Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation

Abstract

Oscillatory behavior is ubiquitous in out-of-equilibrium systems showing spatio-temporal pattern formation. Starting from a linear large-scale oscillatory instability -- a conserved-Hopf instability -- that naturally occurs in many active systems with two conservation laws, we derive a corresponding amplitude equation. It belongs to a hierarchy of such universal equations for the eight types of instabilities in homogeneous isotropic systems resulting from the combination of three features: large-scale vs.\ small-scale instability, stationary vs.\ oscillatory instability, and instability without and with conservation law(s). The derived universal equation generalizes a phenomenological model of considerable recent interest, namely, the nonreciprocal Cahn-Hilliard model, and may be of a similar relevance for the classification of pattern forming systems as the complex Ginzburg-Landau equation.

References in corpus (6)

• Nonequilibrium Physics in Biology
• Nonreciprocity as a generic route to traveling states
• Morphology changes in the evolution of liquid two-layer films
• Gradient dynamics models for liquid films with soluble surfactant
• On the transient and steady state of mass-conserved reaction diffusion systems
• Stationary broken parity states in active matter models

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