一维驱动Allen-Cahn系统的定态和粗化
Steady states and coarsening in one-dimensional driven Allen-Cahn system
摘要：
我们研究了一维受驱动非保守系统的定态和粗化动力学，该系统由所谓的受驱动Allen-Cahn方程（标准Allen-Cahn方程加上一个附加驱动力）模拟。特别是，我们推导出运动方程的相序系统中的相边界服从这个方程使用最近邻相互作用的方法。使用的运动方程，我们探讨扭结的二元和三元相互作用，并分析如何平均域的大小规模相对于时间。此外，我们采用数值方法进行的一个周期的固定的方程的解的分歧分析。然后，我们调查的两个周期的解决方案的线性稳定性，从而确定和研究各种粗化模式。
英文摘要：
We study the steady states and the coarsening dynamics in a one dimensional driven non-conserved system modelled 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 neighbour 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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