Download or read book Homogenization of Multiple Integrals written by Andrea Braides and published by Oxford University Press. This book was released on 1998 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to the mathematical theory of the homogenization of multiple integrals, this book describes the overall properties of such functionals with various applications ranging from cellular elastic materials to Riemannian metrics.

Download or read book Topology Optimization written by Martin Philip Bendsoe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topology optimization method solves the basic enginee- ring problem of distributing a limited amount of material in a design space. The first edition of this book has become the standard text on optimal design which is concerned with the optimization of structural topology, shape and material. This edition, has been substantially revised and updated to reflect progress made in modelling and computational procedures. It also encompasses a comprehensive and unified description of the state-of-the-art of the so-called material distribution method, based on the use of mathematical programming and finite elements. Applications treated include not only structures but also materials and MEMS.

Download or read book Dynamics Games and Science written by Jean-Pierre Bourguignon and published by Springer. This book was released on 2015-07-24 with total page 766 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this volume is research carried out as part of the program Mathematics of Planet Earth, which provides a platform to showcase the essential role of mathematics in addressing problems of an economic and social nature and creating a context for mathematicians and applied scientists to foster mathematical and interdisciplinary developments that will be necessary to tackle a myriad of issues and meet future global economic and social challenges. Earth is a planet with dynamic processes in its mantle, oceans and atmosphere creating climate, causing natural disasters and influencing fundamental aspects of life and life-supporting systems. In addition to these natural processes, human activity has developed highly complex systems, including economic and financial systems; the World Wide Web; frameworks for resource management, transportation, energy production and utilization; health care delivery, and social organizations. This development has increased to the point where it impacts the stability and equilibrium in human societies. Issues such as financial and economic crisis, sustainability, management of resources, risk analysis, and global integration have come to the fore. Written by some of the world’s leading specialists, this book presents the proceedings of the International Conference and Advanced School Planet Earth, Dynamics, Games and Science II, held in Lisbon, Portugal, 28 August -6 September 2013, which was organized by the International Center of Mathematics (CIM) as a partner institution of the international program Mathematics of Planet Earth 2013. The book describes the state of the art in advanced research and ultimate techniques in modeling natural, economic and social phenomena. It constitutes a tool and a framework for researchers and graduate students, both in mathematics and applied sciences, focusing mainly on dynamical systems, game theory and applied sciences.

Download or read book Optimal Control Problems for Partial Differential Equations on Reticulated Domains written by Peter I. Kogut and published by Springer Science & Business Media. This book was released on 2011-09-09 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the development of optimal control, the complexity of the systems to which it is applied has increased significantly, becoming an issue in scientific computing. In order to carry out model-reduction on these systems, the authors of this work have developed a method based on asymptotic analysis. Moving from abstract explanations to examples and applications with a focus on structural network problems, they aim at combining techniques of homogenization and approximation. Optimal Control Problems for Partial Differential Equations on Reticulated Domains is an excellent reference tool for graduate students, researchers, and practitioners in mathematics and areas of engineering involving reticulated domains.

Download or read book Direct Methods in the Calculus of Variations written by Bernard Dacorogna and published by Springer Science & Business Media. This book was released on 2007-11-21 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Download or read book The Complete Works of Gabrio Piola Volume II written by Francesco dell'Isola and published by Springer. This book was released on 2018-10-06 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the second volume of Piola’s original Italian text together with the English-language translation and comments, showing convincingly that Gabrio Piola’s work must still be regarded as a modern theory. Gabrio Piola’s work has had an enormous impact on the development of applied mathematics and continuum mechanics. As such, a committee of scientific experts took it upon themselves to translate his complete works. In a second step, they commented on Piola’s work and compared it to modern theories in mechanics in order to stress Piola’s impact on modern science and prove and confirm that he achieved significant milestones in applied mathematics.

Download or read book Differential Geometry and Continuum Mechanics written by Gui-Qiang G. Chen and published by Springer. This book was released on 2015-08-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the exciting interface between differential geometry and continuum mechanics, now recognised as being of increasing technological significance. Topics discussed include isometric embeddings in differential geometry and the relation with microstructure in nonlinear elasticity, the use of manifolds in the description of microstructure in continuum mechanics, experimental measurement of microstructure, defects, dislocations, surface energies, and nematic liquid crystals. Compensated compactness in partial differential equations is also treated. The volume is intended for specialists and non-specialists in pure and applied geometry, continuum mechanics, theoretical physics, materials and engineering sciences, and partial differential equations. It will also be of interest to postdoctoral scientists and advanced postgraduate research students. These proceedings include revised written versions of the majority of papers presented by leading experts at the ICMS Edinburgh Workshop on Differential Geometry and Continuum Mechanics held in June 2013. All papers have been peer reviewed.

Download or read book Energetic Relaxation to Structured Deformations written by José Matias and published by Springer Nature. This book was released on 2023-04-18 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoretical apparatus for assigning an energy to a structured deformation, thereby providing motivation to researchers in applied mathematics, continuum mechanics, engineering, and materials science to study the deformation of a solid body without committing at the outset to a specific mechanical theory. Researchers will benefit from an approach in which elastic, plastic, and fracture phenomena can be treated in a unified way. ​The book is intended for an audience acquainted with measure theory, the theory of functions of bounded variation, and continuum mechanics. Any students in their last years of undergraduate studies, graduate students, and researchers with a background in applied mathematics, the calculus of variations, and continuum mechanics will have the prerequisite to read this book.

Download or read book Classical and Advanced Theories of Thin Structures written by Antonio Morassi and published by Springer Science & Business Media. This book was released on 2009-06-22 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents an updated state-of-the-art overview of the general aspects and practical applications of the theories of thin structures, through the interaction of several topics, ranging from non-linear thin-films, shells, junctions, beams of different materials and in different contexts (elasticity, plasticity, etc.). Advanced problems like the optimal design and the modeling of thin films made of brittle or phase-transforming materials will be presented as well.

Download or read book Getting Acquainted with Homogenization and Multiscale written by Leonid Berlyand and published by Springer. This book was released on 2018-11-22 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of this book is to navigate beginning graduate students in mathematics and engineering through a mature field of multiscale problems in homogenization theory and to provide an idea of its broad scope. An overview of a wide spectrum of homogenization techniques ranging from classical two-scale asymptotic expansions to Gamma convergence and the rapidly developing field of stochastic homogenization is presented. The mathematical proofs and definitions are supplemented with intuitive explanations and figures to make them easier to follow. A blend of mathematics and examples from materials science and engineering is designed to teach a mixed audience of mathematical and non-mathematical students.

Download or read book Computational Mechanics of Composite Materials written by Marcin Marek Kaminski and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Mechanics of Composite Materials lays stress on the advantages of combining theoretical advancements in applied mathematics and mechanics with the probabilistic approach to experimental data in meeting the practical needs of engineers. Features: Programs for the probabilistic homogenisation of composite structures with finite numbers of components allow composites to be treated as homogeneous materials with simpler behaviours. Treatment of defects in the interfaces within heterogeneous materials and those arising in composite objects as a whole by stochastic modelling. New models for the reliability of composite structures. Novel numerical algorithms for effective Monte-Carlo simulation. Computational Mechanics of Composite Materials will be of interest to academic and practising civil, mechanical, electronic and aerospatial engineers, to materials scientists and to applied mathematicians requiring accurate and usable models of the behaviour of composite materials.

Download or read book Metamaterials and Plasmonics Fundamentals Modelling Applications written by Said Zouhdi and published by Springer Science & Business Media. This book was released on 2008-12-16 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metamaterials and plasmonics are cross-disciplinary fields that are emerging into the mainstream of many scientific areas. Examples of scientific and technical fields which are concerned are electrical engineering, micro- and nanotechnology, microwave engineering, optics, optoelectronics, and semiconductor technologies. In plasmonics, the interplay between propagating electromagnetic waves and free-electron oscillations in materials are exploited to create new components and applications. On the other hand, metamaterials refer to artificial composites in which small artificial elements, through their collective interaction, creates a desired and unexpected macroscopic response function that is not present in the constituent materials. This book charts the state of the art of these fields. In May 2008, world-leading experts in metamaterials and plasmonics gathered into a NATO Advanced Research Workshop in Marrakech, Morocco. The present book contains extended versions of 22 of the presentations held in the workshop, covering the general aspects of the field, as well as design and modelling questions of plasmonics and metamaterials, fabrication issues, and applications like absorbers and antennas.

Download or read book Handbook of Differential Equations Evolutionary Equations written by C.M. Dafermos and published by Elsevier. This book was released on 2008-10-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material collected in this volume discusses the present as well as expected future directions of development of the field with particular emphasis on applications. The seven survey articles present different topics in Evolutionary PDE's, written by leading experts.- Review of new results in the area- Continuation of previous volumes in the handbook series covering Evolutionary PDEs- Written by leading experts

Download or read book Local Minimization Variational Evolution and Convergence written by Andrea Braides and published by Springer. This book was released on 2014-07-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses new questions related to the asymptotic description of converging energies from the standpoint of local minimization and variational evolution. It explores the links between Gamma-limits, quasistatic evolution, gradient flows and stable points, raising new questions and proposing new techniques. These include the definition of effective energies that maintain the pattern of local minima, the introduction of notions of convergence of energies compatible with stable points, the computation of homogenized motions at critical time-scales through the definition of minimizing movement along a sequence of energies, the use of scaled energies to study long-term behavior or backward motion for variational evolutions. The notions explored in the book are linked to existing findings for gradient flows, energetic solutions and local minimizers, for which some generalizations are also proposed.

Download or read book Variational Methods for Discontinuous Structures written by Gianni Dal Maso and published by Springer Science & Business Media. This book was released on 2002 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the Proceedings of the International Workshop "Variational Methods For Discontinuous Structures", held at Villa Erba Antica (Cernobbio) on the Lago di Como, July 4-6, 2001. The workshop was jointly organized by the Dipartimento di Matematica Francesco Brioschi of Milano Politecnico and the International School for Advanced Studies (SISSA) of Trieste. In past years the calculus of variations faced mainly the study of continuous structures, particularly problems with smooth solutions. One of the deepest and more delicate problems was the regularity of weak solutions. More recently, new sophisticated tools have been introduced in order to study discontinuities. In many variational problems solutions develop singularities, and sometimes the most interesting part of a solution is the singularity itself. The conference intended to focus on recent developments in this direction. Some of the talks were devoted to differential or variational modelling of image segmentation, occlusion and textures synthesizing in image analysis, variational description of micro-magnetic materials, dimension reduction and structured deformations in elasticity and plasticity, phase transitions, irrigation and drainage, evolution of crystalline shapes. In most cases theoretical and numerical analysis of these models were provided. Other talks were dedicated to specific problems of the calculus of variations: variational theory of weak or lower-dimensional structures, optimal transport problems with free Dirichlet regions, higher order variational problems, symmetrization in the BV framework. This volume contains contributions by 12 of the 16 speakers invited to deliver lectures in the workshop. Most of the contributions present original results in fields which are rapidly evolving at present.

Download or read book Modern Methods in the Calculus of Variations written by Irene Fonseca and published by Springer Science & Business Media. This book was released on 2007-08-22 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Download or read book Calculus of Variations on Thin Prestressed Films written by Marta Lewicka and published by Springer Nature. This book was released on 2023-04-17 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph considers the analytical and geometrical questions emerging from the study of thin elastic films that exhibit residual stress at free equilibria. It provides the comprehensive account, the details and background on the most recent results in the combined research perspective on the classical themes: in Differential Geometry – that of isometrically embedding a shape with a given metric in an ambient space of possibly different dimension, and in Calculus of Variations – that of minimizing non-convex energy functionals parametrized by a quantity in whose limit the functionals become degenerate. Prestressed thin films are present in many contexts and applications, such as: growing tissues, plastically strained sheets, engineered swelling or shrinking gels, petals and leaves of flowers, or atomically thin graphene layers. While the related questions about the physical basis for shape formation lie at the intersection of biology, chemistry and physics, fundamentally they are of the analytical and geometrical character, and can be tackled using the techniques of the dimension reduction, laid out in this book. The text will appeal to mathematicians and graduate students working in the fields of Analysis, Calculus of Variations, Partial Differential Equations, and Applied Math. It will also be of interest to researchers and graduate students in Engineering (especially fields related to Solid Mechanics and Materials Science), who would like to gain the modern mathematical insight and learn the necessary tools.