Deviation of the power-law by geometric aging effect

Authored by J. K. Shin, G. S. Shin

Date Published: 2007-06

DOI: 10.1142/s0218348x07003514

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

An agent- based model is employed for the study of the group size distributions. A fixed number of homogeneous agents are distributed on a two- dimensional lattice system. The dynamics of the agents is described in terms of the inverse distance potential and the friction factor. From a random initial distribution, the agents move forming groups until all the agents come to a stationary position. For a squared system with L x L cells, the group size distribution showed a well defined power- law behavior up to the cut-off size. But when the system changed to an L x H non- squared one, a “geometric aging effect” emerged. Together with the phase transition, the geometric aging effect is considered to be a generic mechanism of the deviated power-law distributions, such as the “fall-off” and the three- bent- line distributions. The results are discussed in relation to the well- known physical or social phenomena such as the King Effect in the city size distributions, the fall-off distribution of the fish schools, the three- bent- line distributions of the Earth- crossing asteroids and 2D percolation problem.

Tags

Power-law fall-off geometric aging effect king effect percolation three-bent-line distribution