Coarsening and universality on a growing surface

Abstract

We introduce a model in which cells belonging to two species proliferate with volume exclusion on an expanding surface. If the surface expands uniformly, we show that the domains formed by the two species present a critical behavior. We compute the critical exponents characterizing the decay of interfaces and the size distribution of domains using a mean-field theory. These mean-field exponents agree very accurately with those fitted in numerical simulations, suggesting that the theory is exact.