Random Polymer Models

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Random Polymer Models

Author : Giambattista Giacomin
Publisher : Imperial College Press
ISBN 13 : 1860947867
Total Pages : 259 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Random Polymer Models by : Giambattista Giacomin

Download or read book Random Polymer Models written by Giambattista Giacomin and published by Imperial College Press. This book was released on 2007 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Polymer Models

Author : Giambattista Giacomin
Publisher : Imperial College Press
ISBN 13 : 1860948294
Total Pages : 259 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Random Polymer Models by : Giambattista Giacomin

Download or read book Random Polymer Models written by Giambattista Giacomin and published by Imperial College Press. This book was released on 2007 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random polymer models and their applications -- The homogeneous pinning model -- Weakly inhomogeneous models -- The free energy of disordered polymer chains -- Disordered pinning models: The hase diagram -- Disordered copolymers and selective interfaces: The phase diagram -- The localized phase of disordered polymers -- The delocalized phase of disordered polymers -- Numerical algorithms and computations

Random Polymers

Author : Frank Hollander
Publisher : Springer Science & Business Media
ISBN 13 : 364200332X
Total Pages : 271 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Random Polymers by : Frank Hollander

Download or read book Random Polymers written by Frank Hollander and published by Springer Science & Business Media. This book was released on 2009-05-14 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Directed Polymers in Random Environments

Author : Francis Comets
Publisher : Springer
ISBN 13 : 3319504878
Total Pages : 210 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Directed Polymers in Random Environments by : Francis Comets

Download or read book Directed Polymers in Random Environments written by Francis Comets and published by Springer. This book was released on 2017-01-26 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Statistical Physics of Polymers

Author : Toshihiro Kawakatsu
Publisher : Springer Science & Business Media
ISBN 13 : 366210024X
Total Pages : 223 pages
Book Rating : 4.6/5 (621 download)

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Book Synopsis Statistical Physics of Polymers by : Toshihiro Kawakatsu

Download or read book Statistical Physics of Polymers written by Toshihiro Kawakatsu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "...This book is a very useful addition to polymer literature, and it is a pleasure to recommend it to the polymer community." (J.E. Mark, University of Cincinnati, POLYMER NEWS)

Lattice Models of Polymers

Author : Carlo Vanderzande
Publisher : Cambridge University Press
ISBN 13 : 0521559936
Total Pages : 240 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Lattice Models of Polymers by : Carlo Vanderzande

Download or read book Lattice Models of Polymers written by Carlo Vanderzande and published by Cambridge University Press. This book was released on 1998-04-30 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Random Walk Models and Probabilistic Techniques for Inhomogeneous Polymer Chains

Author : Francesco Caravenna
Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (491 download)

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Book Synopsis Random Walk Models and Probabilistic Techniques for Inhomogeneous Polymer Chains by : Francesco Caravenna

Download or read book Random Walk Models and Probabilistic Techniques for Inhomogeneous Polymer Chains written by Francesco Caravenna and published by . This book was released on 2005 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Physical Polymer Science

Author : Leslie H. Sperling
Publisher : John Wiley & Sons
ISBN 13 : 1119103746
Total Pages : 815 pages
Book Rating : 4.1/5 (191 download)

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Book Synopsis Introduction to Physical Polymer Science by : Leslie H. Sperling

Download or read book Introduction to Physical Polymer Science written by Leslie H. Sperling and published by John Wiley & Sons. This book was released on 2015-02-02 with total page 815 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Updated Edition of the Classic Text Polymers constitute the basis for the plastics, rubber, adhesives, fiber, and coating industries. The Fourth Edition of Introduction to Physical Polymer Science acknowledges the industrial success of polymers and the advancements made in the field while continuing to deliver the comprehensive introduction to polymer science that made its predecessors classic texts. The Fourth Edition continues its coverage of amorphous and crystalline materials, glass transitions, rubber elasticity, and mechanical behavior, and offers updated discussions of polymer blends, composites, and interfaces, as well as such basics as molecular weight determination. Thus, interrelationships among molecular structure, morphology, and mechanical behavior of polymers continue to provide much of the value of the book. Newly introduced topics include: Nanocomposites, including carbon nanotubes and exfoliated montmorillonite clays The structure, motions, and functions of DNA and proteins, as well as the interfaces of polymeric biomaterials with living organisms The glass transition behavior of nano-thin plastic films In addition, new sections have been included on fire retardancy, friction and wear, optical tweezers, and more. Introduction to Physical Polymer Science, Fourth Edition provides both an essential introduction to the field as well as an entry point to the latest research and developments in polymer science and engineering, making it an indispensable text for chemistry, chemical engineering, materials science and engineering, and polymer science and engineering students and professionals.

Random Growth Models

Author : Michael Damron
Publisher : American Mathematical Soc.
ISBN 13 : 1470435535
Total Pages : 274 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Random Growth Models by : Michael Damron

Download or read book Random Growth Models written by Michael Damron and published by American Mathematical Soc.. This book was released on 2018-09-27 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Disorder and Critical Phenomena Through Basic Probability Models

Author : Giambattista Giacomin
Publisher : Springer Science & Business Media
ISBN 13 : 3642211550
Total Pages : 140 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Disorder and Critical Phenomena Through Basic Probability Models by : Giambattista Giacomin

Download or read book Disorder and Critical Phenomena Through Basic Probability Models written by Giambattista Giacomin and published by Springer Science & Business Media. This book was released on 2011-07-16 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the effect of disorder on critical phenomena is a central issue in statistical mechanics. In probabilistic terms: what happens if we perturb a system exhibiting a phase transition by introducing a random environment? The physics community has approached this very broad question by aiming at general criteria that tell whether or not the addition of disorder changes the critical properties of a model: some of the predictions are truly striking and mathematically challenging. We approach this domain of ideas by focusing on a specific class of models, the "pinning models," for which a series of recent mathematical works has essentially put all the main predictions of the physics community on firm footing; in some cases, mathematicians have even gone beyond, settling a number of controversial issues. But the purpose of these notes, beyond treating the pinning models in full detail, is also to convey the gist, or at least the flavor, of the "overall picture," which is, in many respects, unfamiliar territory for mathematicians.

Random and Restricted Walks

Author : Michael N. Barber
Publisher : CRC Press
ISBN 13 : 9780677026206
Total Pages : 190 pages
Book Rating : 4.0/5 (262 download)

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Book Synopsis Random and Restricted Walks by : Michael N. Barber

Download or read book Random and Restricted Walks written by Michael N. Barber and published by CRC Press. This book was released on 1970 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Analysis and Stochastics of Growth Processes and Interface Models

Author : Peter Mörters
Publisher : OUP Oxford
ISBN 13 : 019155359X
Total Pages : 348 pages
Book Rating : 4.1/5 (915 download)

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Book Synopsis Analysis and Stochastics of Growth Processes and Interface Models by : Peter Mörters

Download or read book Analysis and Stochastics of Growth Processes and Interface Models written by Peter Mörters and published by OUP Oxford. This book was released on 2008-07-24 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.

The Random-Cluster Model

Author : Geoffrey R. Grimmett
Publisher : Springer Science & Business Media
ISBN 13 : 3540328912
Total Pages : 392 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis The Random-Cluster Model by : Geoffrey R. Grimmett

Download or read book The Random-Cluster Model written by Geoffrey R. Grimmett and published by Springer Science & Business Media. This book was released on 2006-12-13 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Pinning and Wetting Models for Polymers with Semi-Flexible Interaction

Author : Martin Hubert Borecki
Publisher : Sudwestdeutscher Verlag Fur Hochschulschriften AG
ISBN 13 : 9783838120065
Total Pages : 156 pages
Book Rating : 4.1/5 (2 download)

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Book Synopsis Pinning and Wetting Models for Polymers with Semi-Flexible Interaction by : Martin Hubert Borecki

Download or read book Pinning and Wetting Models for Polymers with Semi-Flexible Interaction written by Martin Hubert Borecki and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2010-09 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are several examples of matter consisting of polymers like: plastic, rubber or soap and some more complicated biopolymers like: cellulose, DNA or filaments, which form the cytoskeleton of cells. The variety and numerous applications of these objects interested originally chemists, biologists, physicists and material scientists. Recently also mathematicians showed an active interest in a stochastic description of polymers, resulted in a field called "Random Polymer Models." This book deals with the stochastic description of models motivated from the point of view of semi-flexible polymers. These are chain-like molecules build up from small molecular units (monomers) and, depending on the length-scale, displaying different flexibility properties. In particular, the focus is on the behavior of such a polymer chain in the proximity of an attractive environment, e.g. a membrane. An important question in this situation is whether the polymer sticks close to the membrane (localization) or fluctuates away from it (delocalization). This book provides technics and new results on phase transitions corresponding to some localization behavior.

Disorder Relevance for Continuous Time Polymer Models

Author : Kenn Huber
Publisher :
ISBN 13 : 9781267528643
Total Pages : 46 pages
Book Rating : 4.5/5 (286 download)

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Book Synopsis Disorder Relevance for Continuous Time Polymer Models by : Kenn Huber

Download or read book Disorder Relevance for Continuous Time Polymer Models written by Kenn Huber and published by . This book was released on 2012 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: Given a measure P on continuous time random walk paths x on some countable state space S and a Hamiltonian H, the Gibbs pertubation of P defined by [equation] gives a new measure on paths which can be viewed as a measure on polymers. In the case of H (t, x) = [equation], we say the resulting measure is concentrated on "homopolymers" which have an attraction to the origin. Similarly, we can examine the perturbation governed by an independent random source H (t, x, w) defined by [equation] gives a measure closely resembling that of the discrete polymer with disorder. Letting H (t, x, w) = [equation] and H (t, x) as before, we mirror the discrete polymer models with Gaussian disorder. In this paper we examine the critical values of both the annealed and quenched models, and see for which random walks we have disorder relevance. We show that, as expected, the continuous model results correspond nicely with those of the discrete polymer models.

Statistics of Linear Polymers in Disordered Media

Author : Bikas K. Chakrabarti
Publisher : Elsevier
ISBN 13 : 008046047X
Total Pages : 368 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Statistics of Linear Polymers in Disordered Media by : Bikas K. Chakrabarti

Download or read book Statistics of Linear Polymers in Disordered Media written by Bikas K. Chakrabarti and published by Elsevier. This book was released on 2005-06-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: With the mapping of the partition function graphs of the n-vector magnetic model in the n to 0 limit as the self-avoiding walks, the conformational statistics of linear polymers was clearly understood in early seventies. Various models of disordered solids, percolation model in particular, were also established by late seventies. Subsequently, investigations on the statistics of linear polymers or of self-avoiding walks in, say, porous medium or disordered lattices were started in early eighties. Inspite of the brilliant ideas forwarded and extensive studies made for the next two decades, the problem is not yet completely solved in its generality. This intriguing and important problem has remained since a topic of vigorous and active research. This book intends to offer the readers a first hand and extensive review of the various aspects of the problem, written by the experts in the respective fields. We hope, the contents of the book will provide a valuable guide for researchers in statistical physics of polymers and will surely induce further research and advances towards a complete understanding of the problem. First book on statistics of polymers in random media. Contents straight away from research labs. Chapters written by foremost experts in the respective fields. Theories, experiments and computer simulations extensively discussed. Includes latest developments in understanding related important topics like DNA unzipping, Travelling salesman problem, etc. Comprehensive index for quick search for keywords.

Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory

Author : Roberto Fernandez
Publisher : Springer Science & Business Media
ISBN 13 : 3662028662
Total Pages : 446 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory by : Roberto Fernandez

Download or read book Random Walks, Critical Phenomena, and Triviality in Quantum Field Theory written by Roberto Fernandez and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.