title: Universality in two-dimensional cellular structures evolving by cell division and disappearance.
abstract: The dynamics of two-dimensional cellular networks is written in terms of coupled population equations, which describe how the population of s-sided cells is affected by cell division and disappearance. In these equations the effect of the rest of the foam on the disappearing or dividing cell is treated as a local mean field. Under not too restrictive conditions, the equilibrium distribution P(s) of cells satisfies a linear difference equation of order two or higher. The population equations are asymptotically integrable. The asymptotic integrability implies a "universal" distribution P(s) approximately Cs-kZs for large values of s, which is also the Boltzmann distribution associated with the maximum entropy inference. Asymptotic integrability of the population equations is absent in a global mean-field approximation. The importance of short-range topological information to control the evolution of foams is thus confirmed.
authors.affiliation: Institute for Advanced Studies in Basic Sciences, Zanjan 45195-1159, Iran.
authors.forename: MirFaez
authors.initials: M
authors.lastname: Miri
authors.forename: Nicolas
authors.initials: N
authors.lastname: Rivier
mesh_terms: D017209:Apoptosis / Q000502:physiology; D002448:Cell Adhesion / Q000502:physiology; D002455:Cell Division / Q000502:physiology; D002465:Cell Movement / Q000502:physiology; D049109:Cell Proliferation; D002478:Cells, Cultured; D003198:Computer Simulation; D000078404:Epidermal Cells; D004817:Epidermis / Q000502:physiology*; D004847:Epithelial Cells / Q000166:cytology / Q000502:physiology*; D006801:Humans; D008954:Models, Biological