Analysis reveals dynamic transitions and pattern formations in binary systems on two-dimensional lattices, suggesting geometry impacts outcomes.
Key Points
This article aims to explore how geometry and physical parameters influence dynamic phase transitions and pattern formations in binary systems modeled by the Cahn-Hilliard equation.
Examined dynamic phase transitions in a two-dimensional lattice structure using Cahn-Hilliard equation.
Analyzed the influence of spanning vectors on dynamical transitions and pattern formations.
Decomposed function space into stable and unstable eigenspaces and calculated the center manifold.
Investigated geometry-dependent properties of critical eigenvalues and their multiplicities.
Considered long-range interaction model and its effects compared to the original model.
Observed emergence of hexagonally-packed circles, rolls, and square structures in non-rectangular domains.
Dynamic transitions were shown to correlate with the geometry of the domain and parameter choices.
Identified geometry-dependent multiplicities of critical eigenvalues affecting stability.