Stochastic Homogenization of Rate-dependent Models of Monotone Type in Plasticity PDF Download
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Author: Martin Heida
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatrick's function helps us to introduce and show the existence of the weak solutions for rate-dependent systems. The derivations of the homogenization results presented in this work are based on the stochastic two-scale convergence in Sobolev spaces. For completeness, we also present some two-scale homogenization results for convex functionals, which are related to the classical Gamma-convergence theory.
Author: Martin Heida
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatrick's function helps us to introduce and show the existence of the weak solutions for rate-dependent systems. The derivations of the homogenization results presented in this work are based on the stochastic two-scale convergence in Sobolev spaces. For completeness, we also present some two-scale homogenization results for convex functionals, which are related to the classical Gamma-convergence theory.
Author: G. Bard Ermentrout
Publisher: Springer Science & Business Media
ISBN: 0387877088
Category : Mathematics
Languages : en
Pages : 434
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Book Description
This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
Author: Barbara L. Keyfitz
Publisher: Springer Science & Business Media
ISBN: 1461390494
Category : Mathematics
Languages : en
Pages : 297
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Book Description
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.
Author: Ulrich Hornung
Publisher: Springer Science & Business Media
ISBN: 1461219205
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This book offers a systematic, rigorous treatment of upscaling procedures related to physical modeling for porous media on micro-, meso- and macro-scales, including detailed studies of micro-structure systems and computational results for dual-porosity models.
Author: Dieter Weichert
Publisher: Springer Science & Business Media
ISBN: 9781402003820
Category : Technology & Engineering
Languages : en
Pages : 400
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Book Description
The question whether a structure or a machine component can carry the applied loads, and with which margin of safety, or whether it will become unserviceable due to collapse or excessive inelastic deformations, has always been a major concern for civil and mechanical engineers. The development of methods to answer this technologically crucial question without analysing the evolution of the system under varying loads, has a long tradition that can be traced back even to the times of emerging mechanical sciences in the early 17th century. However, the scientific foundations of the theories underlying these methods, nowadays frequently called "direct", were established sporadically in the Thirties of the 20th century and systematically and rigorously in the Fifties. Further motivations for the development of direct analysis techniques in applied mechanics of solids and structures arise from the circumstance that in many engineering situations the external actions fluctuate according to time histories not a priori known except for some essential features, e.g. variation intervals. In such situations the critical events (or "limit states") to consider, besides plastic collapse, are incremental collapse (or "ratchetting") and alternating plastic yielding, namely lack of "shakedown". Non evolutionary, direct methods for ultimate limit state analysis of structures subjected to variably-repeated external actions are the objectives of most papers collected in this book, which also contains a few contributions on related topics.
Author: Siegfried Schmauder
Publisher: Springer
ISBN: 9789811068836
Category : Science
Languages : en
Pages : 0
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Book Description
This book provides a comprehensive reference for the studies of mechanical properties of materials over multiple length and time scales. The topics include nanomechanics, micromechanics, continuum mechanics, mechanical property measurements, and materials design. The handbook employs a consistent and systematic approach offering readers a user friendly reference ideal for frequent consultation. It is appropriate for an audience at of graduate students, faculties, researchers, and professionals in the fields of Materials Science, Mechanical Engineering, Civil Engineering, Engineering Mechanics, and Aerospace Engineering.
Author: Augusto Visintin
Publisher: Springer Science & Business Media
ISBN: 1461240786
Category : Mathematics
Languages : en
Pages : 334
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Book Description
... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Author: Tomás Roubicek
Publisher: Springer Science & Business Media
ISBN: 3764373970
Category : Mathematics
Languages : en
Pages : 415
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Book Description
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Author: Jean-Pierre Aubin
Publisher: Courier Corporation
ISBN: 0486453243
Category : Mathematics
Languages : en
Pages : 530
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Book Description
Nonlinear analysis, formerly a subsidiary of linear analysis, has advanced as an individual discipline, with its own methods and applications. Moreover, students can now approach this highly active field without the preliminaries of linear analysis. As this text demonstrates, the concepts of nonlinear analysis are simple, their proofs direct, and their applications clear. No prerequisites are necessary beyond the elementary theory of Hilbert spaces; indeed, many of the most interesting results lie in Euclidean spaces. In order to remain at an introductory level, this volume refrains from delving into technical difficulties and sophisticated results not in current use. Applications are explained as soon as possible, and theoretical aspects are geared toward practical use. Topics range from very smooth functions to nonsmooth ones, from convex variational problems to nonconvex ones, and from economics to mechanics. Background notes, comments, bibliography, and indexes supplement the text.
Author: Pavel Drabek
Publisher: CRC Press
ISBN: 1000673499
Category : Mathematics
Languages : en
Pages : 212
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Book Description
Working with mathematical models today requires in-depth knowledge of recent methods developed for solving nonlinear differential equations. Keeping abreast of these developments is the goal of the regular meetings of nonlinear analysts held in the Czech Republic, the most recent of which formed the basis of this volume. The subject addressed by these authors is the theory of nonlinear differential equations, with focus on the quasilinear elliptic differential equations of the degenerate type.
