Fogedby Hans C, Ren Weiqing
Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Oct;80(4 Pt 1):041116. doi: 10.1103/PhysRevE.80.041116. Epub 2009 Oct 15.
We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for the height profile of a growing interface. In one dimension we find that the transition pathway between different height configurations is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise-driven Burgers equation. This transition scenario is in accordance with recent analytical studies of the one-dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit. We also briefly discuss transitions in two dimensions.
我们将一种源自温策尔 - 弗雷德林大偏差理论的数值最小作用量方法应用于描述生长界面高度轮廓的 Kardar - Parisi - Zhang 方程。在一维情况下，我们发现不同高度构型之间的转变路径由小平面或台阶的成核及随后的传播所决定，这对应于基础噪声驱动的伯格斯方程中的移动畴壁或生长模式。这种转变情形与一维 Kardar - Parisi - Zhang 方程在渐近弱噪声极限下的近期解析研究结果相符。我们还简要讨论了二维情况下的转变。
