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 twodimensional 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 D0 and the characteristic Stokes time τ 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, (τ, D0), identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.