Figure 4. Numerical simulations.

The (a–c,e–g) time sequences show that active particles gather in a smooth Gaussian potential, while they disperse in a rough spatially disordered potential. The particles move with a position-dependent velocity v(r) that is constant within the dashed circle in a and then fades gradually to zero when radially moving away from it. These simulations are in very good agreement with the experimental time sequences reported in Fig. 1f–h,o–q, respectively. The scale bars correspond to 20 μm. Sample intensity distributions are shown in the background for the two time sequences. The shaded areas in d and h, respectively, show the time evolution of the active particles for the two previous cases. The dashed lines are linear fits whose slopes give the initial rate of particle gathering or dispersal. To directly compare smooth and rough potentials, the time evolution of d is also shown as a solid line in h. The simulation parameters are chosen to closely mimic the corresponding experimental values.