Effect of energy input on long-term velocity correlations of a rotating sphere in a vibrated sphere-beads system

Abstract

We explore the use of time-resolved Hurst exponent analysis to characterize the degree and nature of correlations in empirical time series corresponding to translational and rotational velocity magnitudes of a rotating sphere on the free surface of vibrated granular matter. For the range of vibration parameters considered, the sphere's translational and rotational motions both display self-similarity or positive, long-term correlations, which indicate persistent dynamical behavior different from that of random 'Brownian' motion. While the degree of long-term correlations in the sphere's rotational motion decreases with increasing vibrational energy input, the nature of correlations remain in the persistent, non-Brownian regime.