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Register a new userNonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility
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Alessandro Sarracino
Publication date
2016
fields
Physics
and research's language is
English
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We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional 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.
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Transport of an inertial particle advected by a two-dimensional steady laminar flow is numerically investigated in the presences of a constant force and a periodic potential. Within particular parameter regimes this system exhibits absolute negative mobility, which means that the particle can travel in a direction opposite to the constant force. It is found that the profile of the periodic potential plays an important role in the nonlinear response regime. Absolute negative mobility can be drastically enhanced by applying appropriate periodic potential, the parameter regime for this phenomenon becomes larger and the amplitude of negative mobility grows exceedingly large (giant negative mobility). In addition, giant positive mobility is also observed in the presence of appropriate periodic potential.
We study, via extensive numerical simulations, the force-velocity curve of an active particle advected by a steady laminar flow, in the nonlinear response regime. Our model for an active particle relies on a colored noise term that mimics its persistent motion over a time scale $tau_A$. We find that the active particle dynamics shows non-trivial effects, such as negative differential and absolute mobility (NDM and ANM, respectively). We explore the space of the model parameters and compare the observed behaviors with those obtained for a passive particle ($tau_A=0$) advected by the same laminar flow. Our results show that the phenomena of NDM and ANM are quite robust with respect to the details of the considered noise: in particular for finite $tau_A$ a more complex force-velocity relation can be observed.
Driven particles in presence of crowded environment, obstacles or kinetic constraints often exhibit negative differential mobility (NDM) due to their decreased dynamical activity. We propose a new mechanism for complex many-particle systems where slowing down of certain {it non-driven} degrees of freedom by the external field can give rise to NDM. This phenomenon, resulting from inter-particle interactions, is illustrated in a pedagogical example of two interacting random walkers, one of which is biased by an external field while the same field only slows down the other keeping it unbiased. We also introduce and solve exactly the steady state of several driven diffusive systems, including a two species exclusion model, asymmetric misanthrope and zero-range processes, to show explicitly that this mechanism indeed leads to NDM.
Reaction currents in chemical networks usually increase when increasing their driving affinities. But far from equilibrium the opposite can also happen. We find that such negative differential response (NDR) occurs in reaction schemes of major biological relevance, namely, substrate inhibition and autocatalysis. We do so by deriving the full counting statistics of two minimal representative models using large deviation methods. We argue that NDR implies the existence of optimal affinities that maximize the robustness against environmental and intrinsic noise at intermediate values of dissipation. An analogous behavior is found in dissipative self-assembly, for which we identify the optimal working conditions set by NDR.
In self-gravitating stars, two dimensional or geophysical flows and in plasmas, long range interactions imply a lack of additivity for the energy; as a consequence, the usual thermodynamic limit is not appropriate. However, by contrast with many claims, the equilibrium statistical mechanics of such systems is a well understood subject. In this proceeding, we explain briefly the classical approach to equilibrium and non equilibrium statistical mechanics for these systems, starting from first principles. We emphasize recent and new results, mainly a classification of equilibrium phase transitions, new unobserved equilibrium phase transition, and out of equilibrium phase transitions. We briefly discuss what we consider as challenges in this field.
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