Velocity Distribution and Cumulants in the Unsteady Uniform Longitudinal Flow of a Granular Gas

The uniform longitudinal flow is characterized by a linear longitudinal velocity field $u_x(x,t)=a(t)x$, where $a(t)={a_0}/({1+a_0t})$ is the strain rate, a uniform density $n(t)\propto a(t)$, and a uniform granular temperature $T(t)$. Direct simulation Monte Carlo solutions of the Boltzmann equation for inelastic hard spheres are presented for three (one positive and two negative) representative values of the initial strain rate $a_0$. Starting from different initial conditions, the temporal evolution of the reduced strain rate $a^*\propto a_0/\sqrt{T}$, the non-Newtonian viscosity, the second and third velocity cumulants, and three independent marginal distribution functions has been recorded. Elimination of time in favor of the reduced strain rate $a^*$ shows that, after a few collisions per particle, different initial states are attracted to common "hydrodynamic" curves. Strong deviations from Maxwellian properties are observed from the analysis of the cumulants and the marginal distributions.Comment: 8 pages; 4 figures; contributed paper at the 28th International Symposium on Rarefied Gas Dynamics (Zaragoza, Spain, July 9-13, 2012

Unsteady non-Newtonian hydrodynamics in granular gases

The temporal evolution of a dilute granular gas, both in a compressible flow (uniform longitudinal flow) and in an incompressible flow (uniform shear flow), is investigated by means of the direct simulation Monte Carlo method to solve the Boltzmann equation. Emphasis is laid on the identification of a first "kinetic" stage (where the physical properties are strongly dependent on the initial state) subsequently followed by an unsteady "hydrodynamic" stage (where the momentum fluxes are well-defined non-Newtonian functions of the rate of strain). The simulation data are seen to support this two-stage scenario. Furthermore, the rheological functions obtained from simulation are well described by an approximate analytical solution of a model kinetic equation.Comment: 19 pages, 3 tables, 14 figure

A granular fluid modeled as a driven system of elastic hard spheres

Publicado en: The Physics of Complex Systems. New Advances and Perspectives, F. Mallamace and H. E. Stanley, eds. (IOS Press, Amsterdam, 2004), pp. 475-480 DOI: 10.3254/978-1-61499-011-6-475Exploramos la posibilidad de describir las principales propiedades de transporte de un gas granular por medio de un modelo que consiste en esferas duras elásticas bajo la acción de una fuerza de arrastre que imita el enfriamiento inelástico del gas granular. Simulaciones directas de Monte Carlo sobre la ecuación de Boltzmann muestran una buena concordancia entre los resultados para un gas de esferas duras inelásticas y las de un gas de esferas duras elásticas impulsadas en el estado de flujo de cizallamiento simple. Esta equivalencia aproximada entre ambos sistemas se aprovecha para extender los modelos cinéticos conocidos por colisiones elásticas al caso inelástico.We explore the possibility of describing the main transport properties of a granular gas by means of a model consisting of elastic hard spheres under the action of a drag force that mimics the inelastic cooling of the granular gas. Direct Monte Carlo simulations of the Boltzmann equation show a good agreement between the results for a gas of inelastic hard spheres and those for a gas of driven elastic hard spheres in the simple shear flow state. This approximate equivalence between both systems is exploited to extend known kinetic models for elastic collisions to the inelastic case

Uniform shear flow in dissipative gases. Computer simulations of inelastic hard spheres and (frictional) elastic hard spheres

In the preceding paper (cond-mat/0405252), we have conjectured that the main transport properties of a dilute gas of inelastic hard spheres (IHS) can be satisfactorily captured by an equivalent gas of elastic hard spheres (EHS), provided that the latter are under the action of an effective drag force and their collision rate is reduced by a factor $(1+\alpha)/2$ (where $\alpha$ is the constant coefficient of normal restitution). In this paper we test the above expectation in a paradigmatic nonequilibrium state, namely the simple or uniform shear flow, by performing Monte Carlo computer simulations of the Boltzmann equation for both classes of dissipative gases with a dissipation range $0.5\leq \alpha\leq 0.95$ and two values of the imposed shear rate $a$. The distortion of the steady-state velocity distribution from the local equilibrium state is measured by the shear stress, the normal stress differences, the cooling rate, the fourth and sixth cumulants, and the shape of the distribution itself. In particular, the simulation results seem to be consistent with an exponential overpopulation of the high-velocity tail. The EHS results are in general hardly distinguishable from the IHS ones if $\alpha\gtrsim 0.7$, so that the distinct signature of the IHS gas (higher anisotropy and overpopulation) only manifests itself at relatively high dissipationsComment: 23 pages; 18 figures; Figs. 2 and 9 include new simulations; two new figures added; few minor changes; accepted for publication in PR

System of elastic hard spheres which mimics the transport properties of a granular gas

The prototype model of a fluidized granular system is a gas of inelastic hard spheres (IHS) with a constant coefficient of normal restitution $\alpha$. Using a kinetic theory description we investigate the two basic ingredients that a model of elastic hard spheres (EHS) must have in order to mimic the most relevant transport properties of the underlying IHS gas. First, the EHS gas is assumed to be subject to the action of an effective drag force with a friction constant equal to half the cooling rate of the IHS gas, the latter being evaluated in the local equilibrium approximation for simplicity. Second, the collision rate of the EHS gas is reduced by a factor $(1+\alpha)/2$, relative to that of the IHS gas. Comparison between the respective Navier-Stokes transport coefficients shows that the EHS model reproduces almost perfectly the self-diffusion coefficient and reasonably well the two transport coefficients defining the heat flux, the shear viscosity being reproduced within a deviation less than 14% (for $\alpha\geq 0.5$). Moreover, the EHS model is seen to agree with the fundamental collision integrals of inelastic mixtures and dense gases. The approximate equivalence between IHS and EHS is used to propose kinetic models for inelastic collisions as simple extensions of known kinetic models for elastic collisionsComment: 20 pages; 6 figures; change of title; few minor changes; accepted for publication in PR

Eficacia de la actuación de los payasos sobre el miedo a procedimientos dolorosos en oncohematología pediátrica

Objectives: To assess the effectiveness of the performance of a couple of hospital clowns on the fear response in patients in Oncohematology unit before applying a painful medical procedure (lumbar puncture or bone marrow aspiration).Patients and methods: 30 children aged 3-11 years-old (M = 6.93, SD = 2.78) underwent lumbar puncture or bone marrow aspirate in the ‘Virgen de la Arrixaca’ Hospital. The assessment consisted of the administration of: 5-Facial scale, the observation scale “modified Yale Preoperative Anxiety Scale” (m-YPAS), and physiological measures of pulse and mean blood pressure.Results: In the between-subjects-analysis, statistically significant differences in all measures, except for the scale of faces, after the performance of hospital clowns was obtained. After the hospital clowns left, groups were matched on their scores. In the within-subject analysis, significant differences between pretest and posttest were achieved in all measures for the control group.The effect size analysis indicates values on the Facial scale d = 0.22 (small effect size) and large effect size for pulse (d = 1.02), mean arterial pressure (d = 1.20), and the m-YPAS scale (d=0.99), before application of painful medical procedure.Conclusions: The presence of clowns helps to reduce the fear in the application of painful procedures. However, this effect is short-term, because after hospital clown leaves differences disappear between groups</p

Transport coefficients for inelastic Maxwell mixtures

The Boltzmann equation for inelastic Maxwell models is used to determine the Navier-Stokes transport coefficients of a granular binary mixture in $d$ dimensions. The Chapman-Enskog method is applied to solve the Boltzmann equation for states near the (local) homogeneous cooling state. The mass, heat, and momentum fluxes are obtained to first order in the spatial gradients of the hydrodynamic fields, and the corresponding transport coefficients are identified. There are seven relevant transport coefficients: the mutual diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity, the Dufour coefficient, the pressure energy coefficient, and the thermal conductivity. All these coefficients are {\em exactly} obtained in terms of the coefficients of restitution and the ratios of mass, concentration, and particle sizes. The results are compared with known transport coefficients of inelastic hard spheres obtained analytically in the leading Sonine approximation and by means of Monte Carlo simulations. The comparison shows a reasonably good agreement between both interaction models for not too strong dissipation, especially in the case of the transport coefficients associated with the mass flux.Comment: 9 figures, to be published in J. Stat. Phy

Estudio mediante la teoría cinética de medios granulares en régimen de flujo rápido

En esta tesis se abordará el estudio de las propiedades dinámicas y de transporte en medios granulares en condiciones de flujo rápido. Se utilizará una descripción basada en la mecánica estadística y en la teoría cinética y se emplearán técnicas analíticas, numéricas y de simulación en ordenador