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 Variational Methods for Crystalline Microstructure written by Georg Dolzmann and published by . This book was released on 2002 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 2001-08-28 with total page 336 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 Analysis and Computation of Microstructure in Finite Plasticity written by Sergio Conti and published by Springer. This book was released on 2015-04-23 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.
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 Variational Methods in Nonlinear Elasticity written by Pablo Pedregal and published by SIAM. This book was released on 2000-01-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.
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 Weak Convergence Methods for Variational Models of Crystalline Solids written by Bo Li and published by Springer. This book was released on 2016-08-18 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims at a quick introduction to the modelling of martensitic phase transformationcs and therefore will be particularly welcoming to graduate students, post-doctorals, and researchers who like to understand the main concepts and methods of the subject. It covers the related mathematical theories (such as quasiconvexity, compensated compactness, and Young measures), the application of these theories to the analysis of martensitic microstructure, and the numerical approximation of microstructure. These mathematical theories have increasing applications in many scientific areas. The book includes in each chapter exercise problems that are not only for practice but also provide examples, proofs, and supplemental material.
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 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 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 617 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 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 The Computation of Crystalline Microstructure written by Mithcell Luskin and published by . This book was released on 1992 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: We describe a two-dimensional model of crystalline martensitic microstructure, and we present a new visualization of computational results for the finite element approximation of solutions to the variational problem with microstructure on a sequence of refined meshes.
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 Numerical Methods for Nonlinear Partial Differential Equations written by Sören Bartels and published by Springer. This book was released on 2015-01-19 with total page 394 pages. Available in PDF, EPUB and Kindle. Book excerpt: The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.
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.
