Universal, statistically scale-invariant regime in 3D cellular systems

We perform extensive Potts model simulations of 3D dry foam coarsening and we report reaching a scaling state. Starting with 2.25 million bubbles, we have enough time for the transient to end and reach the scaling state; enough time in the scaling state to characterize its properties; and finally, enough bubbles at the end to avoid spurious finite size effects. In the scaling state, we find that the number of bubbles decreases as t-1.5 and we obtain a time independent distribution in relative bubble size.