Structural characterization of a magnetic granular system under a time-dependent magnetic field: Voronoi tessellation and multifractal analysis

The structure of a two-dimensional magnetic granular system was determined by multifractal and Voronoi polygon analysis for a wide range of particle concentrations. Randomizing of the particle motions are produced by applying to the system a time-dependent sinusoidal magnetic field directed along the vertical direction. Both repulsive and attractive short-range interactions between the particles are induced. A direct observation of such system shows qualitatively that, as particle concentration increases, the structure evolves from being liquid-like at low particle concentrations to solid-like at high concentrations. We observe the formation of clusters which are small and weakly bonded and short-lived at low concentrations. Above a threshold particle concentration, clusters grow larger and are more strongly attached. In the system, one can distinguish the mobile particles from the immobile particles belonging to clusters, they can be considered separately as two different phases, a fluid and a solid. We determined the information entropy of the system as a whole and separately from each phase as particle concentration increases. The distribution of the Voronoi polygon areas are well fitted by a two-parameter gamma distribution and we have found that the regularity factor shows a notable change when pieces of the solid phase start to form. The methods we use here show that they can use even when the system is heterogeneous and they provide information when changes start.