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

T. Hattori; K. Hattori

doi:10.1088/0305-4470/21/14/013

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

T. Hattori, K. Hattori

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Article number	013
Pages (from-to)	3117-3129
Number of pages	13
Journal	Journal of Physics A: General Physics
Volume	21
Issue number	14
DOIs	https://doi.org/10.1088/0305-4470/21/14/013
Publication status	Published - 1988 Dec 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Physics and Astronomy(all)
Mathematical Physics

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abstract = "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.",

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AB - 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.

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