Asymptotic Methods For Relaxation Oscillations And Applications
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Asymptotic Methods For Relaxation Oscillations And Applications
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Author : Johan Grasman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Asymptotic Methods For Relaxation Oscillations And Applications written by Johan Grasman 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 Science categories.
In various fields of science, notably in physics and biology, one is con fronted with periodic phenomena having a remarkable temporal structure: it is as if certain systems are periodically reset in an initial state. A paper of Van der Pol in the Philosophical Magazine of 1926 started up the investigation of this highly nonlinear type of oscillation for which Van der Pol coined the name "relaxation oscillation". The study of relaxation oscillations requires a mathematical analysis which differs strongly from the well-known theory of almost linear oscillations. In this monograph the method of matched asymptotic expansions is employed to approximate the periodic orbit of a relaxation oscillator. As an introduction, in chapter 2 the asymptotic analysis of Van der Pol's equation is carried out in all detail. The problem exhibits all features characteristic for a relaxation oscillation. From this case study one may learn how to handle other or more generally formulated relaxation oscillations. In the survey special attention is given to biological and chemical relaxation oscillators. In chapter 2 a general definition of a relaxation oscillation is formulated.
Inverse Problems For Partial Differential Equations
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Author : Victor Isakov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Inverse Problems For Partial Differential Equations written by Victor Isakov 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 2013-06-29 with Mathematics categories.
This book describes the contemporary state of the theory and some numerical aspects of inverse problems in partial differential equations. The topic is of sub stantial and growing interest for many scientists and engineers, and accordingly to graduate students in these areas. Mathematically, these problems are relatively new and quite challenging due to the lack of conventional stability and to nonlinearity and nonconvexity. Applications include recovery of inclusions from anomalies of their gravitational fields; reconstruction of the interior of the human body from exterior electrical, ultrasonic, and magnetic measurements, recovery of interior structural parameters of detail of machines and of the underground from similar data (non-destructive evaluation); and locating flying or navigated objects from their acoustic or electromagnetic fields. Currently, there are hundreds of publica tions containing new and interesting results. A purpose of the book is to collect and present many of them in a readable and informative form. Rigorous proofs are presented whenever they are relatively short and can be demonstrated by quite general mathematical techniques. Also, we prefer to present results that from our point of view contain fresh and promising ideas. In some cases there is no com plete mathematical theory, so we give only available results. We do not assume that a reader possesses an enormous mathematical technique. In fact, a moderate knowledge of partial differential equations, of the Fourier transform, and of basic functional analysis will suffice.
Nonlinear Theory Of Shallow Shells
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Author : Iosif I. Vorovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08
Nonlinear Theory Of Shallow Shells written by Iosif I. Vorovich 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 2008-01-08 with Technology & Engineering categories.
This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.
Theory Of Multicomponent Fluids
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Author : Donald A. Drew
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-10
Theory Of Multicomponent Fluids written by Donald A. Drew 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 2006-05-10 with Mathematics categories.
In this book, we give a rational treatment of multicomponent materials as intera- ingcontinua.Weoffertwoderivationsoftheequationsofmotionfortheinteracting continua; one which uses the concepts of continua for the components, and one which applies an averaging operation to the continuum equations for each c- ponent. Arguments are given for constitutive equations appropriate for dispersed multicomponent ?ow. The forms of the constitutive equations are derived from the principles of continuum mechanics applied to the components and their int- actions. The solutions of problems of hydromechanics of ordinary continua are used as motivation for the forms of certain constitutive equations in multicom- nent materials. The balance of the book is devoted to the study of problems of hydrodynamics of multicomponent ?ows. Many materials are homogeneous in the sense that each part of the material has the same response to a given set of stimuli as all of the other parts. An example of such a material is pure water. Formulation of equations describing the behavior of homogeneous materials is well understood, and is described in numerous standard textbooks. Many other materials, both manufactured and occurring in nature, are not - mogeneous. Such materials are often given names such as mixtures or composites.
The Nonlinear Schr Dinger Equation
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Author : Catherine Sulem
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-30
The Nonlinear Schr Dinger Equation written by Catherine Sulem 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 2007-06-30 with Mathematics categories.
Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.
Configurational Forces As Basic Concepts Of Continuum Physics
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Author : Morton E. Gurtin
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-20
Configurational Forces As Basic Concepts Of Continuum Physics written by Morton E. Gurtin 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 2008-01-20 with Science categories.
For the last decade, the author has been working to extend continuum mechanics to treat moving boundaries in materials focusing, in particular, on problems of metallurgy. This monograph presents a rational treatment of the notion of configurational forces; it is an effort to promote a new viewpoint. Included is a presentation of configurational forces within a classical context and a discussion of their use in areas as diverse as phase transitions and fracture. The work should be of interest to materials scientists, mechanicians, and mathematicians.
Analysis And Simulation Of Chaotic Systems
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Author : Frank C. Hoppensteadt
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Analysis And Simulation Of Chaotic Systems written by Frank C. Hoppensteadt 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 2013-03-09 with Mathematics categories.
Analysis and Simulation of Chaotic Systems is a text designed to be used at the graduate level in applied mathematics for students from mathematics, engineering, physics, chemistry and biology. The book can be used as a stand-alone text for a full year course or it can be heavily supplemented with material of more mathematical, more engineering or more scientific nature. Computations and computer simulations are used throughout this text to illustrate phenomena discussed and to supply readers with probes to use on new problems.
Vorticity And Turbulence
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Author : Alexandre J. Chorin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Vorticity And Turbulence written by Alexandre J. Chorin 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 2013-12-01 with Mathematics categories.
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.
Weakly Connected Neural Networks
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Author : Frank C. Hoppensteadt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Weakly Connected Neural Networks written by Frank C. Hoppensteadt 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.
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all physiological attributes of the ith neuron, n is the number of neurons, Ii describes the dynam ics of the ith neuron, and gi describes the interactions between neurons. The small parameter € indicates the strength of connections between the neurons. Weakly connected systems have attracted much attention since the sec ond half of seventeenth century, when Christian Huygens noticed that a pair of pendulum clocks synchronize when they are attached to a light weight beam instead of a wall. The pair of clocks is among the first weakly connected systems to have been studied. Systems of the form (0.1) arise in formal perturbation theories developed by Poincare, Liapunov and Malkin, and in averaging theories developed by Bogoliubov and Mitropolsky.
Homogenization Of Reticulated Structures
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Author : Doina Cioranescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization Of Reticulated Structures written by Doina Cioranescu 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.
This book presents recent works on lattice type structure. Some of the results discussed here have already been published in mathematical journals, but we give here a comprehensive and unified presentation. We have also added some new topics such as those contained in Chapter 4 treating elastic problems for gridworks. The aim of this book is to give continuous simple models for thin reticulated structures (which may have a very complex pattern). This means that we have to treat partial differential equations depending on several small parameters and give the asymptotic behavior with respect to these parameters (which can be the period, the thickness of the material, or the thickness of a plate or of a beam). This book is written from the point of view of the applied mathematician, atten tion being paid to the mathematical rigor, convergence results, and error estimates. It consists of six chapters and more than a hundred figures. The basic ideas are presented in the first two chapters, while the four last ones study some particular models, using the ideas of Chapters 1 and 2. Chapter 1 is an introduction to homogenization methods in perforated domains. Here the parameter to be taken into consideration is the period. After describing the multiple-scale method (which consists in asymptotic expansions), we focus our attention on the variational method introduced by Tartar, whose main idea is the construction of rapidly oscillating test functions.