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Titolo:
IN SEARCH OF A GOOD POLYGONAL KNOT ENERGY
Autore:
DIAO Y; ERNST C; VANRENSBURG EJJ;
Indirizzi:
UNIV N CAROLINA,DEPT MATH CHARLOTTE NC 28223 WESTERN KENTUCKY UNIV,DEPT MATH BOWLING GREEN KY 42101 YORK UNIV,DEPT MATH & STAT N YORK ON M3J 1P3 CANADA
Titolo Testata:
Journal of knot theory and its ramifications
fascicolo: 5, volume: 6, anno: 1997,
pagine: 633 - 657
SICI:
0218-2165(1997)6:5<633:ISOAGP>2.0.ZU;2-2
Fonte:
ISI
Lingua:
ENG
Keywords:
KNOTS; EQUILATERAL POLYGONS; POLYGONAL KNOTS; ENERGIES OF KNOTS; SIMULATED ANNEALING;
Tipo documento:
Article
Natura:
Periodico
Settore Disciplinare:
CompuMath Citation Index
Science Citation Index Expanded
Citazioni:
16
Recensione:
Indirizzi per estratti:
Citazione:
Y. Diao et al., "IN SEARCH OF A GOOD POLYGONAL KNOT ENERGY", Journal of knot theory and its ramifications, 6(5), 1997, pp. 633-657

Abstract

An energy function on knots is a scale-invariant function from knot conformations into non-negative red numbers. The infimum of an energy function is an invariant which defines ''canonical conformation(s)'' ofa knot in three space. These are not necessarily unique, and, in somecases, may even be singular. Many hierarchies of energy functions forknots in the mathematical and physical science literature have been studied, each energy function with its own characteristic set of properties. In this paper we focus on the energy functions of equilateral polygonal knots. These energy functions are important in computer studies of knot energies, and are often defined as discrete versions of energy functions defined on smooth knots. Energy functions on equilateral polygonal knots turn out to be ill-behaved in many cases. To characterize a ''good'' polygonal knot energy we introduce the concepts of asymptotically finite and asymptotically smooth energy functions of equilateral polygonal knots. Energy functions which are both asymptotically finite and smooth tend to have good limiting behavior (as the number of edges goes to infinity). We introduce a new energy function of equilateral polygonal knots, and show that it is both asymptotically finiteand smooth. In addition, we compute this energy for several knots using simulated annealing.

ASDD Area Sistemi Dipartimentali e Documentali, Università di Bologna, Catalogo delle riviste ed altri periodici
Documento generato il 05/08/20 alle ore 12:35:17