Granular Brownian motion

Sarracino, Alessandro; Villamaina, Dario; Costantini, Giulio; Puglisi, Andrea

doi:10.1088/1742-5468/2010/04/p04013

Cited by 50 publications

(76 citation statements)

References 38 publications

(94 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Motivation for this model is twofold: 1) the main features of the vpds, i.e. an elastic resonance (region III) and a plateau revealing loss of memory at larger times (region II); 2) in the dilute limit it can be rigorously derived [28], while at intermediate densities a series of studies showed that memory effects (coming from correlated collisions) are well described by a coupling with an additional degree of freedom fluctuating at slower time-scales [23]. The vpds of the above model can be calculated and reads…”

mentioning

confidence: 99%

Cages and Anomalous Diffusion in Vibrated Dense Granular Media

et al. 2015

View full text Add to dashboard Cite

A vertically shaken granular medium hosts a blade rotating around a fixed vertical axis, which acts as a mesorheological probe. At high densities, independently from the shaking intensity, the blade's dynamics show strong caging effects, marked by transient sub-diffusion and a maximum in the velocity power density spectrum (vpds), at a resonant frequency ∼ 10 Hz. Interpreting the data through a diffusing harmonic cage model allows us to retrieve the elastic constant of the granular medium and its collective diffusion coefficient. For high frequencies f , a tail ∼ 1/f in the vpds reveals non-trivial correlations in the intra-cage micro-dynamics. At very long times (larger than 10 s), a super-diffusive behavior emerges, ballistic in the most extreme cases. Consistently, the distribution of slow velocity inversion times τ displays a power-law decay, likely due to persistent collective fluctuations of the host medium.

show abstract

mentioning

confidence: 99%

Cages and Anomalous Diffusion in Vibrated Dense Granular Media

et al. 2015

View full text Add to dashboard Cite

show abstract

“…The dilute limit here is obtained for Γ ∼ M → ∞. In such a limit indeed U → 0 and the equation for V comes back in the form discussed above [22]. In such a form (2), the dynamics of the tracer is remarkably simple: indeed V follows a Langevin equation in a Lagrangian frame with respect to a field U , which is the local average velocity field of the gas particles colliding with the tracer.…”

mentioning

confidence: 77%

“…At low packing fractions, φ < 0.1, and in the large mass limit, m/M 1, using the Enskog approximation it has been shown [22] that the dynamics of the intruder is described by a linear Langevin equation:…”

mentioning

confidence: 99%

Dynamics of a massive intruder in a homogeneously driven granular fluid

et al. 2012

View full text Add to dashboard Cite

A massive intruder in a homogeneously driven granular fluid, in dilute configurations, performs a memory-less Brownian motion with drag and temperature simply related to the average density and temperature of the fluid. At volume fraction ∼10-50% the intruder's velocity correlates with the local fluid velocity field: such situation is approximately described by a system of coupled linear Langevin equations equivalent to a generalized Brownian motion with memory. Here one may verify the breakdown of the Fluctuation-Dissipation relation and the presence of a net entropy flux -from the fluid to the intruder-whose fluctuations satisfy the Fluctuation Relation.Keywords Granular materials · Non-equilibrium fluctuations Granular fluids represent a valid benchmark for modern theories of non-equilibrium statistical mechanics [9]. Due to dissipative interactions among the microscopic constituents, energy is not conserved and an external source is necessary to maintain a stationary state. The consequence is a breakdown of time reversal invariance and the failure of properties such as the Equilibrium Fluctuation-Dissipation relation (EFDR) [6]. In recent years, a systematic theory for the dilute limit has been developed, in good agreement with numerical simulations [1,2], while a general understanding of dense granular fluids is still lacking. A common approach is the so-called Enskog correction [2,3], which reduces the breakdown of Molecular Chaos to a renormalization of the collision frequency. In cooling regimes, the Enskog theory may describe strong non-equilibrium effects, due to the explicit cooling time-dependence [21]. Nevertheless it cannot describe dynamical effects in stationary regimes, such as multiple characteristic times or different decays of response and autocorrelation [5,17].Here we review a recent model [23] for the dynamics of a massive tracer moving in a gas of smaller granular particles, both coupled to an external bath. Taking as reference point the dilute limit, where the system has a closed analytical description [22], a Langevin equation linearly coupled to a fluctuating local velocity field is proposed as first approximation capable of describing the dense case. Its main features are: (i) the decay of correlation and response functions is not simply exponential and shows backscattering [14,4] and (ii) the EFDR [10,13] of the first and second kind do not hold. In such a model, detailed balance is not necessarily satisfied, and a fluctuating entropy production [24] can be measured, which fairly verifies the Fluctuation Relation [11][12][13].The model reviewed here is the following: an "intruder" disc of mass m 0 = M and radius R, moving in a gas of N granular discs with mass m i = m (i > 0) and radius r , in a two dimensional box of area A = L 2 . We denote by n = N /A the number density of the gas and by φ the occupied volume fraction, i.e. φ = π(Nr 2 + R 2 )/A and we denote by V (or v 0 ) and v (or v i with i > 0) the velocity vector of the tracer and of the gas particles, respectively. Interactio...

show abstract

“…It has been shown in the case of the large mass limit and homogeous energy injection, that Equation (1) for a particle can be written as a Langevin equation corresponding to a granular brownian particle [42]. On the other hand, collisions between two grains follow the inelastic smooth hard sphere collisional model…”

Section: Description Of the Systemmentioning

confidence: 99%

Hydrodynamics of a Granular Gas in a Heterogeneous Environment

Reyes

Lasanta

2017

Entropy

View full text Add to dashboard Cite

Abstract:We analyze the transport properties of a low density ensemble of identical macroscopic particles immersed in an active fluid. The particles are modeled as inelastic hard spheres (granular gas). The non-homogeneous active fluid is modeled by means of a non-uniform stochastic thermostat. The theoretical results are validated with a numerical solution of the corresponding the kinetic equation (direct simulation Monte Carlo method). We show a steady flow in the system that is accurately described by Navier-Stokes (NS) hydrodynamics, even for high inelasticity. Surprisingly, we find that the deviations from NS hydrodynamics for this flow are stronger as the inelasticity decreases. The active fluid action is modeled here with a non-uniform fluctuating volume force. This is a relevant result given that hydrodynamics of particles in complex environments, such as biological crowded environments, is still a question under intense debate.

show abstract

Granular Brownian motion

Cited by 50 publications

References 38 publications

Cages and Anomalous Diffusion in Vibrated Dense Granular Media

Cages and Anomalous Diffusion in Vibrated Dense Granular Media

Dynamics of a massive intruder in a homogeneously driven granular fluid

Hydrodynamics of a Granular Gas in a Heterogeneous Environment

Contact Info

Product

Resources

About