Concentric ring patterns beyond Turing instability

Abstract

Various out-of-equilibrium physical systems exhibit concentric ring patterns. However, these patterns are expected to be unstable due to the interaction of spatial modes. Here, we show that concentric ring patterns are stable beyond Turing instability. Based on a prototype pattern forming model, we show that these solutions are stable and identify the main ingredients for their stability: curvature, characteristic wavelength, and bistability. We further characterize the propagation of stable concentric ring patterns. Experimentally, we observe stable concentric ring patterns in an illuminated dye-doped liquid crystal cell with sufficiently high intensity. The formation of the concentric rings is in agreement with our predicted theoretical findings.