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Register a new userAnomalous mobility of a driven active particle in a steady laminar flow
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Added by
Alessandro Sarracino
Publication date
2018
fields
Physics
and research's language is
English
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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.
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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.
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {em anomalous} diffusive behavior even in the {em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $alpha = 2/(2 u +2 - gamma_1)$, where $ u$ is the Flory exponent and $gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $tau propto f^{-1}N^{frac{2}{alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > propto t^{alpha}$ and $< s(t)^2 > propto t^{2alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.
We study pattern formation, fluctuations and scaling induced by a growth-promoting active walker on an otherwise static interface. Active particles on an interface define a simple model for energy consuming proteins embedded in the plasma membrane, responsible for membrane deformation and cell movement. In our model, the active particle overturns local valleys of the interface into hills, simulating growth, while itself sliding and seeking new valleys. In 1D, this overturn-slide-search dynamics of the active particle causes it to move superdiffusively in the transverse direction while pulling the immobile interface upwards. Using Monte Carlo simulations, we find an emerging tent-like mean profile developing with time, despite large fluctuations. The roughness of the interface follows scaling with the growth, dynamic and roughness exponents, derived using simple arguments as $beta=2/3, z=3/2, alpha=1/2$ respectively, implying a breakdown of the usual scaling law $beta = alpha/z$, owing to very local growth of the interface. The transverse displacement of the puller on the interface scales as $sim t^{2/3}$ and the probability distribution of its displacement is bimodal, with an unusual linear cusp at the origin. Both the mean interface pattern and probability distribution display scaling. A puller on a static 2D interface also displays aspects of scaling in the mean profile and probability distribution. We also show that a pusher on a fluctuating interface moves subdiffusively leading to a separation of time scale in pusher motion and interface response.
The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier transform of the distribution function $f(c)$. In this paper we have inverted the Fourier transform to express $f(c)$ in the form of an infinite series of exponentially decaying terms. The dominant high energy tail is exponential, $f(c)simeq A_0exp(-a|c|)$, where $aequiv 2/sqrt{1-alpha^2}$ and the amplitude $A_0$ is given in terms of a converging sum. This is explicitly shown in the totally inelastic limit ($alphato 0$) and in the quasi-elastic limit ($alphato 1$). In the latter case, the distribution is dominated by a Maxwellian for a very wide range of velocities, but a crossover from a Maxwellian to an exponential high energy tail exists for velocities $|c-c_0|sim 1/sqrt{q}$ around a crossover velocity $c_0simeq ln q^{-1}/sqrt{q}$, where $qequiv (1-alpha)/2ll 1$. In this crossover region the distribution function is extremely small, $ln f(c_0)simeq q^{-1}ln q$.
As a result of nonequilibrium forces, purely repulsive self-propelled particles undergo macrophase separation between a dense and a dilute phase. We present a thorough study of the ordering kinetics of such motility-induced phase separation (MIPS) in active Brownian particles in two dimensions, and we show that it is generically accompanied by microphase separation. The growth of the dense phase follows a law akin to the one of liquid-gas phase separation. However, it is made of a mosaic of hexatic microdomains whose size does not coarsen indefinitely, leaving behind a network of extended topological defects from which microscopic dilute bubbles arise. The characteristic length of these finite-size structures increases with activity, independently of the choice of initial conditions.
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