Mean-field and Monte Carlo analysis of multi-species agent dynamics
We propose a mean-field (MF) approximation as a recurrence relation governing the dynamics of m species of particles on a square lattice. We simultaneously perform Monte Carlo (MC) simulations under identical initial conditions to emulate the intricate motion observed in environments such as subway...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-08-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2025.1648895/full |
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| author | Eduardo Velasco Stock Roberto Da Silva Sebastian Gonçalves |
| author_facet | Eduardo Velasco Stock Roberto Da Silva Sebastian Gonçalves |
| author_sort | Eduardo Velasco Stock |
| collection | DOAJ |
| description | We propose a mean-field (MF) approximation as a recurrence relation governing the dynamics of m species of particles on a square lattice. 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 “Gaussian-to-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. |
| format | Article |
| id | doaj-art-dd8dac9c78e24e4e8694ddac9e79822f |
| institution | Kabale University |
| issn | 2296-424X |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj-art-dd8dac9c78e24e4e8694ddac9e79822f2025-08-26T04:12:45ZengFrontiers Media S.A.Frontiers in Physics2296-424X2025-08-011310.3389/fphy.2025.16488951648895Mean-field and Monte Carlo analysis of multi-species agent dynamicsEduardo Velasco StockRoberto Da SilvaSebastian GonçalvesWe propose a mean-field (MF) approximation as a recurrence relation governing the dynamics of m species of particles on a square lattice. 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 “Gaussian-to-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.https://www.frontiersin.org/articles/10.3389/fphy.2025.1648895/fullpedestrian dynamicsmean-fieldtransport equationlattice gasstochastic processmulti-species |
| spellingShingle | Eduardo Velasco Stock Roberto Da Silva Sebastian Gonçalves Mean-field and Monte Carlo analysis of multi-species agent dynamics Frontiers in Physics pedestrian dynamics mean-field transport equation lattice gas stochastic process multi-species |
| title | Mean-field and Monte Carlo analysis of multi-species agent dynamics |
| title_full | Mean-field and Monte Carlo analysis of multi-species agent dynamics |
| title_fullStr | Mean-field and Monte Carlo analysis of multi-species agent dynamics |
| title_full_unstemmed | Mean-field and Monte Carlo analysis of multi-species agent dynamics |
| title_short | Mean-field and Monte Carlo analysis of multi-species agent dynamics |
| title_sort | mean field and monte carlo analysis of multi species agent dynamics |
| topic | pedestrian dynamics mean-field transport equation lattice gas stochastic process multi-species |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2025.1648895/full |
| work_keys_str_mv | AT eduardovelascostock meanfieldandmontecarloanalysisofmultispeciesagentdynamics AT robertodasilva meanfieldandmontecarloanalysisofmultispeciesagentdynamics AT sebastiangoncalves meanfieldandmontecarloanalysisofmultispeciesagentdynamics |