Disrupted coarsening in complex Cahn-Hilliard dynamics.

Area of Science:

• Materials Science
• Condensed Matter Physics
• Chemical Engineering

Background:

• Predicting pattern formation in systems far from equilibrium is complex.
• Disrupted coarsening, where wavelength is pinned, can be predicted by the long-time order parameter.
• The asymptotic form of the order parameter is unknown for some dynamics, like those in the Cahn-Hilliard-like equation for irradiated solids.

Purpose of the Study:

• To present an alternative method for predicting patterning in systems governed by Cahn-Hilliard-like equations.
• To analyze the disrupted coarsening phenomenon in irradiated solids.
• To establish a criterion for disrupted coarsening.

Main Methods:

• Developed a simple ansatz to calculate the form factor.
• Performed bifurcation analysis of the characteristic length (k_{m}^{∞})^{-1} against an irradiation control parameter.
• Supported theoretical analysis with direct numerical simulations.

Main Results:

• Proved that disrupted coarsening occurs in the studied dynamics.
• Identified the bifurcation of the equation linking characteristic length to the control parameter as the cause.
• Demonstrated that this bifurcation is a reliable criterion for disrupted coarsening.

Conclusions:

• The bifurcation of k_{m}^{∞} serves as a robust criterion for predicting disrupted coarsening.
• The proposed method offers a way to predict patterning even when the asymptotic order parameter is unknown.
• This work advances the understanding of pattern formation under irradiation.