Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

# 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)

How to cite: Guo, T. Study on the Kinetics of a Special Particle Swarm. Preprints 2020, 2020090307 (doi: 10.20944/preprints202009.0307.v3). Guo, T. Study on the Kinetics of a Special Particle Swarm. Preprints 2020, 2020090307 (doi: 10.20944/preprints202009.0307.v3).

## Abstract

For randomly-moving-particle swarm, the past researches only focused on its whole behavior and few people have studied the special particle swarm formed in it, which leading to the phenomenon and reasons for the spontaneous aggregation of particles in the special particle swarm being still unknown. For such a special particle swarm, we have previously studied the causes of its special relativity phenomenon. Here we show the causes of spontaneous aggregation of “randomly moving” particles. The diffusion kinetics of particles in a special circumstance (that is, in a moving reference frame $\mathcal{R}_u$ relative to the stationary reference frame $\mathcal{R}_0$) are studied theoretically. For the first time, the effects of the location aggregation and velocity direction aggregation of randomly moving particles on the diffusion coefficient are considered, and the corresponding generalized diffusion equation is deduced employing concise mathematical logic and Mathematica software.

## Keywords

Randomly Moving Particles; Effects of Location Aggregation; Non-diffusion Particle Swarm; Generalized Diffusion Equation

## Subject

PHYSICAL SCIENCES, Mathematical Physics

Comment 1
Received: 15 November 2021
Commenter: Tao Guo
Commenter's Conflict of Interests: Author
Comment: I have completely revised and optimized it.
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