In a significant academic achievement, Dr Soumyajyoti Biswas, Assistant Professor and Scholars Ms Diksha and Mr Gunnemeda Eswar in the Department of Physics, has published an insightful paper in the prestigious Q1 journal, Physical Review E. The paper, titled “Prediction of depinning transitions in interface models using Gini and Kolkata indices,” presents a novel approach to understanding the complex phenomena of depinning transitions in physical systems.
The research introduces the use of Gini and Kolkata indices as predictive tools, offering a fresh perspective that could pave the way for new discoveries in the field. This publication not only underscores Dr. Biswas’s expertise but also enhances the university’s reputation as a hub for cutting-edge research.
The Department of Physics congratulates Dr. Biswas on this remarkable accomplishment and looks forward to the continued impact of his work on the scientific community.
Abstract
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.
Explanation of Research in Layperson’s Terms
Many different physical systems, from cracking in materials to the movement of magnetic fields, share a common underlying behavior – they all involve an “interface” or boundary that moves through a disordered, or irregular, medium. As this interface moves, it often gets “pinned” or stuck in place by the disorder in the medium. However, as the driving force on the interface increases, there comes a point where the interface suddenly “depins” and starts moving much more freely. This transition from a pinned to a depinned state is called the “depinning transition” and it’s an important phenomenon in many areas of science and engineering.
In this work we have found a way to detect when this depinning transition is about to happen, before it actually occurs. We do this by looking at the sizes or magnitudes of the intermittent, or irregular, responses of the system as the driving force increases. Specifically, we use two measures that are traditionally used to quantify economic inequality – the Gini index and the Kolkata index. These give a way to track how “unequal” or unevenly distributed the sizes of the responses are. We found that when these two inequality measures cross each other, it serves as a precursor or early warning sign that the depinning transition is imminent. This is a powerful result because being able to predict when depinning will happen is very useful in fields like material science, superconductivity, and fluid dynamics, where controlling these phase transitions is important. By monitoring these inequality measures, one can may be able to forecast depinning events before they occur, which could lead to better design and control of these systems.
Title of Research paper in the Citation Format
Diksha, G. Eswar, and S. Biswas, Prediction of depinning transitions in interface models using Gini and Kolkata indices, Physical Review E 109, 044113 (2024).
DOI: https://doi.org/10.1103/PhysRevE.109.044113
Practical Implementation or the Social Implications Associated with it
Prediction of imminent transition has implications in a wide range of disciplines, including stability of mechanical structures (buildings, aircraft, bridges, etc.), extraction of oil (fracking) to the largest scale of mechanical failure i.e., earthquakes.
In this fig. the time series of avalanche sizes is shown along with the time variations of g and k for the quenched Edwards-Wilkinson model as a prototype. Here the crossing of g and k occurs prior to the depinning transition point (the last avalanche in the series). Therefore, the crossing of g and k can serve as a good indicator of an imminent depinning transition.
Collaborations
This work is done with the PhD student Ms Diksha and the BSc student Mr Gunnemeda Eswar.
Future Research Plans
Future research plans include applications of the methods developed here to be applied to real-life physical structures for their stability analysis and predictions of impending catastrophes.