The General Theory of Homogenization PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The General Theory of Homogenization PDF full book. Access full book title The General Theory of Homogenization by Luc Tartar. Download full books in PDF and EPUB format.
Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3642051952
Category : Science
Languages : en
Pages : 466
Get Book Here
Book Description
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.
Author: Luc Tartar
Publisher: Springer Science & Business Media
ISBN: 3642051952
Category : Science
Languages : en
Pages : 466
Get Book Here
Book Description
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.
Author: Doïna Cioranescu
Publisher: Oxford University Press on Demand
ISBN: 9780198565543
Category : Mathematics
Languages : en
Pages : 262
Get Book Here
Book Description
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.
Author: Chiang C Mei
Publisher: World Scientific
ISBN: 9814466964
Category : Mathematics
Languages : en
Pages : 349
Get Book Here
Book Description
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.
Author: Andrea Braides
Publisher: Oxford University Press
ISBN: 9780198502463
Category : Mathematics
Languages : en
Pages : 322
Get Book Here
Book Description
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.
Author: Gregoire Allaire
Publisher: Springer Science & Business Media
ISBN: 1468492861
Category : Technology & Engineering
Languages : en
Pages : 470
Get Book Here
Book Description
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.
Author: Ulrich Hornung
Publisher: Springer Science & Business Media
ISBN: 1461219205
Category : Mathematics
Languages : en
Pages : 290
Get Book Here
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: Zhongwei Shen
Publisher: Springer
ISBN: 3319912143
Category : Mathematics
Languages : en
Pages : 295
Get Book Here
Book Description
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.
Author: Julien Yvonnet
Publisher: Springer
ISBN: 3030183831
Category : Computers
Languages : en
Pages : 234
Get Book Here
Book Description
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.
Author: Folkmar Bornemann
Publisher: Springer Science & Business Media
ISBN: 9783540644477
Category : Mathematics
Languages : en
Pages : 172
Get Book Here
Book Description
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.
Author: Hershel Markovitz
Publisher: Springer Science & Business Media
ISBN: 3642759750
Category : Technology & Engineering
Languages : en
Pages : 575
Get Book Here
Book Description
Reprinted from Archive for Rational Mechanics and Analysis edited by C. Truesdell
