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Statistics Of Knots And Entangled Random Walks
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Book Synopsis Statistics of Knots and Entangled Random Walks by : Sergei K. Nechaev
Download or read book Statistics of Knots and Entangled Random Walks written by Sergei K. Nechaev and published by World Scientific. This book was released on 1996 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the author announces the class of problems called ?entropy of knots? and gives an overview of modern physical applications of existing topological invariants.He constructs statistical models on knot diagrams and braids using the representations of Jones-Kauffman and Alexander invariants and puts forward the question of limit distribution of these invariants for randomly generated knots. The relation of powers of corresponding algebraic invariants to the Lyapunov exponents of the products of noncommutative matrices is described. Also the problem of conditional joint limit distributions for ?brownian bridges? on braids is discussed. Special cases of noncommutative groups PSL(2, R), PSL(2, Z) and braid groups are considered in detail.In this volume, the author also discusses the application of conformal methods for explicit construction of topological invariants for random walks on multiconnected manifolds. The construction of these topological invariants and the monodromy properties of correlation function of some conformal theories are also discussed.The author also considers the physical applications of ?knot entropy? problem in various physical systems, focussing on polymer
Book Synopsis Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems by : A. Comtet
Download or read book Aspects topologiques de la physique en basse dimension. Topological aspects of low dimensional systems written by A. Comtet and published by Springer Science & Business Media. This book was released on 2000-01-20 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: Session LXIX. 7 - 31 July 1998
Book Synopsis Statphys 19 - Proceedings Of The 19th Iupap International Conference On Statistical Physics by : Bailin Hao
Download or read book Statphys 19 - Proceedings Of The 19th Iupap International Conference On Statistical Physics written by Bailin Hao and published by World Scientific. This book was released on 1996-03-18 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 19th IUPAP International Conference on Statistical Physics is devoted to the general field of statistical physics, including traditional topics such as statistical methods concerning the static and dynamic properties of mesoscopic and macroscopic states of matter, as well as hot topics of current interest in applications of statistical physics. These include quantum chaos and turbulence, structures and patterns, fractals, neural networks, computer simulation and visualization in statistical physics, disordered systems and heterogeneous systems, simple and complex fluids.
Book Synopsis Soft Order in Physical Systems by : R. Bruinsma
Download or read book Soft Order in Physical Systems written by R. Bruinsma and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: A humoristic view of the physics of soft matter, which nevertheless has a ring of truth to it, is that it is an ill-defined subject which deals with ill-condensed matter by ill-defined methods. Although, since the Nobel prize was awarded to Pierre-Gilles de Gennes, this subject can be no longer shrugged-away as "sludge physics" by the physics community, it is still not viewed universally as "main stream" physics. While, at first glance, this may be considered as another example of inertia, a case of the "establishment" against the "newcomer", the roots of this prejudice are much deeper and can be traced back to Roger Bacon's conception about the objectivity of science. All of us would agree with the weaker form of this idea which simply says that the final results of our work should be phrased in an observer-independent way and be communicable to anybody who made the effort to learn this language. There exists, however, a stronger form of this idea according to which the above criteria of "objectivity" and "communicability" apply also to the process of scientific inquiry. The fact that major progress in the physics of soft matter was made in apparent violation of this approach, by applying intuition to problems which appeared to defy rigorous analysis, may explain why many physicists feel somewhat ill-at-ease with this subject.
Book Synopsis Physical and Numerical Models in Knot Theory by : Jorge Alberto Calvo
Download or read book Physical and Numerical Models in Knot Theory written by Jorge Alberto Calvo and published by World Scientific. This book was released on 2005 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appreciated and valuable progress continues to be made each year. This volume presents several contributions from researchers using computers to study problems that would otherwise be intractable. While computations have long been used to analyze problems, formulate conjectures, and search for special structures in knot theory, increased computational power has made them a staple in many facets of the field. The volume also includes contributions concentrating on models researchers use to understand knotting, linking, and entanglement in physical and biological systems. Topics include properties of knot invariants, knot tabulation, studies of hyperbolic structures, knot energies, the exploration of spaces of knots, knotted umbilical cords, studies of knots in DNA and proteins, and the structure of tight knots. Together, the chapters explore four major themes: physical knot theory, knot theory in the life sciences, computational knot theory, and geometric knot theory.
Book Synopsis Engineering Applications of Noncommutative Harmonic Analysis by : Gregory S. Chirikjian
Download or read book Engineering Applications of Noncommutative Harmonic Analysis written by Gregory S. Chirikjian and published by CRC Press. This book was released on 2021-02-25 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2001. The classical Fourier transform is one of the most widely used mathematical tools in engineering. However, few engineers know that extensions of harmonic analysis to functions on groups holds great potential for solving problems in robotics, image analysis, mechanics, and other areas. For those that may be aware of its potential value, there is still no place they can turn to for a clear presentation of the background they need to apply the concept to engineering problems. Engineering Applications of Noncommutative Harmonic Analysis brings this powerful tool to the engineering world. Written specifically for engineers and computer scientists, it offers a practical treatment of harmonic analysis in the context of particular Lie groups (rotation and Euclidean motion). It presents only a limited number of proofs, focusing instead on providing a review of the fundamental mathematical results unknown to most engineers and detailed discussions of specific applications. Advances in pure mathematics can lead to very tangible advances in engineering, but only if they are available and accessible to engineers. Engineering Applications of Noncommutative Harmonic Analysis provides the means for adding this valuable and effective technique to the engineer's toolbox.
Author :Michael I. Monastyrsky Publisher :Springer Science & Business Media ISBN 13 :0817647791 Total Pages :220 pages Book Rating :4.8/5 (176 download)
Book Synopsis Riemann, Topology, and Physics by : Michael I. Monastyrsky
Download or read book Riemann, Topology, and Physics written by Michael I. Monastyrsky and published by Springer Science & Business Media. This book was released on 2009-06-08 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: The significantly expanded second edition of this book combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter.
Download or read book Physics, Uspekhi written by and published by . This book was released on 1998 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Random Knotting and Linking by : Kenneth C. Millett
Download or read book Random Knotting and Linking written by Kenneth C. Millett and published by World Scientific. This book was released on 1994 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume includes both rigorous asymptotic results on the inevitability of random knotting and linking, and Monte Carlo simulations of knot probability at small lengths. The statistical mechanics and topology of surfaces on the d-dimensional simple cubic lattice are investigated. The energy of knots is studied both analytically and numerically. Vassiliev invariants are investigated and used in random knot simulations. A mutation scheme which leaves the Jones polynomial unaltered is described. Applications include the investigation of RNA secondary structure using Vassiliev invariants, and the direct experimental measurement of DNA knot probability as a function of salt concentration in random cyclization experiments on linear DNA molecules. The papers in this volume reflect the diversity of interest across science and mathematics in this subject, from topology to statistical mechanics to theoretical chemistry to wet-lab molecular biology.
Download or read book The Cumulative Book Index written by and published by . This book was released on 1997 with total page 2312 pages. Available in PDF, EPUB and Kindle. Book excerpt: A world list of books in the English language.
Book Synopsis Intersections of Random Walks by : Gregory F. Lawler
Download or read book Intersections of Random Walks written by Gregory F. Lawler and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: A more accurate title for this book would be "Problems dealing with the non-intersection of paths of random walks. " These include: harmonic measure, which can be considered as a problem of nonintersection of a random walk with a fixed set; the probability that the paths of independent random walks do not intersect; and self-avoiding walks, i. e. , random walks which have no self-intersections. The prerequisite is a standard measure theoretic course in probability including martingales and Brownian motion. The first chapter develops the facts about simple random walk that will be needed. The discussion is self-contained although some previous expo sure to random walks would be helpful. Many of the results are standard, and I have made borrowed from a number of sources, especially the ex cellent book of Spitzer [65]. For the sake of simplicity I have restricted the discussion to simple random walk. Of course, many of the results hold equally well for more general walks. For example, the local central limit theorem can be proved for any random walk whose increments have mean zero and finite variance. Some of the later results, especially in Section 1. 7, have not been proved for very general classes of walks. The proofs here rely heavily on the fact that the increments of simple random walk are bounded and symmetric.
Book Synopsis Knots '96: Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan by : S Suzuki
Download or read book Knots '96: Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan written by S Suzuki and published by World Scientific. This book was released on 1997-04-19 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of an international conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The conference was attended by nearly 180 mathematicians from Japan and 14 other countries. Most of them were specialists in knot theory. The volume contains 43 papers, which deal with significant current research in knot theory, low-dimensional topology and related topics.The volume includes papers by the following invited speakers: G Burde, R Fenn, L H Kauffman, J Levine, J M Montesinos(-A), H R Morton, K Murasugi, T Soma, and D W Sumners.
Book Synopsis Introduction to Path-integral Methods in Physics and Polymer Science by : F W Wiegel
Download or read book Introduction to Path-integral Methods in Physics and Polymer Science written by F W Wiegel and published by World Scientific Publishing Company. This book was released on 1986-09-01 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph distills material prepared by the author for class lectures, conferences and research seminars. It fills in a much-felt gap between the older and original work by Feynman and Hibbs and the more recent and advanced volume by Schulman. After presenting an elementary account on the Wiener path integral as applied to Brownian motion, the author progresses on to the statistics of polymers and polymer entanglements. The next three chapters provide an introduction to quantum statistical physics with emphasis on the conceptual understanding of many-variable systems. A chapter on the renormalization group provides material for starting on research work. The final chapter contains an over view of the role of path integrals in recent developments in physics. A good bibliography is provided for each chapter. Request Inspection Copy
Book Synopsis Braid Group, Knot Theory and Statistical Mechanics II by : C N Yang
Download or read book Braid Group, Knot Theory and Statistical Mechanics II written by C N Yang and published by World Scientific. This book was released on 1994-02-24 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors. Contents:On the Combinatorics of Vassiliev Invariants (J S Birman)Solvable Methods, Link Invariants and Their Applications to Physics (T Deguchi & M Wadati)Quantum Symmetry in Conformal Field Theory by Hamiltonian Methods (L D Faddeev)Yang-Baxterization & Algebraic Structures (M L Ge, K Xue, Y S Wu)Spin Networks, Topology and Discrete Physics (L H Kauffman)Tunnel Numbers of Knots and Jones-Witten Invariants (T Kohno)Knot Invariants and Statistical Mechanics: A Physicist's Perspective (F Y Wu)and other papers Readership: Mathematical physicists. keywords:Braid Group;Knot Theory;Statistical Mechanics “It has been four years since the publication in 1989 of the previous volume bearing the same title as the present one. Enormous amounts of work have been done in the meantime. We hope the present volume will provide a summary of some of these works which are still progressing in several directions.” from the foreword by C N Yang
Download or read book Physical Review written by and published by . This book was released on 2000-04 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publishes papers that report results of research in statistical physics, plasmas, fluids, and related interdisciplinary topics. There are sections on (1) methods of statistical physics, (2) classical fluids, (3) liquid crystals, (4) diffusion-limited aggregation, and dendritic growth, (5) biological physics, (6) plasma physics, (7) physics of beams, (8) classical physics, including nonlinear media, and (9) computational physics.
Download or read book Conformations written by Alan E. Tonelli and published by CRC Press. This book was released on 2020-04-06 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among the materials found in Nature’s many diverse living organisms or produced by human industry, those made from polymers are dominant. In Nature, they are not only dominant, but they are, as well, uniquely necessary to life. Conformations: Connecting the Chemical Structures and Material Behaviors of Polymers explores how the detailed chemical structures of polymers can be characterized, how their microstructural-dependent conformational preferences can be evaluated, and how these conformational preferences can be connected to the behaviors and properties of their materials. The authors examine the connections between the microstructures of polymers and the rich variety of physical properties they evidence. Detailed polymer architectures, including the molecular bonding and geometries of backbone and side-chain groups, monomer stereo- and regiosequences, comonomer sequences, and branching, are explicitly considered in the analysis of the conformational characteristics of polymers. This valuable reference provides practicing materials engineers as well as polymer and materials science students a means of understanding the differences in behaviors and properties of materials made from chemically distinct polymers. This knowledge can assist the reader design polymers with chemical structures that lead to their desired material behaviors and properties.
Book Synopsis Revista Matemática Iberoamericana by :
Download or read book Revista Matemática Iberoamericana written by and published by . This book was released on 2002 with total page 820 pages. Available in PDF, EPUB and Kindle. Book excerpt:
