SeSP Plinko: Dynamics of C-Shaped Particles Moving Through an Obstacle Field

We examine the behavior of C-shaped superellipse sector particles (SeSPs) as they travel through an obstacle field. SeSPs are two-dimensional particles parameterized by corner sharp- ness, aspect ratio, and opening angle; these parameters are sufficient to represent a large variety of shapes, including discs, rods, and concave and convex particles. Our obstacle field is a rhombic Galton Board, an array with alternating rows of pegs. Galton Boards are common not just in experiments but in popular media, such as in boardwalk games and in The Price is Right’s game segment known as "Plinko." Round particles dropped through a Galton Board distribute normally; due to their irregular shape, c-shaped SeSPs can self-clog on individual pegs, a behavior which is not observed for circular and elliptical particles. We examine and characterize the translational and rotational motion using Mean-Squared Displacements of SeSPs. In the horizontal direction, particles tend to have more diffusive, if not superdiffusive, motion in early timesteps (⟨x^2⟩ = t^(1.22±0.01)), and more subdiffusive motion in later timesteps (⟨x^2⟩ = t^((0.61±0.01)). The vertical motion is observed to be more superdiffusive (⟨y^2⟩ = t^(1.7±0.1)), and the rotational motion to be more subdiffusive with a value ⟨θ^2⟩ = t^(0.77±0.02) in the earlier timesteps and a smaller degree in the later timesteps (⟨θ^2⟩ = t^(0.10±0.02). We explore the distribution of SeSPs exiting the obstacle field–and compare this to the distribution of Galton Boards. The distribution of SeSPs exiting the board has a slight leftward skew in comparison to the normal distribution of a Galton Board with round particles (exiting most commonly in the midleft bin as opposed to the center bin). However, this skew is likely due to board tilt. We consider how soon the initial orientation of a SeSP is lost, finding that the orientation falls rapidly out of alignment with a time constant τ of 1.325 ± 0.001 before plateauing into a more gradual decline. Finally, we present how SeSP collisions within the field impact their probability of getting stuck on an obstacle, and the link between number of collisions and location of sticking, finding that the probability of a SeSP getting stuck increases by approximately 7% the further it travels down the board.