Boundary asymmetry and curvature


 Net force on an isolated box (note the absence of momentum conservation)?

vs.

No boundary torque (zero net force)                             vs.                                       Boundary torque  (net force)

yellow ball In the absence of external torques, a net force is constrained as averaging active particle equations of motion gives:

yellow ball For a closed box the total force and current will both be zero independent of wall potential, suggesting an equation of state.

However, there remain important consequences of activity even in the absence of wall-induced reorientation:

Wall shape and curvature:

N. Nikola, A.P. Solon, Y. Kafri, M. Kardar, J. Tailleur, R. Voituriez, Phys. Rev. Lett. 117, 098001 (2016);

yellow ball   Tangential Ratchet force: Asymmetric walls support a current and net tangential force:

(Another macroscopic consequence of the absence of time reversibility at microscopic scale.)

 Random motions of bacteria:        (R. Di Leonardo, et al PNAS 2010)

yellow ball   Normal force variations for sinusoidal wall:    

           

                    

Variation of pressure with curvature is reminiscent of Laplace's law, implying an activity-induced line (surface) tension:


red ball Bendable soft boundary:

yellow ballReduction in line tension leads to modulational instability:

yellow ballConfirmation for a granular chain held on a vibrating plate of shaken particles (Physics Viewpoint)

G. Junot, G. Briand, R. Ledesma-Alonso, and O. Dauchot, PRL 119, 028002 (2017)