Figure 4. Active Brownian rod swimming on a ‘symmetric’ striped surface with curvature radii equal in magnitude but opposite in sign.
Trajectories for (a) narrow (L/R = 0.25) and (b) broad (L/R = 6) stripes from simulations of duration t = 80τr with starting points indicated in dark blue. The rotational diffusion time is τr = 1/Dr = 18 s (see Methods section). (c) The ratio of mean square displacement (MSD) parallel (x) and perpendicular (y) to the stripes as a function of stripe width L for Δt = τr and Δt → ∞. (d) Rescaled MSD. The blue dotted line corresponds to a free circle swimmer.34 (e) Probability distribution of turning angle ϑ defined in Eq. (6) between successive trajectory segments of duration Δt for L/R = 6. High and low probabilities are shown in red and blue, respectively. (f) Density profile ρ across two stripes. (g) Crossover time τc between ballistic and diffusive regime along the stripes and the mean first-passage time τMFP for the rod to cross the stripe scale both quadratically with L. The white dashed and dotted lines in (e) indicate the corresponding τc and τMFP, respectively.