The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles

Author : E. J. Janse Van Rensburg
Publisher : Oxford Lecture Mathematics and
Page : 641 pages
File Size : 51,8 Mb
Release : 2015
Category : Mathematics
ISBN : 9780199666577

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The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles by E. J. Janse Van Rensburg Pdf

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.

Author : E. J. Janse VanRensburg
Publisher : Unknown
Page : 379 pages
File Size : 55,5 Mb
Release : 2024-06-03
Category : Electronic
ISBN : OCLC:615143313

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The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles by E. J. Janse VanRensburg Pdf

Author : E. J. Janse van Rensburg
Publisher : OUP Oxford
Page : 640 pages
File Size : 47,6 Mb
Release : 2015-05-14
Category : Mathematics
ISBN : 9780191644665

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The Statistical Mechanics of Interacting Walks, Polygons, Animals and Vesicles by E. J. Janse van Rensburg Pdf

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.

Author : A. J. Guttmann
Publisher : Springer
Page : 490 pages
File Size : 51,8 Mb
Release : 2009-03-30
Category : Science
ISBN : 9781402099274

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Polygons, Polyominoes and Polycubes by A. J. Guttmann Pdf

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.

Author : Ali Taheri
Publisher : OUP Oxford
Page : 500 pages
File Size : 54,5 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9780191047824

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Function Spaces and Partial Differential Equations by Ali Taheri Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 776 pages
File Size : 54,8 Mb
Release : 2000
Category : Mechanics, Applied
ISBN : OSU:32435065742082

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Applied Mechanics Reviews by Anonim Pdf

Author : Frank den Hollander
Publisher : Springer
Page : 266 pages
File Size : 47,7 Mb
Release : 2009-04-09
Category : Mathematics
ISBN : 9783642003332

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Random Polymers by Frank den Hollander Pdf

Polymer chains that interact with themselves and/or with their environment are fascinating objects, displaying a range of interesting physical and chemical phenomena. The focus in this monograph is on the mathematical description of some of these phenomena, with particular emphasis on phase transitions as a function of interaction parameters, associated critical behavior and space-time scaling. Topics include: self-repellent polymers, self-attracting polymers, polymers interacting with interfaces, charged polymers, copolymers near linear or random selective interfaces, polymers interacting with random substrate and directed polymers in random environment. Different techniques are exposed, including the method of local times, large deviations, the lace expansion, generating functions, the method of excursions, ergodic theory, partial annealing estimates, coarse-graining techniques and martingales. Thus, this monograph offers a mathematical panorama of polymer chains, which even today holds plenty of challenges.

Author : Gordon Slade
Publisher : Springer
Page : 233 pages
File Size : 54,7 Mb
Release : 2006-08-29
Category : Mathematics
ISBN : 9783540355182

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The Lace Expansion and its Applications by Gordon Slade Pdf

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.

Author : Andrea Braides
Publisher : Clarendon Press
Page : 230 pages
File Size : 55,8 Mb
Release : 2002-07-25
Category : Mathematics
ISBN : 9780191523199

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Gamma-Convergence for Beginners by Andrea Braides Pdf

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.

Author : Pavel Etingof,Frederic Latour
Publisher : OUP Oxford
Page : 152 pages
File Size : 43,5 Mb
Release : 2005-03-24
Category : Mathematics
ISBN : 9780191523922

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The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems by Pavel Etingof,Frederic Latour Pdf

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.

Author : Pavol Hell,Jaroslav Nesetril
Publisher : OUP Oxford
Page : 260 pages
File Size : 51,6 Mb
Release : 2004-07-22
Category : Mathematics
ISBN : 9780191523724

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Graphs and Homomorphisms by Pavol Hell,Jaroslav Nesetril Pdf

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.

Author : Juan Luis Vázquez
Publisher : Oxford University Press
Page : 249 pages
File Size : 47,8 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 9780199202973

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Smoothing and Decay Estimates for Nonlinear Diffusion Equations by Juan Luis Vázquez Pdf

This text is concerned with quantitative aspects of the theory of nonlinear diffusion equations, whichappear as mathematical models in different branches of Physics, Chemistry, Biology and Engineering.

Author : Jean-Yves Chemin,Benoit Desjardins,Isabelle Gallagher,Emmanuel Grenier
Publisher : Oxford University Press on Demand
Page : 263 pages
File Size : 41,5 Mb
Release : 2006-04-13
Category : Mathematics
ISBN : 9780198571339

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Mathematical Geophysics by Jean-Yves Chemin,Benoit Desjardins,Isabelle Gallagher,Emmanuel Grenier Pdf

Aimed at graduate students and researchers in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The Navier-Stokes equations are examined in both incompressible and rapidly rotating forms.

Author : Antonín Novotny,Ivan Straskraba
Publisher : OUP Oxford
Page : 528 pages
File Size : 40,7 Mb
Release : 2004-06-17
Category : Mathematics
ISBN : 9780191523953

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Introduction to the Mathematical Theory of Compressible Flow by Antonín Novotny,Ivan Straskraba Pdf

This book provides a comprehensive introduction to the mathematical theory of compressible flow, describing both inviscid and viscous compressible flow, which are governed by the Euler and the Navier-Stokes equations respectively. The method of presentation allows readers with different backgrounds to focus on various modules of the material, either in part or more fully. Chapters include detailed heuristic arguments providing motivation for technical aspects that are rigorously presented later on in the text; for instance, the existence theory for steady and unsteady Navier-Stokes equations of isentropic compressible flow, and two-by-two systems of Euler equations in one space dimension. These parts are presented in a textbook style with auxiliary material in supporting sections and appendices. The book includes a rich index and extensive bibliography, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of compressible flow, as well as in the book itself.

Author : Luigi Ambrosio,Paolo Tilli
Publisher : Oxford University Press, USA
Page : 148 pages
File Size : 41,8 Mb
Release : 2004
Category : Mathematics
ISBN : 0198529384

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Topics on Analysis in Metric Spaces by Luigi Ambrosio,Paolo Tilli Pdf

This book presents the main mathematical prerequisites for analysis in metric spaces. It covers abstract measure theory, Hausdorff measures, Lipschitz functions, covering theorums, lower semicontinuity of the one-dimensional Hausdorff measure, Sobolev spaces of maps between metric spaces, and Gromov-Hausdorff theory, all developed ina general metric setting. The existence of geodesics (and more generally of minimal Steiner connections) is discussed on general metric spaces and as an application of the Gromov-Hausdorff theory, even in some cases when the ambient space is not locally compact. A brief and very general description of the theory of integration with respect to non-decreasing set functions is presented following the Di Giorgi method of using the 'cavalieri' formula as the definition of the integral. Based on lecture notes from Scuola Normale, this book presents the main mathematical prerequisites for analysis in metric spaces. Supplemented with exercises of varying difficulty it is ideal for a graduate-level short course for applied mathematicians and engineers.