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Physical and Numerical Models in Knot Theory
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 ...
New Developments In The Theory Of Knots
This reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics.
Lectures at Knots '96
This volume consists of ten lectures given at an international workshop/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 workshop was attended by nearly 170 mathematicians from Japan and 14 other countries, most of whom were specialists in knot theory. The lectures can serve as an introduction to the field for advanced undergraduates, graduates and also researchers working in areas such as theoretical physics.
Random Knotting And Linking
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.
Quantum Topology - Proceedings Of The Conference
This volume contains the conference on quantum topology, held at Kansas State University, Manhattan, KS, 24 - 28 March 1993.Quantum topology is a rapidly growing field of mathematics dealing with the recently discovered interactions between low-dimensional topology, the theory of quantum groups, category theory, Cā-algebra theory, gauge theory, conformal and topological field theory and statistical mechanics. The conference, attended by over 60 mathematicians and theoretical physicists from Canada, Denmark, England, France, Japan, Poland and the United States, was highlighted by lecture series given by Louis Kauffman, Univ. of Illinois at Chicago and Nicholai Reshetikhin, Univ. of Califonia, Berkeley.
Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$
The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volumediscusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others d...
Topological Polymer Chemistry
There are examples aplenty in the macroscopic world that demonstrate the form of objects directing their functions and properties. On the other hand, the fabrication of extremely small objects having precisely defined structures has only recently become an attractive challenge, which is now opening the door to nanoscience and nanotechnology.In the field of synthetic polymer chemistry, a number of critical breakthroughs have been achieved during the first decade of this century to produce an important class of polymers having a variety of cyclic and multicyclic topologies. These developments now offer unique opportunities in polymer materials design to create unprecedented properties and func...
Topology and Geometry of Biopolymers
This book contains the proceedings of the AMS Special Session on Topology of Biopolymers, held from April 21ā22, 2018, at Northeastern University, Boston, MA. The papers cover recent results on the topology and geometry of DNA and protein knotting using techniques from knot theory, spatial graph theory, differential geometry, molecular simulations, and laboratory experimentation. They include current work on the following topics: the density and supercoiling of DNA minicircles; the dependence of DNA geometry on its amino acid sequence; random models of DNA knotting; topological models of DNA replication and recombination; theories of how and why proteins knot; topological and geometric approaches to identifying entanglements in proteins; and topological and geometric techniques to predict protein folding rates. All of the articles are written as surveys intended for a broad interdisciplinary audience with a minimum of prerequisites. In addition to being a useful reference for experts, this book also provides an excellent introduction to the fast-moving field of topology and geometry of biopolymers.
Topology of Polymers
Plastics, films, and synthetic fibers are among typical examples of polymer materials fabricated industrially in massive quantities as the basis of modern social life. By comparison, polymers from biological resources, including proteins, DNAs, and cotton fibers, are essential in various processes in living systems. Such polymers are molecular substances, constituted by the linking of hundreds to tens of thousands of small chemical unit (monomer) components. Thus, the form of polymer molecules is frequently expressed by line geometries, and their linear and non-linear forms are believed to constitute the fundamental basis for their properties and functions. In the field of polymer chemistry ...
Integrable Systems in Quantum Field Theory and Statistical Mechanics
Integrable Sys Quantum Field Theory
