Valizadeh N, Hamzehpour H, Samadpour M, Najafi M N
Department of Physics, K.N. Toosi University of Technology, Tehran, 15875-4416, Iran.
Department of Physics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran.
Sci Rep. 2023 Jul 29;13(1):12300. doi: 10.1038/s41598-023-39191-6.
There are various reports about the critical exponents associated with the depinning transition. In this study, we investigate how the disorder strength present in the support can account for this diversity. Specifically, we examine the depinning transition in the quenched Edwards-Wilkinson (QEW) model on a correlated square lattice, where the correlations are modeled using fractional Brownian motion (FBM) with a Hurst exponent of H.We identify a crossover time [Formula: see text] that separates the dynamics into two distinct regimes: for [Formula: see text], we observe the typical behavior of pinned surfaces, while for [Formula: see text], the behavior differs. We introduce a novel three-variable scaling function that governs the depinning transition for all considered H values. The associated critical exponents exhibit a continuous variation with H, displaying distinct behaviors for anti-correlated ([Formula: see text]) and correlated ([Formula: see text]) cases. The critical driving force decreases with increasing H, as the host medium becomes smoother for higher H values, facilitating fluid mobility. This fact causes the asymptotic velocity exponent [Formula: see text] to increase monotonically with H.
关于与脱钉转变相关的临界指数有各种各样的报道。在本研究中，我们研究支撑体中存在的无序强度如何解释这种多样性。具体而言，我们研究了相关正方形晶格上的淬火爱德华兹 - 威尔金森（QEW）模型中的脱钉转变，其中相关性是使用具有赫斯特指数H的分数布朗运动（FBM）来建模的。我们确定了一个交叉时间[公式：见正文]，它将动力学分为两个不同的区域：对于[公式：见正文]，我们观察到被钉扎表面的典型行为，而对于[公式：见正文]，行为则有所不同。我们引入了一种新颖的三变量标度函数，它控制所有考虑的H值下的脱钉转变。相关的临界指数随H连续变化，在反相关（[公式：见正文]）和相关（[公式：见正文]）情况下表现出不同的行为。临界驱动力随着H的增加而减小，因为对于更高的H值，主体介质变得更平滑，有利于流体流动。这一事实导致渐近速度指数[公式：见正文]随H单调增加。
