Wavelength selection by interrupted coarsening in reaction-diffusion systems.

Wavelength selection in reaction-diffusion systems can be understood as a coarsening process that is interrupted by counteracting processes at a certain wavelength. We show that coarsening in mass-conserving reaction-diffusion systems is driven by self-amplifying mass transport between neighboring high-density domains. We derive a general coarsening criterion and show that coarsening in two-component systems is generically uninterrupted. The theory is then generalized to study interrupted coarsening and anti-coarsening due to weakly-broken mass conservation, providing a general path to analyze wavelength selection in pattern formation far from equilibrium.