Using fluctuating hydrodynamics we describe the slow buildup of long range spatial correlations in a freely evolving fluid of inelastic hard spheres. In the incompressible limit, the behavior of spatial velocity correlations (including r 2d behavior) is governed by vorticity fluctuations only and agrees well with two-dimensional simulations up to 50 to 100 collisions per particle. The incompressibility assumption breaks down beyond a distance that diverges in the elastic limit. [S0031-9007(97) In the characterization of granular matter as an unusual solid, fluid, or gas by Jaeger et al. [1], this Letter addresses the granular gas regime, controlled by inelasticity, clustering [2], and collapse [3]. Clustering is a long wavelength, low frequency (hydrodynamic) phenomenon and inelastic collapse a short wavelength, high frequency (kinetic) phenomenon. In the granular gas regime, also called rapid granular flows, the dynamics is dominated by inelastic collisions. Here the methods of nonequilibrium statistical mechanics, molecular dynamics, kinetic theory, and hydrodynamics are most suitable for describing the observed average macroscopic behavior [2][3][4][5][6][7] and the fluctuations around it.The lack of energy conservation makes the granular gas, whether driven or freely evolving, behave very differently from molecular fluids. The essential physical processes and detailed dynamics are described in [2,3] and references therein: the similarities and differences with molecular fluids; lack of separation of microscales and macroscales, not only because the grains themselves are macroscopic, but also because of the existence of intermediate intrinsic scales which are controlled by the inelasticity and are only well separated when the system is nearly elastic. A simple model which incorporates the inelasticity of the granular collisions consists of inelastic hard spheres (IHS), taken here of unit mass and diameter, with momentum conserving dynamics. The energy loss in a collision is proportional to the inelasticity parameter e 1 2 a 2 where a is the coefficient of normal restitution.For an understanding of what follows, we recall two important properties of the undriven granular gas: (i) the existence of a homogeneous cooling state (HCS) and (ii) its instability against spatial fluctuations. The hydrodynamic equations for an IHS fluid, started in a uniform equilibrium state with temperature T 0 , admit an HCS solution (see, e.g., [2,3,7]) with a homogeneous temperature T ͑t͒, described by ≠ t T 22g 0 vT. Here the collision frequency is v͑T͒ ϳ p T͞l 0 with a mean free path l 0 ,given by the Enskog theory [8] for a dense system of hard disks or spheres (d 2, 3) and g 0 e͞2d. Then T ͑t͒ T 0 ͓͞1 1 g 0 v͑T 0 ͒t͔ 2 T 0 exp͑22g 0 t͒, where t is the average number of collisions suffered per particle within a time t. It is found by integrating dt v͑T ͑t͒͒dt. Moreover, this HCS solution is linearly unstable once the linear extent L of the system exceeds some dynamic correlation length, which increases with decreasing e, and is ...

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The time dependence of deviations from the Gaussian state in a freely cooling homogeneous system of smooth inelastically colliding spheres is investigated by kinetic theory. We determine the full time dependence of the coefficients of an expansion around the Gaussian state in Generalized Laguerre polynomials. Approximating this system of equations to sixth order, we find that the asymptotic state, where the mean energy T follows Haff's law with time independent cooling rate, is reached within a few collisions per particle. Two-dimensional molecular dynamics simulations confirm our results and show exponential behavior in the high-energy tails.

An initially homogeneous freely evolving fluid of inelastic hard spheres develops inhomogeneities in the flow field u(r, t) (vortices) and in the density field n(r, t) (clusters), driven by unstable fluctuations, δa = {δn, δu}. Their spatial correlations, δa(r, t)δa(r ′ , t) , as measured in molecular dynamics simulations, exhibit long range correlations; the mean vortex diameter grows as ξ(t) ∝ √ ln t; there occur transitions to macroscopic shearing states, etc. The Cahn-Hilliard theory of spinodal decomposition offers a qualitative understanding and quantitative estimates of the observed phenomena. When intrinsic length scales are of the order of the system size, effects of physical boundaries and periodic boundaries (finite size effects in simulations) are important.

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Abstract. The interest in the use of ceilometers for optical aerosol characterization has increased in the last few years. They operate continuously almost unattended and are also much less expensive than lidars; hence, they can be distributed in dense networks over large areas. However, due to the low signal-to-noise ratio it is not always possible to obtain particle backscatter coefficient profiles, and the vast number of data generated require an automated and unsupervised method that ensures the quality of the profiles inversions.In this work we describe a method that uses aerosol optical depth (AOD) measurements from the AERONET network that it is applied for the calibration and automated quality assurance of inversion of ceilometer profiles. The method is compared with independent inversions obtained by colocated multiwavelength lidar measurements. A difference smaller than 15 % in backscatter is found between both instruments. This method is continuously and automatically applied to the Iberian Ceilometer Network (ICENET) and a case example during an unusually intense dust outbreak affecting the Iberian Peninsula between 20 and 24 February 2016 is shown. Results reveal that it is possible to obtain quantitative optical aerosol properties (particle backscatter coefficient) and discriminate the quality of these retrievals with ceilometers over large areas. This information has a great potential for alert systems and model assimilation and evaluation.

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Particulate matter emissions from paved roads are currently one of the main challenges for a sustainable transport in Europe. Emissions are scarcely estimated due to the lack of knowledge about the resuspension process severely hampering a reliable simulation of PM and heavy metals concentrations in large cities and evaluation of population exposure. In this study the Emission Factors from road dust resuspension on a Mediterranean freeway were estimated per single vehicle category and PM component (OC, EC, mineral dust and metals) by means of the deployment of vertical profiles of passive samplers and terminal concentration estimate. The estimated PMio emission factors varied from 12 to 47 mg VKT -1 (VICT: Vehicle Kilometer Traveled) with an average value of 22.7 ± 14.2 mg VKT -1 . Emission Factors for heavy and light duty vehicles, passenger cars and motorbikes were estimated, based on average fleet composition and EPA ratios, in 187-733 mg VKT -1 , 33-131 VKT -1 , 9.4-36.9 VKT" 1 and 0.8-3.3 VKT -1 , respectively. These range of values are lower than previous estimates in Mediterranean urban roads, probably due to the lower dust reservoir on freeways. PM emitted material was dominated by mineral dust (9-10 mg VKT -1 ), but also OC and EC were found to be major components and approximately 14 -25% and 2-9% of average PM exhaust emissions from diesel passenger cars on highways respectively.