Random walks and effective resistances on toroidal and cylindrical grids

被引：45

作者：

Jeng, M ^{[1
]}

机构：

[1] Univ Calif Santa Barbara, Dept Phys, Santa Barbara, CA 93106 USA

来源：

AMERICAN JOURNAL OF PHYSICS | 2000年 / 68卷 / 01期

关键词：

D O I：

10.1119/1.19370

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

A mapping between random walk problems and resistor network problems is described and used to calculate the effective resistance between any two nodes on an infinite two-dimensional square lattice of unit resistors. The superposition principle is then used to find effective resistances on toroidal and cylindrical square lattices. (C) 2000 American Association of Physics Teachers.

引用

页码：37 / 40

页数：4

共 20 条

[1] RESISTANCE BETWEEN ADJACENT POINTS OF LIEBMAN MESH [J].

AITCHISON, RE .

AMERICAN JOURNAL OF PHYSICS, 1964, 32 (07) :566-&

[2]

[Anonymous], THEORETICAL CHEM ADV

[3] Infinite resistive lattices [J].

Atkinson, D ;

van Steenwijk, FJ .

AMERICAN JOURNAL OF PHYSICS, 1999, 67 (06) :486-492

[4] LETS ANALYZE RESISTANCE LATTICE [J].

BARTIS, FJ .

AMERICAN JOURNAL OF PHYSICS, 1967, 35 (04) :354-&

[5]

Cameron D, 1986, MATH SCI, V11, P75

[6]

DOYLE PG, 1984, RANDOM WALKS ELECT N, pCH3

[7] INFINITE NETWORKS .1. RESISTIVE NETWORKS [J].

FLANDERS, H .

IEEE TRANSACTIONS ON CIRCUIT THEORY, 1971, CT18 (03) :326-&

[8] INFINITE NETWORKS .2. RESISTANCE IN AN INFINITE GRID [J].

FLANDERS, H .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1972, 40 (01) :30-&

[9] EXTENDED WATSON INTEGRALS FOR CUBIC LATTICES [J].

GLASSER, ML ;

ZUCKER, IJ .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1977, 74 (05) :1800-1801

[10]

HORIGUCHI T, 1972, J MATH PHYS, V13, P1411, DOI 10.1063/1.1666155

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