Figure 7. Particle dynamics without saturation of the aligning torque.

(a) Calculated trajectories of active Janus particles in a periodic asymmetric velocity profile v_p(x) for different initial angles ϕ₀. Different from the experimental situation, here a linear relation between the angular velocity and the gradient of the translational velocity is considered. Depending on the initial orientation, particles either perform an oscillating motion in a valley of the velocity profile (green and magenta trajectories) or they periodically move in positive or negative x direction (orange and cyan trajectories). (Note that the green trajectory is scaled by a factor of 2/5 in the y direction for reasons of presentation.) In the absence of saturation, the probabilities and the mean velocities of particles moving to the left and to the right are the same. Thus, no net particle current occurs. (b) Particle orientation ϕ versus position x for the trajectories shown in a. Black crosses represent the initial positions, and the arrows indicate the evolution with time.