Superstatistical approach of the anomalous exponent for scaled Brownian motion

TL;DR

This paper explores a superstatistical framework for scaled Brownian motion, analyzing how heterogeneity in anomalous exponents and diffusivity affects diffusion behavior in complex systems.

Contribution

It introduces truncated-Gaussian and truncated chi-squared distributions for anomalous exponents within a superstatistical approach to scaled Brownian motion.

Findings

Heterogeneity in anomalous exponents influences diffusion dynamics.

Coupling between diffusivity and anomalous exponent affects superstatistical behavior.

Simulation and analytical results validate the proposed models.

Abstract

Anomalous diffusion phenomenon is an intriguing process that tracer diffusion presents in numerous complex systems. Current experimental and theoretical investigations have reported the emergence of random diffusivity scenarios accompanied by the heterogeneity of the $\alpha$-anomalous diffusion exponents. In this framework, we investigate a heterogeneous ensemble of tracers governed by scaled Brownian motion (sBm). The heterogeneous features are considered on anomalous diffusion exponent and diffusivity. To analyse such systems, we introduce the truncated-Gaussian and truncated chi-squared distributions for anomalous exponents in the superstatistical framework. We also discuss the role of different temporal scales in sBm for our model. Furthermore, we investigate the effects of coupling between diffusivity and anomalous exponent on superstatistics of sBm. The investigation provides a thorough analysis of simulation and analytical results.