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: 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.
The Statistical Mechanics Of Interacting Walks Polygons Animals And Vesicles
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Author : E. J. Janse Van Rensburg
language : en
Publisher: Oxford University Press (UK)
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 University Press (UK) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematics categories.
This monograph examines the self-avoiding walk, a classical model in statistical mechanics, probability theory and mathematical physics, paying close attention to recent developments in the field, such as models in the hexagonal lattice and 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.
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.
Analytic Combinatorics
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet 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 2009-01-15 with Mathematics categories.
Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.
Introduction To The Mathematical Theory Of Compressible Flow
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Author : Antonín Novotny
language : en
Publisher: OUP Oxford
Release Date : 2004-06-17
Introduction To The Mathematical Theory Of Compressible Flow written by Antonín Novotny and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-17 with Mathematics categories.
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.
Mathematical Geophysics
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Author : Jean-Yves Chemin
language : en
Publisher: Clarendon Press
Release Date : 2006-04-13
Mathematical Geophysics written by Jean-Yves Chemin and has been published by Clarendon Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-13 with Science categories.
Aimed at graduate students, researchers and academics 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 text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed. Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinates and those in R2. In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical layers are introduced, whose study is completely open.