Continuum Models For Phase Transitions And Twinning In Crystals

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Continuum Models for Phase Transitions and Twinning in Crystals

Mario Pitteri,G. Zanzotto
Continuum Models for Phase Transitions and Twinning in Crystals Book PDF

Author : Mario Pitteri,G. Zanzotto
Publisher : CRC Press
Page : 392 pages
File Size : 53,8 Mb
Release : 2002-06-27
Category : Mathematics
ISBN : 9781420036145

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Continuum Models for Phase Transitions and Twinning in Crystals by Mario Pitteri,G. Zanzotto Pdf

Continuum Models for Phase Transitions and Twinning in Crystals presents the fundamentals of a remarkably successful approach to crystal thermomechanics. Developed over the last two decades, it is based on the mathematical theory of nonlinear thermoelasticity, in which a new viewpoint on material symmetry, motivated by molecular theories, plays a central role. This is the first organized presentation of a nonlinear elastic approach to twinning and displacive phase transition in crystalline solids. The authors develop geometry, kinematics, and energy invariance in crystals in strong connection and with the purpose of investigating the actual mechanical aspects of the phenomena, particularly in an elastostatics framework based on the minimization of a thermodynamic potential. Interesting for both mechanics and mathematical analysis, the new theory offers the possibility of investigating the formation of microstructures in materials undergoing martensitic phase transitions, such as shape-memory alloys. Although phenomena such as twinning and phase transitions were once thought to fall outside the range of elastic models, research efforts in these areas have proved quite fruitful. Relevant to a variety of disciplines, including mathematical physics, continuum mechanics, and materials science, Continuum Models for Phase Transitions and Twinning in Crystals is your opportunity to explore these current research methods and topics.

Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials

P. Ponte Castaneda,J.J. Telega,B. Gambin
Nonlinear Homogenization and its Applications to Composites Polycrystals and Smart Materials Book PDF

Author : P. Ponte Castaneda,J.J. Telega,B. Gambin
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 40,9 Mb
Release : 2006-02-17
Category : Technology & Engineering
ISBN : 9781402026232

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Nonlinear Homogenization and its Applications to Composites, Polycrystals and Smart Materials by P. Ponte Castaneda,J.J. Telega,B. Gambin Pdf

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.

Phase Transitions and Crystal Symmetry

Yurii Aleksandrovich Izyumov,V.N. Syromyatnikov
Phase Transitions and Crystal Symmetry Book PDF

Author : Yurii Aleksandrovich Izyumov,V.N. Syromyatnikov
Publisher : Springer Science & Business Media
Page : 462 pages
File Size : 52,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400919204

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Phase Transitions and Crystal Symmetry by Yurii Aleksandrovich Izyumov,V.N. Syromyatnikov Pdf

About half a century ago Landau formulated the central principles of the phe nomenological second-order phase transition theory which is based on the idea of spontaneous symmetry breaking at phase transition. By means of this ap proach it has been possible to treat phase transitions of different nature in altogether distinct systems from a unified viewpoint, to embrace the aforemen tioned transitions by a unified body of mathematics and to show that, in a certain sense, physical systems in the vicinity of second-order phase transitions exhibit universal behavior. For several decades the Landau method has been extensively used to an alyze specific phase transitions in systems and has been providing a basis for interpreting experimental data on the behavior of physical characteristics near the phase transition, including the behavior of these characteristics in systems subject to various external effects such as pressure, electric and magnetic fields, deformation, etc. The symmetry aspects of Landau's theory are perhaps most effective in analyzing phase transitions in crystals because the relevant body of mathemat ics for this symmetry, namely, the crystal space group representation, has been worked out in great detail. Since particular phase transitions in crystals often call for a subtle symmetry analysis, the Landau method has been continually refined and developed over the past ten or fifteen years.

Advances in Continuum Mechanics and Thermodynamics of Material Behavior

Donald E. Carlson,Yi-Chao Chen
Advances in Continuum Mechanics and Thermodynamics of Material Behavior Book PDF

Author : Donald E. Carlson,Yi-Chao Chen
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 43,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401007283

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Advances in Continuum Mechanics and Thermodynamics of Material Behavior by Donald E. Carlson,Yi-Chao Chen Pdf

The papers included in this volume were presented at the Symposium on Advances in the Continuum Mechanics and Thermodynamics of Material Behavior, held as part of the 1999 Joint ASME Applied Mechanics and Materials Summer Conference at Virginia Tech on June 27-30, 1999. The Symposium was held in honor of Professor Roger L. Fosdick on his 60th birthday. The papers are written by prominent researchers in the fields of mechanics, thermodynamics, materials modeling, and applied mathematics. They address open questions and present the latest development in these and related areas. This volume is a valuable reference for researchers and graduate students in universities and research laboratories.

Mechanics and Mathematics of Crystals

Jerald L. Ericksen,Millard F. Beatty,Michael A. Hayes
Mechanics and Mathematics of Crystals Book PDF

Author : Jerald L. Ericksen,Millard F. Beatty,Michael A. Hayes
Publisher : World Scientific
Page : 656 pages
File Size : 41,6 Mb
Release : 2005
Category : Science
ISBN : 9789812562838

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Mechanics and Mathematics of Crystals by Jerald L. Ericksen,Millard F. Beatty,Michael A. Hayes Pdf

This book is a unique and comprehensive collection of pioneering contributions to the mechanics of crystals by J L Ericksen, a prominent and leading contributor to the study of the mechanics and mathematics of crystalline solids over the past 35 years.It presents a splendid corpus of research papers that cover areas on crystal symmetry, constitutive equations, defects and phase transitions — all topics of current importance to a broad group of workers in the field.The volume thus provides in one place material that is frequently referenced by numerous researchers on crystals across a spectrum of activities in areas of continuum mechanics, applied mathematics, engineering and materials science.Each group of papers or chapters in the book is preceded by a summary introduction that describes how the papers on that topic fit together, and in which Ericksen sketches the context of each paper and shares with the reader his thinking and insightfulness in writing it. The volume, edited by internationally renowned scholars whose works in finite elasticity and continuum mechanics have appeared in a variety of books and prestigious journals published over the past four decades, also includes a very interesting brief autobiography by Ericksen. In it he describes his early life in Oregon, his wartime experiences, his student days and postgraduate study, his introduction to scientific work, and what motivated him in his research. An English translation and revision of the first paper in this volume, originally published in Russian, appears here for the first time.

Micro-Macro-Interactions

Albrecht Bertram,Jürgen Tomas
Micro Macro Interactions Book PDF

Author : Albrecht Bertram,Jürgen Tomas
Publisher : Springer Science & Business Media
Page : 301 pages
File Size : 40,8 Mb
Release : 2008-10-23
Category : Science
ISBN : 9783540857150

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Micro-Macro-Interactions by Albrecht Bertram,Jürgen Tomas Pdf

Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.

Continuous Media with Microstructure

Bettina Albers
Continuous Media with Microstructure Book PDF

Author : Bettina Albers
Publisher : Springer Science & Business Media
Page : 389 pages
File Size : 53,5 Mb
Release : 2010-03-15
Category : Science
ISBN : 9783642114458

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Continuous Media with Microstructure by Bettina Albers Pdf

This book discusses the extension of classical continuum models. To the first class addressed belong various thermodynamic models of multicomponent systems, and to the second class belong primarily microstructures created by phase transformations.

Geometric Continuum Mechanics

Reuven Segev,Marcelo Epstein
Geometric Continuum Mechanics Book PDF

Author : Reuven Segev,Marcelo Epstein
Publisher : Springer Nature
Page : 416 pages
File Size : 53,7 Mb
Release : 2020-05-13
Category : Mathematics
ISBN : 9783030426835

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Geometric Continuum Mechanics by Reuven Segev,Marcelo Epstein Pdf

This contributed volume explores the applications of various topics in modern differential geometry to the foundations of continuum mechanics. In particular, the contributors use notions from areas such as global analysis, algebraic topology, and geometric measure theory. Chapter authors are experts in their respective areas, and provide important insights from the most recent research. Organized into two parts, the book first covers kinematics, forces, and stress theory, and then addresses defects, uniformity, and homogeneity. Specific topics covered include: Global stress and hyper-stress theories Applications of de Rham currents to singular dislocations Manifolds of mappings for continuum mechanics Kinematics of defects in solid crystals Geometric Continuum Mechanics will appeal to graduate students and researchers in the fields of mechanics, physics, and engineering who seek a more rigorous mathematical understanding of the area. Mathematicians interested in applications of analysis and geometry will also find the topics covered here of interest.

Poly-, Quasi- and Rank-One Convexity in Applied Mechanics

Jörg Schröder,Patrizio Neff
Poly Quasi and Rank One Convexity in Applied Mechanics Book PDF

Author : Jörg Schröder,Patrizio Neff
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 42,9 Mb
Release : 2010-08-04
Category : Technology & Engineering
ISBN : 9783709101742

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Poly-, Quasi- and Rank-One Convexity in Applied Mechanics by Jörg Schröder,Patrizio Neff Pdf

Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Waves and Stability in Continuous Media

Roberto Monaco,Miriam Pandolfi Bianchi,Salvatore Rionero
Waves and Stability in Continuous Media Book PDF

Author : Roberto Monaco,Miriam Pandolfi Bianchi,Salvatore Rionero
Publisher : World Scientific
Page : 616 pages
File Size : 51,6 Mb
Release : 2002-06-19
Category : Science
ISBN : 9789814488457

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Waves and Stability in Continuous Media by Roberto Monaco,Miriam Pandolfi Bianchi,Salvatore Rionero Pdf

First organized in 1981, the WASCOM conference to bring together researchers and scientists from all over the world to discuss problems, promote collaborations and shape future directions for research in the field of stability and wave propagation in continuous media. This book constitutes the proceedings of the 11th edition of the conference, the first of the third millennium. The main topics are: (1) Linear and nonlinear hyperbolic equations, conservation laws and specific aspects of wave propagation; (2) stability of systems of PDEs, with particular reference to those of fluid and solid mechanics; (3) extended thermodynamics and passage from microscopic to macroscopic description of the medium for systems characterized also by inelastic interactions at the kinetic scale. The proceedings have been selected for coverage in: • Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings) Contents:Recovering the Potential in the Schrödinger Equation from the N-D Map (S Avdonin et al.)Space Homogeneous Solutions of the Linear Boltzmann Equation for Semiconductors: A Semigroup Approach (J Banasiak et al.)Grad's Closure in the Kinetic Theory of a Chemically Reacting Gas (M Bisi et al.)Characteristic Shocks in Exceptional Directions (G Boillat & A Muracchini)Continuum Mechanics and Dynamical Permutations (Y Brenier)Continuum Equations for Rarefied Gases (X Chen & E A Spiegel)Decay and Other Properties of Cross-Sectional Measures in Elasticity (J N Flavin)Dynamics of Lines in the Spreading of Liquids on Solid Surfaces (H Gouin)Integration and Segregation in a Population — A Short Account of Socio-Thermodynamics (I Müller)Second Sound Propagation in Superfluid Helium via Extended Thermodynamics (A Muracchini et al.)An H-Theorem in a Simple Model of Chemically Reactive Dense Gases (J Polewczak)Modelling of Dissipative Processes (K R Rajagopal)On the Geometry of Spatial Hydrodynamic Motions. Solitonic Connections (C Rogers)Thermodynamics and Balance Laws for Processes of Inelastic Deformations (E I Romenski)Kinetic and Fluidynamic Approaches to Four-Wave-Mixing and Thermal Acoustic Phenomena in Quantum Optics (F Schürrer er al.)Unconditional Nonlinear Stability Via the Energy Method (B Straughan)Entropy Methods for the Asymptotic Behaviour of Fourth-order Nonlinear Diffusion Equations (G Toscani)and other papers Readership: Academics, researchers and graduate students in mathematical modeling, mathematical physics, fluid mechanics and thermodynamics. Keywords:Discontinuity and Shock Waves;Hyperbolic Systems;Stability in Fluid Dynamics;Small Parameter Problems;Kinetic Theories towards Continuum Models;Non Equilibrium Thermodynamics;Extended Thermodynamics;Chemically Reacting Mixtures;Mathematical Models of Biology;Numerical Methods of Fluid Dynamics

Variational Methods for Crystalline Microstructure - Analysis and Computation

Georg Dolzmann
Variational Methods for Crystalline Microstructure Analysis and Computation Book PDF

Author : Georg Dolzmann
Publisher : Springer
Page : 217 pages
File Size : 55,9 Mb
Release : 2004-10-25
Category : Mathematics
ISBN : 9783540361251

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Variational Methods for Crystalline Microstructure - Analysis and Computation by Georg Dolzmann Pdf

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.

Phase Transitions in Ferroelastic and Co-elastic Crystals

E. K. Salje
Phase Transitions in Ferroelastic and Co elastic Crystals Book PDF

Author : E. K. Salje
Publisher : Cambridge University Press
Page : 304 pages
File Size : 40,8 Mb
Release : 1993-04-22
Category : Science
ISBN : 0521429366

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Phase Transitions in Ferroelastic and Co-elastic Crystals by E. K. Salje Pdf

This textbook describes the fundamental principles of structural phase transitions in materials in an easily understandable form, suitable for both undergraduate and graduate students.

Discrete and Topological Models in Molecular Biology

Nataša Jonoska,Masahico Saito
Discrete and Topological Models in Molecular Biology Book PDF

Author : Nataša Jonoska,Masahico Saito
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 53,5 Mb
Release : 2013-12-23
Category : Computers
ISBN : 9783642401930

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Discrete and Topological Models in Molecular Biology by Nataša Jonoska,Masahico Saito Pdf

Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

PDEs and Continuum Models of Phase Transitions

Michel Rascle,Denis Serre,Marshall Slemrod
PDEs and Continuum Models of Phase Transitions Book PDF

Author : Michel Rascle,Denis Serre,Marshall Slemrod
Publisher : Springer
Page : 232 pages
File Size : 54,5 Mb
Release : 2014-08-23
Category : Science
ISBN : 3662137666

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PDEs and Continuum Models of Phase Transitions by Michel Rascle,Denis Serre,Marshall Slemrod Pdf

The study of phase transitions is one of the fundamental problems of physics. The goal of this seminar was to understand better the spectacular progress made recently in constructing continuum models. Concentrating on a few examples such as the microstructure of crystals, defects in liquid crystals and liquid-vapor interfaces, several key points are described, for example the structure and evolution of the interfaces, regularization via interfacial energy, and equilibrium theories. The mathematical treatment of these questions involves large-oscillation theories (Young's measures, compensated compactness), spectral theory, admissibility of shock waves, long-time behavior of dynamical systems, high-order perturbations, group actions, solitons, and others.

Applied and Industrial Mathematics, Venice—2, 1998

Renato Spigler
Applied and Industrial Mathematics Venice 2 1998 Book PDF

Author : Renato Spigler
Publisher : Springer Science & Business Media
Page : 298 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401141932

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Applied and Industrial Mathematics, Venice—2, 1998 by Renato Spigler Pdf

In this volume, I have collected several papers which were presented at the international conference called "Venice-2/Symposium on Applied and In dustrial Mathematics". Such a conference was held in Venice, Italy, between June 11 and 16,1998, and was intended as the follow-up of the very successful similar event (called "Venice-1/Symposium on Applied and Industrial Math ematics"), that was also organized in Venice in October 1989. The Venice-1 conference ended up with a Kluwer volume like this one. I am grateful to Kluwer for having accepted to publish the present volume, the aim of which is to update somehow the state-of-the-art in the field of Ap plied Mathematics as well as in that of the nowadays rather more developed area of Industrial Mathematics. The most of the invited (key-note) speakers contributed to this volume with a paper related to their talk. There are, in addition·, a few significant contributed papers, selected on the basis of their quality and relevance to the present-time research activities. The topics considered in the conference range from rather general sub jects in applied and numerical analysis, to more specialized subjects such as polymers and disordered media, granular flow, semiconductor mathematics, superconductors, elasticity, tomography and other inverse problems, financial modeling, photographic sciences, etc. The papers collected in this volume provide a selection of them. It is clear from the previous list that some attention has been paid to relatively new and emerging fields.