Knot energies by ropes

被引:14
作者
Diao, Y [1 ]
Ernst, C
Van Rensburg, EJJ
机构
[1] Univ N Carolina, Dept Math, Charlotte, NC 28223 USA
[2] Western Kentucky Univ, Dept Math, Bowling Green, KY 42101 USA
[3] York Univ, Dept Math & Stat, N York, ON M3J 1P3, Canada
关键词
knots; energy of knots; knot complexity; thickness of knots;
D O I
10.1142/S0218216597000431
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
An energy function for smooth knots is defined using the concept of thickness and proved to be a good indicator of the complexity of knots. This energy function has the advantage that it can be measured experimentally. We carry out an experiment to measure the energies for knots up to 8 crossings and compare our data with energies obtained elsewhere through numerical simulations.
引用
收藏
页码:799 / 807
页数:9
相关论文
共 15 条
[1]  
BUCK G, 1993, TOPOL APPL, V51, P246
[2]  
BUCK G, APPL PROJECTION ENER
[3]  
Buck G.R., 1994, J KNOT THEOR RAMIF, V3, P355
[4]  
Diao Y., 1993, J KNOT THEOR RAMIF, V02, P413, DOI DOI 10.1142/S0218216593000234
[5]  
DIAO Y, THICKNESSES KNOTS
[6]  
DIAO Y, IN PRESS TOPOLOGY GE
[7]   THE NUMBER OF SMALLEST KNOTS ON THE CUBIC LATTICE [J].
DIAO, YN .
JOURNAL OF STATISTICAL PHYSICS, 1994, 74 (5-6) :1247-1254
[8]   MOBIUS ENERGY OF KNOTS AND UNKNOTS [J].
FREEDMAN, MH ;
HE, ZX ;
WANG, ZH .
ANNALS OF MATHEMATICS, 1994, 139 (01) :1-50
[9]  
KIM D, 1993, EXP MATH, V2
[10]  
KUSNER RB, MOBIUS ENERGIES KNOT