Subdiffusion model for granular discharge in a submerged silo.

Silo discharge has been extensively studied for decades although questions remain regarding the nature of the velocity field, particularly for submerged systems. In this work, fluid-driven granular drainage was performed in a quasi-two-dimensional silo with grains submerged in fluid. While the observed Gaussian velocity profiles were generally consistent with current diffusion models, the diffusion length was found to significantly decrease with height in contrast to the increases previously seen in dry silos. We propose a phenomenological anomalous diffusion model for the spreading of the flow upwards in the cell, with the fluid-driven flows we study here falling in the category of subdiffusive behavior. As the viscous characteristics of the system were amplified, the diffusion length increased and the shape of the flowing zone in the silo changed, deviating further from the parabolic form predicted by traditional normal diffusion models, in effect becoming more subdiffusive as quantified by a decreasing diffusion exponent.

Active Brownian particles moving through disordered landscapes.

Disordered media are ubiquitous in systems where self-propelled particles are present, ranging from biological settings to synthetic systems, like in active microfluidic devices. Here we investigate the behavior of active Brownian particles that have an internal energy depot and move through a landscape with a quenched frictional disorder. We consider the cases of very fast internal relaxation processes and the limit of strong disorder. Analytical calculations of the mean-square displacement in the fast-relaxation approximation is shown to agree well with numerically integrated energy depot dynamics and predict normal dispersion for a bounded drag coefficient and anomalous dispersion for power-law dependence of the drag on spatial coordinates. Furthermore, we show that in the strongly disordered limit the self-propulsion speed can, for practical purposes, be considered a fluctuating quantity. Distributions of self-propulsion speeds are investigated numerically for different parameter choices.