DEVIATION OF THE POWER-LAW BY GEOMETRIC AGING EFFECT

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 × 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 × 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.