Regensburg 2022 – wissenschaftliches Programm
DY 16.11: Vortrag
Dienstag, 6. September 2022, 12:45–13:00, H18
Stochastic motion under active driving due to inverted dry (solid) friction — •Andreas M. Menzel — Otto-von-Guericke-Universität Magdeburg, Magdeburg, Germany
It has become common to describe the motion of actively driven or self-propelled objects using a driving force of constant magnitude. We assume that this driving force always acts along the current velocity direction. Moreover, we consider objects featuring a nonpolar axis, along which driving and propagation occur .
In that case, spontaneous symmetry breaking decides on the heading of propagation, that is, “forward” or “backward” along the nonpolar axis. Stochastic effects may reverse the velocity and thus the direction of the driving force.
As it turns out, active driving under these circumstances corresponds to inverted dry (solid) friction of the Coulomb type. Corresponding tools of theoretical analysis can thus be adopted, mapping the velocity spectrum to the one of a quantum-mechanical harmonic oscillator subject to a repulsive delta potential. In this way, the diffusion coefficient can be calculated analytically. We evaluate velocity and displacement statistics. Outward propagating displacement maxima emerge under increased active driving. The trajectories feature pronounced cusps when velocity reversals occur.
Our results should apply, for instance, to certain types of vibrated nonpolar rods and swimming bacteria that may reverse their propagation direction.
 A. M. Menzel, submitted.