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

Rajiv G. Pereira
Phys. Rev. E 106, 014150 – Published 29 July 2022

Abstract

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.

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  • Received 18 March 2022
  • Accepted 18 July 2022

DOI:https://doi.org/10.1103/PhysRevE.106.014150

©2022 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

Rajiv G. Pereira

  • School of Physics, IISER Thiruvananthapuram, Vithura, Kerala 695551, India

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Issue

Vol. 106, Iss. 1 — July 2022

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