Statistics for an object actively driven by spontaneous symmetry breaking into reversible directions

Abstract

Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained until a large enough impulse by an additional stochastic force reverses it. Examples may be provided by self-propelled droplets, gliding bacteria stochastically reversing their propulsion direction, or nonpolar vibrated hoppers. The magnitude of active forcing is regarded as constant, and we include the effect of inertial contributions. Interestingly, this situation can formally be mapped to stochastic motion under (dry, solid) Coulomb friction, however, with a negative friction parameter. Diffusion coefficients are calculated by formal mapping to the situation of a quantum-mechanical harmonic oscillator exposed to an additional repulsive delta-potential. Results comprise a ditched or double-peaked velocity distribution and spatial statistics showing outward propagating maxima when starting from initially concentrated arrangements.

New insight on filamentary charge‐loaded flows originated by pulsating glow‐type unipolar coronas in atmospheric air

“…Based on these premises, the above section has been structured with the final view to claiming that the ion migration in the TR identifies with a convective, rather than drift, motion preserving momentum and energy (Section 2.2) impressed by an auto‐pulsating glow‐type IR (Section 2.3). That insight is proved to be consistent with a steady flow assuming a long‐range ordering, through a multi‐channelled Laplacian pattern (Section 2.4), as result of symmetry rupture [8] (Section 2.5). The given passive swarm is reminiscent in some ways of the self‐organised collective movement of active particles [9–11], while the related multiscale aspect allows the interpretation of the given macroscopic slow flow as though it were continuous and stable, as it is largely the case for the detection mode of the implied electrical quantities.…”

When low-order expansions fail and all higher-order contributions matter—basic example of the mean squared displacement for Brownian motion

“…On the one hand, we wish to outline the unconventional way of calculating the mean squared displacement. Although a bit more complex, this route may open the possibility to calculate diffusion coefficients also in the context of stochastic motion under nonlinear friction [18][19][20][21][22][23][24][25]. On the other hand, we wish to stress, using this basic example, that we always need to scrutinize the strategies of solution that we apply.…”