The General Theory Of Homogenization

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The General Theory of Homogenization

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

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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.

Homogenization Methods For Multiscale Mechanics

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

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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.

An Introduction to Homogenization

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

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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 of Multiple Integrals

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

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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.

Shape Optimization by the Homogenization Method

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

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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.

Homogenization and Porous Media

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

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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.

Periodic Homogenization of Elliptic Systems

Author : Zhongwei Shen
Publisher : Springer
ISBN 13 : 3319912143
Total Pages : 295 pages
Book Rating : 4.3/5 (199 download)

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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 295 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 in Time of Singularly Perturbed Mechanical Systems

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

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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.

Computational Homogenization of Heterogeneous Materials with Finite Elements

Author : Julien Yvonnet
Publisher : Springer
ISBN 13 : 3030183831
Total Pages : 234 pages
Book Rating : 4.0/5 (31 download)

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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 234 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.

State Identities and the Homogenisation of Peoples

Author : Heather Rae
Publisher : Cambridge University Press
ISBN 13 : 9780521797085
Total Pages : 376 pages
Book Rating : 4.7/5 (97 download)

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Book Synopsis State Identities and the Homogenisation of Peoples by : Heather Rae

Download or read book State Identities and the Homogenisation of Peoples written by Heather Rae and published by Cambridge University Press. This book was released on 2002-08-15 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Why are forced displacement, ethnic cleansing and genocide an enduring feature of state systems? In this book, Heather Rae locates these practices of 'pathological homogenisation' in the processes of state building. Political elites have repeatedly used cultural resources to redefine bounded political communities as exclusive moral communities, from which outsiders must be expelled. Showing that these practices predate the age of nationalism, Rae examines cases from both pre-nationalist and nationalist eras: the expulsion of the Jews from fifteenth century Spain, the persecution of the Huguenots under Louis XIV, and in the twentieth century, the Armenian genocide, and ethnic cleansing in former Yugoslavia. She argues that those atrocities prompted the development of international norms of legitimate state behaviour that increasingly define sovereignty as conditional. Rae concludes by examining two 'threshold' cases - the Czech Republic and Macedonia - to identify the factors that may inhibit pathological homogenization as a method of state-building.

The Theory of Composites

Author : Graeme W. Milton
Publisher : SIAM
ISBN 13 : 1611977487
Total Pages : 761 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Theory of Composites by : Graeme W. Milton

Download or read book The Theory of Composites written by Graeme W. Milton and published by SIAM. This book was released on 2022-12-07 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

Topics in the Mathematical Modelling of Composite Materials

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

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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.

Quantitative Stochastic Homogenization and Large-Scale Regularity

Author : Scott Armstrong
Publisher : Springer
ISBN 13 : 3030155455
Total Pages : 548 pages
Book Rating : 4.0/5 (31 download)

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Book Synopsis Quantitative Stochastic Homogenization and Large-Scale Regularity by : Scott Armstrong

Download or read book Quantitative Stochastic Homogenization and Large-Scale Regularity written by Scott Armstrong and published by Springer. This book was released on 2019-05-09 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book is the large-scale statistical behavior of solutions of divergence-form elliptic equations with random coefficients, which is closely related to the long-time asymptotics of reversible diffusions in random media and other basic models of statistical physics. Of particular interest is the quantification of the rate at which solutions converge to those of the limiting, homogenized equation in the regime of large scale separation, and the description of their fluctuations around this limit. This self-contained presentation gives a complete account of the essential ideas and fundamental results of this new theory of quantitative stochastic homogenization, including the latest research on the topic, and is supplemented with many new results. The book serves as an introduction to the subject for advanced graduate students and researchers working in partial differential equations, statistical physics, probability and related fields, as well as a comprehensive reference for experts in homogenization. Being the first text concerned primarily with stochastic (as opposed to periodic) homogenization and which focuses on quantitative results, its perspective and approach are entirely different from other books in the literature.

Social Theory of International Politics

Author : Alexander Wendt
Publisher : Cambridge University Press
ISBN 13 : 1107268435
Total Pages : 264 pages
Book Rating : 4.1/5 (72 download)

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Book Synopsis Social Theory of International Politics by : Alexander Wendt

Download or read book Social Theory of International Politics written by Alexander Wendt and published by Cambridge University Press. This book was released on 1999-10-07 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Drawing upon philosophy and social theory, Social Theory of International Politics develops a theory of the international system as a social construction. Alexander Wendt clarifies the central claims of the constructivist approach, presenting a structural and idealist worldview which contrasts with the individualism and materialism which underpins much mainstream international relations theory. He builds a cultural theory of international politics, which takes whether states view each other as enemies, rivals or friends as a fundamental determinant. Wendt characterises these roles as 'cultures of anarchy', described as Hobbesian, Lockean and Kantian respectively. These cultures are shared ideas which help shape state interests and capabilities, and generate tendencies in the international system. The book describes four factors which can drive structural change from one culture to another - interdependence, common fate, homogenization, and self-restraint - and examines the effects of capitalism and democracy in the emergence of a Kantian culture in the West.

Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization

Author : Houman Owhadi
Publisher : Cambridge University Press
ISBN 13 : 1108484360
Total Pages : 491 pages
Book Rating : 4.1/5 (84 download)

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Book Synopsis Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization by : Houman Owhadi

Download or read book Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization written by Houman Owhadi and published by Cambridge University Press. This book was released on 2019-10-24 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents interplays between numerical approximation and statistical inference as a pathway to simple solutions to fundamental problems.

Maxwell’s Equations

Author : Ulrich Langer
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110542692
Total Pages : 597 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Maxwell’s Equations by : Ulrich Langer

Download or read book Maxwell’s Equations written by Ulrich Langer and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects longer articles on the analysis and numerics of Maxwell’s equations. The topics include functional analytic and Hilbert space methods, compact embeddings, solution theories and asymptotics, electromagnetostatics, time-harmonic Maxwell’s equations, time-dependent Maxwell’s equations, eddy current approximations, scattering and radiation problems, inverse problems, finite element methods, boundary element methods, and isogeometric analysis.

Harmonic Analysis and Applications

Author : Carlos E. Kenig
Publisher : American Mathematical Soc.
ISBN 13 : 1470461277
Total Pages : 345 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Harmonic Analysis and Applications by : Carlos E. Kenig

Download or read book Harmonic Analysis and Applications written by Carlos E. Kenig and published by American Mathematical Soc.. This book was released on 2020-12-14 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: The origins of the harmonic analysis go back to an ingenious idea of Fourier that any reasonable function can be represented as an infinite linear combination of sines and cosines. Today's harmonic analysis incorporates the elements of geometric measure theory, number theory, probability, and has countless applications from data analysis to image recognition and from the study of sound and vibrations to the cutting edge of contemporary physics. The present volume is based on lectures presented at the summer school on Harmonic Analysis. These notes give fresh, concise, and high-level introductions to recent developments in the field, often with new arguments not found elsewhere. The volume will be of use both to graduate students seeking to enter the field and to senior researchers wishing to keep up with current developments.