Variational Methods for Crystalline Microstructure - Analysis and Computation PDF Download
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Author: Georg Dolzmann
Publisher: Springer
ISBN: 3540361251
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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.
Author: Georg Dolzmann
Publisher: Springer
ISBN: 3540361251
Category : Mathematics
Languages : en
Pages : 223
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Book Description
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.
Author: B. Daya Reddy
Publisher: Springer Science & Business Media
ISBN: 1402090900
Category : Technology & Engineering
Languages : en
Pages : 388
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Book Description
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.
Author: Bernard Dacorogna
Publisher: Springer Science & Business Media
ISBN: 0387552499
Category : Mathematics
Languages : en
Pages : 616
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Book Description
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.
Author: James Blowey
Publisher: Springer Science & Business Media
ISBN: 3662043548
Category : Mathematics
Languages : en
Pages : 290
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Book Description
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.
Author: Avner Friedman
Publisher: Springer Science & Business Media
ISBN: 3540743286
Category : Mathematics
Languages : en
Pages : 215
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Book Description
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.
Author: Alexander Mielke
Publisher: Springer Science & Business Media
ISBN: 3540356576
Category : Mathematics
Languages : en
Pages : 704
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Book Description
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.
Author: Kaushik Bhattacharya
Publisher: Oxford University Press
ISBN: 9780198509349
Category : Computers
Languages : en
Pages : 308
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Book Description
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.
Author: Martin Kružík
Publisher: Springer
ISBN: 3030020657
Category : Science
Languages : en
Pages : 624
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Book Description
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.
Author: Gianfranco Capriz
Publisher: Springer Science & Business Media
ISBN: 3540782761
Category : Technology & Engineering
Languages : en
Pages : 228
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Book Description
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.
Author: Tomáš Roubíček
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110590859
Category : Mathematics
Languages : en
Pages : 602
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Book Description
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.
