Physical And Numerical Models In Knot Theory

Author : Jorge Alberto Calvo
Publisher : World Scientific
Page : 640 pages
File Size : 42,6 Mb
Release : 2005
Category : Mathematics
ISBN : 9789812561879

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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.

Author : Jorge Alberto Calvo
Publisher : World Scientific
Page : 642 pages
File Size : 45,7 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.

Author : American Mathematical Society. Short course
Publisher : American Mathematical Soc.
Page : 203 pages
File Size : 49,6 Mb
Release : 2009
Category : DNA
ISBN : 9780821844663

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Applications of Knot Theory by American Mathematical Society. Short course Pdf

Louis Kauffman discusses applications of knot theory to physics, Nadrian Seeman discusses how topology is used in DNA nanotechnology, and Jonathan Simon discusses the statistical and energetic properties of knots and their relation to molecular biology."--BOOK JACKET.

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 577 pages
File Size : 42,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814313001

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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.

Author : Colin Adams,Erica Flapan,Allison Henrich,Louis H. Kauffman,Lewis D. Ludwig,Sam Nelson
Publisher : CRC Press
Page : 954 pages
File Size : 40,9 Mb
Release : 2021-02-10
Category : Education
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

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 55,9 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9789814474030

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Linknot by Anonim Pdf

Author : Yasuyuki Tezuka
Publisher : World Scientific
Page : 365 pages
File Size : 51,6 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814401272

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Topological Polymer Chemistry by Yasuyuki Tezuka Pdf

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 functions simply based on the form, i.e. topology, of polymer molecules. In this book on topological polymer chemistry, the important developments in this growing area will be collected for the first time, with particular emphasis on new conceptual insights for polymer chemistry and polymer materials. The book will systematically review topological polymer chemistry from basic aspects to practice, and give a broad overview of cyclic polymers covering new synthesis, structure characterization, basic properties/functions and the eventual applications.

Author : Erica Flapan,Allison Henrich,Aaron Kaestner,Sam Nelson:
Publisher : American Mathematical Soc.
Page : 189 pages
File Size : 51,7 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.

Author : Craig John Benham,Stephen Harvey,Wilma K. Olson,De Witt Sumners,David Swigon
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 42,6 Mb
Release : 2010-04-29
Category : Medical
ISBN : 9781441906717

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Mathematics of DNA Structure, Function and Interactions by Craig John Benham,Stephen Harvey,Wilma K. Olson,De Witt Sumners,David Swigon Pdf

Propelled by the success of the sequencing of the human and many related genomes, molecular and cellular biology has delivered significant scientific breakthroughs. Mathematics (broadly defined) continues to play a major role in this effort, helping to discover the secrets of life by working collaboratively with bench biologists, chemists and physicists. Because of its outstanding record of interdisciplinary research and training, the IMA was an ideal venue for the 2007-2008 IMA thematic year on Mathematics of Molecular and Cellular Biology. The kickoff event for this thematic year was a tutorial on Mathematics of Nucleic Acids, followed by the workshop Mathematics of Molecular and Cellular Biology, held September 15--21 at the IMA. This volume is dedicated to the memory of Nicholas R. Cozzarelli, a dynamic leader who fostered research and training at the interface between mathematics and molecular biology. It contains a personal remembrance of Nick Cozzarelli, plus 15 papers contributed by workshop speakers. The papers give an overview of state-of-the-art mathematical approaches to the understanding of DNA structure and function, and the interaction of DNA with proteins that mediate vital life processes.

Author : Vassily Olegovich Manturov,Denis Fedoseev,Seongjeong Kim,Igor Nikonov
Publisher : World Scientific
Page : 387 pages
File Size : 40,6 Mb
Release : 2020-04-22
Category : Mathematics
ISBN : 9789811220135

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Invariants And Pictures: Low-dimensional Topology And Combinatorial Group Theory by Vassily Olegovich Manturov,Denis Fedoseev,Seongjeong Kim,Igor Nikonov Pdf

This book contains an in-depth overview of the current state of the recently emerged and rapidly growing theory of Gnk groups, picture-valued invariants, and braids for arbitrary manifolds. Equivalence relations arising in low-dimensional topology and combinatorial group theory inevitably lead to the study of invariants, and good invariants should be strong and apparent. An interesting case of such invariants is picture-valued invariants, whose values are not algebraic objects, but geometrical constructions, like graphs or polyhedra.In 2015, V O Manturov defined a two-parametric family of groups Gnk and formulated the following principle: if dynamical systems describing a motion of n particles possess a nice codimension 1 property governed by exactly k particles then these dynamical systems possess topological invariants valued in Gnk.The book is devoted to various realisations and generalisations of this principle in the broad sense. The groups Gnk have many epimorphisms onto free products of cyclic groups; hence, invariants constructed from them are powerful enough and easy to compare. However, this construction does not work when we try to deal with points on a 2-surface, since there may be infinitely many geodesics passing through two points. That leads to the notion of another family of groups — Γnk, which give rise to braids on arbitrary manifolds yielding invariants of arbitrary manifolds.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,9 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9789814470650

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Topology and Physics by Anonim Pdf

Author : Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 53,6 Mb
Release : 2009-05-05
Category : Mathematics
ISBN : 9783642008368

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Lectures on Topological Fluid Mechanics by Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners Pdf

This volume contains a wide-ranging collection of valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics to DNA tangles and knotted DNAs in sedimentation.

Author : Chen Ning Yang,Mo-Lin Ge
Publisher : World Scientific
Page : 496 pages
File Size : 42,7 Mb
Release : 1994
Category : Science
ISBN : 981021524X

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Braid Group, Knot Theory, and Statistical Mechanics II by Chen Ning Yang,Mo-Lin Ge Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 41,5 Mb
Release : 2024-05-20
Category : Electronic
ISBN : 9789814468367

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The Origin of Discrete Particles by Anonim Pdf

Author : Louis H. Kauffman
Publisher : World Scientific
Page : 865 pages
File Size : 53,9 Mb
Release : 2013
Category : Mathematics
ISBN : 9789814383004

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Knots and Physics by Louis H. Kauffman Pdf

An introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics.