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The Periodic Unfolding Method
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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 508 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.
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.
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.
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 with total page 314 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.
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.
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.
Book Synopsis Multiscale Problems: Theory, Numerical Approximation And Applications by : Alain Damlamian
Download or read book Multiscale Problems: Theory, Numerical Approximation And Applications written by Alain Damlamian and published by World Scientific. This book was released on 2011-10-13 with total page 314 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.
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 476 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.
Book Synopsis Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials by : Jichun Li
Download or read book Time-Domain Finite Element Methods for Maxwell's Equations in Metamaterials written by Jichun Li and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics On Mathematics For Smart Systems - Proceedings Of The European Conference by : Vanda Valente
Download or read book Topics On Mathematics For Smart Systems - Proceedings Of The European Conference written by Vanda Valente and published by World Scientific. This book was released on 2007-01-18 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Topics on Mathematics for Smart Systems by : Bernadette Miara
Download or read book Topics on Mathematics for Smart Systems written by Bernadette Miara and published by World Scientific. This book was released on 2007 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Homogenization by Localized Decomposition by : Axel Målqvist
Download or read book Numerical Homogenization by Localized Decomposition written by Axel Målqvist and published by SIAM. This book was released on 2020-11-23 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the first survey of the Localized Orthogonal Decomposition (LOD) method, a pioneering approach for the numerical homogenization of partial differential equations with multiscale data beyond periodicity and scale separation. The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB. They also reveal how the LOD method relates to classical homogenization and domain decomposition. Illustrated with numerical experiments that demonstrate the significance of the method, the book is enhanced by a survey of applications including eigenvalue problems and evolution problems. Numerical Homogenization by Localized Orthogonal Decomposition is appropriate for graduate students in applied mathematics, numerical analysis, and scientific computing. Researchers in the field of computational partial differential equations will find this self-contained book of interest, as will applied scientists and engineers interested in multiscale simulation.
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.
Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Book Synopsis Gratings: Theory and Numeric Applications by :
Download or read book Gratings: Theory and Numeric Applications written by and published by Popov, Institut Fresnel. This book was released on with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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.
Book Synopsis Recent Advances in Scientific Computing and Applications by : Jichun Li
Download or read book Recent Advances in Scientific Computing and Applications written by Jichun Li and published by American Mathematical Soc.. This book was released on 2013-04-24 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Eighth International Conference on Scientific Computing and Applications, held April 1-4, 2012, at the University of Nevada, Las Vegas. The papers in this volume cover topics such as finite element methods, multiscale methods, finite difference methods, spectral methods, collocation methods, adaptive methods, parallel computing, linear solvers, applications to fluid flow, nano-optics, biofilms, finance, magnetohydrodynamics flow, electromagnetic waves, the fluid-structure interaction problem, and stochastic PDEs. This book will serve as an excellent reference for graduate students and researchers interested in scientific computing and its applications.
