The General Theory Of Homogenization

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The General Theory of Homogenization

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Author : Luc Tartar
Publisher : Springer Science & Business Media
ISBN 13 : 3642051952
Total Pages : 466 pages
Book Rating : 4.6/5 (42 download)

Book Synopsis The General Theory of Homogenization by : Luc Tartar

Download or read book The General Theory of Homogenization written by Luc Tartar and published by Springer Science & Business Media. This book was released on 2009-12-03 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogenization is not about periodicity, or Gamma-convergence, but about understanding which effective equations to use at macroscopic level, knowing which partial differential equations govern mesoscopic levels, without using probabilities (which destroy physical reality); instead, one uses various topologies of weak type, the G-convergence of Sergio Spagnolo, the H-convergence of François Murat and the author, and some responsible for the appearance of nonlocal effects, which many theories in continuum mechanics or physics guessed wrongly. For a better understanding of 20th century science, new mathematical tools must be introduced, like the author’s H-measures, variants by Patrick Gérard, and others yet to be discovered.

An Introduction to Homogenization

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Author : Doïna Cioranescu
Publisher : Oxford University Press on Demand
ISBN 13 : 9780198565543
Total Pages : 262 pages
Book Rating : 4.5/5 (655 download)

Book Synopsis An Introduction to Homogenization by : Doïna Cioranescu

Download or read book An Introduction to Homogenization written by Doïna Cioranescu and published by Oxford University Press on Demand. This book was released on 1999 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composite materials are widely used in industry: well-known examples of this are the superconducting multi-filamentary composites which are used in the composition of optical fibres. Such materials are complicated to model, as different points in the material will have different properties. The mathematical theory of homogenization is designed to deal with this problem, and hence is used to model the behaviour of these important materials. This book provides a self-contained and authoritative introduction to the subject for graduates and researchers in the field.

Homogenization Methods For Multiscale Mechanics

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Author : Chiang C Mei
Publisher : World Scientific
ISBN 13 : 9814466964
Total Pages : 349 pages
Book Rating : 4.8/5 (144 download)

Book Synopsis Homogenization Methods For Multiscale Mechanics by : Chiang C Mei

Download or read book Homogenization Methods For Multiscale Mechanics written by Chiang C Mei and published by World Scientific. This book was released on 2010-09-23 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical problems several scales are present in space or time, caused by inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization.The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.

Periodic Homogenization of Elliptic Systems

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Author : Zhongwei Shen
Publisher : Springer
ISBN 13 : 3319912143
Total Pages : 291 pages
Book Rating : 4.3/5 (199 download)

Book Synopsis Periodic Homogenization of Elliptic Systems by : Zhongwei Shen

Download or read book Periodic Homogenization of Elliptic Systems written by Zhongwei Shen and published by Springer. This book was released on 2018-09-04 with total page 291 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph surveys the theory of quantitative homogenization for second-order linear elliptic systems in divergence form with rapidly oscillating periodic coefficients in a bounded domain. It begins with a review of the classical qualitative homogenization theory, and addresses the problem of convergence rates of solutions. The main body of the monograph investigates various interior and boundary regularity estimates that are uniform in the small parameter e>0. Additional topics include convergence rates for Dirichlet eigenvalues and asymptotic expansions of fundamental solutions, Green functions, and Neumann functions. The monograph is intended for advanced graduate students and researchers in the general areas of analysis and partial differential equations. It provides the reader with a clear and concise exposition of an important and currently active area of quantitative homogenization.

Homogenization of Multiple Integrals

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Author : Andrea Braides
Publisher : Oxford University Press
ISBN 13 : 9780198502463
Total Pages : 322 pages
Book Rating : 4.5/5 (24 download)

Book Synopsis Homogenization of Multiple Integrals by : Andrea Braides

Download or read book Homogenization of Multiple Integrals written by Andrea Braides and published by Oxford University Press. This book was released on 1998 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.

Homogenization and Porous Media

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Author : Ulrich Hornung
Publisher : Springer Science & Business Media
ISBN 13 : 1461219205
Total Pages : 290 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Homogenization and Porous Media by : Ulrich Hornung

Download or read book Homogenization and Porous Media written by Ulrich Hornung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Shape Optimization by the Homogenization Method

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Author : Gregoire Allaire
Publisher : Springer Science & Business Media
ISBN 13 : 1468492861
Total Pages : 470 pages
Book Rating : 4.4/5 (684 download)

Book Synopsis Shape Optimization by the Homogenization Method by : Gregoire Allaire

Download or read book Shape Optimization by the Homogenization Method written by Gregoire Allaire and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the theory and numerical developments of the homogenization method. It's main features are: a comprehensive presentation of homogenization theory; an introduction to the theory of two-phase composite materials; a detailed treatment of structural optimization by using homogenization; a complete discussion of the resulting numerical algorithms with many documented test problems. It will be of interest to researchers, engineers, and advanced graduate students in applied mathematics, mechanical engineering, and structural optimization.

Computational Homogenization of Heterogeneous Materials with Finite Elements

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Author : Julien Yvonnet
Publisher : Springer
ISBN 13 : 3030183831
Total Pages : 223 pages
Book Rating : 4.0/5 (31 download)

Book Synopsis Computational Homogenization of Heterogeneous Materials with Finite Elements by : Julien Yvonnet

Download or read book Computational Homogenization of Heterogeneous Materials with Finite Elements written by Julien Yvonnet and published by Springer. This book was released on 2019-06-11 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.

Homogenization in Time of Singularly Perturbed Mechanical Systems

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Author : Folkmar Bornemann
Publisher : Springer Science & Business Media
ISBN 13 : 9783540644477
Total Pages : 172 pages
Book Rating : 4.6/5 (444 download)

Book Synopsis Homogenization in Time of Singularly Perturbed Mechanical Systems by : Folkmar Bornemann

Download or read book Homogenization in Time of Singularly Perturbed Mechanical Systems written by Folkmar Bornemann and published by Springer Science & Business Media. This book was released on 1998-06-18 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about the explicit elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and our understanding of model hierarchies. The author presents his new direct method, homogenization in time, based on energy principles and weak convergence techniques. How to use this method is shown in several general cases taken from classical and quantum mechanics. The results are applied to special problems from plasma physics, molecular dynamics and quantum chemistry. Background material from functional analysis is provided and explained to make this book accessible for a general audience of graduate students and researchers.

Homogenization Methods for Multiscale Mechanics

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Author : Chiang C. Mei
Publisher : World Scientific
ISBN 13 : 9814282448
Total Pages : 349 pages
Book Rating : 4.8/5 (142 download)

Book Synopsis Homogenization Methods for Multiscale Mechanics by : Chiang C. Mei

Download or read book Homogenization Methods for Multiscale Mechanics written by Chiang C. Mei and published by World Scientific. This book was released on 2010 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the novel approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.

Mechanics and Thermodynamics of Continua

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Author : Hershel Markovitz
Publisher : Springer Science & Business Media
ISBN 13 : 3642759750
Total Pages : 575 pages
Book Rating : 4.6/5 (427 download)

Book Synopsis Mechanics and Thermodynamics of Continua by : Hershel Markovitz

Download or read book Mechanics and Thermodynamics of Continua written by Hershel Markovitz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reprinted from Archive for Rational Mechanics and Analysis edited by C. Truesdell

Homogenization of Partial Differential Equations

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Author : Vladimir A. Marchenko
Publisher : Springer Science & Business Media
ISBN 13 : 0817644687
Total Pages : 407 pages
Book Rating : 4.8/5 (176 download)

Book Synopsis Homogenization of Partial Differential Equations by : Vladimir A. Marchenko

Download or read book Homogenization of Partial Differential Equations written by Vladimir A. Marchenko and published by Springer Science & Business Media. This book was released on 2008-12-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers

Homogenization of Differential Operators and Integral Functionals

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Author : V.V. Jikov
Publisher : Springer Science & Business Media
ISBN 13 : 3642846599
Total Pages : 583 pages
Book Rating : 4.6/5 (428 download)

Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov

Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.

Multiscale Methods

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Author : G A Pavliotis
Publisher : Springer Science & Business Media
ISBN 13 : 0387738282
Total Pages : 314 pages
Book Rating : 4.3/5 (877 download)

Book Synopsis Multiscale Methods by : G A Pavliotis

Download or read book Multiscale Methods written by G A Pavliotis and published by Springer Science & Business Media. This book was released on 2008-02-19 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to multiscale methods gives you a broad overview of the methods’ many uses and applications. The book begins by setting the theoretical foundations of the methods and then moves on to develop models and prove theorems. Extensive use of examples shows how to apply multiscale methods to solving a variety of problems. Exercises then enable you to build your own skills and put them into practice. Extensions and generalizations of the results presented in the book, as well as references to the literature, are provided in the Discussion and Bibliography section at the end of each chapter.With the exception of Chapter One, all chapters are supplemented with exercises.

Topics in the Mathematical Modelling of Composite Materials

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Author : Andrej V. Cherkaev
Publisher : Springer Science & Business Media
ISBN 13 : 1461220327
Total Pages : 329 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Topics in the Mathematical Modelling of Composite Materials by : Andrej V. Cherkaev

Download or read book Topics in the Mathematical Modelling of Composite Materials written by Andrej V. Cherkaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Andrej V. Cherkaev and Robert V. Kohn In the past twenty years we have witnessed a renaissance of theoretical work on the macroscopic behavior of microscopically heterogeneous mate rials. This activity brings together a number of related themes, including: ( 1) the use of weak convergence as a rigorous yet general language for the discussion of macroscopic behavior; (2) interest in new types of questions, particularly the "G-closure problem," motivated in large part by applications of optimal control theory to structural optimization; (3) the introduction of new methods for bounding effective moduli, including one based on "com pensated compactness"; and (4) the identification of deep links between the analysis of microstructures and the multidimensional calculus of variations. This work has implications for many physical problems involving optimal design, composite materials, and coherent phase transitions. As a result it has received attention and support from numerous scientific communities, including engineering, materials science, and physics as well as mathematics. There is by now an extensive literature in this area. But for various reasons certain fundamental papers were never properly published, circu lating instead as mimeographed notes or preprints. Other work appeared in poorly distributed conference proceedings volumes. Still other work was published in standard books or journals, but written in Russian or French. The net effect is a sort of "gap" in the literature, which has made the subject unnecessarily difficult for newcomers to penetrate.

Mathematical Problems in Elasticity and Homogenization

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Author : O.A. Oleinik
Publisher : Elsevier
ISBN 13 : 9780080875477
Total Pages : 397 pages
Book Rating : 4.8/5 (754 download)

Book Synopsis Mathematical Problems in Elasticity and Homogenization by : O.A. Oleinik

Download or read book Mathematical Problems in Elasticity and Homogenization written by O.A. Oleinik and published by Elsevier. This book was released on 1992-11-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.

Acta Numerica 2008: Volume 17

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Author : A. Iserles
Publisher : Cambridge University Press
ISBN 13 : 9780521516426
Total Pages : 424 pages
Book Rating : 4.5/5 (164 download)

Book Synopsis Acta Numerica 2008: Volume 17 by : A. Iserles

Download or read book Acta Numerica 2008: Volume 17 written by A. Iserles and published by Cambridge University Press. This book was released on 2008-06-12 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: A high-impact, prestigious annual publication containing invited surveys by subject leaders: essential reading for all practitioners and researchers.