[PDF] The Periodic Unfolding Method eBook

Author : Doina Cioranescu
Publisher : Springer
Page : 515 pages
File Size : 26,86 MB
Release : 2018-11-03
Category : Mathematics
ISBN : 9811330328

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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.

Author : Ralph C. Smith
Publisher : SIAM
Page : 283 pages
File Size : 34,2 MB
Release : 2003-01-01
Category : Mathematics
ISBN : 0898715482

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Eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameter systems.

Author : Alain Damlamian
Publisher : World Scientific
Page : 314 pages
File Size : 16,9 MB
Release : 2011
Category : Mathematics
ISBN : 9814366889

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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.

Author : Rolf Jeltsch
Publisher : Dr. Vuong Quan Hoang
Page : 24 pages
File Size : 46,31 MB
Release : 2007
Category : Applied mathematics
ISBN : 7040219034

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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.

Author : Isabella Graf
Publisher : Logos Verlag Berlin GmbH
Page : 288 pages
File Size : 40,28 MB
Release : 2013
Category : Mathematics
ISBN : 3832533974

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Many complex chemical processes are responsible for the proper functioning of the human body. A prime example is the finely structured endoplasmic reticulum, which plays an important role in the metabolisms of human cells. To handle mathematical models that account for this fine structure, periodic homogenization methods are derived and applied. Previous results on homogenization of partial differential equations on finely structured manifolds are extended: Using the periodic unfolding method, diffusion terms on manifolds with different scalings with powers of the homogenization parameter, in particular in case of fast diffusion, are homogenized and are applied in three different biological systems: a linear model of carcinogenesis of cells, a nonlinear extension of the linear carcinogenesis model and a model considering T-cell signaling. Simulations and interpretations of the homogeneous T-cell signaling model give an insight into the related biological mechanisms.

Author : Doïna Cioranescu
Publisher : Oxford University Press on Demand
Page : 262 pages
File Size : 19,31 MB
Release : 1999
Category : Mathematics
ISBN : 9780198565543

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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 : Christian Constanda
Publisher : Springer
Page : 478 pages
File Size : 23,13 MB
Release : 2019-07-18
Category : Mathematics
ISBN : 3030160777

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This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.

Author : Jichun Li
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 50,5 MB
Release : 2012-12-15
Category : Computers
ISBN : 3642337899

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The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.

Author : Vanda Valente
Publisher : World Scientific
Page : 283 pages
File Size : 14,33 MB
Release : 2007-01-18
Category : Mathematics
ISBN : 9814476463

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This volume gathers articles presented at a prominent European conference on smart systems and summarizes the activities carried out by a research and training network supported by the European community. The contributions aim to exhibit new research topics in the areas of materials science, advanced mathematical tools, and elements of control and numerical algorithms relevant to the design and optimization of smart systems.