Granger Causality and Cross Recurrence Plots in Rheochaos

TL;DR

This study investigates the causal relationship and shared dynamics between stress and micelle orientation in rheochaos using Granger causality and cross recurrence plots, revealing feedback mechanisms and phase space similarities.

Contribution

It applies Granger causality and cross recurrence plots to rheological data, uncovering causal influences and shared phase space dynamics in micellar systems.

Findings

Orientational order has a stronger causal effect on stress.

Feedback mechanism exists between stress and micelle orientation.

Stress and intensity share similar phase space dynamics.

Abstract

Our stress relaxation measurements on wormlike micelles using a Rheo-SALS (rheology + small angle light scattering) apparatus allow simultaneous measurements of the stress and the scattered depolarised intensity. The latter is sensitive to orientational ordering of the micelles. To determine the presence of causal influences between the stress and the depolarised intensity time series, we have used the technique of linear and nonlinear Granger causality. We find there exists a feedback mechanism between the two time series and that the orientational order has a stronger causal effect on the stress than vice versa. We have also studied the phase space dynamics of the stress and the depolarised intensity time series using the recently developed technique of cross recurrence plots (CRPs). The presence of diagonal line structures in the CRPs unambiguously proves that the two time series share similar phase space dynamics.