Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

Theoretical Study on the Kinetics of a Special Particle Swarm

Version 1 : Received: 12 September 2020 / Approved: 14 September 2020 / Online: 14 September 2020 (00:04:07 CEST)
Version 2 : Received: 31 December 2020 / Approved: 5 January 2021 / Online: 5 January 2021 (11:14:18 CET)
Version 3 : Received: 12 November 2021 / Approved: 15 November 2021 / Online: 15 November 2021 (11:10:16 CET)
Version 4 : Received: 7 June 2022 / Approved: 7 June 2022 / Online: 7 June 2022 (08:32:15 CEST)
Version 5 : Received: 10 November 2022 / Approved: 10 November 2022 / Online: 10 November 2022 (03:53:56 CET)

A peer-reviewed article of this Preprint also exists.

Guo, T. Dynamics of stochastic-constrained particles. Sci Rep 13, 2759 (2023). Guo, T. Dynamics of stochastic-constrained particles. Sci Rep 13, 2759 (2023).


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 Ru 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 < rs), 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.


randomly moving particles; effects of location aggregation; relaxed galaxy clusters; generalized diffusion equation


Physical Sciences, Astronomy and Astrophysics

Comments (1)

Comment 1
Received: 7 June 2022
Commenter: Tao Guo
Commenter's Conflict of Interests: Author
Comment: 1. Added an example to verify the equation.
2. Revised the core paragraph.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.

Leave a public comment
Send a private comment to the author(s)
* All users must log in before leaving a comment
Views 0
Downloads 0
Comments 1
Metrics 0

Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.