and developing connections between spatial ecology