Influence of an Intruder Particle on Wave-like Behavior in Vertically Vibrated Granular Matter

Pattern-forming behavior is widely observed in granular matter, particularly when vertically vibrated, and the study of granular matter is relevant due both to its wide-ranging applications in various industries as well as for its mathematical properties. The existence of surface waves in a bath of vertically vibrated granular matter is well known, as is the segregation of polydisperse mixtures of particles. Of particular interest is the behavior of a single large particle, known as an intruder, in a bath of otherwise monodisperse smaller particles. In this work, we use particle-tracking software to track an intruder in a bath of vertically vibrated granular matter. We systematically vary the shaking amplitude and frequency as well as the bath depth and intruder size and density. By computing the radial distribution of and pairwise distances between coarse-grained bath particles, we show that the intruder is responsible for additional wave-like behavior of the bath particles beyond what they experience from the vertical vibration alone. We also establish the nature of wave-like interactions between multiple intruders mediated by the bath particles. This study sheds light on the interplay between an intruder particle and the collective wave-like behavior in vertically vibrated granular matter.