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Physical Knots
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Book Synopsis Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ by : Jorge Alberto Calvo
Download or read book Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$ written by Jorge Alberto Calvo and published by American Mathematical Soc.. This book was released on 2002 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Body Knots written by Howard Schatz and published by Rizzoli International Publications. This book was released on 2000 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: Body Knots celebrates the human body by transforming it into something larger than life. The bodies assume a wild variety of forms: creative compositions, biologic sculpture, and dazzling design. Sometimes witty, sometimes glamourous and sometimes strange, the images are always captivating, beautiful, compelling and fun. In this book, the human body is twisted and turned into shapes and contortions one would not have dreamed possible.
Download or read book Ideal Knots written by Andrzej Stasiak and published by World Scientific. This book was released on 1998 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis History and Science of Knots by : J C Turner
Download or read book History and Science of Knots written by J C Turner and published by World Scientific. This book was released on 1996-05-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots. Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day. In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot. Contents:Prehistory and Antiquity:Pleistocene KnottingWhy Knot? — Some Speculations on the First KnotsOn Knots and Swamps — Knots in European PrehistoryAncient Egyptian Rope and KnotsNon-European Traditions:The Peruvian QuipuThe Art of Chinese Knots Works: A Short HistoryInuit KnotsWorking Knots:Knots at SeaA History of Life Support KnotsTowards a Science of Knots?:Studies on the Behaviour of KnotsA History of Topological Knot Theory of KnotsTramblesCrochet Work — History and Computer ApplicationsDecorative Knots and Other Aspects:The History of MacraméA History of LaceHeraldic KnotsOn the True Love Knotand other papers Readership: Mathematicians, archeologists, social historians and general readers. keywords:Antiquit;Braiding;Climbing;Heraldry;History;Knots;Lace;Mariners;Prehistory;Quipus;Science;Theory;Topology;Knotting, Pleistocene;Egyptian;Inuit;Chinese;Mountaineering, Topological Knot Theory;Knot Theories;Quipo Knot Mathematics;Knot Strength Efficiency;Heraldic;True Love;Crochet;Computer Aided Design;Trambles “… it is a veritable compendium of information about every aspects of knots, from their links with quantum theory to attempts to measure their strength when tying climbing ropes together … the huge scope of this book makes it one I have turned to many times, for many different purposes.” New Scientists “I enjoyed browsing through all the chapters. They contain material that a mathematician would not normally come across in his work.” The Mathematical Intelligencer
Download or read book Ideal Knots written by A. Stasiak and published by World Scientific. This book was released on 1998 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Energy of Knots and Conformal Geometry by : Jun O'Hara
Download or read book Energy of Knots and Conformal Geometry written by Jun O'Hara and published by World Scientific. This book was released on 2003-03-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis The Complete Book of Knots by : Geoffrey Budworth
Download or read book The Complete Book of Knots written by Geoffrey Budworth and published by Bounty Books. This book was released on 2013-11-20 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text provides easy-to-follow instructions for selecting and tying more than 100 of the most useful knots. With knots for climbing, sailing and fishing, every knot contains information on its history and development, alternative names and its uses.
Author :Stuart G. Whittington Publisher :Springer Science & Business Media ISBN 13 :9780387985800 Total Pages :228 pages Book Rating :4.9/5 (858 download)
Book Synopsis Topology and Geometry in Polymer Science by : Stuart G. Whittington
Download or read book Topology and Geometry in Polymer Science written by Stuart G. Whittington and published by Springer Science & Business Media. This book was released on 1998-08-13 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions from a workshop on topology and geometry of polymers, held at the IMA in June 1996, which brought together topologists, combinatorialists, theoretical physicists and polymer scientists, with a common interest in polymer topology. Polymers can be highly self-entangled even in dilute solution. In the melt the inter- and intra-chain entanglements can dominate the rheological properties of these phenomena. Although the possibility of knotting in ring polymers has been recognized for more than thirty years it is only recently that the powerful methods of algebraic topology have been used in treating models of polymers. This book contains a series of chapters which review the current state of the field and give an up to date account of what is known and perhaps more importantly, what is still unknown. The field abounds with open problems. The book is of interest to workers in polymer statistical mechanics but will also be useful as an introduction to topological methods for polymer scientists, and will introduce mathematicians to an area of science where topological approaches are making a substantial contribution.
Book Synopsis Knots in Hellas '98 by : C. McA. Gordon
Download or read book Knots in Hellas '98 written by C. McA. Gordon and published by World Scientific. This book was released on 2000 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon?Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.
Book Synopsis Knots and Links by : Peter R. Cromwell
Download or read book Knots and Links written by Peter R. Cromwell and published by Cambridge University Press. This book was released on 2004-10-14 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: A richly illustrated 2004 textbook on knot theory; minimal prerequisites but modern in style and content.
Book Synopsis The Geometry and Physics of Knots by : Michael Francis Atiyah
Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by Cambridge University Press. This book was released on 1990-08-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Book Synopsis Physical and Numerical Models in Knot Theory by : Jorge Alberto Calvo
Download or read book Physical and Numerical Models in Knot Theory written by Jorge Alberto Calvo and published by World Scientific. This book was released on 2005 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Knot Book by : Colin Conrad Adams
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Knots and Applications by : Louis H. Kauffman
Download or read book Knots and Applications written by Louis H. Kauffman and published by World Scientific. This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Knots, Topology And Quantum Field Theory: Proceedings Of The 13th Johns Hopkins Workshop by : Luca Lusanna
Download or read book Knots, Topology And Quantum Field Theory: Proceedings Of The 13th Johns Hopkins Workshop written by Luca Lusanna and published by World Scientific. This book was released on 1989-12-01 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book fills a gap in literature for the important interdisciplinary area of biochemical physics, adopting the chemist's view of this topic in the process. The present status of the theory of electron spin effects in fundamental processes such as spin exchange, dipole-dipole interactions, electron transfer, triplet-triplet energy transfer, and annihilation intersystem crossing is reviewed. These effects form a basis for the understanding of the molecular mechanisms essential to chemical and biological reactions including photosynthesis and magnetic field influence, and for the creation of advanced organic magnets and catalysts, as well as the development of new methods of studying the structural and molecular dynamics of biological and non-biological objects.
Book Synopsis Knots, Low-Dimensional Topology and Applications by : Colin C. Adams
Download or read book Knots, Low-Dimensional Topology and Applications written by Colin C. Adams and published by Springer. This book was released on 2019-06-26 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a diverse collection of high-quality, state-of-the-art research and survey articles written by top experts in low-dimensional topology and its applications. The focal topics include the wide range of historical and contemporary invariants of knots and links and related topics such as three- and four-dimensional manifolds, braids, virtual knot theory, quantum invariants, braids, skein modules and knot algebras, link homology, quandles and their homology; hyperbolic knots and geometric structures of three-dimensional manifolds; the mechanism of topological surgery in physical processes, knots in Nature in the sense of physical knots with applications to polymers, DNA enzyme mechanisms, and protein structure and function. The contents is based on contributions presented at the International Conference on Knots, Low-Dimensional Topology and Applications – Knots in Hellas 2016, which was held at the International Olympic Academy in Greece in July 2016. The goal of the international conference was to promote the exchange of methods and ideas across disciplines and generations, from graduate students to senior researchers, and to explore fundamental research problems in the broad fields of knot theory and low-dimensional topology. This book will benefit all researchers who wish to take their research in new directions, to learn about new tools and methods, and to discover relevant and recent literature for future study.
Book Synopsis Knots and Physics by : Louis H. Kauffman
Download or read book Knots and Physics written by Louis H. Kauffman and published by World Scientific. This book was released on 2013 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
