Download or read book Lectures on Viscoelasticity Theory written by Allen C. Pipkin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely de tailed explanation. Furthermore, much of the content of the course is in the prob lems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not given, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA~, 291(1962)) remains the best reference for proofs of theorems.

Download or read book Lectures on Viscoelasticity Theory written by A.C. Pipkin and published by Springer. This book was released on 2011-09-27 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains notes for a one-semester course on viscoelasticity given in the Division of Applied Mathematics at Brown University. The course serves as an introduction to viscoelasticity and as a workout in the use of various standard mathematical methods. The reader will soon find that he needs to do some work on the side to fill in details that are omitted from the text. These are notes, not a completely detailed explanation. Furthermore, much of the content of the course is in the problems assigned for solution by the student. The reader who does not at least try to solve a good many of the problems is likely to miss most of the point. Much that is known about viscoelasticity is not discussed in these notes, and references to original sources are usually not give, so it will be difficult or impossible to use this book as a reference for looking things up. Readers wanting something more like a treatise should see Ferry's Viscoelastic Properties of Polymers, Lodge's Elastic Liquids, the volumes edited by Eirich on Rheology, or any issue of the Transactions of the Society of Rheology. These works emphasize physical aspects of the subject. On the mathematical side, Gurtin and Sternberg's long paper On the Linear Theory of Viscoelasticity (ARMA II, 291 (I962» remains the best reference for proofs of theorems.

Download or read book Theory of Viscoelasticity written by Richard M. Christensen and published by Courier Corporation. This book was released on 2003-01-01 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integration of numerous theoretical developments offers a complete, consistent description of the linear theory of the viscoelastic behavior of materials. Relevant theoretical formulations are derived from a continuum mechanics viewpoint, followed by discussions of problem-solving techniques. "A welcome addition to the literature." — American Scientist. 29 figures. 1982 edition.

Download or read book The Phenomenological Theory of Linear Viscoelastic Behavior written by Nicholas W. Tschoegl and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the principal objects of theoretical research in any department of knowledge is to find the point of view from which the subject appears in its greatest simplicity. J. Willard Gibbs This book is an outgrowth of lectures I have given, on and off over some sixteen years, in graduate courses at the California Institute of Technology, and, in abbreviated form, elsewhere. It is, nevertheless, not meant to be a textbook. I have aimed at a full exposition of the phenomenological theory of linear viscoelastic behavior for the use of the practicing scientist or engineer as well as the academic teacher or student. The book is thus primarily a reference work. In accord with the motto above, I have chosen to describe the theory of linear viscoelastic behavior through the use of the Laplace transformation. The treatment oflinear time-dependent systems in terms of the Laplace transforms of the relations between the excitation add response variables has by now become commonplace in other fields. With some notable exceptions, it has not been widely used in viscoelasticity. I hope that the reader will find this approach useful.

Download or read book Applied Functional Analysis written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second part of an elementary textbook which combines linear functional analysis, nonlinear functional analysis, and their substantial applications. The book addresses undergraduates and beginning graduates of mathematics, physics, and engineering who want to learn how functional analysis elegantly solves mathematical problems which relate to our real world and which play an important role in the history of mathematics. The books approach is to attempt to determine the most important applications. These concern integral equations, differential equations, bifurcation theory, the moment problem, Cebysev approximation, the optimal control of rockets, game theory, symmetries and conservation laws, the quark model, and gauge theory in elementary particle physics. The presentation is self-contained and requires only that readers be familiar with some basic facts of calculus.

Download or read book Global Analysis in Mathematical Physics written by Yuri Gliklikh and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first edition of this book entitled Analysis on Riemannian Manifolds and Some Problems of Mathematical Physics was published by Voronezh Univer sity Press in 1989. For its English edition, the book has been substantially revised and expanded. In particular, new material has been added to Sections 19 and 20. I am grateful to Viktor L. Ginzburg for his hard work on the transla tion and for writing Appendix F, and to Tomasz Zastawniak for his numerous suggestions. My special thanks go to the referee for his valuable remarks on the theory of stochastic processes. Finally, I would like to acknowledge the support of the AMS fSU Aid Fund and the International Science Foundation (Grant NZBOOO), which made possible my work on some of the new results included in the English edition of the book. Voronezh, Russia Yuri Gliklikh September, 1995 Preface to the Russian Edition The present book is apparently the first in monographic literature in which a common treatment is given to three areas of global analysis previously consid ered quite distant from each other, namely, differential geometry and classical mechanics, stochastic differential geometry and statistical and quantum me chanics, and infinite-dimensional differential geometry of groups of diffeomor phisms and hydrodynamics. The unification of these topics under the cover of one book appears, however, quite natural, since the exposition is based on a geometrically invariant form of the Newton equation and its analogs taken as a fundamental law of motion.

Download or read book Analysis of Spherical Symmetries in Euclidean Spaces written by Claus Müller and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book offers a new and direct approach to the theories of special functions with emphasis on spherical symmetry in Euclidean spaces of arbitrary dimensions. Based on many years of lecturing to mathematicians, physicists and engineers in scientific research institutions in Europe and the USA, the author uses elementary concepts to present the spherical harmonics in a theory of invariants of the orthogonal group. One of the highlights is the extension of the classical results of the spherical harmonics into the complex - particularly important for the complexification of the Funk-Hecke formula which successfully leads to new integrals for Bessel- and Hankel functions with many applications of Fourier integrals and Radon transforms. Numerous exercises stimulate mathematical ingenuity and bridge the gap between well-known elementary results and their appearance in the new formations.

Download or read book Asymptotic Analysis written by J.D. Murray and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "A good introduction to a subject important for its capacity to circumvent theoretical and practical obstacles, and therefore particularly prized in the applications of mathematics. The book presents a balanced view of the methods and their usefulness: integrals on the real line and in the complex plane which arise in different contexts, and solutions of differential equations not expressible as integrals. Murray includes both historical remarks and references to sources or other more complete treatments. More useful as a guide for self-study than as a reference work, it is accessible to any upperclass mathematics undergraduate. Some exercises and a short bibliography included. Even with E.T. Copson's Asymptotic Expansions or N.G. de Bruijn's Asymptotic Methods in Analysis (1958), any academic library would do well to have this excellent introduction." (S. Puckette, University of the South) #Choice Sept. 1984#1

Download or read book Infinite Dimensional Dynamical Systems in Mechanics and Physics written by Roger Temam and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author presents the dynamical systems in infinite dimension, especially those generated by dissipative partial differential equations. This book attempts a systematic study of infinite dimensional dynamical systems generated by dissipative evolution partial differential equations arising in mechanics and physics and in other areas of sciences and technology. This second edition has been updated and extended.

Download or read book Configurational Forces as Basic Concepts of Continuum Physics written by Morton E. Gurtin and published by Springer Science & Business Media. This book was released on 2008-01-20 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Nonlinear Schr dinger Equation written by Catherine Sulem and published by Springer Science & Business Media. This book was released on 2007-06-30 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Multiple Scale and Singular Perturbation Methods written by J.K. Kevorkian and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Download or read book Analysis and Simulation of Chaotic Systems written by Frank C. Hoppensteadt and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Acoustic and Electromagnetic Equations written by Jean-Claude Nedelec and published by Springer Science & Business Media. This book was released on 2001-03-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acoustic and electromagnetic waves underlie a range of modern technology from sonar, radio, and television to microwave heating and electromagnetic compatibility analysis. This book, written by an international researcher, presents some of the research in a complete way. It is useful for graduate students in mathematics, physics, and engineering.

Download or read book Weakly Connected Neural Networks written by Frank C. Hoppensteadt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.

Download or read book Semigroups of Linear Operators and Applications to Partial Differential Equations written by Amnon Pazy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Download or read book Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations written by P. Constantin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work was initiated in the summer of 1985 while all of the authors were at the Center of Nonlinear Studies of the Los Alamos National Laboratory; it was then continued and polished while the authors were at Indiana Univer sity, at the University of Paris-Sud (Orsay), and again at Los Alamos in 1986 and 1987. Our aim was to present a direct geometric approach in the theory of inertial manifolds (global analogs of the unstable-center manifolds) for dissipative partial differential equations. This approach, based on Cauchy integral mani folds for which the solutions of the partial differential equations are the generating characteristic curves, has the advantage that it provides a sound basis for numerical Galerkin schemes obtained by approximating the inertial manifold. The work is self-contained and the prerequisites are at the level of a graduate student. The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.