Transfer entropy analysis of ball-fluid interactions during sinusoidal vibration with varying frequencies

Abstract

This present work adapts the information dynamics approach to examine systems involving a fixed-parameter rigid ball, modeled after a polypropylene 'ping-pong' ball, on a vibrating fluid bath simulated via smoothed particle hydrodynamics (SPH). We focus on quantifying the direction and strength of information transfer among various motion-related quantities using a combination of transfer entropy (TE) and Schreiber-Schmitz iterative surrogates. By computing net TE values and comparing them with surrogate counterparts using Z-scores, 26 variable pairs are found to exhibit significant net information transfer, 11 of which involve interactions between the ping-pong ball and the fluid. Notably, the ball's velocity along the z-axis strongly influences the mean and standard deviation of the fluid particles' velocity components and magnitude. Overall, there is no consistent trend observed in the impact of varying frequency across all variable pairs, as some pairs exhibit high net TE at 25 Hz while others show low net TE values.