Dynamical properties of granular rotors

Cleuren, Bart; Eichhorn, Ralf

doi:10.1088/1742-5468/2008/10/p10011

Cited by 29 publications

(64 citation statements)

References 28 publications

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“…To verify the validity of Eqs. (84) and (86), we perform the Monte Carlo simulation to obtain the numerical distribution function P SS (V) and compared it with Eqs. (84) and (86).…”

Section: Numerical Validationmentioning

confidence: 99%

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Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

et al. 2015

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We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601-090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.

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“…To verify the validity of Eqs. (84) and (86), we perform the Monte Carlo simulation to obtain the numerical distribution function P SS (V) and compared it with Eqs. (84) and (86).…”

Section: Numerical Validationmentioning

confidence: 99%

“…[31][32][33][34]44,84] (Gálvez LO, Van der Meer D, 2014, Private communication). We first explain the setup of the granular motor under dry friction, and introduce the Boltzmann-Lorentz model, which is valid for dilute granular gases [78].…”

Section: Example: Granular Motor Under Dry Frictionmentioning

confidence: 99%

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

et al. 2015

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“…The equally essential second ingredient, the symmetry breaking that must be present in order to rectify the stochastic motion due to the noisy environment, is provided by the fact that the two sides of each vane are coated differently. Although similar devices have been considered in a granular gas from a theoretical point of view [6,7], we here present the first experimental realization.…”

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confidence: 99%

“…We find a stable Â position for all studied values of the particle number N, which suggests that the state is present at all densities (although small particle numbers tend to increase the escape rate from the Â position). Since all available theories are based on uncorrelated collisions, the existence of this stable position was not predicted [6,7].…”

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Experimental Realization of a Rotational Ratchet in a Granular Gas

et al. 2010

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We construct a ratchet of the Smoluchowski-Feynman type, consisting of four vanes that are allowed to rotate freely in a vibrofluidized granular gas. The necessary out-of-equilibrium environment is provided by the inelastically colliding grains, and the equally crucial symmetry breaking by applying a soft coating to one side of each vane. The onset of the ratchet effect occurs at a critical shaking strength via a smooth, continuous phase transition. For very strong shaking the vanes interact actively with the gas and a convection roll develops, sustaining the rotation of the vanes. Introduction.-Throughout the ages scientists and laymen alike have tried to find a way to circumvent the second law of thermodynamics and create work out of thermal noise. In 1912, Marian Smoluchowski devised an especially appealing thought experiment [1], which consisted of four vanes and an asymmetrically toothed wheel with a pawl, submerged in a molecular heat bath [ Fig. 1(a)]. At first glance it seems that the wheel can turn in one direction only, in violation of the second law. However, Richard Feynman unambiguously showed that this type of device does not produce work at thermal equilibrium [2]: Since not only the vanes but also the pawl are subject to collisions with the gas molecules, the pawl bounces off the toothed wheel and causes the system to rotate randomly in either direction.In contrast, systems outside of thermal equilibrium are very well capable of creating work (directed motion) out of a noisy environment by means of the ratchet effect [3]. In fact, ratchet type devices have been proposed as the paradigmatic way in which motors operate at Brownian scales [4], and during the last decade scientists have realized (over a limited rotation range) a molecular version of Smoluchowski's device [5]. Here-on a macroscopic level-we construct a fully operational rotational ratchet of the Smoluchowski-Feynman type, capable of any uninterrupted number of revolutions. It consists of four vanes that are allowed to rotate freely in a granular gas. The necessary out-of-equilibrium environment-to bypass the second law of thermodynamics which prohibits the extraction of work from a system at thermal equilibrium-is provided by the granular gas. This is by its very nature out of equilibrium since in order to sustain the gaseous state it requires an external energy input to balance the energy dissipation caused by the inelastically colliding particles. The equally essential second ingredient, the symmetry breaking that must be present in order to rectify the stochastic motion due to the noisy environment, is provided by the fact that the two sides of each vane are coated differently. Although similar devices have been

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Large Deviations of Brownian Motors

Sarracino

Villamaina

2014

Large Deviations in Physics

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Dynamical properties of granular rotors

Cited by 29 publications

References 28 publications

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

Experimental Realization of a Rotational Ratchet in a Granular Gas

Large Deviations of Brownian Motors

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