### 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

*Journal of Physics A: General Physics*,

*21*(14), 3117-3129. [013]. https://doi.org/10.1088/0305-4470/21/14/013

**POP approximation to the spectral dimension of dual three-dimensional Sierpinski carpets.** / Hattori, Tetsuya; Hattori, K.

Research output: Contribution to journal › Article

*Journal of Physics A: General Physics*, vol. 21, no. 14, 013, pp. 3117-3129. https://doi.org/10.1088/0305-4470/21/14/013

}

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.

UR - http://www.scopus.com/inward/record.url?scp=0011381809&partnerID=8YFLogxK

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 -