Biased Random Organization of Ellipses and Needles

The Biased Random Organization (BRO) model exhibits a dynamical phase transition between an absorbing and an active state. At the critical point for spheres in three dimensions it produces Random Close Packed structures. 3D Ellipsoids randomly pack denser than spheres. What happens when we apply BRO to ellipses in 2D? We found the system exhibits dynamical phase transition between absorbing and active states and also belongs to the Manna universality class. However, the hexagonal equivalent of a crystal of ellipses appears to be unstable when the aspect ratio is above a certain threshold. While investigating the nematicity of the ellipse system, we explored needles (infinite aspect ratio ellipses) on a square lattice. We discovered a novel active "checkerboard" phase where needles alternate vertical, horizontal, vertical, horizontal….orientations. This phase exists within a narrow parameter range: when the half-length of the needles (r) slightly exceeds the lattice constant (r/a - 1 ~ 0.001) and the kick size (Δθ) is ~ .1 to .5 radians. We mapped out a phase diagram and examined the properties of transitions at the phase boundaries. The checkerboard phase system exhibits Model A-like coarsening dynamics.