Download or read book Variational Methods for Crystalline Microstructure Analysis and Computation written by Georg Dolzmann and published by Springer. This book was released on 2004-10-23 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: Phase transformations in solids typically lead to surprising mechanical behaviour with far reaching technological applications. The mathematical modeling of these transformations in the late 80s initiated a new field of research in applied mathematics, often referred to as mathematical materials science, with deep connections to the calculus of variations and the theory of partial differential equations. This volume gives a brief introduction to the essential physical background, in particular for shape memory alloys and a special class of polymers (nematic elastomers). Then the underlying mathematical concepts are presented with a strong emphasis on the importance of quasiconvex hulls of sets for experiments, analytical approaches, and numerical simulations.

Download or read book IUTAM Symposium on Theoretical Computational and Modelling Aspects of Inelastic Media written by B. Daya Reddy and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work comprises papers based on some of the talks presented at the IUTAM Symposium of the same name, held in Cape Town, January 14-18, 2008. This volume treats cutting-edge issues in modelling, the behaviour of various classes of inelastic media, and associated algorithms for carrying out computational simulations. A key feature of the contributions are works directed at modelling behaviour at the meso and micro-scales, and at bridging the micro-macro scales.

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 Analysis Modeling and Simulation of Multiscale Problems written by Alexander Mielke and published by Springer Science & Business Media. This book was released on 2006-10-14 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reports recent mathematical developments in the Programme "Analysis, Modeling and Simulation of Multiscale Problems", which started as a German research initiative in 2006. Multiscale problems occur in many fields of science, such as microstructures in materials, sharp-interface models, many-particle systems and motions on different spatial and temporal scales in quantum mechanics or in molecular dynamics. The book presents current mathematical foundations of modeling, and proposes efficient numerical treatment.

Download or read book Theory and Numerics of Differential Equations written by James Blowey and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.

Download or read book Tutorials in Mathematical Biosciences IV written by Avner Friedman and published by Springer Science & Business Media. This book was released on 2007-11-21 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an introduction to fast growing research areas in evolution of species, population genetics, ecological models, and population dynamics. It reviews the concept and methodologies of phylogenetic trees, introduces ecological models, examines a broad range of ongoing research in population dynamics, and deals with gene frequencies under the action of migration and selection. The book features computational schemes, illustrations, and mathematical theorems.

Download or read book Inverse Problems and Imaging written by Ana Carpio and published by Springer Science & Business Media. This book was released on 2008-04-17 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the CIME Summer School on Imaging, experts in mathematical techniques and applications presented useful introductions to many aspects of the field. This volume contains updated lectures as well as additional contributions on other related topics.

Download or read book Mathematical Models of Granular Matter written by Gianfranco Capriz and published by Springer Science & Business Media. This book was released on 2008-04-18 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Granular matter displays a variety of peculiarities that distinguish it from other appearances studied in condensed matter physics and renders its overall mathematical modelling somewhat arduous. Prominent directions in the modelling granular flows are analyzed from various points of view. Foundational issues, numerical schemes and experimental results are discussed. The volume furnishes a rather complete overview of the current research trends in the mechanics of granular matter. Various chapters introduce the reader to different points of view and related techniques. New models describing granular bodies as complex bodies are presented. Results on the analysis of the inelastic Boltzmann equations are collected in different chapters. Gallavotti-Cohen symmetry is also discussed.

Download or read book Microstructure of Martensite written by Kaushik Bhattacharya and published by Oxford University Press. This book was released on 2003-11-06 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Martensites are crystalline solids that display dazzling patterns at the microscopic scales. This microstructure gives rise to unusual macroscopic properties like the shape-memory effect. Starting with the crystalline structure, this book describes a theoretical framework for studying martensites and uses the theory to explain why these materials form microstructure. The macrostructure consequences of the microstructure are subsequently discussed. Complete with a piece of shape-memory wire and numerous examples from real materials, this book represents a successful case study in multiscale modeling, giving a clear understanding of the link between microstructure and macrostructure properties. Beautifully written, in a most clear and pedagogical manner, it holds appeal for a broad audience. On the one hand, it introduces modern modeling techniques to those trained in materials science, mechanics and physics and shows how these techniques can be used in real-world problems. On the other hand, it introduces physical phenomena to those trained in mathematics, and demonstrates how such phenomena give rise to interesting mathematical problems.

Download or read book Mathematical Methods in Continuum Mechanics of Solids written by Martin Kružík and published by Springer. This book was released on 2019-03-02 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily focuses on rigorous mathematical formulation and treatment of static problems arising in continuum mechanics of solids at large or small strains, as well as their various evolutionary variants, including thermodynamics. As such, the theory of boundary- or initial-boundary-value problems for linear or quasilinear elliptic, parabolic or hyperbolic partial differential equations is the main underlying mathematical tool, along with the calculus of variations. Modern concepts of these disciplines as weak solutions, polyconvexity, quasiconvexity, nonsimple materials, materials with various rheologies or with internal variables are exploited. This book is accompanied by exercises with solutions, and appendices briefly presenting the basic mathematical concepts and results needed. It serves as an advanced resource and introductory scientific monograph for undergraduate or PhD students in programs such as mathematical modeling, applied mathematics, computational continuum physics and engineering, as well as for professionals working in these fields.

Download or read book Relaxation in Optimization Theory and Variational Calculus written by Tomáš Roubíček and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-11-09 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: The relaxation method has enjoyed an intensive development during many decades and this new edition of this comprehensive text reflects in particular the main achievements in the past 20 years. Moreover, many further improvements and extensions are included, both in the direction of optimal control and optimal design as well as in numerics and applications in materials science, along with an updated treatment of the abstract parts of the theory.

Download or read book ESAIM written by and published by . This book was released on 2007 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Elements of Nonlinear Analysis written by Michel Chipot and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book covers some of the main aspects of nonlinear analysis. It concentrates on stressing the fundamental ideas instead of elaborating on the intricacies of the more esoteric ones...it encompass[es] many methods of dynamical systems in quite simple and original settings. I recommend this book to anyone interested in the main and essential concepts of nonlinear analysis as well as the relevant methodologies and applications." --MATHEMATICAL REVIEWS

Download or read book Acta Numerica 1996 Volume 5 written by Arieh Iserles and published by Cambridge University Press. This book was released on 1996-07-25 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acta Numerica is an annual volume presenting survey papers in numerical analysis. Each year the editorial board selects significant topics and invites papers from authors who have made notable contributions to the development of that topic. The articles are intended to summarize the field at a level accessible to graduate students and researchers. Acta Numerica has proved to be a valuable tool not only for researchers and professionals wishing to develop their understanding of the subject and follow developments, but also as an advanced teaching aid at colleges and universities. Articles in previous volumes have been expanded into both monographs and textbooks, and many of the original articles themselves have been used as the prime resource for graduate courses.

Download or read book Multifield Problems in Solid and Fluid Mechanics written by Rainer Helmig and published by Springer Science & Business Media. This book was released on 2006-11-28 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an overview of the research projects within the SFB 404 "Mehrfeldprobleme in der Kontinuumsmechanik". The book is for researchers and graduate students in applied mechanics and civil engineering.

Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2006-02-09 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Celebrates the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Containing 32 contributions, this volume covers a range of nonlinear elliptic and parabolic equations, with applications to natural sciences and engineering.

Download or read book Quantum Field Theory I Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.