The Periodic Unfolding Method

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The Periodic Unfolding Method

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Author : Doina Cioranescu
language : en
Publisher: Springer
Release Date : 2018-11-03

The Periodic Unfolding Method written by Doina Cioranescu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.

This is the first book on the subject of the periodic unfolding method (originally called "éclatement périodique" in French), which was originally developed to clarify and simplify many questions arising in the homogenization of PDE's. It has since led to the solution of some open problems. Written by the three mathematicians who developed the method, the book presents both the theory as well as numerous examples of applications for partial differential problems with rapidly oscillating coefficients: in fixed domains (Part I), in periodically perforated domains (Part II), and in domains with small holes generating a strange term (Part IV). The method applies to the case of multiple microscopic scales (with finitely many distinct scales) which is connected to partial unfolding (also useful for evolution problems). This is discussed in the framework of oscillating boundaries (Part III). A detailed example of its application to linear elasticity is presented in the case of thin elastic plates (Part V). Lastly, a complete determination of correctors for the model problem in Part I is obtained (Part VI). This book can be used as a graduate textbook to introduce the theory of homogenization of partial differential problems, and is also a must for researchers interested in this field.

Mathematical Analysis Of Deterministic And Stochastic Problems In Complex Media Electromagnetics

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Author : G. F. Roach
language : en
Publisher: Princeton University Press
Release Date : 2012-03-04

Mathematical Analysis Of Deterministic And Stochastic Problems In Complex Media Electromagnetics written by G. F. Roach and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-04 with Mathematics categories.

Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature. Because of their wide range of important applications, these materials have been intensely studied over the past twenty-five years, mainly from the perspectives of physics and engineering. But a body of rigorous mathematical theory has also gradually developed, and this is the first book to present that theory. Designed for researchers and advanced graduate students in applied mathematics, electrical engineering, and physics, this book introduces the electromagnetics of complex media through a systematic, state-of-the-art account of their mathematical theory. The book combines the study of well posedness, homogenization, and controllability of Maxwell equations complemented with constitutive relations describing complex media. The book treats deterministic and stochastic problems both in the frequency and time domains. It also covers computational aspects and scattering problems, among other important topics. Detailed appendices make the book self-contained in terms of mathematical prerequisites, and accessible to engineers and physicists as well as mathematicians.

Multiscale Problems Theory Numerical Approximation And Applications

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Author : Alain Damlamian
language : en
Publisher: World Scientific
Release Date : 2011-10-13

Multiscale Problems Theory Numerical Approximation And Applications written by Alain Damlamian and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-13 with Mathematics categories.

The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated.

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 Mathematics 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.​

Mystery Of The Periodic Table

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Author : Benjamin D Wiker
language : en
Publisher: Bethlehem Books
Release Date : 2003-04-18

Mystery Of The Periodic Table written by Benjamin D Wiker and has been published by Bethlehem Books this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-18 with Juvenile Fiction categories.

Leads the reader on a delightful and absorbing journey through the ages, on the trail of the elements of the Periodic Table as we know them today. He introduces the young reader to people like Von Helmont, Boyle, Stahl, Priestly, Cavendish, Lavoisier, and many others, all incredibly diverse in personality and approach, who have laid the groundwork for a search that is still unfolding to this day. The first part of Wiker's witty and solidly instructive presentation is most suitable to middle school age, while the later chapters are designed for ages 12-13 and up, with a final chapter somewhat more advanced. Illustrated by Jeanne Bendick and Ted Schluenderfritz.

Modelling And Simulation In Fluid Dynamics In Porous Media

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Author : José A. Ferreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-04

Modelling And Simulation In Fluid Dynamics In Porous Media written by José A. Ferreira 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 2012-12-04 with Mathematics categories.

This volume presents a selection of survey and research articles based on invited lectures and contributed talks presented at the Workshop on Fluid Dynamics in Porous Media that was held in Coimbra, Portugal, in September 12-14, 2011. The contributions are devoted to mathematical modeling, numerical simulation and their applications, providing the readers a state-of-the-art overview on the latest findings and new challenges on the topic. The book includes research work of worldwide recognized leaders in their respective fields and presents advances in both theory and applications, making it appealing to a vast range of audience, in particular mathematicians, engineers and physicists.

Gratings Theory And Numeric Applications

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Author :
language : en
Publisher: Popov, Institut Fresnel
Release Date :

Gratings Theory And Numeric Applications written by and has been published by Popov, Institut Fresnel this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.

Partial Differential Equations Theory Control And Approximation

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Author : Philippe G. Ciarlet
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-29

Partial Differential Equations Theory Control And Approximation written by Philippe G. Ciarlet 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 2013-11-29 with Mathematics categories.

This book collects papers mainly presented at the "International Conference on Partial Differential Equations: Theory, Control and Approximation" (May 28 to June 1, 2012 in Shanghai) in honor of the scientific legacy of the exceptional mathematician Jacques-Louis Lions. The contributors are leading experts from all over the world, including members of the Academies of Sciences in France, the USA and China etc., and their papers cover key fields of research, e.g. partial differential equations, control theory and numerical analysis, that Jacques-Louis Lions created or contributed so much to establishing.

Some Topics In Industrial And Applied Mathematics

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Author : Rolf Jeltsch
language : en
Publisher: Dr. Vuong Quan Hoang
Release Date : 2007

Some Topics In Industrial And Applied Mathematics written by Rolf Jeltsch and has been published by Dr. Vuong Quan Hoang this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Technology & Engineering categories.

The Shanghai Forum on Industrial and Applied Mathematics was organized in May 2006 on the occasion that many famous industrial and applied mathematicians gathered in Shanghai from different countries to participate in the Officers' Meeting and the Board Meeting of the ICIAM (International Council for Industrial and Applied Mathematics). This volume collects the material covered by the majority of the lectures of which reflects panoramically recent results and trends in industrial and applied mathematics. This book will be very useful for graduate students and researchers in industrial and applied mathematics.

Emerging Problems In The Homogenization Of Partial Differential Equations

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Author : Patrizia Donato
language : en
Publisher: Springer Nature
Release Date : 2021-02-01

Emerging Problems In The Homogenization Of Partial Differential Equations written by Patrizia Donato and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-01 with Mathematics categories.

This book contains some of the results presented at the mini-symposium titled Emerging Problems in the Homogenization of Partial Differential Equations, held during the ICIAM2019 conference in Valencia in July 2019. The papers cover a large range of topics, problems with weak regularity data involving renormalized solutions, eigenvalue problems for complicated shapes of the domain, homogenization of partial differential problems with strongly alternating boundary conditions of Robin type with large parameters, multiscale analysis of the potential action along a neuron with a myelinated axon, and multi-scale model of magnetorheological suspensions. The volume is addressed to scientists who deal with complex systems that presents several elements (characteristics, constituents...) of very different scales, very heterogeneous, and search for homogenized models providing an effective (macroscopic) description of their behaviors.