Defect Solutions of the Non-reciprocal Cahn-Hilliard Model: Spirals and Targets

Abstract

We study the defect solutions of the Non-reciprocal Cahn-Hilliard model (NRCH). We find two kinds of defects, spirals with unit magnitude topological charge, and topologically neutral targets. These defects generate radially outward travelling waves and thus break the parity and time-reversal symmetry. For a given strength of non-reciprocity, spirals and targets with unique asymptotic wavenumber and amplitude are selected. We use large-scale simulations to show that at low non-reciprocity $\alpha$, a quenched disordered state evolves into quasi-stationary spiral networks. With increasing $\alpha$, we observe networks composed primarily of targets. Beyond a critical threshold ${\alpha }_c$, a disorder-order transition from defect networks to travelling waves emerges. The transition is marked by a sharp rise in the global polar order.

15 pages including supplemental material

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• Non-reciprocal mixtures in suspension: the role of hydrodynamic interactions
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