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 | |
| Publication status | Published - 1988 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics
Cite this
POP approximation to the spectral dimension of dual three-dimensional Sierpinski carpets. / Hattori, Tetsuya; Hattori, K.
In: Journal of Physics A: General Physics, Vol. 21, No. 14, 013, 1988, p. 3117-3129.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - POP approximation to the spectral dimension of dual three-dimensional Sierpinski carpets
AU - Hattori, Tetsuya
AU - Hattori, K.
PY - 1988
Y1 - 1988
N2 - 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.
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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UR - http://www.scopus.com/inward/citedby.url?scp=0011381809&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/21/14/013
DO - 10.1088/0305-4470/21/14/013
M3 - Article
AN - SCOPUS:0011381809
VL - 21
SP - 3117
EP - 3129
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
SN - 1751-8113
IS - 14
M1 - 013
ER -