Directed transport induced by asymmetric surface vibrations: making use of friction

Fleishman, D.G.; Asscher, Y; Urbakh, Michael

doi:10.1088/0953-8984/19/9/096004

Cited by 28 publications

(23 citation statements)

References 19 publications

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“…On a horizontal plane, asymmetric vibrations may lead to a net transport velocity; this behavior has been studied in detail by Buguin et al [7] and Fleishman et al [8] for a single block. Considering symmetric vibrations, Sanchez et al [9] studied the spreading of a granular pile on a vibrated horizontal plate.…”

Section: Introductionmentioning

confidence: 94%

Angular particle sliding down a transversally vibrated smooth plane

Benedetti

Sornay²,

Dalloz³

et al. 2012

Phys. Rev. E

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We present a theoretical, numerical, and experimental study about the sliding motion of an angular particle down a vibrated smooth plane. The model is based on a Coulomb's friction law with a unique friction coefficient. The model is solved numerically and is tested with controlled experiments. Different motion regimes are identified and the particle behavior is governed by two dimensionless parameters. The comparison between experimental and numerical results gives an indirect access to the dynamic friction coefficient.

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Section: Introductionmentioning

confidence: 94%

Angular particle sliding down a transversally vibrated smooth plane

Benedetti

Sornay²,

Dalloz³

et al. 2012

Phys. Rev. E

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“…where v − is given in Eq. (15) and v + = −(∆ + ∆ * )τ (so that v + is the hypothetical fixed point of Eq. (17) that one would obtain by replacing σ(v) by 1).…”

Section: Exact Solution For One-sided Shotsmentioning

confidence: 99%

Singular features in noise-induced transport with dry friction

Baule

Sollich

2012

EPL

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We present an exactly solvable nonlinear model for the directed motion of an object due to zeromean fluctuations on a uniform featureless surface. Directed motion results from the effect of dry (Coulombic) friction coupled to asymmetric surface vibrations with Poissonian shot noise statistics. We find that the transport of the object exhibits striking non-monotonic and singular features: transport actually improves for increasing dry friction up to a critical dry friction strength ∆ * and undergoes a transition to a unidirectional mode of motion at ∆ * . This transition is indicated by a cusp singularity in the mean velocity of the object. Moreover, the stationary velocity distribution also contains singular features, such as a discontinuity and a delta peak at zero velocity. Our results highlight that dissipation can in fact enhance transport, which might be exploited in artificial small scale systems.

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“…In related work, small objects such as hydrogels, droplets and micron sized particles have been moved over solid surfaces using asymmetric surface oscillations or noisy vibrations without a net force [3][4][5][6][7][8][9]. This kind of noise-induced transport relies on a ratchet effect in the velocity coordinate, which requires in addition to (i) and (ii) a nonlinear resistance of the moving object to the imposed force.…”

Section: Introductionmentioning

confidence: 99%

Rectification of asymmetric surface vibrations with dry friction: An exactly solvable model

Baule

Sollich

2013

Phys. Rev. E

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We consider a stochastic model for the directed motion of a solid object due to the rectification of asymmetric surface vibrations with Poissonian shot-noise statistics. The friction between the object and the surface is given by a piecewise-linear friction force. This models the combined effect of dynamic friction and singular dry friction. We derive an exact solution of the stationary Kolmogorov-Feller (KF) equation in the case of two-sided exponentially distributed amplitudes. The stationary density of the velocity exhibits singular features such as a discontinuity and a delta-peak singularity at zero velocity, and also contains contributions from non-integrable solutions of the KF equation. The mean velocity in our model generally varies non-monotonically as the strength of the dry friction is increased, indicating that transport improves for increased dissipation.

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Directed transport induced by asymmetric surface vibrations: making use of friction

Cited by 28 publications

References 19 publications

Angular particle sliding down a transversally vibrated smooth plane

Angular particle sliding down a transversally vibrated smooth plane

Singular features in noise-induced transport with dry friction

Rectification of asymmetric surface vibrations with dry friction: An exactly solvable model

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