E-Book Overview
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.
E-Book Content
Physical and Numerical Models in Knot Theory Including Applications to the Life Sciences
This page intentionally left blank
Series on Knots and Everything - Vol. 36
Physical and Numerical Models in KnotTheory Including Applications to the Life Sciences
Editors
Jorge A. Calvo Ave Maria University, USA
Kenneth C. Millett University of California, San ta Barbara, USA
Eric J. Rawdon Duquesne University, USA
Andrzej Stasiak Universite de Lausanne, Switzerland
NEW JERSEY
-
r pWorld Scientific LONDON
*
SINGAPORE
-
BElJlNG
*
SHANGHAI * HONG KONG
-
TAIPEI
*
CHENNAI
Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA ofice: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 U K ofice: 57 Shelton Street, Covent Garden, London WC2H 9HE
Library of Congress Cataloging-in-PublicationData Physical and numerical models in knot theory : including applications to the life sciences / editors, Jorge A. Calvo ... [et al.]. p. cm. (series on knots and everything ; v. 36) Includes bibliographical references. ISBN 981-256-187-0(alk. paper) 11. Title. 111. Series. 1. Knot theory. I. Calvo, Jorge Alberto, 1971QA612.2 .P642005 5 14'.2242--dc22 2005049743
British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library.
About the cover: the contact points of the ideal trefoil as architectures-by Ben Laurie
Copyright Q 2005 by World Scientific Publishing Co. Re. Ltd. All rights reserved. This book, or parts thereox may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permissionfrom the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
Printed in Singapore by B & JO Enterprise
To our families and our teachers.
This page intentionally left blank
PREFACE
The physical properties of knotted and linked configurations in space have long been of interest t o mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Th