Fig. 3: Velocity Correlation and Correlation Length vs. Active Force.
a Scaled velocity-velocity spatial auto correlation C(r) as a function of spatial distance r, for different active force magnitudes f as indicated in the legend, and persistence time τp = 3 b The correlation length ξL as a function of the active force f for different persistence times τp as shown; the plot demonstrates that, at fixed persistence time, the correlation length is independent of the magnitude of the active force. 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.
