Random Polymer Models
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Random Polymer Models
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Author : Giambattista Giacomin
language : en
Publisher: World Scientific
Release Date : 2007-03-22
Random Polymer Models written by Giambattista Giacomin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-03-22 with Mathematics categories.
This volume introduces readers to the world of disordered systems and to some of the remarkable probabilistic techniques developed in the field. The author explores in depth a class of directed polymer models to which much attention has been devoted in the last 25 years, in particular in the fields of physical and biological sciences. The models treated have been widely used in studying, for example, the phenomena of polymer pinning on a defect line, the behavior of copolymers in proximity to an interface between selective solvents and the DNA denaturation transition. In spite of the apparent heterogeneity of this list, in mathematical terms, a unified vision emerges. One is in fact dealing with the natural statistical mechanics systems built on classical renewal sequences by introducing one-body potentials.This volume is also a self-contained mathematical account of the state of the art for this class of statistical mechanics models./a
Random Polymers
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Author : Frank Hollander
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-05-14
Random Polymers written by Frank Hollander 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 2009-05-14 with Mathematics categories.
Polymer chains that interact with themselves and/or their environment display a range of physical and chemical phenomena. This text focuses on the mathematical description of some of these phenomena, offering a mathematical panorama of polymer chains.
Lattice Models Of Polymers
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Author : Carlo Vanderzande
language : en
Publisher: Cambridge University Press
Release Date : 1998-04-30
Lattice Models Of Polymers written by Carlo Vanderzande 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 1998-04-30 with Mathematics categories.
This book provides an introduction to lattice models of polymers. This is an important topic both in the theory of critical phenomena and the modelling of polymers. The first two chapters introduce the basic theory of random, directed and self-avoiding walks. The next two chapters develop and expand this theory to explore the self-avoiding walk in both two and three dimensions. Following chapters describe polymers near a surface, dense polymers, self-interacting polymers and branched polymers. The book closes with discussions of some geometrical and topological properties of polymers, and of self-avoiding surfaces on a lattice. The volume combines results from rigorous analytical and numerical work to give a coherent picture of the properties of lattice models of polymers. This book will be valuable for graduate students and researchers working in statistical mechanics, theoretical physics and polymer physics. It will also be of interest to those working in applied mathematics and theoretical chemistry.
The Random Cluster Model
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Author : Geoffrey R. Grimmett
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-13
The Random Cluster Model written by Geoffrey R. Grimmett 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 2006-12-13 with Mathematics categories.
The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Directed Polymers In Random Environments
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Author : Francis Comets
language : en
Publisher: Springer
Release Date : 2017-01-26
Directed Polymers In Random Environments written by Francis Comets and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-26 with Mathematics categories.
Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.
Random Growth Models
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Author : Michael Damron
language : en
Publisher: American Mathematical Soc.
Release Date : 2018-09-27
Random Growth Models written by Michael Damron and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-27 with Mathematics categories.
The study of random growth models began in probability theory about 50 years ago, and today this area occupies a central place in the subject. The considerable challenges posed by these models have spurred the development of innovative probability theory and opened up connections with several other parts of mathematics, such as partial differential equations, integrable systems, and combinatorics. These models also have applications to fields such as computer science, biology, and physics. This volume is based on lectures delivered at the 2017 AMS Short Course “Random Growth Models”, held January 2–3, 2017 in Atlanta, GA. The articles in this book give an introduction to the most-studied models; namely, first- and last-passage percolation, the Eden model of cell growth, and particle systems, focusing on the main research questions and leading up to the celebrated Kardar-Parisi-Zhang equation. Topics covered include asymptotic properties of infection times, limiting shape results, fluctuation bounds, and geometrical properties of geodesics, which are optimal paths for growth.
Microporous Media
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Author : Freddy Romm
language : en
Publisher: CRC Press
Release Date : 2004-03-29
Microporous Media written by Freddy Romm and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-29 with Science categories.
Microporous Media presents new developments from nearly a decade of advancement. Written by a leading researcher in the field, this reference provides examples of the most original scientific and technical research impacting studies in porosity and microporosity, and illustrates methods to forecast the properties of microporous structures for impro
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language : en
Publisher: World Scientific
Release Date :
written by and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Critical Phenomena In Loop Models
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Author : Adam Nahum
language : en
Publisher: Springer
Release Date : 2014-10-01
Critical Phenomena In Loop Models written by Adam Nahum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-01 with Science categories.
When close to a continuous phase transition, many physical systems can usefully be mapped to ensembles of fluctuating loops, which might represent for example polymer rings, or line defects in a lattice magnet, or worldlines of quantum particles. 'Loop models' provide a unifying geometric language for problems of this kind. This thesis aims to extend this language in two directions. The first part of the thesis tackles ensembles of loops in three dimensions, and relates them to the statistical properties of line defects in disordered media and to critical phenomena in two-dimensional quantum magnets. The second part concerns two-dimensional loop models that lie outside the standard paradigms: new types of critical point are found, and new results given for the universal properties of polymer collapse transitions in two dimensions. All of these problems are shown to be related to sigma models on complex or real projective space, CP^{n−1} or RP^{n−1} -- in some cases in a 'replica' limit -- and this thesis is also an in-depth investigation of critical behaviour in these field theories.
Simulation Methods For Polymers
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Author : Michael Kotelyanskii
language : en
Publisher: CRC Press
Release Date : 2004-03-01
Simulation Methods For Polymers written by Michael Kotelyanskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-03-01 with Technology & Engineering categories.