Theoretical Study on the Kinetics of a Special Particle Swarm

Prior studies have focused on the overall behavior of randomly moving particle swarms. However, the characteristics of ubiquitous special particle swarms that form in these swarms remain unknown. This study demonstrates a generalized diffusion equation for randomly moving particles that considers the velocity and location aggregation effects in a special circumstance (that is, in a moving reference frame R_u relative to a stationary reference frame R₀). This equation can be approximated as the Schrodinger equation in the microcosmic case and describes the kinetics of the total mass distribution in the macrocosmic case. The predicted density distribution of the particle swarm in the stable aggregation state is consistent with the total mass distribution of massive, relaxed galaxy clusters (at least in the range of r < r_s), preventing cuspy problems in the empirical Navarro-Frenk-White (NFW) profile. This article is helpful for inspiring people to think about the essence of universal gravitation.