Physical and Numerical Models in Knot Theory

Physical and Numerical Models in Knot Theory
Author: Jorge Alberto Calvo
Publisher: World Scientific
Total Pages: 642
Release: 2005
Genre: Mathematics
ISBN: 9812703462

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.

Body Knots

Body Knots
Author: Howard Schatz
Publisher: Rizzoli International Publications
Total Pages: 170
Release: 2000
Genre: Art
ISBN:

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.

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

Physical Knots: Knotting, Linking, and Folding Geometric Objects in $\mathbb {R}^3$
Author: Jorge Alberto Calvo
Publisher: American Mathematical Soc.
Total Pages: 356
Release: 2002
Genre: Mathematics
ISBN: 082183200X

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.

Ideal Knots

Ideal Knots
Author: Andrzej Stasiak
Publisher: World Scientific
Total Pages: 426
Release: 1998
Genre: Mathematics
ISBN: 9810235305

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.

History And Science Of Knots

History And Science Of Knots
Author: John C Turner
Publisher: World Scientific
Total Pages: 463
Release: 1996-05-30
Genre: Mathematics
ISBN: 9814499641

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.

Knots

Knots
Author: Gunnhild Øyehaug
Publisher: Macmillan + ORM
Total Pages: 128
Release: 2017-07-11
Genre: Fiction
ISBN: 0374714991

A mesmerizing collection of playfully surreal stories from one of Norway’s most celebrated writers First published in Norway in 2004, Knots is Gunnhild Øyehaug’s radical collection of short stories that range from the surreal to the oddly mundane, and prod the discomforts of mental, sexual, and familial bonds. In both precise short-shorts and ruminative longer tales, Øyehaug meanders through the tangled, jinxed, and unavoidable conflicts of love and desire. From young Rimbaud’s thwarted passions to the scandalous disappearance of an entire family, these stories do the chilling work of tracing the outlines of what could have been in both the quietly morbid and the delightfully comical. A young man is born with an uncuttable umbilical cord and spends his life physically tethered to his mother; a tipsy uncle makes an uncomfortable toast with unforeseeable repercussions; and a dissatisfied deer yearns to be seen. As one character reflects, “You never know how things might turn out, you never know how anything will turn out, tomorrow the walls might fall down, the room disappear.” Cleverly balancing the sensuous, the surreal, and the comical, Øyehaug achieves a playful familiarity with the absurd that never overreaches the needs of her stories. Full of characters who can’t help tying knots in themselves and each other, these tales make the world just a little more strange, and introduce a major international voice of searing vision, grace, and humor.

Physical and Numerical Models in Knot Theory

Physical and Numerical Models in Knot Theory
Author: Jorge Alberto Calvo
Publisher: World Scientific
Total Pages: 640
Release: 2005
Genre: Mathematics
ISBN: 9812561870

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.

The Book of Knots

The Book of Knots
Author: Geoffrey Budworth
Publisher: Ivy Press
Total Pages: 178
Release: 2021-07-13
Genre: Crafts & Hobbies
ISBN: 0711257426

The fundamental skill of tying knots is useful in countless situations, both indoors and out. The Book of Knots teaches you which knot to choose and exactly how to tie it, whether you’re constructing a trout fly, repairing a hammock, mooring a boat, securing a load to a car roof rack, or engaging in a rescue or survival situation. This invaluable manual explains through clear line diagrams and step-by-step descriptions how to tie more than 125 practical knots.

Ideal Knots

Ideal Knots
Author: A. Stasiak
Publisher: World Scientific
Total Pages: 426
Release: 1998
Genre: Crafts & Hobbies
ISBN: 981279607X

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.

Knots And Physics (Second Edition)

Knots And Physics (Second Edition)
Author: Louis H Kauffman
Publisher: World Scientific
Total Pages: 739
Release: 1994-01-15
Genre: Mathematics
ISBN: 9814502375

In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum 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. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.