Homogenization
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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.
Homogenization
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Author : Gregori A. Chechkin
language : en
Publisher: American Mathematical Soc.
Release Date :
Homogenization written by Gregori A. Chechkin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
This book focuses on both classical results of homogenization theory and modern techniques developed over the past decade. The powerful techniques in partial differential equations are illustrated with many exercises and examples to enhance understanding of the material. Several of the modern topics that are presented have not previously appeared in any monograph.
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.
Computational Homogenization Of Heterogeneous Materials With Finite Elements
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Author : Julien Yvonnet
language : en
Publisher: Springer
Release Date : 2019-06-11
Computational Homogenization Of Heterogeneous Materials With Finite Elements written by Julien Yvonnet and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-11 with Computers categories.
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 And Porous Media
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Author : Ulrich Hornung
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization And Porous Media written by Ulrich Hornung 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.
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.
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.
Homogenization Of Coupled Phenomena In Heterogenous Media
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Author : Jean-Louis Auriault
language : en
Publisher: John Wiley & Sons
Release Date : 2010-01-05
Homogenization Of Coupled Phenomena In Heterogenous Media written by Jean-Louis Auriault and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-05 with Technology & Engineering categories.
Both naturally-occurring and man-made materials are often heterogeneous materials formed of various constituents with different properties and behaviours. Studies are usually carried out on volumes of materials that contain a large number of heterogeneities. Describing these media by using appropriate mathematical models to describe each constituent turns out to be an intractable problem. Instead they are generally investigated by using an equivalent macroscopic description - relative to the microscopic heterogeneity scale - which describes the overall behaviour of the media. Fundamental questions then arise: Is such an equivalent macroscopic description possible? What is the domain of validity of this macroscopic description? The homogenization technique provides complete and rigorous answers to these questions. This book aims to summarize the homogenization technique and its contribution to engineering sciences. Researchers, graduate students and engineers will find here a unified and concise presentation. The book is divided into four parts whose main topics are Introduction to the homogenization technique for periodic or random media, with emphasis on the physics involved in the mathematical process and the applications to real materials. Heat and mass transfers in porous media Newtonian fluid flow in rigid porous media under different regimes Quasi-statics and dynamics of saturated deformable porous media Each part is illustrated by numerical or analytical applications as well as comparison with the self-consistent approach.
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
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.