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

TL;DR

This paper investigates defect solutions in the Non-reciprocal Cahn-Hilliard model, identifying spiral and target defects that generate waves and lead to a transition from disordered states to ordered traveling wave patterns as non-reciprocity increases.

Contribution

It characterizes the types of defects in the NRCH model and reveals how defect networks evolve and transition to traveling waves with increasing non-reciprocity.

Findings

Identified spiral and target defects with unique asymptotic properties.

Observed a transition from disordered to ordered states at a critical non-reciprocity threshold.

Demonstrated the emergence of traveling waves beyond the critical point.

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.