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Physical And Numerical Models In Knot Theory: Including Applications To The Life Sciences

Physical And Numerical Models In Knot Theory: Including Applications To The Life Sciences
Author: Jorge Alberto Calvo
Publisher: World Scientific
Total Pages: 640
Release: 2005-09-20
Genre: Mathematics
ISBN: 9814480851

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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.


Encyclopedia of Knot Theory

Encyclopedia of Knot Theory
Author: Colin Adams
Publisher: CRC Press
Total Pages: 954
Release: 2021-02-10
Genre: Education
ISBN: 1000222381

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"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


Lectures on Topological Fluid Mechanics

Lectures on Topological Fluid Mechanics
Author: Mitchell A. Berger
Publisher: Springer Science & Business Media
Total Pages: 240
Release: 2009-05-05
Genre: Mathematics
ISBN: 3642008364

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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.


Non-equilibrium Soft Matter Physics

Non-equilibrium Soft Matter Physics
Author: Shigeyuki Komura
Publisher: World Scientific
Total Pages: 435
Release: 2012
Genre: Science
ISBN: 9814360635

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Soft matter is a concept which covers polymers, liquid crystals, colloids, amphiphilic molecules, glasses, granular and biological materials. One of the fundamental characteristic features of soft matter is that it exhibits various mesoscopic structures originating from a large number of internal degrees of freedom of each molecule. Due to such intermediate structures, soft matter can easily be brought into non-equilibrium states and cause non-linear responses by imposing external fields such as an electric field, a mechanical stress or a shear flow. Volume 4 of the series in Soft Condensed Matter focuses on the non-linear and non-equilibrium properties of soft matter. It contains a collection of review articles on the current topics of non-equilibrium soft matter physics written by leading experts in the field. The topics dealt with in this volume includes rheology of polymers and liquid crystals, dynamical properties of Langmuir monolayers at the air/water interface, hydrodynamics of membranes and twisted filaments as well as dynamics of deformable self-propelled particles and migration of biological cells. This book serves both as an introduction to students as well as a useful reference to researchers.


Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday

Topology And Dynamics Of Chaos: In Celebration Of Robert Gilmore's 70th Birthday
Author: Christophe Letellier
Publisher: World Scientific
Total Pages: 362
Release: 2013-01-11
Genre: Mathematics
ISBN: 9814434876

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The book surveys how chaotic behaviors can be described with topological tools and how this approach occurred in chaos theory. Some modern applications are included.The contents are mainly devoted to topology, the main field of Robert Gilmore's works in dynamical systems. They include a review on the topological analysis of chaotic dynamics, works done in the past as well as the very latest issues. Most of the contributors who published during the 90's, including the very well-known scientists Otto Rössler, René Lozi and Joan Birman, have made a significant impact on chaos theory, discrete chaos, and knot theory, respectively.Very few books cover the topological approach for investigating nonlinear dynamical systems. The present book will provide not only some historical — not necessarily widely known — contributions (about the different types of chaos introduced by Rössler and not just the “Rössler attractor”; Gumowski and Mira's contributions in electronics; Poincaré's heritage in nonlinear dynamics) but also some recent applications in laser dynamics, biology, etc.


Knot Theory and Its Applications

Knot Theory and Its Applications
Author: Kunio Murasugi
Publisher: Springer Science & Business Media
Total Pages: 350
Release: 2007-10-03
Genre: Mathematics
ISBN: 081764718X

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This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.


Knot Entropy

Knot Entropy
Author: Nathan Thomas Moore
Publisher:
Total Pages: 206
Release: 2006
Genre:
ISBN:

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Knots And Applications

Knots And Applications
Author: Thaddeus M Cowan
Publisher: World Scientific
Total Pages: 492
Release: 1995-03-06
Genre:
ISBN: 9814501433

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This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.


Applications of Knot Theory

Applications of Knot Theory
Author: American Mathematical Society. Short Course
Publisher: American Mathematical Soc.
Total Pages: 203
Release: 2009
Genre: Mathematics
ISBN: 0821844660

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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.


The Mathematics of Knots

The Mathematics of Knots
Author: Markus Banagl
Publisher: Springer Science & Business Media
Total Pages: 363
Release: 2010-11-25
Genre: Mathematics
ISBN: 3642156371

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The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.