Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:A2L-B

Session:

Number:106

On the Analysis of a Scaling Law Related to Random Walks -for the distributions of broken fragments of glass, areas enclosed by city roads, and divided faces in network models-

Yukio Hayashi,  

pp.106-109

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.106

PDF download (402KB)

A common distribution of areas (or mass) is observed in fragments of glass, city roads, and cracking patterns. In order to study a generation mechanism of the scaling law, we consider a fractal-like hierarchical network construction 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 show a good fitting with the actual distribution in the averaging behavior of the divisions.

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