Patterns And Dynamics In Reactive Media

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Patterns and Dynamics in Reactive Media

Author : Rutherford Aris
Publisher : Springer Science & Business Media
ISBN 13 : 1461232066
Total Pages : 211 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Patterns and Dynamics in Reactive Media by : Rutherford Aris

Download or read book Patterns and Dynamics in Reactive Media written by Rutherford Aris and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ever since the seminal works on traveling waves and morphogenesis by Fisher, by Kolmogorov, Petrovski and Piscunov, and by Turing, scientists from many disciplines have been fascinated by questions concerning the formation of steady or dynamic patterns in reactive media. Contributions to this volume have been made by chemists, chemical engineers, mathematicians (both pure and applied), and physicists. The topics covered range from reports of experimental studies, through descriptions of numerical experiments, to rather abstract theoretical investigations, each exhibiting different aspects of a very diverse field.

Foundations of Synergetics I

Author : Alexander S. Mikhailov
Publisher : Springer Science & Business Media
ISBN 13 : 3642785565
Total Pages : 198 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Foundations of Synergetics I by : Alexander S. Mikhailov

Download or read book Foundations of Synergetics I written by Alexander S. Mikhailov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to the mathematical theory of cooperative behavior in active systems of various origins, both natural and artificial. It is based on a lecture course in synergetics which I held for almost ten years at the University of Moscow. The first volume deals mainly with the problems of pattern fonnation and the properties of self-organized regular patterns in distributed active systems. It also contains a discussion of distributed analog information processing which is based on the cooperative dynamics of active systems. The second volume is devoted to the stochastic aspects of self-organization and the properties of self-established chaos. I have tried to avoid delving into particular applications. The primary intention is to present general mathematical models that describe the principal kinds of coopera tive behavior in distributed active systems. Simple examples, ranging from chemical physics to economics, serve only as illustrations of the typical context in which a particular model can apply. The manner of exposition is more in the tradition of theoretical physics than of in mathematics: Elaborate fonnal proofs and rigorous estimates are often replaced the text by arguments based on an intuitive understanding of the relevant models. Because of the interdisciplinary nature of this book, its readers might well come from very diverse fields of endeavor. It was therefore desirable to minimize the re quired preliminary knowledge. Generally, a standard university course in differential calculus and linear algebra is sufficient.

Pattern Formation in Continuous and Coupled Systems

Author : Martin Golubitsky
Publisher : Springer Science & Business Media
ISBN 13 : 9780387988740
Total Pages : 354 pages
Book Rating : 4.9/5 (887 download)

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Book Synopsis Pattern Formation in Continuous and Coupled Systems by : Martin Golubitsky

Download or read book Pattern Formation in Continuous and Coupled Systems written by Martin Golubitsky and published by Springer Science & Business Media. This book was released on 1999-06-22 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems that generate new types of pattern such as discrete coupled systems, systems with global coupling, and combustion experiments were stressed, as were new types of pattern."--BOOK JACKET.

Mathematical Models for Biological Pattern Formation

Author : Philip K. Maini
Publisher : Springer Science & Business Media
ISBN 13 : 1461301335
Total Pages : 327 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematical Models for Biological Pattern Formation by : Philip K. Maini

Download or read book Mathematical Models for Biological Pattern Formation written by Philip K. Maini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

Dynamics of Algorithms

Author : Rafael de la Llave
Publisher : Springer Science & Business Media
ISBN 13 : 146121274X
Total Pages : 150 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Dynamics of Algorithms by : Rafael de la Llave

Download or read book Dynamics of Algorithms written by Rafael de la Llave and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles collected in this volume represent the contributions presented at the IMA workshop on "Dynamics of Algorithms" which took place in November 1997. The workshop was an integral part of the 1997 -98 IMA program on "Emerging Applications of Dynamical Systems." The interaction between algorithms and dynamical systems is mutually beneficial since dynamical methods can be used to study algorithms that are applied repeatedly. Convergence, asymptotic rates are indeed dynamical properties. On the other hand, the study of dynamical systems benefits enormously from having efficient algorithms to compute dynamical objects.

Hamiltonian Dynamical Systems

Author : H.S. Dumas
Publisher : Springer Science & Business Media
ISBN 13 : 9780387944371
Total Pages : 418 pages
Book Rating : 4.9/5 (443 download)

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Book Synopsis Hamiltonian Dynamical Systems by : H.S. Dumas

Download or read book Hamiltonian Dynamical Systems written by H.S. Dumas and published by Springer Science & Business Media. This book was released on 1995-03-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Chemomechanical Instabilities in Responsive Materials

Author : Pierre Borckmans
Publisher : Springer Science & Business Media
ISBN 13 : 9048129915
Total Pages : 282 pages
Book Rating : 4.0/5 (481 download)

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Book Synopsis Chemomechanical Instabilities in Responsive Materials by : Pierre Borckmans

Download or read book Chemomechanical Instabilities in Responsive Materials written by Pierre Borckmans and published by Springer Science & Business Media. This book was released on 2009-08-13 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume includes most of the material of the invited lectures delivered at the NATO Advanced Study Institute “Morphogenesis through the interplay of nonlinear chemical instabilities and elastic active media” held from 2th to 14th July 2007 at the Institut d’Etudes Scientifiques de Cargèse (http://www.iesc.univ-corse.fr/), in Corsica (France). This traditional place to organize Summer Schools and Workshops in a well equipped secluded location at the border of the Mediterranean sea has, over many years now, earned an increasing deserved reputation. Non-linear dynamics of non equilibrium systems has worked its way into a great number of fields and plays a key role in the understanding of se- organization and emergence phenomena in domains as diverse as chemical reactors, laser physics, fluid dynamics, electronic devices and biological morphogenesis. In the latter case, the viscoelastic properties of tissues are also known to play a key role. The control and formulation of soft responsive or “smart” materials has been a fast growing field of material science, specially in the area of po- mer networks, due to their growing applications in bio-science, chemical sensors, intelligent microfluidic devices, ... . Nature is an important p- vider of active materials whether at the level of tissues or at that of s- cellular structures. As a consequence, the fundamental understanding of the physical mechanisms at play in responsive materials also shines light in the understanding of biological artefacts.

Multiple-Time-Scale Dynamical Systems

Author : Christopher K.R.T. Jones
Publisher : Springer Science & Business Media
ISBN 13 : 1461301173
Total Pages : 278 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multiple-Time-Scale Dynamical Systems by : Christopher K.R.T. Jones

Download or read book Multiple-Time-Scale Dynamical Systems written by Christopher K.R.T. Jones and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Systems with sub-processes evolving on many different time scales are ubiquitous in applications: chemical reactions, electro-optical and neuro-biological systems, to name just a few. This volume contains papers that expose the state of the art in mathematical techniques for analyzing such systems. Recently developed geometric ideas are highlighted in this work that includes a theory of relaxation-oscillation phenomena in higher dimensional phase spaces. Subtle exponentially small effects result from singular perturbations implicit in certain multiple time scale systems. Their role in the slow motion of fronts, bifurcations, and jumping between invariant tori are all explored here. Neurobiology has played a particularly stimulating role in the development of these techniques and one paper is directed specifically at applying geometric singular perturbation theory to reveal the synchrony in networks of neural oscillators.

Nonlinear and Robust Control of PDE Systems

Author : Panagiotis D. Christofides
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641566
Total Pages : 278 pages
Book Rating : 4.6/5 (415 download)

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Book Synopsis Nonlinear and Robust Control of PDE Systems by : Panagiotis D. Christofides

Download or read book Nonlinear and Robust Control of PDE Systems written by Panagiotis D. Christofides and published by Springer Science & Business Media. This book was released on 2001-01-25 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The interest in control of nonlinear partial differential equation (PDE) sys tems has been triggered by the need to achieve tight distributed control of transport-reaction processes that exhibit highly nonlinear behavior and strong spatial variations. Drawing from recent advances in dynamics of PDE systems and nonlinear control theory, control of nonlinear PDEs has evolved into a very active research area of systems and control. This book the first of its kind- presents general methods for the synthesis of nonlinear and robust feedback controllers for broad classes of nonlinear PDE sys tems and illustrates their applications to transport-reaction processes of industrial interest. Specifically, our attention focuses on quasi-linear hyperbolic and parabolic PDE systems for which the manipulated inputs and measured and controlled outputs are distributed in space and bounded. We use geometric and Lyapunov-based control techniques to synthesize nonlinear and robust controllers that use a finite number of measurement sensors and control actuators to achieve stabilization of the closed-loop system, output track ing, and attenuation of the effect of model uncertainty. The controllers are successfully applied to numerous convection-reaction and diffusion-reaction processes, including a rapid thermal chemical vapor deposition reactor and a Czochralski crystal growth process. The book includes comparisons of the proposed nonlinear and robust control methods with other approaches and discussions of practical implementation issues.

Mathematical Modeling

Author : Rutherford Aris
Publisher : Elsevier
ISBN 13 : 0080511244
Total Pages : 503 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Mathematical Modeling by : Rutherford Aris

Download or read book Mathematical Modeling written by Rutherford Aris and published by Elsevier. This book was released on 1999-07-16 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical modeling is the art and craft of building a system of equations that is both sufficiently complex to do justice to physical reality and sufficiently simple to give real insight into the situation. Mathematical Modeling: A Chemical Engineer's Perspective provides an elementary introduction to the craft by one of the century's most distinguished practitioners. Though the book is written from a chemical engineering viewpoint, the principles and pitfalls are common to all mathematical modeling of physical systems. Seventeen of the author's frequently cited papers are reprinted to illustrate applications to convective diffusion, formal chemical kinetics, heat and mass transfer, and the philosophy of modeling. An essay of acknowledgments, asides, and footnotes captures personal reflections on academic life and personalities. Describes pitfalls as well as principles of mathematical modeling Presents twenty examples of engineering problems Features seventeen reprinted papers Presents personal reflections on some of the great natural philosophers Emphasizes modeling procedures that precede extensive calculations

Stochastic Chemical Reaction Systems in Biology

Author : Hong Qian
Publisher : Springer Nature
ISBN 13 : 3030862526
Total Pages : 364 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Stochastic Chemical Reaction Systems in Biology by : Hong Qian

Download or read book Stochastic Chemical Reaction Systems in Biology written by Hong Qian and published by Springer Nature. This book was released on 2021-10-18 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.

Multidimensional Hyperbolic Problems and Computations

Author : James Glimm
Publisher : Springer Science & Business Media
ISBN 13 : 1461391210
Total Pages : 399 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Multidimensional Hyperbolic Problems and Computations by : James Glimm

Download or read book Multidimensional Hyperbolic Problems and Computations written by James Glimm and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a variety of research fields connected with multidimensional hyperbolic problems. A vner Friedman Willard Miller PREFACE A primary goal of the IMA workshop on Multidimensional Hyperbolic Problems and Computations from April 3-14, 1989 was to emphasize the interdisciplinary nature of contemporary research in this field involving the combination of ideas from the theory of nonlinear partial differential equations, asymptotic methods, numerical computation, and experiments. The twenty-six papers in this volume span a wide cross-section of this research including some papers on the kinetic theory of gases and vortex sheets for incompressible flow in addition to many papers on systems of hyperbolic conservation laws. This volume includes several papers on asymptotic methods such as nonlinear geometric optics, a number of articles applying numerical algorithms such as higher order Godunov methods and front tracking to physical problems along with comparison to experimental data, and also several interesting papers on the rigorous mathematical theory of shock waves.

Computer Aided Proofs in Analysis

Author : Kenneth R. Meyer
Publisher : Springer Science & Business Media
ISBN 13 : 1461390923
Total Pages : 264 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Computer Aided Proofs in Analysis by : Kenneth R. Meyer

Download or read book Computer Aided Proofs in Analysis written by Kenneth R. Meyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications COMPUTER AIDED PROOFS IN ANALYSIS is based on the proceedings of an IMA Participating Institutions (PI) Conference held at the University of Cincinnati in April 1989. Each year the 19 Participating Institutions select, through a competitive process, several conferences proposals from the PIs, for partial funding. This conference brought together leading figures in a number of fields who were interested in finding exact answers to problems in analysis through computer methods. We thank Kenneth Meyer and Dieter Schmidt for organizing the meeting and editing the proceedings. A vner Friedman Willard Miller, Jr. PREFACE Since the dawn of the computer revolution the vast majority of scientific compu tation has dealt with finding approximate solutions of equations. However, during this time there has been a small cadre seeking precise solutions of equations and rigorous proofs of mathematical results. For example, number theory and combina torics have a long history of computer-assisted proofs; such methods are now well established in these fields. In analysis the use of computers to obtain exact results has been fragmented into several schools.

Mathematics in Industrial Problems

Author : Avner Friedman
Publisher : Springer Science & Business Media
ISBN 13 : 1461390982
Total Pages : 200 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Mathematics in Industrial Problems by : Avner Friedman

Download or read book Mathematics in Industrial Problems written by Avner Friedman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume in the series "Mathematics in Industrial Prob lems." The motivation for these volumes is to foster interaction between Industry and Mathematics at the "grass roots"; that is, at the level of spe cific problems. These problems come from Industry: they arise from models developed by the industrial scientists in ventures directed at the manufac ture of new or improved products. At the same time, these problems have the potential for mathematical challenge and novelty. To identify such problems, I have visited industries and had discussions with their scientists. Some of the scientists have subsequently presented their problems in the IMA seminar on Industrial Problems. The book is based on questions raised in the seminar and subsequent discussions. Each chapter is devoted to one of the talks and is self-contained. The chap ters usually provide references to the mathematical literature and a list of open problems which are of interest to the industrial scientists. For some problems partial solution is indicated briefly. The last chapter of the book contains a short description of solutions to some of the problems raised in the second volume, as well as references to papers in which such solutions have been published.

Advances in Chemical Engineering

Author :
Publisher : Academic Press
ISBN 13 : 9780080922928
Total Pages : 496 pages
Book Rating : 4.9/5 (229 download)

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Book Synopsis Advances in Chemical Engineering by :

Download or read book Advances in Chemical Engineering written by and published by Academic Press. This book was released on 2008-09-22 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cross-fertilization of physico-chemical and mathematical ideas has a long historical tradition. This volume of Advances in Chemical Engineering is almost completely dedicated to a conference on “Mathematics in Chemical Kinetics and Engineering (MaCKiE-2007), which was held in Houston in February 2007, bringing together about 40 mathematicians, chemists, and chemical engineers from 10 countries to discuss the application and development of mathematical tools in their respective fields. * Updates and informs the reader on the latest research findings using original reviews * Written by leading industry experts and scholars * Reviews and analyzes developments in the field

Solitons in Physics, Mathematics, and Nonlinear Optics

Author : Peter J. Olver
Publisher : Springer Science & Business Media
ISBN 13 : 1461390338
Total Pages : 220 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Solitons in Physics, Mathematics, and Nonlinear Optics by : Peter J. Olver

Download or read book Solitons in Physics, Mathematics, and Nonlinear Optics written by Peter J. Olver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications SOLITONS IN PHYSICS, MATHEMATICS, AND NONLINEAR OPTICS is based on the proceedings of two workshops which were an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshops focussed on the main parts of the theory of solitons and on the applications of solitons in physics, biology and engineering, with a special concentration on nonlinear optics. We thank the Coordinating Committee: James Glimm, Daniel Joseph, Barbara Keyfitz, An Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for drew planning and implementing the stimulating year-long program. We especially thank the Workshop Organizers for Solitons in Physics and Mathematics, Alan Newell, Peter Olver, and David Sattinger, and for Nonlinear Optics and Plasma Physics, David Kaup and Yuji Kodama for their efforts in bringing together many of the major figures in those research fields in which solitons in physics, mathematics, and nonlinear optics theories are used. A vner Friedman Willard Miller, Jr. PREFACE This volume includes some of the lectures given at two workshops, "Solitons in Physics and Mathematics" and "Solitons in Nonlinear Optics and Plasma Physics" held during the 1988-89 LM. A. year on Nonlinear Waves. Since their discovery by Kruskal and Zabusky in the early 1960's, solitons have had a profound impact on many fields, ranging from engineering and physics to algebraic geometry.

Nonlinear Evolution Equations That Change Type

Author : Barbara L. Keyfitz
Publisher : Springer Science & Business Media
ISBN 13 : 1461390494
Total Pages : 297 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Nonlinear Evolution Equations That Change Type by : Barbara L. Keyfitz

Download or read book Nonlinear Evolution Equations That Change Type written by Barbara L. Keyfitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications NONLINEAR EVOLUTION EQUATIONS THAT CHANGE TYPE is based on the proceedings of a workshop which was an integral part of the 1988-89 IMA program on NONLINEAR WAVES. The workshop focussed on prob lems of ill-posedness and change of type which arise in modeling flows in porous materials, viscoelastic fluids and solids and phase changes. We thank the Coordinat ing Committee: James Glimm, Daniel Joseph, Barbara Lee Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the workshop organizers, Barbara Lee Keyfitz and Michael Shearer, for their efforts in bringing together many of the major figures in those research fields in which theories for nonlinear evolution equations that change type are being developed. A vner Friedman Willard Miller, J r. ix PREFACE During the winter and spring quarters of the 1988/89 IMA Program on Non linear Waves, the issue of change of type in nonlinear partial differential equations appeared frequently. Discussion began with the January 1989 workshop on Two Phase Waves in Fluidized Beds, Sedimentation and Granular Flow; some of the papers in the proceedings of that workshop present strategies designed to avoid the appearance of change of type in models for multiphase fluid flow.