The Periodic Unfolding Method

The Periodic Unfolding Method

Author: Doina Cioranescu

Publisher: Springer

Published: 2018-11-03

Total Pages: 515

ISBN-13: 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.


Book Synopsis The Periodic Unfolding Method by : Doina Cioranescu

Download or read book The Periodic Unfolding Method written by Doina Cioranescu and published by Springer. This book was released on 2018-11-03 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiscale Problems

Multiscale Problems

Author: Alain Damlamian

Publisher: World Scientific

Published: 2011-10-13

Total Pages: 316

ISBN-13: 9814458120

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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. Contents:An Introduction to Periodic Homogenization (Alain Damlamian)The Periodic Unfolding Method in Homogenization (Alain Damlamian)Deterministic Homogenization of Stationary Navier–Stokes Type Equations (Gabriel Nguetseng & Lazarus Signing)Homogenization of a Class of Imperfect Transmission Problems (Patricia Donato)Decompositions of Displacements of Thin Structures (Georges Griso)Decomposition of Rods Deformations. Asymptotic Behavior of Nonlinear Elastic Rods (Georges Griso)Junction of a Periodic Family of Rods with a Plate in Elasticity (Dominique Blanchard)Multi-scale Modelling of New Composites: Theory and Numerical Simulation (Bernadette Miara)A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle) Readership: PhD students and researchers in applied mathematics, mechanics, physics and engineering. Keywords:Multiscale Problem;Homogenization;Asymptotic Behavior;Approximation


Book Synopsis Multiscale Problems by : Alain Damlamian

Download or read book Multiscale Problems written by Alain Damlamian and published by World Scientific. This book was released on 2011-10-13 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. Contents:An Introduction to Periodic Homogenization (Alain Damlamian)The Periodic Unfolding Method in Homogenization (Alain Damlamian)Deterministic Homogenization of Stationary Navier–Stokes Type Equations (Gabriel Nguetseng & Lazarus Signing)Homogenization of a Class of Imperfect Transmission Problems (Patricia Donato)Decompositions of Displacements of Thin Structures (Georges Griso)Decomposition of Rods Deformations. Asymptotic Behavior of Nonlinear Elastic Rods (Georges Griso)Junction of a Periodic Family of Rods with a Plate in Elasticity (Dominique Blanchard)Multi-scale Modelling of New Composites: Theory and Numerical Simulation (Bernadette Miara)A Priori and a Posteriori Error Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle) Readership: PhD students and researchers in applied mathematics, mechanics, physics and engineering. Keywords:Multiscale Problem;Homogenization;Asymptotic Behavior;Approximation

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics

Author: G. F. Roach

Publisher: Princeton University Press

Published: 2012-03-04

Total Pages: 400

ISBN-13: 1400842654

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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.


Book Synopsis Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics by : G. F. Roach

Download or read book Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics written by G. F. Roach and published by Princeton University Press. This book was released on 2012-03-04 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Some Topics in Industrial and Applied Mathematics

Some Topics in Industrial and Applied Mathematics

Author: Rolf Jeltsch

Publisher: Dr. Vuong Quan Hoang

Published: 2007

Total Pages: 24

ISBN-13: 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.


Book Synopsis Some Topics in Industrial and Applied Mathematics by : Rolf Jeltsch

Download or read book Some Topics in Industrial and Applied Mathematics written by Rolf Jeltsch and published by Dr. Vuong Quan Hoang. This book was released on 2007 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Emerging Problems in the Homogenization of Partial Differential Equations

Author: Patrizia Donato

Publisher: Springer Nature

Published: 2021-02-01

Total Pages: 122

ISBN-13: 3030620301

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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.


Book Synopsis Emerging Problems in the Homogenization of Partial Differential Equations by : Patrizia Donato

Download or read book Emerging Problems in the Homogenization of Partial Differential Equations written by Patrizia Donato and published by Springer Nature. This book was released on 2021-02-01 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Homogenization

An Introduction to Homogenization

Author: Doïna Cioranescu

Publisher: Oxford University Press on Demand

Published: 1999

Total Pages: 262

ISBN-13: 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.


Book Synopsis An Introduction to Homogenization by : Doïna Cioranescu

Download or read book An Introduction to Homogenization written by Doïna Cioranescu and published by Oxford University Press on Demand. This book was released on 1999 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Partial Differential Equations: Theory, Control and Approximation

Partial Differential Equations: Theory, Control and Approximation

Author: Philippe G. Ciarlet

Publisher: Springer Science & Business Media

Published: 2013-11-29

Total Pages: 431

ISBN-13: 364241401X

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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.


Book Synopsis Partial Differential Equations: Theory, Control and Approximation by : Philippe G. Ciarlet

Download or read book Partial Differential Equations: Theory, Control and Approximation written by Philippe G. Ciarlet and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces

Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces

Author: Isabella Graf

Publisher: Logos Verlag Berlin GmbH

Published: 2013

Total Pages: 288

ISBN-13: 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.


Book Synopsis Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces by : Isabella Graf

Download or read book Multiscale Modeling and Homogenization of Reaction-Diffusion Systems Involving Biological Surfaces written by Isabella Graf and published by Logos Verlag Berlin GmbH. This book was released on 2013 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Research Directions in Distributed Parameter Systems

Research Directions in Distributed Parameter Systems

Author: Ralph C. Smith

Publisher: SIAM

Published: 2003-01-01

Total Pages: 290

ISBN-13: 9780898717525

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Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems. Topics include electromagnetic theory for dielectric and conductive materials, flow control, cardiovascular and respiratory models, homogenization and systems theory, optimal and geometric control, reduced-order models for large-scale systems, smart materials, and nondestructive evaluation and structural health monitoring for systems, including nuclear power plants.


Book Synopsis Research Directions in Distributed Parameter Systems by : Ralph C. Smith

Download or read book Research Directions in Distributed Parameter Systems written by Ralph C. Smith and published by SIAM. This book was released on 2003-01-01 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems. Topics include electromagnetic theory for dielectric and conductive materials, flow control, cardiovascular and respiratory models, homogenization and systems theory, optimal and geometric control, reduced-order models for large-scale systems, smart materials, and nondestructive evaluation and structural health monitoring for systems, including nuclear power plants.

Integral Methods in Science and Engineering

Integral Methods in Science and Engineering

Author: Christian Constanda

Publisher: Springer

Published: 2019-07-18

Total Pages: 478

ISBN-13: 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.


Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda

Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer. This book was released on 2019-07-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.