SCALING EXPONENTS FOR ELECTRICAL RESISTANCE ON HIGHER-DIMENSIONAL GENERALIZATIONS OF FRACTAL CARPETS AND SPONGES

被引：1
|
作者：
Schonfeld, Jonathan F. [1 ]
机构：
[1] Harvard & Smithsonian, Ctr Astrophys, 60 Garden St, Cambridge, MA 02138 USA
来源：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY | 2023年 / 31卷 / 05期
关键词：
Fractals; Sierpinski Carpet; Menger Sponge; Power-Law Scaling; Electrical Resistance; Potential Theory; Dielectric Theory; Perforated Fractal;
D O I：
10.1142/S0218348X23500457
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we calculate electrical resistance scaling exponents for analogues of "carpet" and "sponge" fractals in higher-dimensional embedding spaces. The calculation idealizes the voids that define such fractals as spherical, and exploits the elementary theory of dielectrics. Possible applications include models of elementary particles with "extra" dimensions, and new large-dimension methods for the theory of fractals.
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页数：5
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