Scale invariance in a nonvibrating magnetic granular system

Abstract

A nonvibrating magnetic granular system is studied by using a time series approach. The system consists of steel balls confined inside a circular wall that surrounds a glass plate. Kinetic energy is provided to the particles by the application of an external vertical time-dependent magnetic field of different amplitudes. We carried out a characterization of the system dynamics through the measurement of the correlations present in the time series of positions, in the x-direction, of each particle. In particular, by performing Fourier spectral analysis, we find that the time series are fractal and scale invariant, in such a way that the corresponding Fourier power spectra follow a power law P(f) ∝ 1/f β , with 0 < β < 2.5. More specifically, we find that the values of β , and therefore the strength of the correlations, increase as the magnetic field also increases. In this way, the present system constitutes an experimental model to generate correlated random walks. Additionally, we show how the introduction of a constant magnetic field breaks down this scale invariance property in the positions of each particle. Finally, we confirm the above results by applying detrended fluctuation analysis.

Magnetized granular particles running and tumbling on $S^{1}$

“…In this work, the experimental arrangement described in recent works [21,[40][41][42] is slightly modified to study the stochastic motion of a metallic ball confined to a lithographic circular channel made on an acrylic plate. Briefly speaking, the setup consists of a pair of Helmholtz coils, where a flat and horizontal plate, called observation cell, is placed in the homogeneous magnetic field region as shown schematically in the left of the figure (1).…”