Nonlinear Response of Inertial Tracers in Steady Laminar Flows: Differential and Absolute Negative Mobility

Abstract

We study the mobility and the diffusion coefficient of an inertial tracer advected by a twodimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force which induce the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of non-equilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.

Diffusion of chiral janus particles in convection rolls

“…For instance, in the presence of periodic perturbations the deterministic dynamics of arXiv:2002.06113v1 [cond-mat.soft] 14 Feb 2020 a passive particle exhibits remarkable chaotic properties [12,13]. Especially relevant to the present work are the results reported for the diffusivity [11] and the nonlinear mobility [14,15] of passive tracers subject to thermal fluctuations. Note that in Ref.…”

Life efficiency does not always increase with the dissipation rate

“…The physics of glasses, in which caging is the important effect, and the corresponding studies of changes in dynamical activity have also become biologically relevant [13]. In a different context, when dealing with driven particles, the stalling might be the point at the onset of a regime of negative differential mobility [39,[64][65][66].…”

Giant negative mobility of inertial particles caused by the periodic potential in steady laminar flows

“…The particle travels through a divergenceless cellular flow U = (U x , U y ) and is subjected to a constant force f 0 and a substrate force F p (x) along the x direction. The dynamics of the inertial particle are described by the following equations [24][25][26]:…”

“…As in Ref. [24], we also use times and lengths in units of L/U 0 and L, respectively. Here, we set L = 1.0 and U 0 = 1.0, which defines a typical time scale of the flow τ c = L/U 0 = 1.…”

“…Therefore, how to enhance ANM in this system becomes very important. In this paper, we extend this work [24,25] by applying an additional periodic potential and focus on finding how the periodic potential affects the onset of ANM. It is found that the profile of the potential can strongly affects the force-velocity behaviors.…”