Download or read book Global Solutions of Reaction Diffusion Systems written by Franz Rothe and published by Springer. This book was released on 2006-12-08 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nonlinear Reaction Diffusion Systems written by Roman Cherniha and published by Springer. This book was released on 2017-09-18 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Shock Waves and Reaction Diffusion Equations written by Joel Smoller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Dissipative Solitons in Reaction Diffusion Systems written by Andreas Liehr and published by Springer Science & Business Media. This book was released on 2013-03-27 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why writing a book about a specialized task of the large topic of complex systems? And who will read it? The answer is simple: The fascination for a didactically valuable point of view, the elegance of a closed concept and the lack of a comprehensive disquisition. The fascinating part is that field equations can have localized solutions exhibiting the typical characteristics of particles. Regarding the field equations this book focuses on, the field phenomenon of localized solutions can be described in the context of a particle formalism, which leads to a set of ordinary differential equations covering the time evolution of the position and the velocity of each particle. Moreover, starting from these particle dynamics and making the transition to many body systems, one considers typical phenomena of many body systems as shock waves and phase transitions, which themselves can be described as field phenomena. Such transitions between different level of modelling are well known from conservative systems, where localized solutions of quantum field theory lead to the mechanisms of elementary particle interaction and from this to field equations describing the properties of matter. However, in dissipative systems such transitions have not been considered yet, which is adjusted by the presented book. The elegance of a closed concept starts with the observation of self-organized current filaments in a semiconductor gas discharge system. These filaments move on random paths and exhibit certain particle features like scattering or the formation of bound states. Neither the reasons for the propagation of the filaments nor the laws of the interaction between the filaments can be registered by direct observations. Therefore a model is established, which is phenomenological in the first instance due to the complexity of the experimental system. This model allows to understand the existence of localized structures, their mechanisms of movement, and their interaction, at least, on a qualitative level. But this model is also the starting point for developing a data analysis method that enables the detection of movement and interaction mechanisms of the investigated localized solutions. The topic is rounded of by applying the data analysis to real experimental data and comparing the experimental observations to the predictions of the model. A comprehensive publication covering the interesting topic of localized solutions in reaction diffusion systems in its width and its relation to the well known phenomena of spirals and patterns does not yet exist, and this is the third reason for writing this book. Although the book focuses on a specific experimental system the model equations are as simple as possible so that the discussed methods should be adaptable to a large class of systems showing particle-like structures. Therefore, this book should attract not only the experienced scientist, who is interested in self-organization phenomena, but also the student, who would like to understand the investigation of a complex system on the basis of a continuous description.

Download or read book Numerical Bifurcation Analysis for Reaction Diffusion Equations written by Zhen Mei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the first to provide readers with numerical tools for a systematic analysis of bifurcation problems in reaction-diffusion equations. Many examples and figures illustrate analysis of bifurcation scenario and implementation of numerical schemes. Readers will gain a thorough understanding of numerical bifurcation analysis and the necessary tools for investigating nonlinear phenomena in reaction-diffusion equations.

Download or read book Mathematical Aspects of Reacting and Diffusing Systems written by P. C. Fife and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling and analyzing the dynamics of chemical mixtures by means of differ- tial equations is one of the prime concerns of chemical engineering theorists. These equations often take the form of systems of nonlinear parabolic partial d- ferential equations, or reaction-diffusion equations, when there is diffusion of chemical substances involved. A good overview of this endeavor can be had by re- ing the two volumes by R. Aris (1975), who himself was one of the main contributors to the theory. Enthusiasm for the models developed has been shared by parts of the mathematical community, and these models have, in fact, provided motivation for some beautiful mathematical results. There are analogies between chemical reactors and certain biological systems. One such analogy is rather obvious: a single living organism is a dynamic structure built of molecules and ions, many of which react and diffuse. Other analogies are less obvious; for example, the electric potential of a membrane can diffuse like a chemical, and of course can interact with real chemical species (ions) which are transported through the membrane. These facts gave rise to Hodgkin's and Huxley's celebrated model for the propagation of nerve signals. On the level of populations, individuals interact and move about, and so it is not surprising that here, again, the simplest continuous space-time interaction-migration models have the same g- eral appearance as those for diffusing and reacting chemical systems.

Download or read book Chemistry in Motion written by Bartosz A. Grzybowski and published by John Wiley & Sons. This book was released on 2009-04-03 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book A Closer Look of Nonlinear Reaction Diffusion Equations written by Lakshmanan Rajendran and published by Nova Science Publishers. This book was released on 2020-10 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Stochastic Modelling of Reaction Diffusion Processes written by Radek Erban and published by Cambridge University Press. This book was released on 2020-01-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This practical introduction to stochastic reaction-diffusion modelling is based on courses taught at the University of Oxford. The authors discuss the essence of mathematical methods which appear (under different names) in a number of interdisciplinary scientific fields bridging mathematics and computations with biology and chemistry. The book can be used both for self-study and as a supporting text for advanced undergraduate or beginning graduate-level courses in applied mathematics. New mathematical approaches are explained using simple examples of biological models, which range in size from simulations of small biomolecules to groups of animals. The book starts with stochastic modelling of chemical reactions, introducing stochastic simulation algorithms and mathematical methods for analysis of stochastic models. Different stochastic spatio-temporal models are then studied, including models of diffusion and stochastic reaction-diffusion modelling. The methods covered include molecular dynamics, Brownian dynamics, velocity jump processes and compartment-based (lattice-based) models.

Download or read book Reaction Diffusion Systems written by Gabriela Caristi and published by CRC Press. This book was released on 2020-10-07 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."

Download or read book The Dynamics of Nonlinear Reaction Diffusion Equations with Small L vy Noise written by Arnaud Debussche and published by Springer. This book was released on 2013-10-01 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

Download or read book Reaction diffusion Equations and Their Applications to Biology written by N. F. Britton and published by . This book was released on 1986 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book IPython Interactive Computing and Visualization Cookbook written by Cyrille Rossant and published by Packt Publishing Ltd. This book was released on 2014-09-25 with total page 899 pages. Available in PDF, EPUB and Kindle. Book excerpt: Intended to anyone interested in numerical computing and data science: students, researchers, teachers, engineers, analysts, hobbyists... Basic knowledge of Python/NumPy is recommended. Some skills in mathematics will help you understand the theory behind the computational methods.

Download or read book Patterns and Waves written by Peter Grindrod and published by Oxford University Press, USA. This book was released on 1991 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book 2019 20 MATRIX Annals written by Jan de Gier and published by Springer Nature. This book was released on 2021-02-10 with total page 798 pages. Available in PDF, EPUB and Kindle. Book excerpt: MATRIX is Australia’s international and residential mathematical research institute. It facilitates new collaborations and mathematical advances through intensive residential research programs, each 1-4 weeks in duration. This book is a scientific record of the ten programs held at MATRIX in 2019 and the two programs held in January 2020: · Topology of Manifolds: Interactions Between High and Low Dimensions · Australian-German Workshop on Differential Geometry in the Large · Aperiodic Order meets Number Theory · Ergodic Theory, Diophantine Approximation and Related Topics · Influencing Public Health Policy with Data-informed Mathematical Models of Infectious Diseases · International Workshop on Spatial Statistics · Mathematics of Physiological Rhythms · Conservation Laws, Interfaces and Mixing · Structural Graph Theory Downunder · Tropical Geometry and Mirror Symmetry · Early Career Researchers Workshop on Geometric Analysis and PDEs · Harmonic Analysis and Dispersive PDEs: Problems and Progress The articles are grouped into peer-reviewed contributions and other contributions. The peer-reviewed articles present original results or reviews on a topic related to the MATRIX program; the remaining contributions are predominantly lecture notes or short articles based on talks or activities at MATRIX.

Download or read book Reaction Diffusion Computers written by Andrew Adamatzky and published by Elsevier. This book was released on 2005-10-05 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book introduces a hot topic of novel and emerging computing paradigms and architectures -computation by travelling waves in reaction-diffusion media. A reaction-diffusion computer is a massively parallel computing device, where the micro-volumes of the chemical medium act as elementary few-bit processors, and chemical species diffuse and react in parallel. In the reaction-diffusion computer both the data and the results of the computation are encoded as concentration profiles of the reagents, or local disturbances of concentrations, whilst the computation per se is performed via the spreading and interaction of waves caused by the local disturbances. The monograph brings together results of a decade-long study into designing experimental and simulated prototypes of reaction-diffusion computing devices for image processing, path planning, robot navigation, computational geometry, logics and artificial intelligence. The book is unique because it gives a comprehensive presentation of the theoretical and experimental foundations, and cutting-edge computation techniques, chemical laboratory experimental setups and hardware implementation technology employed in the development of novel nature-inspired computing devices. Key Features: - Non-classical and fresh approach to theory of computation. - In depth exploration of novel and emerging paradigms of nature-inspired computing. - Simple to understand cellular-automata models will help readers/students to design their own computational experiments to advance ideas and concepts described in the book . - Detailed description of receipts and experimental setups of chemical laboratory reaction-diffusion processors will make the book an invaluable resource in practical studies of non-classical and nature-inspired computing architectures . - Step by step explanations of VLSI reaction-diffusion circuits will help students to design their own types of wave-based processors.Key Features: - Non-classical and fresh approach to theory of computation. - In depth exploration of novel and emerging paradigms of nature-inspired computing. - Simple to understand cellular-automata models will help readers/students to design their own computational experiments to advance ideas and concepts described in the book . - Detailed description of receipts and experimental setups of chemical laboratory reaction-diffusion processors will make the book an invaluable resource in practical studies of non-classical and nature-inspired computing architectures . - Step by step explanations of VLSI reaction-diffusion circuits will help students to design their own types of wave-based processors.

Download or read book Recent Progress On Reaction diffusion Systems And Viscosity Solutions written by Yihong Du and published by World Scientific. This book was released on 2009-03-12 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of survey and research articles expanding on the theme of the “International Conference on Reaction-Diffusion Systems and Viscosity Solutions”, held at Providence University, Taiwan, during January 3-6, 2007. It is a carefully selected collection of articles representing the recent progress of some important areas of nonlinear partial differential equations. The book is aimed for researchers and postgraduate students who want to learn about or follow some of the current research topics in nonlinear partial differential equations. The contributors consist of international experts and some participants of the conference, including Nils Ackermann (Mexico), Chao-Nien Chen (Taiwan), Yihong Du (Australia), Alberto Farina (France), Hitoshi Ishii (Japan), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (USA), Kunimochi Sakamoto (Japan), Richard Tsai (USA), Mingxin Wang (China), Yoshio Yamada (Japan), Eiji Yanagida (Japan), and Xiao-Qiang Zhao (Canada).