Author: Sergei Nechaev Publisher: World Scientific ISBN: 9814499501 Category : Science Languages : en Pages : 206
Book Description
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 polymers.
Author: Sergei K. Nechaev Publisher: World Scientific ISBN: 9810225199 Category : Mathematics Languages : en Pages : 206
Book Description
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
Author: Bailin Hao Publisher: World Scientific ISBN: 9814549088 Category : Languages : en Pages : 598
Book Description
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.
Author: S Suzuki Publisher: World Scientific ISBN: 9814546283 Category : Languages : en Pages : 614
Book Description
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.
Author: R. Bruinsma Publisher: Springer Science & Business Media ISBN: 146152458X Category : Science Languages : en Pages : 241
Book Description
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.
Author: Jorge Alberto Calvo Publisher: World Scientific ISBN: 9812703462 Category : Mathematics Languages : en Pages : 642
Book Description
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.
Author: Gregory S. Chirikjian Publisher: CRC Press ISBN: 1000694259 Category : Mathematics Languages : en Pages : 697
Book Description
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: 0817647791 Category : Mathematics Languages : en Pages : 220
Book Description
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.
Author: Sergei Nechaev
Author: Sergei K. Nechaev
Author: A. Comtet
Author: Bailin Hao
Author: S Suzuki
Author: R. Bruinsma
Author: Jorge Alberto Calvo
Author: Gregory S. Chirikjian
Author: Michael I. Monastyrsky
Author: