Resistance in higher-dimensional Sierpinski carpets

被引：12
|
作者：
McGillivray, I [1 ]
机构：
[1] Univ Bristol, Dept Math, Bristol BS8 1TW, Avon, England
来源：
POTENTIAL ANALYSIS | 2002年 / 16卷 / 03期
关键词：
Sierpinski carpets; resistance scaling factor; recurrence; electrical resistance;
D O I：
10.1023/A:1014035414658
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the effective resistance between disjoint compact sets relative to the n-th level approximation F-n to the generalized Sierpinski carpet in d dimensions. This yields a simple criterion for determining recurrence of simple random walk on the associated pre-fractal graph in terms of the resistance scaling factor.
引用
收藏
页码：289 / 303
页数：15
相关论文
共 50 条
  • [1] Resistance in Higher-Dimensional Sierpiński Carpets
    I. McGillivray
    [J]. Potential Analysis, 2002, 16 : 289 - 303
  • [2] GEODESICS OF HIGHER-DIMENSIONAL SIERPINSKI GASKET
    Gu, Jiangwen
    Ye, Qianqian
    Xi, Lifeng
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2019, 27 (04)
  • [3] SCALING EXPONENTS FOR ELECTRICAL RESISTANCE ON HIGHER-DIMENSIONAL GENERALIZATIONS OF FRACTAL CARPETS AND SPONGES
    Schonfeld, Jonathan F.
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2023, 31 (05)
  • [4] RESISTANCE AND SPECTRAL DIMENSION OF SIERPINSKI CARPETS
    BARLOW, MT
    BASS, RF
    SHERWOOD, JD
    [J]. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1990, 23 (06): : L253 - L258
  • [5] MEAN VALUE PROPERTY OF HARMONIC FUNCTION ON THE HIGHER-DIMENSIONAL SIERPINSKI GASKET
    Wu, Yipeng
    Chen, Zhilong
    Zhang, Xia
    Zhao, Xudong
    [J]. FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY, 2020, 28 (05)
  • [6] Uniformization of Sierpinski Carpets by Square Carpets
    Ntalampekos, Dimitrios
    [J]. POTENTIAL THEORY ON SIERPINSKI CARPETS: WITH APPLICATIONS TO UNIFORMIZATION, 2020, 2268 : 91 - 177
  • [7] HIGHER-DIMENSIONAL TARGETING
    KOSTELICH, EJ
    GREBOGI, C
    OTT, E
    YORKE, JA
    [J]. PHYSICAL REVIEW E, 1993, 47 (01): : 305 - 310
  • [8] On higher-dimensional dynamics
    Wesson, PS
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (05) : 2423 - 2438
  • [9] HIGHER-DIMENSIONAL COSMOLOGIES
    LORENZPETZOLD, D
    [J]. PHYSICS LETTERS B, 1984, 148 (1-3) : 43 - 47
  • [10] HIGHER-DIMENSIONAL UNIFICATION
    FREUND, PGO
    [J]. PHYSICA D, 1985, 15 (1-2): : 263 - 269
12345