Fig. 4: Velocity Correlation and Correlation Length vs. Persistence Time.
a The scaled equal-time velocity-velocity correlation as a function of spatial distance r for different persistence times τp as indicated, for active force magnitude f = 0.25. b The correlation length ξL as a function of the persistence time τp for different values of the active force magnitude f. The plot shows that the correlation length ξL grows as a power law (with exponent \(\frac{1}{2}\), black dashed line) with the persistence time τp, and this behaviour is independent of the magnitude of the active force f, which is shown in the legend. The simulations for this figure were conducted at densities ϕa = 0.01 and ϕp = 0.94 of active and passive particles, respectively. To accurately estimate the correlation length, we conducted 50 simulations with random initial configurations, collected 2500 snapshots in a stationary state from these simulations, and averaged the results to ensure precision. The error bars show the standard error of the mean.
