Some Experiments on the Electrical Conductivity of Atmospheric Air

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Chapman-Enskog expansion about nonequilibrium states: the sheared granular fluid

The Chapman-Enskog method of solution of kinetic equations, such as the Boltzmann equation, is based on an expansion in gradients of the deviations fo the hydrodynamic fields from a uniform reference state (e.g., local equilibrium). This paper presents an extension of the method so as to allow for expansions about \emph{arbitrary}, far-from equilibrium reference states. The primary result is a set of hydrodynamic equations for studying variations from the arbitrary reference state which, unlike the usual Navier-Stokes hydrodynamics, does not restrict the reference state in any way. The method is illustrated by application to a sheared granular gas which cannot be studied using the usual Navier-Stokes hydrodynamics.Comment: 23 pages, no figures. Submited to PRE Replaced to correct misc. errors Replaced to correct misc. errors, make notation more consistant, extend discussio

Change in interplanetary shock acceleration preceding STIP Interval 17

The intensity and frequency of shock acceleration events in the interplanetary medium decreased dramatically in early 1985. Low energy ions were observed by IMP 8 at 1 AU and Voyagers 1 and 2 at 22 and 16 AU, respectively. Voyager 1 was at 25 deg heliographic latitude while IMP 8 and Voyager 2 were near the solar equatorial plane. The decrease in low energy shock events led to a drop in the average ion flux by a factor of 20 to 50. It started about day 10 of 1985 in the approximately .5 MeV channel on IMP8 and took approximately 75 days to reach the new, lower, background level. The decrease at the Voyagers started approximately 50 days later. The time delay between the start of the decrease at IMP and at Voyager 2 implies that decrease was convected outward with a velocity of approximately 535 km/sec. The intensity and frequency of interplanetary shock events remained at the lower level for at least 1.5 years

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

Settling Some Open Problems on 2-Player Symmetric Nash Equilibria

Over the years, researchers have studied the complexity of several decision versions of Nash equilibrium in (symmetric) two-player games (bimatrix games). To the best of our knowledge, the last remaining open problem of this sort is the following; it was stated by Papadimitriou in 2007: find a non-symmetric Nash equilibrium (NE) in a symmetric game. We show that this problem is NP-complete and the problem of counting the number of non-symmetric NE in a symmetric game is #P-complete. In 2005, Kannan and Theobald defined the "rank of a bimatrix game" represented by matrices (A, B) to be rank(A+B) and asked whether a NE can be computed in rank 1 games in polynomial time. Observe that the rank 0 case is precisely the zero sum case, for which a polynomial time algorithm follows from von Neumann's reduction of such games to linear programming. In 2011, Adsul et. al. obtained an algorithm for rank 1 games; however, it does not solve the case of symmetric rank 1 games. We resolve this problem

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

True blue: Temporal and spatial stability of pelagic wildlife at a submarine canyon

Funding: This research was funded through the Ian Potter Foundation and the First author.In coastal systems, marine-protected areas (MPAs) have been shown to increase the diversity, abundance, and biomass of wildlife assemblages as well as their resilience to climate change. The effectiveness of pelagic MPAs is less clear, with arguments against their establishment typically based on the highly mobile nature of pelagic taxa. We used mid-water stereo-baited remote underwater video systems (stereo-BRUVS) and spatial predictive models to characterize the pelagic wildlife assemblage at the head of the Perth Canyon, one of the largest submarine canyons in Australia, over a 7-yr period (2013–2019). The total number of unique taxa and mean values of taxonomic richness, abundance, fork length, and biomass demonstrated strong interannual stability, although mean taxonomic richness and abundance were significantly lower in 2018 relative to other years. Seasonal variability was absent in 2016, but in 2018, taxonomic richness and abundance were three times greater in the Austral spring than in the autumn. Some mobile megafauna were only recorded at the Perth Canyon Marine Park (PCMP) in the autumn, suggesting a seasonal component to their occurrence. The fine-scale distribution of pelagic taxa at the canyon head was largely stable over time, with many areas of higher relative probability of presence located outside protected zones. Despite a degree of variability that may relate to the effect of the El Niño Southern Oscillation on the Leeuwin Current, the PCMP assemblage demonstrates a relatively high degree of spatiotemporal stability. Stronger protection of the PCMP (IUCN II or higher) would potentially improve conservation outcomes for many species of pelagic wildlife.Publisher PDFPeer reviewe

English indices of deprivation 2010 : technical report

The English indices of deprivation 2010 is the third release in a series of statistics produced to measure multiple forms of deprivation at the small spatial scale. It updates the indices of deprivation 2007 and 2004, retaining broadly the same methodology, domains and indicators. This report outlines the conceptualisation underpinning the model of multiple deprivation used and describes the indicators and domains that make up the indices

Hydrodynamic modes, Green-Kubo relations, and velocity correlations in dilute granular gases

It is shown that the hydrodynamic modes of a dilute granular gas of inelastic hard spheres can be identified, and calculated in the long wavelength limit. Assuming they dominate at long times, formal expressions for the Navier-Stokes transport coefficients are derived. They can be expressed in a form that generalizes the Green-Kubo relations for molecular systems, and it is shown that they can also be evaluated by means of $N$-particle simulation methods. The form of the hydrodynamic modes to zeroth order in the gradients is used to detect the presence of inherent velocity correlations in the homogeneous cooling state, even in the low density limit. They manifest themselves in the fluctuations of the total energy of the system. The theoretical predictions are shown to be in agreement with molecular dynamics simulations. Relevant related questions deserving further attention are pointed out

Segregation of an intruder in a heated granular dense gas

A recent segregation criterion [V. Garz\'o, Phys. Rev. E \textbf{78}, 020301(R) (2008)] based on the thermal diffusion factor $\Lambda$ of an intruder in a heated granular gas described by the inelastic Enskog equation is revisited. The sign of $\Lambda$ provides a criterion for the transition between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE). The present theory incorporates two extra ingredients not accounted for by the previous theoretical attempt. First, the theory is based upon the second Sonine approximation to the transport coefficients of the mass flux of intruder. Second, the dependence of the temperature ratio (intruder temperature over that of the host granular gas) on the solid volume fraction is taken into account in the first and second Sonine approximations. In order to check the accuracy of the Sonine approximation considered, the Enskog equation is also numerically solved by means of the direct simulation Monte Carlo (DSMC) method to get the kinetic diffusion coefficient $D_0$. The comparison between theory and simulation shows that the second Sonine approximation to $D_0$ yields an improvement over the first Sonine approximation when the intruder is lighter than the gas particles in the range of large inelasticity. With respect to the form of the phase diagrams for the BNE/RBNE transition, the kinetic theory results for the factor $\Lambda$ indicate that while the form of these diagrams depends sensitively on the order of the Sonine approximation considered when gravity is absent, no significant differences between both Sonine solutions appear in the opposite limit (gravity dominates the thermal gradient). In the former case (no gravity), the first Sonine approximation overestimates both the RBNE region and the influence of dissipation on thermal diffusion segregation.Comment: 9 figures; to be published in Phys. Rev.