The Generation of Random Equilateral Polygons

被引:20
作者
Alvarado, Sotero [2 ]
Calvo, Jorge Alberto [1 ]
Millett, Kenneth C. [3 ]
机构
[1] Ave Maria Univ, Ave Maria, FL 34142 USA
[2] Arizona Western Coll, Yuma, AZ 85365 USA
[3] Univ Calif Santa Barbara, Santa Barbara, CA 93106 USA
关键词
Knot space; Probability of knotting; Monte Carlo method; Pivot method; Polygonal folding; Crankshaft rotations; Hedgehog method; Triangle method; MONTE-CARLO; SCALING BEHAVIOR; TOTAL CURVATURE; RING POLYMERS; TOTAL TORSION; DNA; KNOTS; ROPELENGTH; GYRATION; LENGTHS;
D O I
10.1007/s10955-011-0164-4
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Freely jointed random equilateral polygons serve as a common model for polymer rings, reflecting their statistical properties under theta conditions. To generate equilateral polygons, researchers employ many procedures that have been proved, or at least are believed, to be random with respect to the natural measure on the space of polygonal knots. As a result, the random selection of equilateral polygons, as well as the statistical robustness of this selection, is of particular interest. In this research, we study the key features of four popular methods: the Polygonal Folding, the Crankshaft Rotation, the Hedgehog, and the Triangle Methods. In particular, we compare the implementation and efficacy of these procedures, especially in regards to the population distribution of polygons in the space of polygonal knots, the distribution of edge vectors, the local curvature, and the local torsion. In addition, we give a rigorous proof that the Crankshaft Rotation Method is ergodic.
引用
收藏
页码:102 / 138
页数:37
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