Gibbs Measures And Phase Transitions
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Gibbs Measures And Phase Transitions
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Author : Hans-Otto Georgii
language : en
Publisher: Walter de Gruyter
Release Date : 2011-05-31
Gibbs Measures And Phase Transitions written by Hans-Otto Georgii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-05-31 with Mathematics categories.
"This book is much more than an introduction to the subject of its title. It covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics and as an up to date reference in its chosen topics it is a work of outstanding scholarship. It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert. In its latter function it informs the reader about the state of the art in several directions. It is introductory in the sense that it does not assume any prior knowledge of statistical mechanics and is accessible to a general readership of mathematicians with a basic knowledge of measure theory and probability. As such it should contribute considerably to the further growth of the already lively interest in statistical mechanics on the part of probabilists and other mathematicians." Fredos Papangelou, Zentralblatt MATH The second edition has been extended by a new section on large deviations and some comments on the more recent developments in the area.
Gibbs Measures And Phase Transitions
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Author : Hans-Otto Georgii
language : en
Publisher: Walter de Gruyter
Release Date : 2011
Gibbs Measures And Phase Transitions written by Hans-Otto Georgii and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
From a review of the first edition: "This book [...] covers in depth a broad range of topics in the mathematical theory of phase transition in statistical mechanics. [...] It is in fact one of the author's stated aims that this comprehensive monograph should serve both as an introductory text and as a reference for the expert." (F. Papangelou
Statistical Mechanics Of Lattice Systems
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Author : Sacha Friedli
language : en
Publisher: Cambridge University Press
Release Date : 2017-11-23
Statistical Mechanics Of Lattice Systems written by Sacha Friedli 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 2017-11-23 with Mathematics categories.
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Phase Transitions In Surface Films
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Author : J.G. Dash
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Phase Transitions In Surface Films written by J.G. Dash 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 Science categories.
The Advanced Study Institute on Phase Transitions in Surface Films was held at the Ettore Majorana Centre for Scientific Cul ture in Erice, Sicily, during June 11 to June 25, 1979. This Institute was the second course of the International School of Low Temperature Physics which was established at the Centre in 1977, with the guidance and inspiration of T. Regge and A. Zichichi. The 1979 course selected a topic on one of the most rapidly advancing fields of condensed matter physics in the late 70's. The program of topics and speakers was developed with the advice of the Organizing Committee, composed of J. Friedel, N. D. Mermin, R. E. Peierls, T. Regge and J. Wheatley. These two weeks were memorable for the range and depth of the lectures and seminars, and the sustained high interest of the students and faculty through a damanding schedule of over 5 hours a day of formal sessions. A large fraction of the leading researchers in the field were there. It would have been impossible to gather such a large group five years earlier, for the field itself is hardly 10 years old. Although the foundations of the thermodynamics of surface films were laid down by Gibbs about 100 years ago, and experiments on oil/water monolayers were carried out by Pockels and Rayleigh at about the same time, the beginnings of the modern field were much more recent.
Microcanonical Thermodynamics
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Author : Dieter H. E. Gross
language : en
Publisher: World Scientific
Release Date : 2001
Microcanonical Thermodynamics written by Dieter H. E. Gross and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Science categories.
Boltzmann's formula S = In(W(E) defines the microcanonical ensemble. The usual textbooks on statistical mechanics start with the microensemble but rather quickly switch to the canonical ensemble introduced by Gibbs. This has the main advantage of easier analytical calculations, but there is a price to pay -- for example, phase transitions can only be defined in the thermodynamic limit of infinite system size. The question how phase transitions show up from systems with, say, 100 particles with an increasing number towards the bulk can only be answered when one finds a way to define and classify phase transitions in small systems. This is all possible within Boltzmann's original definition of the microcanonical ensemble. Starting from Boltzmann's formula, the book formulates the microcanonical thermodynamics entirely within the frame of mechanics. This way the thermodynamic limit is avoided and the formalism applies to small as well to other nonextensive systems like gravitational ones. Phasetransitions of first order, continuous transitions, critical lines and multicritical points can be unambiguously defined by the curvature of the entropy S(E, N). Special attention is given to the fragmentation of nuclei and atomic clusters as a peculiar phase transition of small systems controlled, among others, by angular momentum. The dependence of the liquid-gas transition of small atomic clusters under prescribed pressure is treated. Thus the analogue to the bulk transition can be studied. New insights into the many facets of the many-body physics of the critical point are presented. The book also describes the microcanonical statistics of the collapse of a self-gravitating system under large angular momentum.
Gibbs Measures In Biology And Physics The Potts Model
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Author : Utkir A Rozikov
language : en
Publisher: World Scientific
Release Date : 2022-07-28
Gibbs Measures In Biology And Physics The Potts Model written by Utkir A Rozikov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-28 with Mathematics categories.
This book presents recently obtained mathematical results on Gibbs measures of the q-state Potts model on the integer lattice and on Cayley trees. It also illustrates many applications of the Potts model to real-world situations in biology, physics, financial engineering, medicine, and sociology, as well as in some examples of alloy behavior, cell sorting, flocking birds, flowing foams, and image segmentation.Gibbs measure is one of the important measures in various problems of probability theory and statistical mechanics. It is a measure associated with the Hamiltonian of a biological or physical system. Each Gibbs measure gives a state of the system.The main problem for a given Hamiltonian on a countable lattice is to describe all of its possible Gibbs measures. The existence of some values of parameters at which the uniqueness of Gibbs measure switches to non-uniqueness is interpreted as a phase transition.This book informs the reader about what has been (mathematically) done in the theory of Gibbs measures of the Potts model and the numerous applications of the Potts model. The main aim is to facilitate the readers (in mathematical biology, statistical physics, applied mathematics, probability and measure theory) to progress into an in-depth understanding by giving a systematic review of the theory of Gibbs measures of the Potts model and its applications.
Statistical Mechanics
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Author : James Sethna
language : en
Publisher: OUP Oxford
Release Date : 2006-04-07
Statistical Mechanics written by James Sethna and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-07 with Science categories.
In each generation, scientists must redefine their fields: abstracting, simplifying and distilling the previous standard topics to make room for new advances and methods. Sethna's book takes this step for statistical mechanics - a field rooted in physics and chemistry whose ideas and methods are now central to information theory, complexity, and modern biology. Aimed at advanced undergraduates and early graduate students in all of these fields, Sethna limits his main presentation to the topics that future mathematicians and biologists, as well as physicists and chemists, will find fascinating and central to their work. The amazing breadth of the field is reflected in the author's large supply of carefully crafted exercises, each an introduction to a whole field of study: everything from chaos through information theory to life at the end of the universe.
Phase Transitions And Critical Phenomena
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Author :
language : en
Publisher: Elsevier
Release Date : 2000-09-15
Phase Transitions And Critical Phenomena written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-09-15 with Science categories.
The field of phase transitions and critical phenomena continues to be active in research, producing a steady stream of interesting and fruitful results. No longer an area of specialist interest, it has acquired a central focus in condensed matter studies. The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.The two review articles in this volume complement each other in a remarkable way. Both deal with what might be called the modern geometricapproach to the properties of macroscopic systems. The first article by Georgii (et al.) describes how recent advances in the application ofgeometric ideas leads to a better understanding of pure phases and phase transitions in equilibrium systems. The second article by Alava (et al.)deals with geometrical aspects of multi-body systems in a hands-on way, going beyond abstract theory to obtain practical answers. Thecombination of computers and geometrical ideas described in this volume will doubtless play a major role in the development of statisticalmechanics in the twenty-first century.
Phase Transitions In Foods
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Author : Yrjö H. Roos
language : en
Publisher: Academic Press
Release Date : 1995-06-12
Phase Transitions In Foods written by Yrjö H. Roos and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-06-12 with Technology & Engineering categories.
Assembling recent research and theories, this book describes the phase and state transitions that affect technological properties of biological materials occurring in food processing and storage. It covers the role of water as a plasticizer, the effect of transitions on mechanical and chemical changes, and the application of modeling in predicting stability rates of changes. The volume presents methods for detecting changes in the physical state and various techniques used to analyze phase behavior of biopolymers and food components. This book should become a valuable resource for anyone involved with food engineering, processing, storage, and quality, as well as those working on related properties of pharmaceuticals and other biopolymers. - Contains descriptions of nonfat food solids as"biopolymers"which exhibit physical properties that are highly dependent on temperature, time, and water content - Details the effects of water on the state and stability of foods - Includes information on changes occuring in state and physicochemical properties during processing and storage - The only book on phase and state transitions written specifically for the applications in food industry, product development, and research - No recent competition
The Physics Of Phase Transitions
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Author : Pierre Papon
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
The Physics Of Phase Transitions written by Pierre Papon 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 2013-06-29 with Science categories.
We learned in school that matter exists in three forms: solid, liquid and gas, as well as other more subtle things such as the fact that "evaporation produces cold. " The science of the states of matter was born in the 19th century. It has now grown enormously in two directions: 1) The transitions have multiplied: first between a solid and a solid, par ticularly for metallurgists. Then for magnetism, illustrated in France by Louis Neel, and ferro electricity. In addition, the extraordinary phenomenon of su perconductivity in certain metals appeared at the beginning of the 20th cen tury. And other superfluids were recognized later: helium 4, helium 3, the matter constituting atomic nuclei and neutron stars . . . There is now a real zoology of transitions, but we know how to classify them based on Landau's superb idea. 2) Our profound view of the mechanisms has evolved: in particular, the very universal properties of fluctuations near a critical point - described by Kadanoff's qualitative analysis and specified by an extraordinary theoretical tool: the renormalization group. Without exaggerating, we can say that our view of condensed matter has undergone two revolutions in the 20th century: first, the introduction of quantum physics in 1930, then the recognition of "self-similar" structures and the resulting scaling laws around 1970. .