The Homogeneous Cooling State Revisited

Goldhirsch, I.; Noskowicz, S. H.; Bar-Lev, O.

doi:10.1007/978-3-540-39843-1_2

Cited by 17 publications

(11 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Freely cooling systems -mainly examined numerically and theoretically -are almost impossible to realize experimentally. Only in the last years, laboratory experiments were performed, where clustering could be examined in driven systems [14][15][16][17][18][19][20], where also kinetic theory approaches [21][22][23][24][25][26][27][28][29][30][31][32] complemented by numerical simulations have proven to be successful [12,25,[33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Driven Granular Gases

Luding

Cafiero

Herrmann

2003

Granular Gas Dynamics

View full text Add to dashboard Cite

Abstract. In this paper, a two-dimensional granular gas of inelastic, rough spheres subject to driving is examined. Either the translational degrees of freedom are agitated proportional to a power |v( x)| δ of the local particle velocity v( x), or the rotational degrees are agitated randomly with respect to the angular velocity ω( x).The steady state properties of the model, with respect to energy, partition of energy, and velocity distributions, are examined for different values of δ, and compared with the homogeneous driving case δ = 0. A driving linearly proportional to v( x) seems to reproduce some experimental observations which could not be reproduced by a homogeneous driving. Furthermore, we obtain that the system can be homogenized even for strong dissipation, if a driving inversely proportional to the velocity is used (δ < 0). In the case of rotational driving, the system is well randomized and clusters are hindered. Even though rotational driving may be difficult to realize experimentally, this is an opportunity to avoid or delay the often unwanted effect of clustering.

show abstract

Section: Introductionmentioning

confidence: 99%

Driven Granular Gases

Luding

Cafiero

Herrmann

2003

Granular Gas Dynamics

View full text Add to dashboard Cite

show abstract

“…This is achieved by applying the general equation (16) for the evolution of a dynamical variable to T (t), R(t) and b(t) and using our Ansatz for ρ(t), see Eqs. (17), (19). Due to the specific functional form of our ansatz -a product of polynomials and gaussians in the velocities -the set of self-consistent equations can be determined analytically.…”

Section: The European Physical Journal Special Topicsmentioning

confidence: 99%

“…The main (and very important) difference between a granular gas and a molecular gas is the dissipative nature of particle interactions, which are described by the macroscopic mechanics of solids rather than by a microscopic interaction potential. The consequences of the dissipative interactions are quite substantial: A spatially homogeneous state is unstable [7][8][9], velocities are not distributed according to a Maxwell-Boltzmann distribution [10][11][12][13][14][15][16][17][18] and the diffusion or self-diffusion is anomalous [19][20][21][22][23]. These properties of a granular gas have been observed for the case of smooth particles, when grain collisions do not affect their rotational motion.…”

Section: Introductionmentioning

confidence: 98%

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

Kranz

Brilliantov

Pöschel

et al. 2009

Eur. Phys. J. Spec. Top.

View full text Add to dashboard Cite

Abstract. In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.

show abstract

“…Although an explicit solution has not yet been obtained, its form at large and small velocities has been determined by good analytic approximations [8,9]. More generally the universality of the HCS as the attractor for a wide class of initial conditions, its functional form, and the scaling property have been verified by Monte Carlo simulation [11].…”

Section: Boltzmann Equation and Homogeneous Cooling Solutionmentioning

confidence: 99%

“…This is similar to the rapid velocity relaxation to a Maxwell distribution in normal gases. A great deal is known about this special solution, the "homogeneous cooling solution" (HCS), from both analytic [8,9,10] and Monte Carlo simulation studies [11].…”

Section: Introductionmentioning

confidence: 99%

Some Aspects of the Boltzmann Equation for a Granular Gas

Dufty¹

2005

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. The Boltzmann equation for a gas of smooth, inelastic hard spheres is introduced and its homogeneous solution for an isolated system is discussed. The possibility of hydrodynamic excitations is explored using the linearized Boltzmann equation for small spatial perturbations of the homogeneous state. It is shown that the spectrum of the generator for this linear dynamics contains five points at long wavelengths that are the origin of hydrodynamic excitations. With this knowledge, response functions are introduced that allow the formal derivation of linear hydrodynamic equations and associated GreenKubo expressions for the transport coefficients at Navier-Stokes order.

show abstract

The Homogeneous Cooling State Revisited

Cited by 17 publications

References 15 publications

Driven Granular Gases

Driven Granular Gases

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

Some Aspects of the Boltzmann Equation for a Granular Gas

Contact Info

Product

Resources

About