Steady states and coarsening in one-dimensional driven Allen-Cahn system

We study the steady states and the coarsening dynamics in a one-dimensional driven nonconserved system modeled by the so-called driven Allen-Cahn equation, which is the standard Allen-Cahn equation with an additional driving force. In particular, we derive equations of motion for the phase boundaries in a phase ordering system obeying this equation using a nearest-neighbor interaction approach. Using the equations of motion we explore kink binary and ternary interactions and analyze how the average domain size scale with respect to time. Further, we employ numerical techniques to perform a bifurcation analysis of the one-period stationary solutions of the equation. We then investigate the linear stability of the two-period solutions and thereby identify and study various coarsening modes.

Automated summary

Studied the steady states and coarsening dynamics in a one-dimensional driven nonconserved system, derived equations of motion for phase boundaries in a phase ordering system, explored kink interactions, and analyzed scaling of average domain size with time using numerical techniques.