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Homogenization Methods In Partial Differential Equations And Modeling Multiphase Materials
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Book Synopsis Homogenization Methods in Partial Differential Equations and Modeling Multiphase Materials by : Chaocheng Huang
Download or read book Homogenization Methods in Partial Differential Equations and Modeling Multiphase Materials written by Chaocheng Huang and published by . This book was released on 1995 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :Vladimir A. Marchenko Publisher :Springer Science & Business Media ISBN 13 :0817644687 Total Pages :407 pages Book Rating :4.8/5 (176 download)
Book Synopsis Homogenization of Partial Differential Equations by : Vladimir A. Marchenko
Download or read book Homogenization of Partial Differential Equations written by Vladimir A. Marchenko and published by Springer Science & Business Media. This book was released on 2008-12-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive study of homogenized problems, focusing on the construction of nonstandard models Details a method for modeling processes in microinhomogeneous media (radiophysics, filtration theory, rheology, elasticity theory, and other domains) Complete proofs of all main results, numerous examples Classroom text or comprehensive reference for graduate students, applied mathematicians, physicists, and engineers
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 The authors provide a careful error analysis, including previously unpublished results, and a complete implementation of the method in MATLAB.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 Optimal Design of Multi-Phase Materials by : Juan Casado-Díaz
Download or read book Optimal Design of Multi-Phase Materials written by Juan Casado-Díaz and published by . This book was released on 2022 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims the optimal design of a material (thermic or electrical) obtained as the mixture of a finite number of original materials, not necessarily isotropic. The problem is to place these materials in such a way that the solution of the corresponding state equation minimizes a certain functional that can depend nonlinearly on the gradient of the state function. This is the main novelty in the book. It is well known that this type of problems has no solution in general and therefore that it is needed to work with a relaxed formulation. The main results in the book refer to how to obtain such formulation, the optimality conditions, and the numerical computation of the solutions. In the case of functionals that do not depend on the gradient of the state equation, it is known that a relaxed formulation consists of replacing the original materials with more general materials obtained via homogenization. This includes materials with different properties of the originals but whose behavior can be approximated by microscopic mixtures of them. In the case of a cost functional depending nonlinearly on the gradient, it is also necessary to extend the cost functional to the set of these more general materials. In general, we do not dispose of an explicit representation, and then, to numerically solve the problem, it is necessary to design strategies that allow the functional to be replaced by upper or lower approximations. The book is divided in four chapters. The first is devoted to recalling some classical results related to the homogenization of a sequence of linear elliptic partial differential problems. In the second one, we define the control problem that we are mainly interested in solving in the book. We obtain a relaxed formulation and their main properties, including an explicit representation of the new cost functional, at least in the boundary of its domain. In the third chapter, we study the optimality conditions of the relaxed problem, and we describe some algorithms to numerically solve the problem. We also provide some numerical experiments carried out using such algorithms. Finally, the fourth chapter is devoted to briefly describe some extensions of the results obtained in Chapters 2 and 3 to the case of dealing with several state equations and the case of evolutive problems. The problems covered in the book are interesting for mathematicians and engineers whose work is related to mathematical modeling and the numerical resolution of optimal design problems in material sciences. The contents extend some previous results obtained by the author in collaboration with other colleagues.
Book Synopsis Composite Media And Homogenization Theory: Proceedings Of The Second Workshop by : Gianni Dal Maso
Download or read book Composite Media And Homogenization Theory: Proceedings Of The Second Workshop written by Gianni Dal Maso and published by World Scientific. This book was released on 1995-09-30 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: A rigorous mathematical treatment of the properties of composite materials has been made possible by recent mathematical results in the fields of partial differential equations and the calculus of variations. The progress in the mathematical models for composite media has led to a deeper understanding of the overall behaviour of composite structures and to significant applications in physics and engineering, including a new approach to optimal design problems.Many new, relevant results are presented in this volume, which contains 16 invited papers from the Second Workshop on Composite Media and Homogenization Theory held at the International Centre for Theoretical Physics in Trieste, Italy, from September 20 to October 1, 1993. Topics include homogenization of problems singularly depending on small or large parameters, homogenization of nonlinear problems, optimal bounds for effective moduli, asymptotic analysis of problems in perforated domains, laminate structures in phase transitions, optimal design and relaxation. Mathematicians and engineers interested in mathematical models of composite materials will find this book to be an important reference.
Book Synopsis Dissertation Abstracts International by :
Download or read book Dissertation Abstracts International written by and published by . This book was released on 2008 with total page 1006 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homogenization by : Gregori A. Chechkin
Download or read book Homogenization written by Gregori A. Chechkin and published by American Mathematical Soc.. This book was released on 2007 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homogenization is a collection of powerful techniques in partial differential equations that are used to study differential operators with rapidly oscillating coefficients, boundary value problems with rapidly varying boundary conditions, equations in perforated domains, equations with random coefficients, and other objects of theoretical and practical interest. The book focuses on various aspects of homogenization theory and related topics. It comprises classical results and methods of homogenization theory, as well as modern subjects and techniques developed in the last decade. Special attention is paid to averaging of random parabolic equations with lower order terms, to homogenization of singular structures and measures, and to problems with rapidly alternating boundary conditions. The book contains many exercises, which help the reader to better understand the material presented. All the main results are illustrated with a large number of examples, ranging from very simple to rather advanced.
Book Synopsis Shape Optimization, Homogenization and Optimal Control by : Volker Schulz
Download or read book Shape Optimization, Homogenization and Optimal Control written by Volker Schulz and published by Springer. This book was released on 2018-09-05 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume give an insight into current research activities in Shape Optimization, Homogenization and Optimal Control performed in Africa, Germany and internationally. Seeds for collaboration can be found in the first four papers in the field of homogenization. Modelling and optimal control in partial differential equations is the topic of the next six papers, again mixed from Africa and Germany. Finally, new results in the field of shape optimization are discussed in the final international three papers. This workshop, held at the AIMS Center Senegal, March 13-16, 2017, has been supported by the Deutsche Forschungsgemeinschaft (DFG) and by the African Institute for Mathematical Sciences (AIMS) in Senegal, which is one of six centres of a pan-African network of centres of excellence for postgraduate education, research and outreach in mathematical sciences.
Book Synopsis Multiscale Models in Mechano and Tumor Biology by : Alf Gerisch
Download or read book Multiscale Models in Mechano and Tumor Biology written by Alf Gerisch and published by Springer. This book was released on 2018-03-16 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.
Book Synopsis Homogenization and Effective Moduli of Materials and Media by : Jerry L Ericksen
Download or read book Homogenization and Effective Moduli of Materials and Media written by Jerry L Ericksen and published by . This book was released on 1986-06-11 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homogenization and Porous Media by : Ulrich Hornung
Download or read book Homogenization and Porous Media written by Ulrich Hornung and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics by : Felix Fritzen
Download or read book Machine Learning, Low-Rank Approximations and Reduced Order Modeling in Computational Mechanics written by Felix Fritzen and published by MDPI. This book was released on 2019-09-18 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: The use of machine learning in mechanics is booming. Algorithms inspired by developments in the field of artificial intelligence today cover increasingly varied fields of application. This book illustrates recent results on coupling machine learning with computational mechanics, particularly for the construction of surrogate models or reduced order models. The articles contained in this compilation were presented at the EUROMECH Colloquium 597, « Reduced Order Modeling in Mechanics of Materials », held in Bad Herrenalb, Germany, from August 28th to August 31th 2018. In this book, Artificial Neural Networks are coupled to physics-based models. The tensor format of simulation data is exploited in surrogate models or for data pruning. Various reduced order models are proposed via machine learning strategies applied to simulation data. Since reduced order models have specific approximation errors, error estimators are also proposed in this book. The proposed numerical examples are very close to engineering problems. The reader would find this book to be a useful reference in identifying progress in machine learning and reduced order modeling for computational mechanics.
Book Synopsis Homogenization Methods for Multiscale Mechanics by : Chiang C. Mei
Download or read book Homogenization Methods for Multiscale Mechanics written by Chiang C. Mei and published by World Scientific. This book was released on 2010 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many physical problems several scales present either in space or in time, caused by either 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 novel 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.
Book Synopsis Mathematical Problems in Elasticity and Homogenization by : O.A. Oleinik
Download or read book Mathematical Problems in Elasticity and Homogenization written by O.A. Oleinik and published by Elsevier. This book was released on 1992-11-02 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based on research undertaken by the authors during the last ten years. The main part of the work deals with homogenization problems in elasticity as well as some mathematical problems related to composite and perforated elastic materials. This study of processes in strongly non-homogeneous media brings forth a large number of purely mathematical problems which are very important for applications. Although the methods suggested deal with stationary problems, some of them can be extended to non-stationary equations. With the exception of some well-known facts from functional analysis and the theory of partial differential equations, all results in this book are given detailed mathematical proof. It is expected that the results and methods presented in this book will promote further investigation of mathematical models for processes in composite and perforated media, heat-transfer, energy transfer by radiation, processes of diffusion and filtration in porous media, and that they will stimulate research in other problems of mathematical physics and the theory of partial differential equations.
Book Synopsis Homogenization of Differential Operators and Integral Functionals by : V.V. Jikov
Download or read book Homogenization of Differential Operators and Integral Functionals written by V.V. Jikov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 583 pages. Available in PDF, EPUB and Kindle. Book excerpt: It was mainly during the last two decades that the theory of homogenization or averaging of partial differential equations took shape as a distinct mathe matical discipline. This theory has a lot of important applications in mechanics of composite and perforated materials, filtration, disperse media, and in many other branches of physics, mechanics and modern technology. There is a vast literature on the subject. The term averaging has been usually associated with the methods of non linear mechanics and ordinary differential equations developed in the works of Poincare, Van Der Pol, Krylov, Bogoliubov, etc. For a long time, after the works of Maxwell and Rayleigh, homogeniza tion problems for· partial differential equations were being mostly considered by specialists in physics and mechanics, and were staying beyond the scope of mathematicians. A great deal of attention was given to the so called disperse media, which, in the simplest case, are two-phase media formed by the main homogeneous material containing small foreign particles (grains, inclusions). Such two-phase bodies, whose size is considerably larger than that of each sep arate inclusion, have been discovered to possess stable physical properties (such as heat transfer, electric conductivity, etc.) which differ from those of the con stituent phases. For this reason, the word homogenized, or effective, is used in relation to these characteristics. An enormous number of results, approximation formulas, and estimates have been obtained in connection with such problems as electromagnetic wave scattering on small particles, effective heat transfer in two-phase media, etc.
Book Synopsis Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials by : P. Ponte Castaneda
Download or read book Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials written by P. Ponte Castaneda and published by Springer Science & Business Media. This book was released on 2006-02-17 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although several books and conference proceedings have already appeared dealing with either the mathematical aspects or applications of homogenization theory, there seems to be no comprehensive volume dealing with both aspects. The present volume is meant to fill this gap, at least partially, and deals with recent developments in nonlinear homogenization emphasizing applications of current interest. It contains thirteen key lectures presented at the NATO Advanced Workshop on Nonlinear Homogenization and Its Applications to Composites, Polycrystals and Smart Materials. The list of thirty one contributed papers is also appended. The key lectures cover both fundamental, mathematical aspects of homogenization, including nonconvex and stochastic problems, as well as several applications in micromechanics, thin films, smart materials, and structural and topology optimization. One lecture deals with a topic important for nanomaterials: the passage from discrete to continuum problems by using nonlinear homogenization methods. Some papers reveal the role of parameterized or Young measures in description of microstructures and in optimal design. Other papers deal with recently developed methods – both analytical and computational – for estimating the effective behavior and field fluctuations in composites and polycrystals with nonlinear constitutive behavior. All in all, the volume offers a cross-section of current activity in nonlinear homogenization including a broad range of physical and engineering applications. The careful reader will be able to identify challenging open problems in this still evolving field. For instance, there is the need to improve bounding techniques for nonconvex problems, as well as for solving geometrically nonlinear optimum shape-design problems, using relaxation and homogenization methods.
Book Synopsis Advances in Materials Science and Engineering by : Chander Prakash
Download or read book Advances in Materials Science and Engineering written by Chander Prakash and published by Springer Nature. This book was released on 2020-05-21 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the select proceedings of the International Conference on Functional Material, Manufacturing and Performances (ICFMMP) 2019. The book provides the state-of-the-art research, development, and commercial prospective of recent advances in materials science and engineering. The contents cover various synthesis and fabrication routes of functional and smart materials for applications in mechanical engineering, manufacturing, metrology, nanotechnology, physics, chemical and biological sciences, civil engineering, food science among others. It also provides the evolutionary behavior of materials science for industrial applications. This book will be a useful resource for researchers as well as professionals interested in the highly interdisciplinary field of materials science.
