Far-from-equilibrium Ostwald ripening in electrostatically driven granular powders

We report the first experimental study of cluster size distributions in electrostatically driven granular submonolayers. The cluster size distribution in this far-from-equilibrium process exhibits dynamic scaling behavior characteristic of the (nearly equilibrium) Ostwald ripening, controlled by the attachment and detachment of the "gas" particles. The scaled size distribution, however, is different from the classical Wagner distribution obtained in the limit of a vanishingly small area fraction of the clusters. A much better agreement is found with the theory of Conti et al. [Phys. Rev. E 65, 046117 (2002)] which accounts for the cluster merger.Comment: 5 pages, to appear in PR

Hydrodynamic singularities and clustering in a freely cooling inelastic gas

We employ hydrodynamic equations to follow the clustering instability of a freely cooling dilute gas of inelastically colliding spheres into a well-developed nonlinear regime. We simplify the problem by dealing with a one-dimensional coarse-grained flow. We observe that at a late stage of the instability the shear stress becomes negligibly small, and the gas flows solely by inertia. As a result the flow formally develops a finite time singularity, as the velocity gradient and the gas density diverge at some location. We argue that flow by inertia represents a generic intermediate asymptotic of unstable free cooling of dilute inelastic gases.Comment: 4 pages, 4 figure

Attempted density blowup in a freely cooling dilute granular gas: hydrodynamics versus molecular dynamics

It has been recently shown (Fouxon et al. 2007) that, in the framework of ideal granular hydrodynamics (IGHD), an initially smooth hydrodynamic flow of a granular gas can produce an infinite gas density in a finite time. Exact solutions that exhibit this property have been derived. Close to the singularity, the granular gas pressure is finite and almost constant. This work reports molecular dynamics (MD) simulations of a freely cooling gas of nearly elastically colliding hard disks, aimed at identifying the "attempted" density blowup regime. The initial conditions of the simulated flow mimic those of one particular solution of the IGHD equations that exhibits the density blowup. We measure the hydrodynamic fields in the MD simulations and compare them with predictions from the ideal theory. We find a remarkable quantitative agreement between the two over an extended time interval, proving the existence of the attempted blowup regime. As the attempted singularity is approached, the hydrodynamic fields, as observed in the MD simulations, deviate from the predictions of the ideal solution. To investigate the mechanism of breakdown of the ideal theory near the singularity, we extend the hydrodynamic theory by accounting separately for the gradient-dependent transport and for finite density corrections.Comment: 11 pages, 9 figures, accepted for publication on Physical Review

Thermal Instability-Induced Interstellar Turbulence

We study the dynamics of phase transitions in the interstellar medium by means of three-dimensional hydrodynamic numerical simulations. We use a realistic cooling function and generic nonequilibrium initial conditions to follow the formation history of a multiphase medium in detail in the absence of gravity. We outline a number of qualitatively distinct stages of this process, including a linear isobaric evolution, transition to an isochoric regime, formation of filaments and voids (also known as "thermal" pancakes), the development and decay of supersonic turbulence, an approach to pressure equilibrium, and final relaxation of the multiphase medium. We find that 1%-2% of the initial thermal energy is converted into gas motions in one cooling time. The velocity field then randomizes into turbulence that decays on a dynamical timescale E_k ~ t^-n, 1 < n < 2. While not all initial conditions yield a stable two-phase medium, we examine such a case in detail. We find that the two phases are well mixed with the cold clouds possessing a fine-grained structure near our numerical resolution limit. The amount of gas in the intermediate unstable phase roughly tracks the rms turbulent Mach number, peaking at 25% when M_rms ~ 8, decreasing to 11% when M_rms ~ 0.4.Comment: To appear in the ApJ Letters, April 2002; 5 pages, 3 color figures, mpeg animations available at http://akpc.ucsd.edu/ThermalLetter/thermal.htm

The Knudsen temperature jump and the Navier-Stokes hydrodynamics of granular gases driven by thermal walls

Thermal wall is a convenient idealization of a rapidly vibrating plate used for vibrofluidization of granular materials. The objective of this work is to incorporate the Knudsen temperature jump at thermal wall in the Navier-Stokes hydrodynamic modeling of dilute granular gases of monodisperse particles that collide nearly elastically. The Knudsen temperature jump manifests itself as an additional term, proportional to the temperature gradient, in the boundary condition for the temperature. Up to a numerical pre-factor of order unity, this term is known from kinetic theory of elastic gases. We determine the previously unknown numerical pre-factor by measuring, in a series of molecular dynamics (MD) simulations, steady-state temperature profiles of a gas of elastically colliding hard disks, confined between two thermal walls kept at different temperatures, and comparing the results with the predictions of a hydrodynamic calculation employing the modified boundary condition. The modified boundary condition is then applied, without any adjustable parameters, to a hydrodynamic calculation of the temperature profile of a gas of inelastic hard disks driven by a thermal wall. We find the hydrodynamic prediction to be in very good agreement with MD simulations of the same system. The results of this work pave the way to a more accurate hydrodynamic modeling of driven granular gases.Comment: 7 pages, 3 figure

Weak selection and stability of localized distributions in Ostwald ripening

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed that, when combined with an exact invariance property of the system, yields the selection rule, predicts a power-law convergence towards the selected self-similar DF and agrees well with our numerical simulations for the interface- and diffusion-controlled OR.Comment: 4 pages, 2 figures, submitted to PR

A nonlinear theory of non-stationary low Mach number channel flows of freely cooling nearly elastic granular gases

We use hydrodynamics to investigate non-stationary channel flows of freely cooling dilute granular gases. We focus on the regime where the sound travel time through the channel is much shorter than the characteristic cooling time of the gas. As a result, the gas pressure rapidly becomes almost homogeneous, while the typical Mach number of the flow drops well below unity. Eliminating the acoustic modes, we reduce the hydrodynamic equations to a single nonlinear and nonlocal equation of a reaction-diffusion type in Lagrangian coordinates. This equation describes a broad class of channel flows and, in particular, can follow the development of the clustering instability from a weakly perturbed homogeneous cooling state to strongly nonlinear states. If the heat diffusion is neglected, the reduced equation is exactly soluble, and the solution develops a finite-time density blowup. The heat diffusion, however, becomes important near the attempted singularity. It arrests the density blowup and brings about novel inhomogeneous cooling states (ICSs) of the gas, where the pressure continues to decay with time, while the density profile becomes time-independent. Both the density profile of an ICS, and the characteristic relaxation time towards it are determined by a single dimensionless parameter that describes the relative role of the inelastic energy loss and heat diffusion. At large values of this parameter, the intermediate cooling dynamics proceeds as a competition between low-density regions of the gas. This competition resembles Ostwald ripening: only one hole survives at the end.Comment: 20 pages, 15 figures, final versio

Coarsening of granular clusters: two types of scaling behaviors

We report on an experimental study of small cluster dynamics during the coarsening process in driven granular submonolayers of 120mkm bronze particles. The techniques of electrostatic and vertical mechanical vibration were employed to excite the granular gas. We measure the scaling exponent for the evaporation of small clusters during coarsening. It was found that the surface area of small clusters S vs time t behaves as S ~ (t_0-t)^(2/3) for lower frequencies and S ~ (t_0-t) for higher frequencies. We argue that the change in the scaling exponent is related to the transition from three dimensional to two dimensional character of motion in the granular gas.Comment: 4 pages,5 figures, submitted to Phys.Rev.

Noise driven unlimited population growth

Demographic noise causes unlimited population growth in a broad class of models which, without noise, would predict a stable finite population. We study this effect on the example of a stochastic birth-death model which includes immigration, binary reproduction and death. The unlimited population growth proceeds as an exponentially slow decay of a metastable probability distribution (MPD) of the population. We develop a systematic WKB theory, complemented by the van Kampen system size expansion, for the MPD and for the decay time. Important signatures of the MPD is a power-law tail (such that all the distribution moments, except the zeroth one, diverge) and the presence in the solution of two different WKB modes.Comment: 4 pages, 2 figure