POP approximation to the spectral dimension of dual three-dimensional Sierpinski carpets

T. Hattori, K. Hattori

研究成果: Article査読

2 被引用数 (Scopus)

抄録

The spectral dimension d of a network governs the massless singularity of a free field and the asymptotic behaviour of the diffusion on the network. Approximate values of d for two types of three-dimensional generalisations of the dual Sierpinski carpet are obtained using the POP approximation method. For one of them which is generated by a cube of side length three, with one block at the centre taken away, the value obtained is d(POP)=2 log 26/log(884/93) approximately=2.89. For the other one with seven cubes taken away, d(POP)=2 log 20/log (40/3) approximately=2.31. The algorithm of the POP method is explained. The results for 2D symmetric dual Sierpinski-type carpets are also reported.

本文言語English
論文番号013
ページ(範囲)3117-3129
ページ数13
ジャーナルJournal of Physics A: General Physics
21
14
DOI
出版ステータスPublished - 1988 12月 1
外部発表はい

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 物理学および天文学(全般)
  • 数理物理学

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