Statistical analysis of self-similar behaviour in the shear induced melting model

TL;DR

This paper investigates the shear melting model under additive noise, revealing power-law distributions and self-similarity in the order parameter, with self-similarity increasing as noise intensity decreases.

Contribution

It provides a detailed analysis of self-similar behavior in shear melting models using multifractal analysis, highlighting the impact of noise intensity.

Findings

Power-law distribution in the order parameter

Self-similarity increases with decreasing noise

Generalized Hurst exponent indicates multifractality

Abstract

The analysis of the system behavior under the effect of the additive noises has been done using a simple model of shear melting. The situation with low intensity of the order parameter noise has been investigated in detail, and time dependence of the order parameter has been calculated. A distinctive feature of the obtained dependence is power-law distribution and self-similarity. The generalized Hurst exponent of the time series has been found within multifractal detrended fluctuation analysis. It is shown that the self-similarity of the time series increases when the noise intensity reduces.