Defect Solutions of the Nonreciprocal Cahn-Hilliard Model: Spirals and Targets.

Abstract

We study the defect solutions of the nonreciprocal Cahn-Hilliard model. We find two kinds of defects, spirals with unit magnitude topological charge, and topologically neutral targets. These defects generate radially outward traveling waves and thus break the parity and time-reversal symmetry. For a given strength of nonreciprocity, spirals and targets with unique asymptotic wave number and amplitude are selected. We use large-scale simulations to show that at low nonreciprocity α, disordered states evolve into quasistationary spiral networks. With increasing α, we observe networks composed primarily of targets. Beyond a critical threshold α_{c}, a disorder-order transition from defect networks to traveling waves emerges. The transition is marked by a sharp rise in the global polar order.