Version 1
: Received: 18 January 2023 / Approved: 19 January 2023 / Online: 19 January 2023 (02:08:53 CET)
Version 2
: Received: 6 February 2023 / Approved: 7 February 2023 / Online: 7 February 2023 (06:08:54 CET)
Version 3
: Received: 5 September 2023 / Approved: 6 September 2023 / Online: 6 September 2023 (10:37:58 CEST)
Version 4
: Received: 14 October 2023 / Approved: 16 October 2023 / Online: 16 October 2023 (08:45:20 CEST)
How to cite:
Guo, T. Biased Stochastic Process of Randomly Moving Particles with Constant Average Velocities. Preprints2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v1
Guo, T. Biased Stochastic Process of Randomly Moving Particles with Constant Average Velocities. Preprints 2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v1
Guo, T. Biased Stochastic Process of Randomly Moving Particles with Constant Average Velocities. Preprints2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v1
APA Style
Guo, T. (2023). Biased Stochastic Process of Randomly Moving Particles with Constant Average Velocities. Preprints. https://doi.org/10.20944/preprints202301.0342.v1
Chicago/Turabian Style
Guo, T. 2023 "Biased Stochastic Process of Randomly Moving Particles with Constant Average Velocities" Preprints. https://doi.org/10.20944/preprints202301.0342.v1
Abstract
In a randomly moving particle swarm with fixed kinetic energy, the particle speeds follow the Maxwell distribution. In a certain period, the moving directions of particles in a sub-particle swarm may aggregate. Thus, the movements of the particles have the characteristics of biased stochastic movement. Regarding the biased particle swarm formed by a series of randomly moving particles (with a uniform average velocity c) with a greater probability of moving in a certain direction and the same probability of moving in other directions, there is a certain group velocity u in this direction, while the diffusion rate in other directions is slower than that of unbiased moving particles with the same average speed c. Moreover, the degree of slowing follows the Lorentz-like factor. In this article, the characteristics of this kind of biased random process are deduced starting from a biased random walk by using probability theory, and the expression of the Ito equation is provided. This article is expected to provide a reference to understand the nature of the special relativity effect.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
