Coarsening and universality on a growing surface

TL;DR

This paper introduces a model of two-species cell proliferation on an expanding surface, revealing critical behavior and universal exponents that match mean-field predictions and simulations.

Contribution

The study presents a new model of proliferating cells on an expanding surface and demonstrates the universality of critical exponents through analytical and numerical methods.

Findings

Domains exhibit critical behavior with universal exponents.

Mean-field theory accurately predicts critical exponents.

Numerical simulations confirm theoretical predictions.

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.