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We study the force-velocity relation of a tracer particle driven by an external force in two different systems. First, we present analytical results in the case of a lattice gas model, where the tracer moves in an environment of mobile hard-core obstacles. We discuss in particular the surprising effect of negative differential mobility (NDM), namely a nonmonotonic behavior of the tracer velocity as a function of the external force. Then, we discuss the case of an inertial particle advected by a laminar flow, where the nonlinear response of the tracer shows a very rich phenomenology.
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