Localized states in coupled Cahn-Hilliard equations

Abstract

The classical Cahn-Hilliard (CH) equation corresponds to a gradient dynamics model that describes phase decomposition in a binary mixture. In the spinodal region, an initially homogeneous state spontaneously decomposes via a large-scale instability into drop, hole or labyrinthine concentration patterns of a typical structure length followed by a continuously ongoing coarsening process. Here we consider the coupled CH dynamics of two concentration fields and show that nonreciprocal (or active, or nonvariational) coupling may induce a small-scale (Turing) instability. At the corresponding primary bifurcation a branch of periodically patterned steady states emerges. Furthermore, there exist localized states that consist of patterned patches coexisting with a homogeneous background. The branches of steady parity-symmetric and parity-asymmetric localized states form a slanted homoclinic snaking structure typical for systems with a conservation law. In contrast to snaking structures in systems with gradient dynamics, here, Hopf instabilities occur at sufficiently large activity which result in oscillating and traveling localized patterns.

References in corpus (5)

• Nonreciprocity as a generic route to traveling states
• Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
• Alternative mechanisms of structuring biomembranes: Self-assembly vs. self-organization
• Localized states in passive and active phase-field-crystal models
• Spatio-temporal dynamics induced by competing instabilities in two asymmetrically coupled nonlinear evolution equations

Cited by in corpus (19)

• Non-reciprocity across scales in active mixtures
• Clustering and flocking of repulsive chiral active particles with non-reciprocal couplings
• Suppression of coarsening and emergence of oscillatory behavior in a Cahn-Hilliard model with nonvariational coupling
• Nonreciprocal Cahn-Hilliard model emerges as a universal amplitude equation
• Defect Solutions of the Non-reciprocal Cahn-Hilliard Model: Spirals and Targets
• Field-Theory of Active Chiral Hard Disks: A First-Principles Approach to Steric Interactions
• Nonreciprocity induces resonances in two-field Cahn-Hilliard model
• Stationary broken parity states in active matter models
• Coexistence of uniform and oscillatory states resulting from nonreciprocity and conservation laws
• Robustness of travelling states in generic non-reciprocal mixtures
• Derivation and analysis of a phase field crystal model for a mixture of active and passive particles
• Enhanced stability and chaotic condensates in multi-species non-reciprocal mixtures
• An amplitude equation for the conserved-Hopf bifurcation -- derivation, analysis and assessment
• Fluctuating hydrodynamics of active particles interacting via taxis and quorum sensing: static and dynamics
• Local Order Controls the Onset of Oscillations in the Nonreciprocal Ising Model
• Pattern dynamics of the nonreciprocal Swift-Hohenberg model
• Traveling spatially localized convective structures in an inclined porous medium
• Stochastic Thermodynamics of Non-reciprocally Interacting Particles and Fields
• Higher-codimension points as organizing centers in nonreciprocal pattern-forming systems with O(2)-symmetry