The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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Author : E. J. Janse Van Rensburg
language : en
Publisher: Oxford Lecture Mathematics and
Release Date : 2015
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles written by E. J. Janse Van Rensburg and has been published by Oxford Lecture Mathematics and this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model. This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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Author : E. J. Janse VanRensburg
language : en
Publisher:
Release Date :
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles written by E. J. Janse VanRensburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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Author : E. J. Janse van Rensburg
language : en
Publisher: OUP Oxford
Release Date : 2015-05-14
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles written by E. J. Janse van Rensburg and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-14 with Mathematics categories.
The self-avoiding walk is a classical model in statistical mechanics, probability theory and mathematical physics. It is also a simple model of polymer entropy which is useful in modelling phase behaviour in polymers. This monograph provides an authoritative examination of interacting self-avoiding walks, presenting aspects of the thermodynamic limit, phase behaviour, scaling and critical exponents for lattice polygons, lattice animals and surfaces. It also includes a comprehensive account of constructive methods in models of adsorbing, collapsing, and pulled walks, animals and networks, and for models of walks in confined geometries. Additional topics include scaling, knotting in lattice polygons, generating function methods for directed models of walks and polygons, and an introduction to the Edwards model. This essential second edition includes recent breakthroughs in the field, as well as maintaining the older but still relevant topics. New chapters include an expanded presentation of directed models, an exploration of methods and results for the hexagonal lattice, and a chapter devoted to the Monte Carlo methods.
Polygons Polyominoes And Polycubes
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Author : A. J. Guttmann
language : en
Publisher: Springer
Release Date : 2009-03-30
Polygons Polyominoes And Polycubes written by A. J. Guttmann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-30 with Science categories.
The problem of counting the number of self-avoiding polygons on a square grid, - therbytheirperimeterortheirenclosedarea,is aproblemthatis soeasytostate that, at ?rst sight, it seems surprising that it hasn’t been solved. It is however perhaps the simplest member of a large class of such problems that have resisted all attempts at their exact solution. These are all problems that are easy to state and look as if they should be solvable. They include percolation, in its various forms, the Ising model of ferromagnetism, polyomino enumeration, Potts models and many others. These models are of intrinsic interest to mathematicians and mathematical physicists, but can also be applied to many other areas, including economics, the social sciences, the biological sciences and even to traf?c models. It is the widespread applicab- ity of these models to interesting phenomena that makes them so deserving of our attention. Here however we restrict our attention to the mathematical aspects. Here we are concerned with collecting together most of what is known about polygons, and the closely related problems of polyominoes. We describe what is known, taking care to distinguish between what has been proved, and what is c- tainlytrue,but has notbeenproved. Theearlierchaptersfocusonwhatis knownand on why the problems have not been solved, culminating in a proof of unsolvability, in a certain sense. The next chapters describe a range of numerical and theoretical methods and tools for extracting as much information about the problem as possible, in some cases permittingexactconjecturesto be made.
Function Spaces And Partial Differential Equations
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Author : Ali Taheri
language : en
Publisher: OUP Oxford
Release Date : 2015-07-30
Function Spaces And Partial Differential Equations written by Ali Taheri and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-30 with Mathematics categories.
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 2000
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mechanics, Applied categories.
The Lace Expansion And Its Applications
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Author : Gordon Slade
language : en
Publisher: Springer
Release Date : 2006-08-29
The Lace Expansion And Its Applications written by Gordon Slade and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-29 with Mathematics categories.
The lace expansion is a powerful and flexible method for understanding the critical scaling of several models of interest in probability, statistical mechanics, and combinatorics, above their upper critical dimensions. These models include the self-avoiding walk, lattice trees and lattice animals, percolation, oriented percolation, and the contact process. This volume provides a unified and extensive overview of the lace expansion and its applications to these models.
Gamma Convergence For Beginners
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Author : Andrea Braides
language : en
Publisher: Clarendon Press
Release Date : 2002-07-25
Gamma Convergence For Beginners written by Andrea Braides and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-07-25 with Mathematics categories.
The theory of Gamma-convergence is commonly recognized as an ideal and flexible tool for the description of the asymptotic behaviour of variational problems. Its applications range from the mathematical analysis of composites to the theory of phase transitions, from Image Processing to Fracture Mechanics. This text, written by an expert in the field, provides a brief and simple introduction to this subject, based on the treatment of a series of fundamental problems that illustrate the main features and techniques of Gamma-convergence and at the same time provide a stimulating starting point for further studies. The main part is set in a one-dimensional framework that highlights the main issues of Gamma-convergence without the burden of higher-dimensional technicalities. The text deals in sequence with increasingly complex problems, first treating integral functionals, then homogenisation, segmentation problems, phase transitions, free-discontinuity problems and their discrete and continuous approximation, making stimulating connections among those problems and with applications. The final part is devoted to an introduction to higher-dimensional problems, where more technical tools are usually needed, but the main techniques of Gamma-convergence illustrated in the previous section may be applied unchanged. The book and its structure originate from the author's experience in teaching courses on this subject to students at PhD level in all fields of Applied Analysis, and from the interaction with many specialists in Mechanics and Computer Vision, which have helped in making the text addressed also to a non-mathematical audience. The material of the book is almost self-contained, requiring only some basic notion of Measure Theory and Functional Analysis.
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems
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Author : Pavel Etingof
language : en
Publisher: OUP Oxford
Release Date : 2005-03-24
The Dynamical Yang Baxter Equation Representation Theory And Quantum Integrable Systems written by Pavel Etingof and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-03-24 with Mathematics categories.
The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.
Graphs And Homomorphisms
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Author : Pavol Hell
language : en
Publisher: OUP Oxford
Release Date : 2004-07-22
Graphs And Homomorphisms written by Pavol Hell and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
This is a book about graph homomorphisms. Graph theory is now an established discipline but the study of graph homomorphisms has only recently begun to gain wide acceptance and interest. The subject gives a useful perspective in areas such as graph reconstruction, products, fractional and circular colourings, and has applications in complexity theory, artificial intelligence, telecommunication, and, most recently, statistical physics. Based on the authors' lecture notes for graduate courses, this book can be used as a textbook for a second course in graph theory at 4th year or master's level and has been used for courses at Simon Fraser University (Vancouver), Charles University (Prague), ETH (Zurich), and UFRJ (Rio de Janeiro). The exercises vary in difficulty. The first few are usually intended to give the reader an opportunity to practice the concepts introduced in the chapter; the later ones explore related concepts, or even introduce new ones. For the harder exercises hints and references are provided. The authors are well known for their research in this area and the book will be invaluable to graduate students and researchers alike.