Anomalous phenomena and intermittency in the dynamics of multiple particles in a funnel

Abstract

In this thesis, we investigate a granular system of multiple inelastic, frictionless, spherical particles falling under gravity through a symmetric two-dimensional funnel with different particle injection frequencies. Intuitively, one might expect that the average durations which particles spend in the funnel would increase monotonically as the particle injection frequency increases, since, due to inter-particle collisions, the more particles in the funnel, the more likely the particles would slow down and consequently more difficult to pass through the funnel. However we show surprisingly that the duration is not a monotonic function of the injection frequency. We provide an explanation for the seemingly counterintuitive phenomena. We further conduct detailed studies on how the coefficient of restitution and dynamics of inter-particle collisions affect the duration. We also identify the phenomena of intermittency in the system with steep walls. Namely, the behaviors of the system keep altering between two completely different states at certain range of injection frequency. In one state, the particles have very few inter-particle collisions, short durations and simple trajectories; in the other, they have considerably more inter-particle collisions, much longer durations and more complicated trajectories. We provide an explanation for these phenomena, and develop a method of classifying these two states.