Structure of random cellular networks and their evolution

Abstract

The methods of statistical mechanics are applied to the structure of random, space-filling, cellular structures (foams, metallurgical grain aggregates, biological tissues). Microreversibility of the structural properties under elementary transformations is demonstrated. Maximum entropy inference under a few constraints yields structural equations of state, relating the size of cells to their topological shape. These equations of state classify the structures, and are criteria for their randomness. Quasistatic evolution is obtained if the structure remains in statistical equilibrium at all times. In 2D, it is governed by von Neumann's law.