Random Knotting And Linking

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Random Knotting and Linking

Kenneth C. Millett
Random Knotting and Linking Book PDF

Author : Kenneth C. Millett
Publisher : World Scientific
Page : 207 pages
File Size : 46,5 Mb
Release : 1994
Category : Mathematics
ISBN : 9789810220051

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Random Knotting and Linking by Kenneth C. Millett Pdf

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.

Random Knotting and Linking

K C Millett,D W Sumners
Random Knotting and Linking Book PDF

Author : K C Millett,D W Sumners
Publisher : World Scientific
Page : 208 pages
File Size : 51,5 Mb
Release : 1994-12-09
Category : Science
ISBN : 9789814501422

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Random Knotting and Linking by K C Millett,D W Sumners Pdf

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. Contents:Graph Invariants and the Topology of RNA Folding (L H Kauffman & Y Magarshak)The Functoriality of Vassiliev-Type Invariants of Links, Braids, and Knotted Graphs (T Stanford)Knotting of Regular Polygons in 3-Space (K C Millett)An Elementary Invariant of Knots (R Randell)DNA Knot Formation in Aqueous Solutions (S Y Shaw & J C Wang)Energy Functions for Polygonal Knots (J K Simon)A Statistical Study of Random Knotting Using the Vassiliev Invariants (T Deguchi & K Tsurusaki)Random Knots and Energy: Elementary Considerations (G R Buck)Statistical Mechanics and Topology of Surfaces in Zd (E J Janse van Rensburg)Unsplittability of Random Links (Y A Diao)Twist Sequences and Vassiliev Invariants (R Trapp)Global Mutation of Knots (D Rolfsen)On Random Knots (Y A Diao et al.) Readership: Mathematicians and mathematical physicists. keywords:Knots;Links;Polygonal Knots;Invariants;DNA;RNA;Energy Functions;Statistical Knot Theory;Random Knots;Mutation;Statistical Mechanics;Topology of Surfaces

Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$

Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon
Physical Knots Knotting Linking and Folding Geometric Objects in mathbb R 3 Book PDF

Author : Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 45,9 Mb
Release : 2002
Category : Knot theory
ISBN : 9780821832004

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Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ by Jorge Alberto Calvo,AMS Special Session on Physical Knotting,Kenneth C. Millett,Eric J. Rawdon Pdf

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 deal with applications of mathematics to theoretical computer science, engineering,physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.

Lectures at Knots '96

S Suzuki
Lectures at Knots 96 Book PDF

Author : S Suzuki
Publisher : World Scientific
Page : 300 pages
File Size : 55,8 Mb
Release : 1997-07-04
Category : Science
ISBN : 9789814497541

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Lectures at Knots '96 by S Suzuki Pdf

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. Contents:Tunnel Number and Connected Sum of Knots (K Morimoto)Topological Imitations (A Kawauchi)Surfaces in 4-Space: A View of Normal Forms and Braidings (S Kamada)Knot Types of Satellite Knots and Twisted Knots (K Motegi)Random Knots and Links and Applications to Polymer Physics (T Deguchi & K Tsurusaki)Knots and Diagrams (L H Kauffman)On Spatial Graphs (K Taniyama)Energy and Length of Knots (G Buck & J Simon)Chern-Simons Perturbative Invariants (T Kohno)Combinatorial Methods in Dehn Surgery (C M Gordon) Readership: Mathematicians and mathematical physicists. keywords:Lectures;Knots;Conference;Proceedings;Tokyo (Japan)

The Knot Book

Colin Conrad Adams
The Knot Book Book PDF

Author : Colin Conrad Adams
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 46,9 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821836781

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The Knot Book by Colin Conrad Adams Pdf

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Knots, Links, Spatial Graphs, and Algebraic Invariants

Erica Flapan,Allison Henrich,Aaron Kaestner,Sam Nelson:
Knots Links Spatial Graphs and Algebraic Invariants Book PDF

Author : Erica Flapan,Allison Henrich,Aaron Kaestner,Sam Nelson:
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 41,8 Mb
Release : 2017-05-19
Category : Combinatorics -- Graph theory -- Planar graphs
ISBN : 9781470428471

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Knots, Links, Spatial Graphs, and Algebraic Invariants by Erica Flapan,Allison Henrich,Aaron Kaestner,Sam Nelson: Pdf

This volume contains the proceedings of the AMS Special Session on Algebraic and Combinatorial Structures in Knot Theory and the AMS Special Session on Spatial Graphs, both held from October 24–25, 2015, at California State University, Fullerton, CA. Included in this volume are articles that draw on techniques from geometry and algebra to address topological problems about knot theory and spatial graph theory, and their combinatorial generalizations to equivalence classes of diagrams that are preserved under a set of Reidemeister-type moves. The interconnections of these areas and their connections within the broader field of topology are illustrated by articles about knots and links in spatial graphs and symmetries of spatial graphs in and other 3-manifolds.

Physical and Numerical Models in Knot Theory

Jorge Alberto Calvo
Physical and Numerical Models in Knot Theory Book PDF

Author : Jorge Alberto Calvo
Publisher : World Scientific
Page : 642 pages
File Size : 40,9 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812703460

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Physical and Numerical Models in Knot Theory by Jorge Alberto Calvo Pdf

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.

Energy of Knots and Conformal Geometry

Jun O'Hara
Energy of Knots and Conformal Geometry Book PDF

Author : Jun O'Hara
Publisher : World Scientific
Page : 304 pages
File Size : 51,5 Mb
Release : 2003-03-25
Category : Mathematics
ISBN : 9789814486408

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Energy of Knots and Conformal Geometry by Jun O'Hara Pdf

Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents:In Search of the “Optimal Embedding” of a Knot:α-Energy Functional E(α)On E(2)Lp Norm Energy with Higher IndexNumerical ExperimentsStereo Pictures of E(2)MinimizersEnergy of Knots in a Riemannian ManifoldPhysical Knot EnergiesEnergy of Knots from a Conformal Geometric Viewpoint:Preparation from Conformal GeometryThe Space of Non-Trivial Spheres of a KnotThe Infinitesimal Cross RatioThe Conformal Sin Energy Esin θMeasure of Non-Trivial SpheresAppendices:Generalization of the Gauss Formula for the Linking NumberThe 3-Tuple Map to the Set of Circles in S3Conformal Moduli of a Solid TorusKirchhoff ElasticaOpen Problems and Dreams Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics. Keywords:Energy of Knots;Optimal Embedding;Conformal Geometry;Möbius Transformation;Infinitesimal Cross RatioReviews:“… this book gives an excellent, state of the art account of many of the important results in this field. A strong point of the book is that almost all proofs of the theorems stated are included.”Zentralblatt MATH

Knots and Links

Peter R. Cromwell
Knots and Links Book PDF

Author : Peter R. Cromwell
Publisher : Cambridge University Press
Page : 356 pages
File Size : 45,8 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 0521548314

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Knots and Links by Peter R. Cromwell Pdf

A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.

Physical Knots

Jorge Alberto Calvo,Kenneth C. Millett,Eric J. Rawdon
Physical Knots Book PDF

Author : Jorge Alberto Calvo,Kenneth C. Millett,Eric J. Rawdon
Publisher : American Mathematical Soc.
Page : 358 pages
File Size : 54,5 Mb
Release : 2002-11-15
Category : Mathematics
ISBN : 0821856405

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Physical Knots by Jorge Alberto Calvo,Kenneth C. Millett,Eric J. Rawdon Pdf

Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volume discusses critical questions and new ideas in the areas of knotting and folding of curves in surfaces in three-dimensional space and applications of these ideas to biology, chemistry, computer science, and engineering. Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering, physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.

Statistical Models, Yang–Baxter Equation and Related Topics; Symmetry, Statistical Mechanical Models and Applications

M L Ge,F Y Wu
Statistical Models Yang Baxter Equation and Related Topics Symmetry Statistical Mechanical Models and Applications Book PDF

Author : M L Ge,F Y Wu
Publisher : World Scientific
Page : 460 pages
File Size : 44,6 Mb
Release : 1996-09-20
Category : Electronic
ISBN : 9789814547567

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Statistical Models, Yang–Baxter Equation and Related Topics; Symmetry, Statistical Mechanical Models and Applications by M L Ge,F Y Wu Pdf

This book contains the proceedings of two international conferences: a satellite meeting of the IUPAP Statphys-19 Conference and the Seventh Nankai Workshop, held in Tianjin, China in August 1995. The central theme of the two conferences, which drew participants from 18 countries, was the Yang–Baxter equation and its development and applications. With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in statistical mechanics. Contents:Satellite Meeting of Statphys-19:Boundary Yang–Baxter in the RSOS/SOS Representation (C Ahn & W M Koo)Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains (F C Alcaraz et al.)The Generalized Chiral Clock Model and Its Phase Diagram (H Au-Yang & J H H Perk)Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals (M Baake)Reflection Equations and Surface Critical Phenomena (M T Batchelor)Quantum Field Theories in Terms of Group-Valued Local Fields: An Overview (L-L Chau)U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model (C Destri)Dilute Algebras and Solvable Lattice Models (U Grimm)Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition (Y Hatsugai et al.) Quantum Group and the Hofstadter Problem (Y Hatsugai et al.)Domain Walls in the Spin-S Quantum Ising Chain (M Henkel)Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction (A R Its & V E Korepin)Stochastic Reaction-Diffusion Processes, Operator Algebras and Integrable Quantum Spin Chains (G M Schütz)Vertex-Face Correspondence in Elliptic Solutions of the Yang–Baxter Equation (Y Shibukawa)Logarithmic Anomalies of Susceptibility for Solvable Models (M Takahashi)On Chiral Hubbard Model at Strong Interaction (D F Wang)Soluble Free-Fermion Models in d Dimensions (F Y Wu)Bosonization Based on Bethe Ansatz Equations and Proof of the Conformal Conjecture (Y-S Wu & Y Yu)and other papersThe Seventh Nankai Workshop:Corner Transfer Matrix of Asymmetric Vertex Models (H-P Eckle)Scaling Properties of the Ising Model in a Field (U Grimm & B Nienhuis)One Dimensional Lattice Models of Electrons with r–2 Hopping and Exchange (Ch Gruber & D F Wang)Symmetry Group Invariants for Spontaneous Magnetization (J-M Maillard)Experimental Realizations of Integrable Reaction-Diffusion Processes in Biological and Chemical Systems (G M Schütz)Zamolodchikov–Faddeev Algebra in 2-Component Anyons (Y-L Shen & M-L Ge)and other papers Readership: Theoretical physicists and mathematicians. keywords:

Encyclopedia of Knot Theory

Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Encyclopedia of Knot Theory Book PDF

Author : Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Publisher : CRC Press
Page : 941 pages
File Size : 52,8 Mb
Release : 2021-02-10
Category : Mathematics
ISBN : 9781000222388

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Encyclopedia of Knot Theory by Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson Pdf

"Knot theory is a fascinating mathematical subject, with multiple links to theoretical physics. This enyclopedia is filled with valuable information on a rich and fascinating subject." – Ed Witten, Recipient of the Fields Medal "I spent a pleasant afternoon perusing the Encyclopedia of Knot Theory. It’s a comprehensive compilation of clear introductions to both classical and very modern developments in the field. It will be a terrific resource for the accomplished researcher, and will also be an excellent way to lure students, both graduate and undergraduate, into the field." – Abigail Thompson, Distinguished Professor of Mathematics at University of California, Davis Knot theory has proven to be a fascinating area of mathematical research, dating back about 150 years. Encyclopedia of Knot Theory provides short, interconnected articles on a variety of active areas in knot theory, and includes beautiful pictures, deep mathematical connections, and critical applications. Many of the articles in this book are accessible to undergraduates who are working on research or taking an advanced undergraduate course in knot theory. More advanced articles will be useful to graduate students working on a related thesis topic, to researchers in another area of topology who are interested in current results in knot theory, and to scientists who study the topology and geometry of biopolymers. Features Provides material that is useful and accessible to undergraduates, postgraduates, and full-time researchers Topics discussed provide an excellent catalyst for students to explore meaningful research and gain confidence and commitment to pursuing advanced degrees Edited and contributed by top researchers in the field of knot theory

Ideal Knots

A Stasiak,V Katritch,L H Kauffman
Ideal Knots Book PDF

Author : A Stasiak,V Katritch,L H Kauffman
Publisher : World Scientific
Page : 424 pages
File Size : 40,7 Mb
Release : 1998-12-31
Category : Mathematics
ISBN : 9789814495936

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Ideal Knots by A Stasiak,V Katritch,L H Kauffman Pdf

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter. Contents:Ideal Knots and Their Relation to the Physics of Real Knots (A Stasiak et al.)Knots with Minimal Energies (Y Diao et al.)The Writhe of Knots and Links (E J Janse van Rensburg et al.)Entropy of a Knot: Simple Arguments About Difficult Problem (A Yu Grosberg)Knots and Fluid Dynamics (H K Moffatt)Möbius-Invariant Knot Energies (R B Kusner & J M Sullivan)Fourier Knots (L H Kauffman)and other papers Readership: Mathematicians, physicists, chemists and biologists. Keywords:Knots;Topology;Theory of Knots;Energy of Knots;Knot's Invariants;Geometry of Knots;Physics of KnotsReviews: “The authors of the articles in this book manage to put together a wide variety of ideas related to the notion of a simple representation of a knot.” Mathematical Reviews

Ideal Knots

Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman
Ideal Knots Book PDF

Author : Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman
Publisher : World Scientific
Page : 426 pages
File Size : 46,8 Mb
Release : 1998
Category : Mathematics
ISBN : 9789810235307

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Ideal Knots by Andrzej Stasiak,Vsevolod Katritch,Louis H. Kauffman Pdf

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.

Introductory Lectures on Knot Theory

Louis H. Kauffman
Introductory Lectures on Knot Theory Book PDF

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 578 pages
File Size : 52,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814307994

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Introductory Lectures on Knot Theory by Louis H. Kauffman Pdf

More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.