Combinatorial and approximative analyses in a spatially random division process

• 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.

identifier:https://dspace.jaist.ac.jp/dspace/handle/10119/11650

Journal

• Physica A: Statistical Mechanics and its Applications

  Physica A: Statistical Mechanics and its Applications 329 (9), 2212-2225, 2013-01-17

  Elsevier

Keywords

• Random division process
• Universal spatoal characteristic
• Hierarchical structure
• Self-organization
• Complex System

Details

• CRID: 1050001337538421120
• NII Article ID: 120005367956
• ISSN: 03784371
• Web Site: http://hdl.handle.net/10119/11650
• Text Lang: en
• Article Type: journal article
• Data Source:
  • IRDB
  • CiNii Articles