Dynamics of particle-particle collisions in a viscous liquid

When two solid spheres collide in a liquid, the dynamic collision process is slowed by viscous dissipation and the increased pressure in the interparticle gap as compared with dry collisions. This paper investigates liquid-immersed head-on and oblique collisions, which complements previously investigated particle-on-wall immersed collisions. By defining the normal from the line of centers at contact, the experimental findings support the decomposition of an oblique collision into its normal and tangential components of motion. The normal relative particle motion is characterized by an effective coefficient of restitution and a binary Stokes number with a correlation that follows the particle-wall results. The tangential motion is described by a collision model using a normal coefficient of restitution and a friction coefficient that are modified for the liquid effects

On the Einstein relation in a heated granular gas

Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $\epsilon\equiv D/(T_0\lambda)=1$ between the diffusion $D$ and mobility $\lambda$ coefficients when the temperature of the gas $T$ is replaced by the temperature of the impurity $T_0$ in the usual Einstein relation. This problem is analyzed in this paper by solving analytically the Boltzmann-Lorentz equation from the Chapman-Enskog method. The gas is heated by the action of an external driving force (thermostat) which does work to compensate for the collisional loss of energy. Two types of thermostats are considered: (a) a deterministic force proportional to the particle velocity (Gaussian thermostat), and (b) a white noise external force (stochastic thermostat). The diffusion and mobility coefficients are given in terms of the solutions of two linear integral equations, which are approximately solved up to the second order in a Sonine polynomial expansion. The results show that the violation of the Einstein relation ($\epsilon\neq 1$) is only due to the non-Maxwellian behavior of the impurity velocity distribution function (absence of the Gibbs state). At a quantitative level, the kinetic theory results also show that the deviation of $\epsilon$ from 1 is more significant in the case of the Gaussian thermostat than in the case of the stochastic one, in which case the deviation of the Einstein relation is in general smaller than 1%. This conclusion agrees quite well with the results found in computer simulations.Comment: 7 figures. to appear in Physica

Agricultural labour adjustment and the impact of Institutions

The economic transformation in countries of Central and Eastern Europe as well as Asia resulted in a diverse picture of change in agricultural labour use. Based on a measure of sectoral labour adjustment, the paper explores the determinants of occupational labour flows paying special attention to the impact of institutions. Annual rates of occupational migration between agriculture and non-agriculture over the period 1978-2005 are calculated for a panel of 30 transition countries. Annual migration from agriculture ranges from outflows of nearly 8 percent of the agricultural labour force to immigration into agriculture about 9 percent on average. Fixed-effects panel models are used to explain the annual intersectoral labour flow. The most important determinants of the migration rate are the relative income differences between non-agricultural and agricultural sectors, the relative magnitude of agricultural labour, the development of terms of trade and the level of unemployment. Furthermore, the speed of economic reforms and the way of land privatization affect occupational migration significantly. An increasing intersectoral income difference points to still existing mobility restrictions for agricultural labour in some of the countries analyzed

Mass transport of an impurity in a strongly sheared granular gas

Transport coefficients associated with the mass flux of an impurity immersed in a granular gas under simple shear flow are determined from the inelastic Boltzmann equation. A normal solution is obtained via a Chapman-Enskog-like expansion around a local shear flow distribution that retains all the hydrodynamic orders in the shear rate. Due to the anisotropy induced by the shear flow, tensorial quantities are required to describe the diffusion process instead of the conventional scalar coefficients. The mass flux is determined to first order in the deviations of the hydrodynamic fields from their values in the reference state. The corresponding transport coefficients are given in terms of the solutions of a set of coupled linear integral equations, which are approximately solved by considering the leading terms in a Sonine polynomial expansion. The results show that the deviation of these generalized coefficients from their elastic forms is in general quite important, even for moderate dissipation.Comment: 6 figure

Fluctuation-Dissipation relations in Driven Granular Gases

We study the dynamics of a 2d driven inelastic gas, by means of Direct Simulation Monte Carlo (DSMC) techniques, i.e. under the assumption of Molecular Chaos. Under the effect of a uniform stochastic driving in the form of a white noise plus a friction term, the gas is kept in a non-equilibrium Steady State characterized by fractal density correlations and non-Gaussian distributions of velocities; the mean squared velocity, that is the so-called {\em granular temperature}, is lower than the bath temperature. We observe that a modified form of the Kubo relation, which relates the autocorrelation and the linear response for the dynamics of a system {\em at equilibrium}, still holds for the off-equilibrium, though stationary, dynamics of the systems under investigation. Interestingly, the only needed modification to the equilibrium Kubo relation is the replacement of the equilibrium temperature with an effective temperature, which results equal to the global granular temperature. We present two independent numerical experiment, i.e. two different observables are studied: (a) the staggered density current, whose response to an impulsive shear is proportional to its autocorrelation in the unperturbed system and (b) the response of a tracer to a small constant force, switched on at time $t_w$, which is proportional to the mean-square displacement in the unperturbed system. Both measures confirm the validity of Kubo's formula, provided that the granular temperature is used as the proportionality factor between response and autocorrelation, at least for not too large inelasticities.Comment: 11 pages, 7 figures, submitted for publicatio

A note on the violation of the Einstein relation in a driven moderately dense granular gas

The Einstein relation for a driven moderately dense granular gas in $d$-dimensions is analyzed in the context of the Enskog kinetic equation. The Enskog equation neglects velocity correlations but retains spatial correlations arising from volume exclusion effects. As expected, there is a breakdown of the Einstein relation $\epsilon=D/(T_0\mu)\neq 1$ relating diffusion $D$ and mobility $\mu$, $T_0$ being the temperature of the impurity. The kinetic theory results also show that the violation of the Einstein relation is only due to the strong non-Maxwellian behavior of the reference state of the impurity particles. The deviation of $\epsilon$ from unity becomes more significant as the solid volume fraction and the inelasticity increase, especially when the system is driven by the action of a Gaussian thermostat. This conclusion qualitatively agrees with some recent simulations of dense gases [Puglisi {\em et al.}, 2007 {\em J. Stat. Mech.} P08016], although the deviations observed in computer simulations are more important than those obtained here from the Enskog kinetic theory. Possible reasons for the quantitative discrepancies between theory and simulations are discussed.Comment: 6 figure

Study of the trajectories of visually guided movement of unimanual and bimanual tasks

Restitution of upper limb mobility following stroke is one of the major challenges facing clinicians in the country today. The complexity of performing skilled tasks with fine movements makes restitution of mobility all the more complex for rehabilitation specialists. Although several techniques have been evolved for, limited success with transfer of training from the clinical environment to functional performance clearly indicates a need for research and development in the area of upper extremity rehabilitation. Bimanual coordination has recently surfaced as a novel and effective way to fast and lasting recovery. The success of bimanually coordinated training encourages a better understanding of the underlying neural, physiological and engineering principles involved which in turn would result in improved treatments for people with hemiparesis. An apparatus developed in this project enables such an understanding, by successfully being able to collect, record and analyze the movement trajectories of both the hands simultaneously with a high degree of accuracy

Wavelength Scaling and Square/Stripe and Grain Mobility Transitions in Vertically Oscillated Granular Layers

Laboratory experiments are conducted to examine granular wave patterns near onset as a function of the container oscillation frequency f and amplitude A, layer depth H, and grain diameter D. The primary transition from a flat grain layer to standing waves occurs when the layer remains dilated after making contact with the container. With a flat layer and increasing dimensionless peak container acceleration G = 4 pi^2 f^2 A/g (g is the acceleration due to gravity), the wave transition occurs for G=2.6, but with decreasing G the waves persist to G=2.2. For 2.2<G<3.8, patterns are squares for f<f_ss and stripes for f>f_ss; H determines the square/stripe transition frequency f_ss=0.33(g/H)^0.5. The dispersion relations for layers with varying H collapse onto the curve L/H=1.0+1.1[f(H/g)^0.5]^(-1.32 +/- 0.03) (L is the wavelength) when the peak container velocity v exceeds a critical value v_gm of approximately 3 (Dg)^0.5. Local collision pressure measurements suggest that v_gm is associated with a transition in the horizontal grain mobility: for v>v_gm, there is a hydrodynamic-like horizontal sloshing motion, while for v<v_gm, the grains are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at v_gm less than f_ss and v<v_gm, patterns are tenuous and disordered.Comment: 21 pages, 15 figures, submitted to Physica

What is the temperature of a granular medium?

In this paper we discuss whether thermodynamical concepts and in particular the notion of temperature could be relevant for the dynamics of granular systems. We briefly review how a temperature-like quantity can be defined and measured in granular media in very different regimes, namely the glassy-like, the liquid-like and the granular gas. The common denominator will be given by the Fluctuation-Dissipation Theorem, whose validity is explored by means of both numerical and experimental techniques. It turns out that, although a definition of a temperature is possible in all cases, its interpretation is far from being obvious. We discuss the possible perspectives both from the theoretical and, more importantly, from the experimental point of view