Anomalous force-velocity relation of driven inertial tracers in steady laminar flows

We study the nonlinear response to an external force of an inertial tracer advected by a two-dimensional incompressible laminar flow and subject to thermal noise. In addition to the driving external field $F$, the main parameters in the system are the noise amplitude $D_0$ and the characteristic Stokes time $\tau$ of the tracer. The relation velocity vs force shows interesting effects, such as negative differential mobility (NDM), namely a non-monotonic behavior of the tracer velocity as a function of the applied force, and absolute negative mobility (ANM), i.e. a net motion against the bias. By extensive numerical simulations, we investigate the phase chart in the parameter space of the model, $(\tau,D_0)$, identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.