Mathematical Methods And Models In Phase Transitions
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Mathematical Methods And Models In Phase Transitions
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Author : Alain Miranville
language : en
Publisher: Nova Publishers
Release Date : 2005
Mathematical Methods And Models In Phase Transitions written by Alain Miranville and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The modelling and the study of phase transition phenomena are capital issues as they have essential applications in material sciences and in biological and industrial processes. We can mention, e.g., phase separation in alloys, ageing of materials, microstructure evolution, crystal growth, solidification in complex alloys, surface diffusion in the presence of stress, evolution of the surface of a thin flow in heteroepitaxial growth, motion of voids in interconnects in integrated circuits, treatment of airway closure disease by surfactant injection, fuel injection, fire extinguishers etc., This book consists of 11 contributions from specialists in the mathematical modelling and analysis of phase transitions. The content of these contributions ranges from the modelling to the mathematical and numerical analysis. Furthermore, many numerical simulations are presented. Finally, the contributors have tried to give comprehensive and accurate reference lists. This book should thus serve as a reference book for researchers interested in phase transition phenomena.
Mathematical Methods And Models In Phase Transitions
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Author :
language : en
Publisher:
Release Date : 2006
Mathematical Methods And Models In Phase Transitions written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with categories.
Continuum Models For Phase Transitions And Twinning In Crystals
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Author : Mario Pitteri
language : en
Publisher: CRC Press
Release Date : 2002-06-27
Continuum Models For Phase Transitions And Twinning In Crystals written by Mario Pitteri and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-27 with Mathematics categories.
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 c
Mathematical Models For Phase Change Problems
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Author : J.F. Rodriques
language : en
Publisher: Birkhäuser
Release Date : 2013-03-07
Mathematical Models For Phase Change Problems written by J.F. Rodriques and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-07 with Social Science categories.
This monograph collects research and expository articles reflect ing the interaction and the cooperation of different groups in several European institut ions concerning current research on mathematical models for the behaviour of materials with phase change. These papers were presented and discussed in a Workshop held at Obidos, Portugal, du ring the first three days of October, 1988, and grew out of a two year period of intensive exploitation of differ ent abilities and mathematical experiences of the six participating groups, namely, in the University of Augsburg, wh ich was the co ordination center of this project, the Laboratoire Central des Ponts et Chaussees of Paris, the Aristoteles University of Thessaloniki, the University of Florence, the University of Lisbon and the University of Oxford. This project was carried out under the title "Mathemat ical Models of Phase Transitions and Numerical Simulation", in the framework of twinning program for stimulation of cooperation and scientific interchange, sponsored by the European Community. The underlying idea of the project was to create and study the mathematical models arising in applied engineering problems with free boundaries in a broad sense, namely in melting and freezing problems, diffusion-reaction processes, solid-solid phase transition, hysteresis phenomena, "mushy region" descriptions, contact prob lems with friction andjor adhesion, elastoplastic deformations, etc. vi This large spectrum of applied problems have in common the main feature of brusque transitions of their qualitative behaviour that correspond, in general, to non-classical discontinuous monotone or non monotone strong nonlinearities in the mathematical equations
Models Of Phase Transitions
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Author : Augusto Visintin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Models Of Phase Transitions written by Augusto Visintin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
... "What do you call work?" "Why ain't that work?" Tom resumed his whitewashing, and answered carelessly: "Well. lI1a), he it is, and maybe it aill't. All I know, is, it suits Tom Sawvc/:" "Oil CO/lll!, IIOW, Will do not mean to let 011 that you like it?" The brush continued to move. "Likc it? Well, I do not see wlzy I oughtn't to like it. Does a hoy get a chance to whitewash a fence every day?" That put the thing ill a Ilew light. Ben stopped nibhling the apple ... (From Mark Twain's Adventures of Tom Sawyer, Chapter II.) Mathematics can put quantitative phenomena in a new light; in turn applications may provide a vivid support for mathematical concepts. This volume illustrates some aspects of the mathematical treatment of phase transitions, namely, the classical Stefan problem and its generalizations. The in tended reader is a researcher in application-oriented mathematics. An effort has been made to make a part of the book accessible to beginners, as well as physicists and engineers with a mathematical background. Some room has also been devoted to illustrate analytical tools. This volume deals with research I initiated when I was affiliated with the Istituto di Analisi Numerica del C.N.R. in Pavia, and then continued at the Dipartimento di Matematica dell'Universita di Trento. It was typeset by the author in plain TEX
Nonequilibrium Phase Transitions In Lattice Models
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Author : Joaquin Marro
language : en
Publisher: Cambridge University Press
Release Date : 1999-05-06
Nonequilibrium Phase Transitions In Lattice Models written by Joaquin Marro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-05-06 with Mathematics categories.
This book provides an introduction to nonequilibrium statistical physics via lattice models. Beginning with an introduction to the basic driven lattice gas, the early chapters discuss the relevance of this lattice model to certain natural phenomena and examine simulation results in detail. Several possible theoretical approaches to the driven lattice gas are presented. In the next two chapters, absorbing-state transitions are discussed in detail. The later chapters examine a variety of systems subject to dynamic disorder before returning to look at the more surprising effects of multiparticle rules, nonunique absorbing-states and conservation laws. Examples are given throughout the book, the emphasis being on using simple representations of nature to describe ordering in real systems. The use of methods such as mean-field theory, Monte Carlo simulation, and the concept of universality to study and interpret these models is described. Detailed references are included.
Phase Transitions In Complex Fluids
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Author : Pierre Toldano
language : en
Publisher: World Scientific
Release Date : 1998
Phase Transitions In Complex Fluids written by Pierre Toldano and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Science categories.
This important and timely book deals with the theoretical and experimental investigation of the phase transitions which occur in complex fluid systems, namely lyotropic systems, microemulsions, colloids, gels, polymers, biological membranes, Langmuir monolayers, and ferrofluids. It contains 20-odd review papers from the major contributors to this rapidly growing field of research, summarizing the main results obtained in the description and understanding of the phase transitions taking place between the isotopic, nematic, cholesteric, lamellar, hexagonal, and cubic mesophases of complex fluids.
Equilibrium Statistical Mechanics Of Lattice Models
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Author : David A. Lavis
language : en
Publisher: Springer
Release Date : 2015-01-31
Equilibrium Statistical Mechanics Of Lattice Models written by David A. Lavis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-31 with Science categories.
Most interesting and difficult problems in equilibrium statistical mechanics concern models which exhibit phase transitions. For graduate students and more experienced researchers this book provides an invaluable reference source of approximate and exact solutions for a comprehensive range of such models. Part I contains background material on classical thermodynamics and statistical mechanics, together with a classification and survey of lattice models. The geometry of phase transitions is described and scaling theory is used to introduce critical exponents and scaling laws. An introduction is given to finite-size scaling, conformal invariance and Schramm—Loewner evolution. Part II contains accounts of classical mean-field methods. The parallels between Landau expansions and catastrophe theory are discussed and Ginzburg--Landau theory is introduced. The extension of mean-field theory to higher-orders is explored using the Kikuchi--Hijmans--De Boer hierarchy of approximations. In Part III the use of algebraic, transformation and decoration methods to obtain exact system information is considered. This is followed by an account of the use of transfer matrices for the location of incipient phase transitions in one-dimensionally infinite models and for exact solutions for two-dimensionally infinite systems. The latter is applied to a general analysis of eight-vertex models yielding as special cases the two-dimensional Ising model and the six-vertex model. The treatment of exact results ends with a discussion of dimer models. In Part IV series methods and real-space renormalization group transformations are discussed. The use of the De Neef—Enting finite-lattice method is described in detail and applied to the derivation of series for a number of model systems, in particular for the Potts model. The use of Pad\'e, differential and algebraic approximants to locate and analyze second- and first-order transitions is described. The realization of the ideas of scaling theory by the renormalization group is presented together with treatments of various approximation schemes including phenomenological renormalization. Part V of the book contains a collection of mathematical appendices intended to minimise the need to refer to other mathematical sources.
Quantum Phase Transitions
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Author : Subir Sachdev
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-07
Quantum Phase Transitions written by Subir Sachdev and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-07 with Science categories.
Describing the physical properties of quantum materials near critical points with long-range many-body quantum entanglement, this book introduces readers to the basic theory of quantum phases, their phase transitions and their observable properties. This second edition begins with a new section suitable for an introductory course on quantum phase transitions, assuming no prior knowledge of quantum field theory. It also contains several new chapters to cover important recent advances, such as the Fermi gas near unitarity, Dirac fermions, Fermi liquids and their phase transitions, quantum magnetism, and solvable models obtained from string theory. After introducing the basic theory, it moves on to a detailed description of the canonical quantum-critical phase diagram at non-zero temperatures. Finally, a variety of more complex models are explored. This book is ideal for graduate students and researchers in condensed matter physics and particle and string theory.
Dissipative Phase Transitions
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Author : Pierluigi Colli
language : en
Publisher: World Scientific
Release Date : 2006-03-06
Dissipative Phase Transitions written by Pierluigi Colli and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-03-06 with Mathematics categories.
Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity.The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area.This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects.