Driven fragmentation of granular gases

Jamming and tiling in fragmentation of rectangles

We investigate a stochastic process where a rectangle breaks into smaller rectangles through a series of horizontal and vertical fragmentation events. We focus on the case where both the vertical size and the horizontal size of a rectangle are discrete variables. Because of this constraint, the system reaches a jammed state where all rectangles are sticks, that is, rectangles with minimal width. Sticks are frozen as they cannot break any further. The average number of sticks in the jammed state, S, grows as S≃A/sqrt[2πlnA] with rectangle area A in the large-area limit, and remarkably, this behavior is independent of the aspect ratio. The distribution of stick length has a power-law tail, and further, its moments are characterized by a nonlinear spectrum of scaling exponents. We also study an asymmetric breakage process where vertical and horizontal fragmentation events are realized with different probabilities. In this case, there is a phase transition between a weakly asymmetric phase where the length distribution is independent of system size and a strongly asymmetric phase where this distribution depends on system size.

Dynamical scaling of fragment distribution in drying paste

Crack patterns of drying paste and their statistical properties are investigated through smoothed particle hydrodynamics, which is one method for solving continuum equations in the Lagrangian description. In addition to reproducing a realistic crack pattern, we also find that the average area of a fragment decays inversely with time in the case of linearly increasing desiccation stress. We find that the distribution can be scaled with the average area of the fragment over the corresponding time, even though the distribution function of the fragment area changes the functional form during evolution.