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 Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities. Preprints2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v3
Guo, T. Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities. Preprints 2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v3
Guo, T. Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities. Preprints2023, 2023010342. https://doi.org/10.20944/preprints202301.0342.v3
APA Style
Guo, T. (2023). Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities. Preprints. https://doi.org/10.20944/preprints202301.0342.v3
Chicago/Turabian Style
Guo, T. 2023 "Biased Random Process of Randomly Moving Particles with Fixed Mean and Group Velocities" Preprints. https://doi.org/10.20944/preprints202301.0342.v3
Abstract
In a particle swarm with a fixed kinetic energy, the constituent particles move randomly and their velocity magnitudes follow a Maxwell distribution characterized by specific parameters. Within a certain time frame, particles in a sub-swarm may exhibit a bias in their movement direction. Thus, the particles may exhibit a special characteristic (biased random motion), where the group velocity in a particular direction remains constant u. For this biased particle swarm, composed of randomly moving particles with a fixed average speed c, particles have a higher probability of moving in a specific direction. Conversely, their likelihood of moving in all other directions is equally reduced. This study starts from the perspective of biased random walks and using Mathematica software proves that the diffusion rate of particles (in the reference frame Ru observed from R0) in all directions is slower than that of an unbiased particle swarm with the same average speed c. Specifically, the degree of reduction is determined by the Lorentz-like factor. Lastly, we present the Ito equation for this biased random motion and provide associated verification examples. This study aims to serve as a reference for comprehending the underlying principles of the special relativity effect.
Keywords
Biased Random Process; Randomly Moving Particles; Special Relativity Effect; Lorentz-like factor
Subject
Physical Sciences, Mathematical Physics
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.
Commenter: Tao Guo
Commenter's Conflict of Interests: Author
2. Thoroughly strengthened the manuscript.