Jamming from Stochastic Dynamics with Interactive Noise

Random close packing of spheres has been studied using dynamical models such as biased random organization (BRO) and gradient descent. In this study, we develop a continuous-time stochastic model of particle dynamics called Stochastic Dynamics with Interactive Noise (SDIN). This model incorporates repulsive interactions and athermal noise stemming from particle interactions. Due to the anisotropic and inhomogeneous nature of the particles' microenvironment, we model fluctuations using multiplicative, anisotropic noise. We then demonstrate that SDIN approximates both biased random organization (BRO) and mini-batch gradient descent (MGD) in the limit of small step size (or learning rate), hence BRO and MGD are equivalent in this limit, and they converge to the same random close packing fraction. Furthermore, we show that the behavior of MGD near the critical (jamming) point is consistent with the Manna universality class and exhibits hyperuniformity at the jamming point.