Mathematical Aspects Of Reacting And Diffusing Systems

Author : P. C. Fife
Publisher : Springer Science & Business Media
Page : 192 pages
File Size : 55,9 Mb
Release : 2013-03-08
Category : Mathematics
ISBN : 9783642931116

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Mathematical Aspects of Reacting and Diffusing Systems by P. C. Fife Pdf

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.

Author : Paul C. Fife
Publisher : Unknown
Page : 185 pages
File Size : 52,7 Mb
Release : 1979
Category : Biology
ISBN : 0387091173

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Lecture Notes in Biomathematics by Paul C. Fife Pdf

Author : Gabriela Caristi
Publisher : CRC Press
Page : 428 pages
File Size : 46,9 Mb
Release : 2020-10-07
Category : Mathematics
ISBN : 9781000117196

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Reaction Diffusion Systems by Gabriela Caristi Pdf

"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."

Author : Andreas Liehr
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 41,9 Mb
Release : 2013-03-27
Category : Science
ISBN : 9783642312519

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Dissipative Solitons in Reaction Diffusion Systems by Andreas Liehr Pdf

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.

Author : Péter Érdi,János Tóth
Publisher : Manchester University Press
Page : 296 pages
File Size : 50,7 Mb
Release : 1989
Category : Chemical reactions
ISBN : 0719022088

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Mathematical Models of Chemical Reactions by Péter Érdi,János Tóth Pdf

Author : János Tóth,Attila László Nagy,Dávid Papp
Publisher : Springer
Page : 469 pages
File Size : 48,5 Mb
Release : 2018-09-18
Category : Science
ISBN : 9781493986439

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Reaction Kinetics: Exercises, Programs and Theorems by János Tóth,Attila László Nagy,Dávid Papp Pdf

Fifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.

Author : Yihong Du,Hitoshi Ishii,Wei-Yueh Lin
Publisher : World Scientific
Page : 373 pages
File Size : 53,6 Mb
Release : 2009
Category : Mathematics
ISBN : 9789812834737

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Recent Progress on Reaction-diffusion Systems and Viscosity Solutions by Yihong Du,Hitoshi Ishii,Wei-Yueh Lin Pdf

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 (Waseda), N Ishimura (Japan), Shigeaki Koike (Japan), Chu-Pin Lo (Taiwan), Peter Polacik (Minnesota), Kunimochi Sakamoto (Hiroshima), Richard Tsai (Texas), Mingxin Wang (China), Yoshio Yamada (Waseda), Eiji Yanagida (Tohoku), and Xiao-Qiang Zhao (Canada).

Author : J.A. Leach,D.J. Needham
Publisher : Springer Science & Business Media
Page : 290 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780857293961

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Matched Asymptotic Expansions in Reaction-Diffusion Theory by J.A. Leach,D.J. Needham Pdf

This volume contains a wealth of results and methodologies applicable to a wide range of problems arising in reaction-diffusion theory. It can be viewed both as a handbook, and as a detailed description of the methodology. The authors present new methods based on matched asymptotic expansions.

Author : Roman Cherniha,Mykola Serov,Oleksii Pliukhin
Publisher : CRC Press
Page : 244 pages
File Size : 48,8 Mb
Release : 2017-11-02
Category : Mathematics
ISBN : 9781351650878

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Nonlinear Reaction-Diffusion-Convection Equations by Roman Cherniha,Mykola Serov,Oleksii Pliukhin Pdf

It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.

Author : Robert Stephen Cantrell,Chris Cosner
Publisher : John Wiley & Sons
Page : 428 pages
File Size : 42,9 Mb
Release : 2004-01-09
Category : Mathematics
ISBN : 9780470871287

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Spatial Ecology via Reaction-Diffusion Equations by Robert Stephen Cantrell,Chris Cosner Pdf

Many ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models. * Rapidly expanding area of research for biologists and applied mathematicians * Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models * Provides the reader with the tools needed to construct and interpret models * Offers specific applications of both the models and the methods * Authors have played a dominant role in the field for years Essential reading for graduate students and researchers working with spatial modelling from mathematics, statistics, ecology, geography and biology.

Author : Joel Smoller
Publisher : Springer
Page : 618 pages
File Size : 47,5 Mb
Release : 1983-01-31
Category : Mathematics
ISBN : UOM:39015016355649

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Shock Waves and Reaction—Diffusion Equations by Joel Smoller Pdf

The purpose of this book is to make easily available the basics of the theory of hyperbolic conservation laws and the theory of systems of reaction-diffusion equations, including the generalized Morse theory as developed by Charles Conley. It presents the modern ideas in these fields in a way that is accessible to a wider audience than just mathematicians.The book is divided into four main parts: linear theory, reaction-diffusion equations, shock-wave theory, and the Conley index. For the second edition numerous typographical errors and other mistakes have been corrected and a new chapter on recent results has been added. The new chapter contains discussions of the stability of traveling waves, symmetry-breaking bifurcations, compensated compactness, viscous profiles for shock waves, and general notions for construction traveling-wave solutions for systems of nonlinear equations.

Author : Warren E. Stewart,W. Harmon Ray,Charles C. Conley
Publisher : Academic Press
Page : 426 pages
File Size : 40,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262062

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Dynamics and Modelling of Reactive Systems by Warren E. Stewart,W. Harmon Ray,Charles C. Conley Pdf

Dynamics and Modelling of Reactive Systems contains the proceedings of the Advanced Seminar on Dynamics and Modeling of Reactive Systems, held at the University of Wisconsin on October 1979. The book presents papers that assess the level of understanding of the dynamics of chemically reacting systems. The topics discussed include the hierarchies of models in reactive systems; model reduction of chemically reacting systems; and some consequences of nonlinearity in the diffusion process. Time-periodic and spatially irregular patterns; important aspects in simulating the dynamics of aerosols; and the diffusion and reaction in carbon burning are covered as well. Engineers and applied mathematicians will find the book highly insightful.

Author : James D. Murray
Publisher : Springer Science & Business Media
Page : 783 pages
File Size : 41,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662085424

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Mathematical Biology by James D. Murray Pdf

Mathematics has always benefited from its involvement with developing sciences. Each successive interaction revitalises and enhances the field. Biomedical science is clearly the premier science of the foreseeable future. For the continuing health of their subject mathematicians must become involved with biology. With the example of how mathematics has benefited from and influenced physics, it is clear that if mathematicians do not become involved in the biosciences they will simply not be a part of what are likely to be the most important and exciting scientific discoveries of all time. Mathematical biology is a fast growing, well recognised, albeit not clearly defined, subject and is, to my mind, the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biol ogy becomes more quantitative. The complexity of the biological sciences makes interdisciplinary involvement essential. For the mathematician, biology opens up new and exciting branches while for the biologist mathematical modelling offers another research tool commmensurate with a new powerful laboratory technique but only if used appropriately and its limitations recognised. However, the use of esoteric mathematics arrogantly applied to biological problems by mathemati cians who know little about the real biology, together with unsubstantiated claims as to how important such theories are, does little to promote the interdisciplinary involvement which is so essential. Mathematical biology research, to be useful and interesting, must be relevant biologically.

Author : Peter Grindrod
Publisher : Oxford University Press, USA
Page : 264 pages
File Size : 47,8 Mb
Release : 1991
Category : Mathematics
ISBN : STANFORD:36105002077340

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Patterns and Waves by Peter Grindrod Pdf

Author : Arthur T. Winfree
Publisher : Springer Science & Business Media
Page : 543 pages
File Size : 52,9 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662224922

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The Geometry of Biological Time by Arthur T. Winfree Pdf

As 1 review these pages, the last of them written in Summer 1978, some retrospec tive thoughts come to mind which put the whole business into better perspective for me and might aid the prospective reader in choosing how to approach this volume. The most conspicuous thought in my mind at present is the diversity of wholly independent explorations that came upon phase singularities, in one guise or another, during the past decade. My efforts to gather the published literature during the last phases of actually writing a whole book about them were almost equally divided between libraries of Biology, Chemistry, Engineering, Mathematics, Medicine, and Physics. A lot of what 1 call "gathering " was done somewhat in anticipation in the form of cönjecture, query, and prediction based on analogy between developments in different fields. The consequence throughout 1979 was that our long-suffering publisher re peatedly had to replace such material by citation of unexpected flurries of papers giving substantive demonstration. 1 trust that the authors of these many excellent reports, and especially of those I only found too late, will forgive the brevity of allusion I feIt compelled to observe in these substitutions. A residue of loose ends is largely collected in the index under "QUERIES. " It is c1ear to me already that the materials I began to gather several years ago represented only the first flickering of what turns out to be a substantial conflagration.