Anisotropic Isometric Fluctuation Relations in experiment and theory on a self-propelled rod (original) (raw)
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Phys. Rev. Lett. 106, 118001 (2011) -- Editor's suggestion, 2011
A geometrically polar granular rod confined in 2D geometry, subjected to a sinusoidal vertical oscillation, undergoes noisy self-propulsion in a direction determined by its polarity. When surrounded by a medium of crystalline spherical beads, it displays substantial negative fluctuations in its velocity. We find that the large-deviation function (LDF) for the normalized velocity is strongly non-Gaussian with a kink at zero velocity, and that the antisymmetric part of the LDF is linear, resembling the fluctuation relation known for entropy production, even when the velocity distribution is clearly non-Gaussian. We extract an analogue of the phase-space contraction rate and find that it compares well with an independent estimate based on the persistence of forward and reverse velocities.
Journal of Statistical Physics, 2017
The effect of a change of noise amplitudes in overdamped diffusive systems is linked to their unperturbed behavior by means of a nonequilibrium fluctuation-response relation. This formula holds also for systems with state-independent nontrivial diffusivity matrices, as we show with an application to an experiment of two trapped and hydrodynamically coupled colloids, one of which is subject to an external random forcing that mimics an effective temperature. The nonequilibrium susceptibility of the energy to a variation of this driving is an example of our formulation, which improves an earlier version, as it does not depend on the time-discretization of the stochastic dynamics. This scheme holds for generic systems with additive noise and can be easily implemented numerically, thanks to matrix operations.
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Chaos: An Interdisciplinary Journal of Nonlinear Science, 1998
The constructive role of random fluctuations is studied in the context of transport in stochastic ratchets. We discuss the interplay of independent white ͑thermal͒ and discrete ͑external͒ noises and their generation of transport in anisotropic potentials. The constructive cooperation of such fluctuations is most apparent in the asymptotic limit of fast discrete-valued noise, a limit which presents some interesting mathematical features. We describe the asymptotic analysis of the current in the limit of fast external noise, pointing out the strong qualitative dependence of the current on the interplay of the independent noise sources and its surprising sensitivity to the regularity of the underlying anisotropic ratchet potential.
Role of translational noise on current reversals of active particles on ratchet
Scientific Reports
In this study, we explore using Langevin dynamics simulations, the role of thermal fluctuations on the rectification of non-interacting inertial active (self-propelled) particles in a rocking ratchet setup in the absence and in the presence of the external time periodic drive. The system is first studied in the absence of the external drive. It is found that the average velocity is always positive and a peaked function of the translational noise, indicating that the asymmetry effects dominate at intermediate values of the strength of the thermal noise. In the second part of this work, we study the effect of the external drive on the dynamics of the system by exploring a phase diagram in the parameter space of translational noise and driving frequency for two different strengths of rotational diffusion. For a given constant amplitude of the active force and amplitude of external drive less than the maximum force due to the potential, the average velocity magnitude as well as the dire...
Fluctuations and pattern formation in self-propelled particles
Physical Review E, 2010
We consider a coarse-grained description of a system of self-propelled particles given by hydrodynamic equations for the density and polarization fields. We find that the ordered moving or flocking state of the system is unstable to spatial fluctuations beyond a threshold set by the self-propulsion velocity of the individual units. In this region, the system organizes itself into an inhomogeneous state of well-defined propagating stripes of flocking particles interspersed with low density disordered regions. Further, we find that even in the regime where the homogeneous flocking state is stable, the system exhibits large fluctuations in both density and orientational order. We study the hydrodynamic equations analytically and numerically to characterize both regimes.
Statistical behaviour of isotropic and anisotropic fluctuations in homogeneous turbulence
Physica D: Nonlinear Phenomena, 2008
We review recent progresses on anomalous scaling and universality in anisotropic and homogeneous hydrodynamic turbulent flows. As a central matter, we discuss the validity and the limits of classical ideas of statistical isotropy restoration. Finally, we comment on a still open issue, the observed different scaling behaviour of longitudinal and transverse velocity increment moments in purely statistically isotropic ensemble.
Langevin Dynamics Driven by a Telegraphic Active Noise
Frontiers in Physics
Self-propelled or active particles are referred to as the entities which exhibit anomalous transport violating the fluctuation-dissipation theorem by means of taking up an athermal energy source from the environment. Currently, a variety of active particles and their transport patterns have been quantified based on novel experimental tools such as single-particle tracking. However, the comprehensive theoretical understanding for these processes remains challenging. Effectively the stochastic dynamics of these active particles can be modeled as a Langevin dynamics driven by a particular class of active noise. In this work, we investigate the corresponding Langevin dynamics under a telegraphic active noise. By both analytical and computational approaches, we study in detail the transport and nonequilibrium properties of this process in terms of physical observables such as the velocity autocorrelation, heat current, and the mean squared displacement. It is shown that depending on the properties of the amplitude and duration time of the telegraphic noise various transport patterns emerge. Comparison with other active dynamics models such as the run-and-tumble and Lévy walks is also presented.
Fokker-Planck and Langevin descriptions of fluctuations in uniform shear flow
Journal of Statistical Physics, 1983
The Boltzmann description of the preceding paper for tagged particle fluctuations in a nonequilibrium gas is further analyzed in the limit of small mass ratio between the gas and the tagged particles. For a large class of nonequilibrium states the Boltzmann-Lorentz collision operator for the tagged particle distribution is expanded to leading order in the mass ratio, resulting in a Fokker-Planck operator. The drift vector and diffusion tensor are calculated exactly for Maxwell molecules. The Fokker-Planck operator depends on the nonequilibrium state only through the hydrodynamic variables for the fluid. The diffusion tensor is a measure of the "noise" amplitude and is not simply determined from the nonequilibrium temperature; instead, it depends on the fluid stress tensor components as well. For the special case of uniform shear flow, the Fokker-Planck equation is of the linear type and may be solved exactly. The associated set of Langevin equations is also identified and used to describe spatial diffusion in the Lagrangian coordinates of the fluid. The effect of viscous heating on diffusion is discussed and the dependence of the diffusion coefficient on the shear rate is calculated.
Concentration Dependent Diffusion of Self-Propelled Rods
Physical Review Letters, 2010
We examine the persistent random motion of self-propelled rods (SPR) as a function of the area fraction and study the effect of steric interactions on their diffusion properties. SPR of length l and width w are fabricated with a spherocylindrical head attached to a beaded chain tail, and show directed motion on a vibrated substrate. The mean square displacement (MSD) on the substrate grows linearly with time t for < w=l, before displaying caging as is increased, and stops well below the close packing limit. Direction autocorrelations decay progressively slower with. We describe the observed decrease of SPR propagation speed cðÞ with a tube model. Further, MSD parallel to the SPR collapse with ¼ l=cðÞ and scales as ðlt=Þ 2 , and MSD in the perpendicular direction grows progressively slower than l 2 t= with , consistent with dynamics inside a thinning tube.