Morphology from the maximum entropy principle: domains in a phase ordering system and a crack pattern in broken glass

The maximum entropy principle is applied to study the morphology of a phase ordering two-dimensional system below the critical point. The distribution of domain area A is a function of ratio of the area to contour length L, R=A/L(A), and is given by exp(-lambda R(mu)) with exponent mu=2, which follows from the Lifshitz-Cahn-Allen theory. A and L are linked through the relation L approximately A(nu). We find two types of domain in the system: large of elongated shape (nu=0.88) and small of circular shape (nu=0.5). A crack pattern in broken glass belongs to the same morphology class with mu=1 and nu=0.72.