An Introduction To Homogenization
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An Introduction To Homogenization
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Author : Doïna Cioranescu
language : en
Publisher: Oxford University Press on Demand
Release Date : 1999
An Introduction To Homogenization written by Doïna Cioranescu and has been published by Oxford University Press on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.
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.
The Homogenization Method
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Author : Lars-Erik Persson
language : en
Publisher:
Release Date : 1993
The Homogenization Method written by Lars-Erik Persson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.
Homogenization Theory For Multiscale Problems
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Author : Xavier Blanc
language : en
Publisher: Springer Nature
Release Date : 2023-04-29
Homogenization Theory For Multiscale Problems written by Xavier Blanc and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Mathematics categories.
The book provides a pedagogic and comprehensive introduction to homogenization theory with a special focus on problems set for non-periodic media. The presentation encompasses both deterministic and probabilistic settings. It also mixes the most abstract aspects with some more practical aspects regarding the numerical approaches necessary to simulate such multiscale problems. Based on lecture courses of the authors, the book is suitable for graduate students of mathematics and engineering.
The General Theory Of Homogenization
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Author : Luc Tartar
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-03
The General Theory Of Homogenization written by Luc Tartar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-03 with Science categories.
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.
Introduction To Homogenization Methods In Continuum Mechanics
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Author : William Parnell
language : en
Publisher:
Release Date : 2007
Introduction To Homogenization Methods In Continuum Mechanics written by William Parnell and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.
Homogenization Of Multiple Integrals
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Author : Andrea Braides
language : en
Publisher: Oxford University Press
Release Date : 1998
Homogenization Of Multiple Integrals written by Andrea Braides and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
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.
Periodic Homogenization Of Elliptic Systems
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Author : Zhongwei Shen
language : en
Publisher: Springer
Release Date : 2018-09-04
Periodic Homogenization Of Elliptic Systems written by Zhongwei Shen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-04 with Mathematics categories.
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.
Shape Optimization By The Homogenization Method
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Author : Gregoire Allaire
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shape Optimization By The Homogenization Method written by Gregoire Allaire and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
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 Of Reticulated Structures
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Author : Doina Cioranescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization Of Reticulated Structures written by Doina Cioranescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Materials science is an area of growing research as composite materials become widely used in such areas as civil engineering, electrotechnics, and the aerospace industry. This mathematically rigorous treatment of lattice-type structures will appeal to both applied mathematicians, as well as engineers looking for a solid mathematical foundation of the methodology.
Homogenization Of Partial Differential Equations
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Author : Vladimir A. Marchenko
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-22
Homogenization Of Partial Differential Equations written by Vladimir A. Marchenko and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-22 with Mathematics categories.
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