Eswar Gunnemeda, Biswas Soumyajyoti
Department of Physics, SRM University - AP, Andhra Pradesh 522240, India.
Phys Rev E. 2024 Apr;109(4-1):044113. doi: 10.1103/PhysRevE.109.044113.
The intermittent dynamics of driven interfaces through disordered media and its subsequent depinning for large enough driving force is a common feature for a myriad of diverse systems, starting from mode-I fracture, vortex lines in superconductors, and magnetic domain walls to invading fluid in a porous medium, to name a few. In this work, we outline a framework that can give a precursory signal of the imminent depinning transition by monitoring the variations in sizes or the inequality of the intermittent responses of a system that are seen prior to the depinning point. In particular, we use measures traditionally used to quantify economic inequality, i.e., the Gini index and the Kolkata index, for the case of the unequal responses of precritical systems. The crossing point of these two indices serves as a precursor to imminent depinning. Given a scale-free size distribution of the responses, we calculate the expressions for these indices, evaluate their crossing points, and give a recipe for forecasting depinning transitions. We apply this method to the Edwards-Wilkinson, Kardar-Parisi-Zhang, and fiber bundle model interface with variable interaction strengths and quenched disorder. The results are applicable for any interface dynamics undergoing a depinning transition. The results also explain previously observed near-universal values of Gini and Kolkata indices in self-organized critical systems.
驱动界面在无序介质中的间歇动力学及其在足够大驱动力作用下随后的脱钉现象，是众多不同系统的一个共同特征，从I型断裂、超导体中的涡旋线、磁畴壁到多孔介质中侵入的流体等等。在这项工作中，我们概述了一个框架，通过监测系统在脱钉点之前所表现出的间歇响应的大小变化或不平等性，能够给出即将发生脱钉转变的先兆信号。特别地，对于临界前系统的不平等响应情况，我们使用传统上用于量化经济不平等的度量，即基尼指数和加尔各答指数。这两个指数的交叉点作为即将脱钉的先兆。给定响应的无标度大小分布，我们计算这些指数的表达式，评估它们的交叉点，并给出预测脱钉转变的方法。我们将此方法应用于具有可变相互作用强度和淬火无序的爱德华兹 - 威尔金森模型、卡达尔 - 帕里西 - 张模型以及纤维束模型界面。结果适用于任何经历脱钉转变的界面动力学。这些结果还解释了在自组织临界系统中先前观察到的基尼指数和加尔各答指数近乎普遍的值。
