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Combinatorial and approximative analyses in a spatially random division process

Author

Listed:
  • Hayashi, Yukio
  • Komaki, Takayuki
  • Ide, Yusuke
  • Machida, Takuya
  • Konno, Norio

Abstract

For a spatial characteristic, there exist commonly fat-tail frequency distributions of fragment-size and -mass of glass, areas enclosed by city roads, and pore size/volume in random packings. In order to give a new analytical approach for the distributions, we consider a simple model which constructs a fractal-like hierarchical network based on random divisions of rectangles. The stochastic process makes a Markov chain and corresponds to directional random walks with splitting into four particles. We derive a combinatorial analytical form and its continuous approximation for the distribution of rectangle areas, and numerically show a good fitting with the actual distribution in the averaging behavior of the divisions.

Suggested Citation

  • Hayashi, Yukio & Komaki, Takayuki & Ide, Yusuke & Machida, Takuya & Konno, Norio, 2013. "Combinatorial and approximative analyses in a spatially random division process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2212-2225.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:2212-2225
    DOI: 10.1016/j.physa.2013.01.025
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