Emergence of scale invariance in the dynamics of an ellipsoidal particle on a granular magnetic bath

Abstract

Recently, scale invariance in the position time series of particles constituting a non-vibrating magnetic granular system was determined, employing Fourier analysis (FA) and detrended fluctuation analysis (DFA). Such system consists of steel balls confined inside a circular wall that surrounds a glass plate, where kinetic energy is provided to the particles by means of the application of an external vertical time-dependent magnetic field. Now, in the present contribution, the magnetic particles are considered as an agitated granular bath where a single non-magnetic ellipsoidal particle lies. In this work, we carry out experiments considering two different sizes of the ellipsoidal particle, and, in addition to the oscillating magnetic field, we also consider a constant magnetic field. In this new scenario, we found that the Fourier power spectra of the time series of the ellipsoidal particle positions in x-direction, and the angular time series constructed from rotational movements, follow a power law, P(f)∝1∕fβ with β≈2, indicating Brownian-type motion. Additionally, we observed that this scale invariance property is not true for the position time series of the particles in the granular bath. These results are confirmed by applying DFA. In this way, by employing time series analysis techniques, a characterization of the emergence of Brownian paths in this model of active matter is achieved.