TOPOLOGICAL CORRELATIONS IN CELLULAR STRUCTURES AND PLANAR GRAPH-THEORY

被引：57

作者：

GODRECHE, C ^{[1
]}

KOSTOV, I ^{[1
]}

YEKUTIELI, I ^{[1
]}

机构：

[1] CTR ETUD SACLAY,SERV PHYS THEOR,F-91191 GIF SUR YVETTE,FRANCE

来源：

PHYSICAL REVIEW LETTERS | 1992年 / 69卷 / 18期

关键词：

D O I：

10.1103/PhysRevLett.69.2674

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We study the topological properties of the ensemble of cells with trivalent vertices in the plane. The problem is equivalent to counting planar Feynman diagrams with a cubic interaction. This ensemble is also the equilibrium state of a topological model of cellular structure, obtained by applying repetitively a topological flip transformation to any initial configuration of cells with trivalent vertices. We give analytical expressions for two-cell correlations; in particular, we give the analytical form of the average number m(n) of edges of cells adjacent to an n-sided cell. These results are confirmed by simulations.

引用

页码：2674 / 2677

页数：4

共 7 条

[1]

Aboav D. A., 1970, Metallography, V3, P383, DOI 10.1016/0026-0800(70)90038-8

[2] ARRANGEMENT OF CELLS IN A NET [J].

ABOAV, DA .

METALLOGRAPHY, 1980, 13 (01) :43-58

[3] ANALYTICAL AND NUMERICAL STUDY OF A MODEL OF DYNAMICALLY TRIANGULATED RANDOM SURFACES [J].

BOULATOV, DV ;

KAZAKOV, VA ;

KOSTOV, IK ;

MIGDAL, AA .

NUCLEAR PHYSICS B, 1986, 275 (04) :641-686

[4] PLANAR DIAGRAMS [J].

BREZIN, E ;

ITZYKSON, C ;

PARISI, G ;

ZUBER, JB .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1978, 59 (01) :35-51

[5]

Gibson L.J., 1988, CELLULAR SOLIDS

[6] ENTROPIC PREDICTIONS FOR CELLULAR NETWORKS [J].

PESHKIN, MA ;

STRANDBURG, KJ ;

RIVIER, N .

PHYSICAL REVIEW LETTERS, 1991, 67 (13) :1803-1806

[7] SOAP, CELLS AND STATISTICS - RANDOM PATTERNS IN 2 DIMENSIONS [J].

WEAIRE, D ;

RIVIER, N .

CONTEMPORARY PHYSICS, 1984, 25 (01) :59-99

← 1 →