Transformation Methods for Nonlinear Partial Differential Equations

Edelen, D. G. B.: Isovector Methods for Equations of Balance, Sijthoff & Noordhoff, Alphen aan den Rijn, The Netherlands, 1980. . Edelen, D. G. B.: Isovector fields for problems in the mechanics of solids and fluids, Int. J. Engng. Sci.


Author: Dominic G B Edelen

Publisher: World Scientific

ISBN: 9789814505680

Category: Science

Page: 340

View: 527

The purpose of the book is to provide research workers in applied mathematics, physics, and engineering with practical geometric methods for solving systems of nonlinear partial differential equations. The first two chapters provide an introduction to the more or less classical results of Lie dealing with symmetries and similarity solutions. The results, however, are presented in the context of contact manifolds rather than the usual jet bundle formulation and provide a number of new conclusions. The remaining three chapters present essentially new methods of solution that are based on recent publications of the authors'. The text contains numerous fully worked examples so that the reader can fully appreciate the power and scope of the new methods. In effect, the problem of solving systems of nonlinear partial differential equations is reduced to the problem of solving families of autonomous ordinary differential equations. This allows the graphs of solutions of the system of partial differential equations to be realized as certain leaves of a foliation of an appropriately defined contact manifold. In fact, it is often possible to obtain families of solutions whose graphs foliate an open subset of the contact manifold. These ideas are extended in the final chapter by developing the theory of transformations that map a foliation of a contact manifold onto a foliation. This analysis gives rise to results of surprising depth and practical significance. In particular, an extended Hamilton-Jacobi method for solving systems of partial differential equations is obtained. Contents:ForwardContact Manifolds, Ideals and Partial Differential EquationsAn Order Independent Method of CharacteristicsHorizontal Ideals, Foliations, and SolutionsPrimitive Integrals, Isovectors and ResolutionsExtended Canonical TransformationsAppendix A: An Alternative Treatment of Extended Canonical TransformationsAppendix B: Multiple Integral Variational ProblemsReferencesIndex Readership: Applied mathematicians, physicists and engineers. keywords:Bäcklund Theorem;Classical Symmetry;Similarity Methods;Contact Manifolds of Finite Order;Systems of Cartan Annihilating Vector Fields;Extended Canonical Transformations;Korteweg-De Vries Equation;Klein-Gordon;Sine-Gordon;Liouville;Monge-Ampère;Navier-Stokes Equations

The Breadth and Depth of Continuum Mechanics

Suppose that the original balance system consisted of laws of conservation; that is F = F = 0. ... EDELEN, D. G. B., Isovector Methods for Equations of Balance (Sijthoff and Noordhoff, Alphen aan den Rijn, The Netherlands, 1980). 3.


Author: Constantine M. Dafermos

Publisher: Springer Science & Business Media

ISBN: 9783642616341

Category: Science

Page: 778

View: 866

This volume collects papers dedicated to Jerry Ericksen on his sixtieth birthday, December 20, 1984. They first appeared in Volumes 82-90 (1983-1985) of the Archive for Rational Mechanics and Analysis. At the request of the Editors the list of authors to be invited was drawn up by C. M. Dafermos, D. D. Joseph, and F. M. Leslie. The breadth and depth of the works here reprinted reflect the corresponding qualities in Jerry Ericksen's research, teaching, scholarship, and inspiration. His interests and expertness center upon the mechanics of materials and extend to everything that may contribute to it: pure analysis, algebra, geometry, through all aspects of theoretical mechanics to fundamental experiment, all of these illumi nated by an intimate and deep familiarity with the sources, even very old ones. He is independent of school and contemptuous of party spirit; his generosity in giving away his ideas is renowned, but not everyone is capable of accepting what is offered. His writings are totally free of broad claims and attributions beyond his own study. Some are decisive, some are prophetic, and all are forthright. His work has served as a beacon of insight and simple honesty in an age of ever more trivial and corrupt science. The authors of the memoirs in this volume are his students, colleagues, admirers, and (above all) his friends.

Differential Geometric Methods in Mathematical Physics

[ 10 ] Edelen , D.G.B. , Isovector Methods for Equations of Balance , Sijthoff and Noordhoff , 1980 . [ 11 ] Flato , M. , Pinczon , G. , and Simon , J. , Nonlinear representations of Lie groups , Ann . Sci . Ec . Norm . Sup .


Author: S. Sternberg

Publisher: Springer Science & Business Media

ISBN: 1402003412

Category: Science

Page: 296

View: 563

The following pages represent the Proceedings of the XI Annual Conference on Differential Geometric Methods in Mathematical Physics which was held in Jerusalem from August 5 through 11, 1982 under the auspices of the Tel Aviv University and the Israel Academy of Sciences and Humanities. In addition to the above mentioned institutions, partial financial support was received form the Bank Leumi Lelsrael Fund for International Conferences, the American Friends of the Tel Aviv Institute of Mathematical Sciences and the Mathematics and Physics Branch of the United States Army Research, Development and Standardization Group (UK). We are grateful to all of these organizations for their financial support. GAUGE THEORY AND NUCLEAR STRUCTURE K. Bleuler Institut fur Theoretische Kernphysik der Universitat Bonn NuBallee 14-16, D-5300 Bonn, West-Germany I. INTRODUCTION The recent, most impressive verification of the Salam­ -Weinberg theory of electro-weak interactions through the experimental discovery of the so-called inter­ mediate bosons represents, at the same time, a success of the general gauge theoretical viewpoints in modern particle physics (quantum chromodynamics, 0CD). This theory leads to a deeper and by far more natural inter­ pretation of particle interaction and induces, as we shall see, also a profound change in our understanding of nuclear structure.

Symmetries of Partial Differential Equations

Edelen, D. G. B.: Isovector Methods for Equations of Balance, Sijthoff & Nordhoff, Alphen a/d Rijn, 1981. . Gragert, P. K. H., Kersten, P. H. M., and Martini, R.: Symbolic computations in applied differential geometry, Acta Appl. Math.


Author: A.M. Vinogradov

Publisher: Springer Science & Business Media

ISBN: 9789400919488

Category: Mathematics

Page: 456

View: 854

2 The authors of these issues involve not only mathematicians, but also speci alists in (mathematical) physics and computer sciences. So here the reader will find different points of view and approaches to the considered field. A. M. VINOGRADOV 3 Acta Applicandae Mathematicae 15: 3-21, 1989. © 1989 Kluwer Academic Publishers. Symmetries and Conservation Laws of Partial Differential Equations: Basic Notions and Results A. M. VINOORADOV Department of Mathematics, Moscow State University, 117234, Moscow, U. S. S. R. (Received: 22 August 1988) Abstract. The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed. AMS subject classifications (1980). 35A30, 58005, 58035, 58H05. Key words. Higher symmetries, conservation laws, partial differential equations, infinitely prolonged equations, generating functions. o. Introduction In this paper we present the basic notions and results from the general theory of local symmetries and conservation laws of partial differential equations. More exactly, we will focus our attention on the main conceptual points as well as on the problem of how to find all higher symmetries and conservation laws for a given system of partial differential equations. Also, some general views and perspectives will be discussed.

Applications of Lie Groups to Differential Equations

Isovector Methods for Equations of Balance, Sijthoff and Noordhoff, Germantown, Md., 1980. Ehresmann, C. 1. Les prolongements d'une variété différentiable, C.R. Acad. Sci. Paris 233 (1951), 598–600, 777-779, 1081–1083; 234 (1952), ...


Author: Peter J. Olver

Publisher: Springer Science & Business Media

ISBN: 9781468402742

Category: Mathematics

Page: 497

View: 731

This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Fluid Mechanics of Mixing

Modelling, Operations and Experimental Techniques R. King ... With Application to Finite Element Methods and Other Problems. 1979 ISBN 90-286-0.008-6 5. D.G.B. Edelen: Isovector Methods for Equations of Balance.


Author: R. King

Publisher: Springer Science & Business Media

ISBN: 9789401579735

Category: Science

Page: 269

View: 204

This volume is a selection of the material presented at the 7th European Mixing Congress. It is concerned exclusively with mixing in circular section vessels, using centrally mounted paddles or similar impellers. The contents are arranged under three classifications: Modelling of Mixing Processes, Mixing Operations and Experimental Techniques. The classifications result in the original material appearing in a different order to that of the Congress. This arrangement is intended to assist the reader in identifying the topic area by function or application, rather than by technology. In this book the section on Modelling contains papers which focus on the representation of the mixing process, whether by equation, scale-up criteria, or fluid dynamic simulation. Similarly, Mixing Operations are concerned with the application or function of the mixing process, such as mass transfer, heat transfer or mixing time. Experimental Techniques addresses the tools the researcher needs to use at the data gathering experimental stage. It collects together advances made in the various methods used by some of the foremost researchers, and indicates those areas still in need of additional instrumentation or methods of data reduction. The book is intended for researchers, designers and users of mixing equipment, and for those planning research and development programmes and who wish to keep up to date with advances in the basic technology and its applications.

Solution of Crack Problems

The Distributed Dislocation Technique D.A. Hills, P.A. Kelly, D.N. Dai, A.M. Korsunsky ... With Application to Finite Element Methods and Other Problems. ... D.G.B. Edelen: Isovector Methods for Equations of Balance.


Author: D.A. Hills

Publisher: Springer Science & Business Media

ISBN: 9789401586481

Category: Science

Page: 308

View: 584

This book is concerned with the numerical solution of crack problems. The techniques to be developed are particularly appropriate when cracks are relatively short, and are growing in the neighbourhood of some stress raising feature, causing a relatively steep stress gradient. It is therefore practicable to represent the geometry in an idealised way, so that a precise solution may be obtained. This contrasts with, say, the finite element method in which the geometry is modelled exactly, but the subsequent solution is approximate, and computationally more taxing. The family of techniques presented in this book, based loosely on the pioneering work of Eshelby in the late 1950's, and developed by Erdogan, Keer, Mura and many others cited in the text, present an attractive alternative. The basic idea is to use the superposition of the stress field present in the unfiawed body, together with an unknown distribution of 'strain nuclei' (in this book, the strain nucleus employed is the dislocation), chosen so that the crack faces become traction-free. The solution used for the stress field for the nucleus is chosen so that other boundary conditions are satisfied. The technique is therefore efficient, and may be used to model the evolution of a developing crack in two or three dimensions. Solution techniques are described in some detail, and the book should be readily accessible to most engineers, whilst preserving the rigour demanded by the researcher who wishes to develop the method itself.

Progress in Structural Engineering

D.G.B. Edelen: Isovector Methods for Equations of Balance. With Programs for Computer Assistance in Operator Calculations and an Exposition of Practical Topics of the Exterior Calculus. 1980 ISBN 90-286-0420-0 6.


Author: Donald E. Grierson

Publisher: Springer Science & Business Media

ISBN: 9789401136167

Category: Technology & Engineering

Page: 573

View: 556

We three editors of this volume are former Ph. D. students of Professor Mircea Cohn at the University of Waterloo, Canada. Donald Grierson obtained his Ph. D. degree in 1968, Alberto Franchi in 1977, and Paolo Riva in 1988, and as such, we span almost the entire career of Professor Cohn at Waterloo. Even though we graduated during different decades in his life, we share similar views of Mircea Cohn as an educator, researcher and man. Together we recall that he was very firm in his resolve that we get the most out of the education he was facilitating for us. Together we agree that he was inspirational in his desire to have us carry out the very best research work we were capable of. Together we feel particularly fortunate to have had such a dedicated and distinguished individual as Professor Cohn as our Ph. D. research advisor. It is with great pleasure that we ack nowledge him as our mentor and friend. We began in 1989 to plan this volume as a tribute to Professor Cohn on the occasion of his 65th birthday in 1991. Upon contacting his many former students and research associates from around the world, we were not surprised to find that they too shared our feelings of respect and admiration for Mircea Cohn as an educator, researcher and man.

Finite Element Analysis of Composite Laminates

D.G.B. Edelen: Isovector Methods for Equations of Balance. With Programs for Computer Assistance in Operator Calculations and an Exposition of Practical Topics of the Exterior Calculus. 1980 ISBN 90-286-0420-0 6.


Author: O.O. Ochoa

Publisher: Springer Science & Business Media

ISBN: 9789401579957

Category: Science

Page: 213

View: 807

Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and Iaminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in Chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses, and sample examples of laminated plates in bending and vibration are discussed. Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.