ORIGINAL RESEARCH article
Front. Phys.
Sec. Social Physics
Volume 13 - 2025 | doi: 10.3389/fphy.2025.1648895
This article is part of the Research TopicInnovative Approaches to Pedestrian Dynamics: Experiments and Mathematical ModelsView all 4 articles
Mean-field and Monte Carlo Analysis of Multi-Species Dynamics of agents
Provisionally accepted
- Institute of Physics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil
Select one of your emails
You have multiple emails registered with Frontiers:
Notify me on publication
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
We propose a mean-field (MF) approximation for the recurrence relation governing the dynamics of m species of particles on a square lattice, and we simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to emulate the intricate motion observed in environments such as subway corridors and scramble crossings in large cities. Each species moves according to transition probabilities influenced by its respective static floor field and the state of neighboring cells. To illustrate the methodology, we analyze statistical fluctuations in the spatial distribution for m = 1, m = 2, and m = 4 and for different regimes of average density and biased movement. A numerical comparison is conducted to determine the best agreement between the MC simulations and the MF approximation considering a renormalization exponent β that optimizes the fit between methods. Finally, we report a phenomenon we term "Gaussianto-Gaussian" behavior, in which an initially normal distribution of particles becomes distorted due to interactions among same and opposing species, passes through a transient regime, and eventually returns to a Gaussian-like profile in the steady state, after multiple rounds of motion under periodic boundary conditions.
Keywords: Pedestrian dynamics, mean-field, transport equation, Lattice gas, stochastic process, Multi-species
Received: 17 Jun 2025; Accepted: 29 Jul 2025.
Copyright: © 2025 Stock, Da Silva and Gonçalves. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Roberto Da Silva, Institute of Physics, Federal University of Rio Grande do Sul, Porto Alegre, Brazil
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.