title: Evolution of power law distributions in science and society.
abstract: Power law distributions have been observed in numerous physical and social systems; for example, the size distributions of particles, aerosols, corporations, and cities are often power laws. Each system is an ensemble of clusters, comprising units that combine with or dissociate from the cluster. Constructing models and investigating their properties are needed to understand how such clusters evolve. To describe the growth of clusters, we hypothesize that a distribution obeys a governing population dynamics equation based on a reversible association-dissociation process. The rate coefficients are considered to depend on the cluster size as power expressions, thus providing an explanation for the asymptotic evolution of power law distributions.
authors.affiliation: Department of Chemical Engineering, Louisiana State University, Baton Rouge, Louisiana 70803, USA.
authors.forename: Young-Pyo
authors.initials: YP
authors.lastname: Jeon
authors.forename: Benjamin J
authors.initials: BJ
authors.lastname: McCoy
mesh_terms: D000222:Adaptation, Physiological / Q000502:physiology*; D000818:Animals; D005075:Biological Evolution; D003198:Computer Simulation; D017753:Ecosystem; D006128:Growth / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011158:Population Growth; D012586:Science; D012931:Social Environment