Force on curved & soft walls
In the absence of external torques, averaging active particle equations of motion gives:
For a closed box the total force and current will both be zero, independent of wall potential.
Curved wall?
N. Nikola, A.P. Solon, Y. Kafri, M. Kardar, J. Tailleur, R. Voituriez, arXiv:1512.05697;
Sinusoidal wall: Density is non-uniform, depending on curvature as well as potential
Sinusoidal wall: Pressure is curvature dependent, largest at the bottom of the trench!
Ratchet: Asymmetric walls support a current and net force:
Soft boundaries with bending?
Increase/decrease of pressure on the concave/convex side can lead to modulational instability:
A flexible chain (worm) spontaneously curves and moves:
