Inequality of avalanche sizes in models of fracture

Abstract

Prediction of an imminent catastrophic event in a driven disordered system is of paramount importance - from the laboratory scale controlled fracture experiment to the largest scale of mechanical failure i.e., earthquakes. It has been long conjectured that the statistical regularities in the energy emission time series mirrors the "health" of such driven systems and hence have the potential for forecasting imminent catastrophe. Among other statistical regularities, a measure of how unequal the avalanche sizes are, is potentially a crucial indicator of imminent failure. The inequalities of avalanche sizes are quantified using inequality indices traditionally used in socio-economic systems: the Gini index (g), the Hirsch index (h) and the Kolkata index (k). It is then shown analytically (for mean field) and numerically (for non mean field) in models of quasi-brittle materials that the indices show universal behavior near the breaking points in such models and hence could serve as indicators of imminent breakdown of stressed disordered systems.