Intrinsic statistical regularity of topological charges revealed in dynamical disk model

Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive particles confined on a disk under the Hamiltonian dynamics by the recently developed algorithm called the random batch method. This algorithm is specifically designed for reducing the computational complexity of long-range interacting particle systems. We highlight the revealed intrinsic statistical regularity of topological charges that is otherwise unattainable by the continuum analysis of particle density. We also identify distinct collective dynamics of the interacting particles under short- and long-range repulsive forces. This work shows the robustness and effectiveness of the concept of topological charge for characterizing the convoluted particle dynamics, and it demonstrates the promising potential of the random batch method for exploring fundamental scientific questions arising in a variety of long-range interacting particle systems in soft matter physics and other relevant fields.