Transport Far From Equilibrium --- Uniform Shear Flow

The BGK model kinetic equation is applied to spatially inhomogeneous states near steady uniform shear flow. The shear rate of the reference steady state can be large so the states considered include those very far from equilibrium. The single particle distribution function is calculated exactly to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding non-linear hydrodynamic equaitons are obtained and the set of transport coefficients are identified as explicit functions of the shear rate. The spectrum of the linear hydrodynamic equation is studied in detail and qualitative differences from the spectrum for equilibrium fluctuations are discussed. Conditions for instabilities at long wavelengths are identified and disccused.Comment: 32 pages, 1 figure, RevTeX, submitted to Phys. Rev.

Linear Response for Granular Fluids

The linear response of an isolated, homogeneous granular fluid to small spatial perturbations is studied by methods of non-equilibrium statistical mechanics. The long wavelength linear hydrodynamic equations are obtained, with formally exact expressions for the susceptibilities and transport coefficients. The latter are given in equivalent Einstein-Helfand and Green-Kubo forms. The context of these results and their contrast with corresponding results for normal fluids are discussed.Comment: Submitted to PR

Diffusion in a Granular Fluid - Simulation

The linear response description for impurity diffusion in a granular fluid undergoing homogeneous cooling is developed in the preceeding paper. The formally exact Einstein and Green-Kubo expressions for the self-diffusion coefficient are evaluated there from an approximation to the velocity autocorrelation function. These results are compared here to those from molecular dynamics simulations over a wide range of density and inelasticity, for the particular case of self-diffusion. It is found that the approximate theory is in good agreement with simulation data up to moderate densities and degrees of inelasticity. At higher density, the effects of inelasticity are stronger, leading to a significant enhancement of the diffusion coefficient over its value for elastic collisions. Possible explanations associated with an unstable long wavelength shear mode are explored, including the effects of strong fluctuations and mode coupling

Endo- vs. Exo-genous shocks and relaxation rates in book and music "sales"

In this paper, we analyze the response of music and book sales to an external field and to buyer herding. We distinguish endogenous and exogenous shocks. We focus on some case studies, whose data have been collected from ranking on amazon.com. We show that an ensemble of equivalent systems quantitatively respond in a similar way to a similar ''external shock'', indicating roads to universality features. In contrast to Sornette et al. [Phys. Rev. Lett. {93}, 228701 (2004)] who seemed to find power law behaviors, in particular at long times, - a law interpreted in terms of an epidemic activity, we observe that the relaxation process can be as well seen as an exponential one that saturates toward an asymptotic state, itself different from the pre-shock state. By studying an ensemble of 111 shocks, on books or records, we show that exogenous and endogenous shocks are discriminated by their short-time behaviour: the relaxation time seems to be twice shorter in endogenous shocks than in exogenous ones. We interpret the finding through a simple thermodynamic model with a dissipative force.Comment: to be published in physica

Stability of Uniform Shear Flow

The stability of idealized shear flow at long wavelengths is studied in detail. A hydrodynamic analysis at the level of the Navier-Stokes equation for small shear rates is given to identify the origin and universality of an instability at any finite shear rate for sufficiently long wavelength perturbations. The analysis is extended to larger shear rates using a low density model kinetic equation. Direct Monte Carlo Simulation of this equation is computed with a hydrodynamic description including non Newtonian rheological effects. The hydrodynamic description of the instability is in good agreement with the direct Monte Carlo simulation for $t < 50t_0$, where $t_0$ is the mean free time. Longer time simulations up to $2000t_0$ are used to identify the asymptotic state as a spatially non-uniform quasi-stationary state. Finally, preliminary results from molecular dynamics simulation showing the instability are presented and discussed.Comment: 25 pages, 9 figures (Fig.8 is available on request) RevTeX, submitted to Phys. Rev.

Theoretical Description of Coulomb Balls - Fluid Phase

A theoretical description for the radial density profile of a finite number of identical charged particles confined in a harmonic trap is developed for application over a wide range of Coulomb coupling (or, equivalently, temperatures) and particle numbers. A simple mean field approximation neglecting correlations yields a density profile which is monotonically decreasing with radius for all temperatures, in contrast to molecular dynamics simulations and experiments showing shell structure at lower temperatures. A more complete theoretical description including charge correlations is developed here by an extension of the hypernetted chain approximation, developed for bulk fluids, to the confined charges. The results reproduce all of the qualitative features observed in molecular dynamics simulations and experiments. These predictions are then tested quantitatively by comparison with new benchmark Monte Carlo simulations. Quantitative accuracy of the theory is obtained for the selected conditions by correcting the hypernetted chain approximation with a representation for the associated bridge functions.Comment: 10 figures, submitted to Physical Review

Corticosterone and the Stress Response in Young Western Screech-Owls: Effects of Captivity, Gender, and Activity Period

We used a standard handling protocol to examine the stress response of captive young western screech-owls during their active (nighttime) and inactive (daytime) periods and to compare the stress responses of captive and free-living owls. Circulating corticosterone levels were significantly higher during the inactive period than in the active period in this nocturnal species. This suggests that the daily pattern of corticosterone secretion is reversed in nocturnal birds and is correlated with activity period rather than with the light/dark cycle. Young (ca. 4-5 mo old) screech-owls of both sexes showed increases in plasma corticosterone up to 30 min after capture, followed by significant decreases at 60 min. This pattern is similar to those of other species of birds examined previously, except that decreases in corticosterone at 60 min rarely have been observed. Such decreases may be the result of physiological differences between adult and young birds, habituation to handling in captive birds, or the effects of body condition. Corticosterone levels and the response to capture and handling were comparable in captive and free-living owls, which suggests that the captive owls were not subjected to chronically high levels of stress

Kinetic Theory of Response Functions for the Hard Sphere Granular Fluid

The response functions for small spatial perturbations of a homogeneous granular fluid have been described recently. In appropriate dimensionless variables, they have the form of stationary state time correlation functions. Here, these functions are expressed in terms of reduced single particle functions that are expected to obey a linear kinetic equation. The functional assumption required for such a kinetic equation, and a Markov approximation for its implementation are discussed. If, in addition, static velocity correlations are neglected, a granular fluid version of the linearized Enskog kinetic theory is obtained. The derivation makes no a priori limitation on the density, space and time scale, nor degree of inelasticity. As an illustration, recently derived Helfand and Green-Kubo expressions for the Navier-Stokes order transport coefficients are evaluated with this kinetic theory. The results are in agreement with those obtained from the Chapman-Enskog solution to the nonlinear Enskog kinetic equation.Comment: Submitted to J. Stat. Mec

Aging to non-Newtonian hydrodynamics in a granular gas

The evolution to the steady state of a granular gas subject to simple shear flow is analyzed by means of computer simulations. It is found that, regardless of its initial preparation, the system reaches (after a transient period lasting a few collisions per particle) a non-Newtonian (unsteady) hydrodynamic regime, even at strong dissipation and for states where the time scale associated with inelastic cooling is shorter than the one associated with the irreversible fluxes. Comparison with a simplified rheological model shows a good agreement.Comment: 6 pages, 4 figures; v2: improved version to be published in EP

Plumage Variation, Plasma Steroids and Social Dominance in Male House Finches

In male House Finches (Carpodacusm exicanus), the extent and color of plumage varies depending on access to carotenoid pigments. Colorful males exhibit extensive red pigmentation, while less colorful (i.e., drab ) males exhibit carotenoid pigmentation over a smaller percentage of their plumage, pigmentation of a color besides red (e.g., yellow, gold, orange, or pink), or both. One explanation for maintenance of plumage variation is that it reliably reflects social status, allowing males to correctly assess their status in relation to others and avoid or minimize costly fights. Social relationships may also be related to endogenous factors, such as circulating levels of the hormones testosterone and corticosterone. High levels of testosterone may promote or facilitate increased aggression, and stress associated with receiving aggression from individuals of higher status may increase adrenal activity and secretion of corticosterone. We examined the relationship between plumage variability, steroid hormones, and social status in captive male House Finches during the non-breeding period in: (1) groups of males in which individuals varied by age, size, and plumage, and (2) pairs (dyads) of males matched for several measurable parameters except plumage. Testosterone and social status were not related in males competing in either groups or dyads, and levels of testosterone were routinely low. Corticosterone and status were not related in groups but, in dyads where subordinate individuals had little chance of escaping aggression from more dominant birds, subordinates exhibited significantly greater levels of corticosterone. Although drab males tended to achieve higher status than colorful males in both experiments, which is consistent with previous studies on free-living individuals, we could not reject the null hypothesis that plumage and status were unrelated. We conclude that dominance relationships among male House Finches during the non-breeding season may not be related to testosterone, but they are reflected by levels of corticosterone in some circumstances. Additionally, colorful plumage appears to be a poor predictor of high social status among male House Finches during the non-breeding season