Scale invariance in a nonvibrating magnetic granular system

G Torres-Vargas,C Tapia-Ignacio,R Fossion,F López-González,F Donado

doi:10.1038/s41598-020-68345-z

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)propto 1/f^beta, with 0<beta <2.5. More specifically, we find that the values of beta, 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.

Highlights

A nonvibrating magnetic granular system is studied by using a time series approach
In order to avoid a wrong detection of apparent long-range correlations, we analyze the fractal properties of the time series by applying detrended fluctuation analysis (DFA), to confirm the results found by applying Fourier analysis (FA)
We have introduced two mathematical tools from time series and signal analysis, Fourier analysis (FA) and detrended fluctuation analysis (DFA), to perform a characterization of the particles dynamics in a non-vibrating magnetic granular system, under the action of a magnetic field, B

Summary

Introduction

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. One of the advantages of such systems, for instance, is that the interparticle interactions can be modulated by active controls[15,16,17,18] Another advantage is that their dynamics and structural properties can be studied directly from the positions of the particles, in a straightforward way. We calculate the Fourier power spectrum, P(f), from the time series of positions, in the x-direction, of each particle in the aforementioned experimental model, where f is the frequency of the periodic modes in which the time series is decomposed In this way, a set of power spectra is obtained from the entire system for each value of Bo. In this way, a set of power spectra is obtained from the entire system for each value of Bo From all these spectra, an average power spectrum is calculated, which follows a power law, P(f ) ∝ 1/f β ,

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Conclusion