Cauchy problem for the Boltzmann-BGK model near a global Maxwellian

In this paper, we are interested in the Cauchy problem for the Boltzmann-BGK model for a general class of collision frequencies. We prove that the Boltzmann-BGK model linearized around a global Maxwellian admits a unique global smooth solution if the initial perturbation is sufficiently small in a high order energy norm. We also establish an asymptotic decay estimate and uniform $L^2$-stability for nonlinear perturbations.Comment: 26 page

Higher-order Continuum Approximation for Rarefied Gases

The Hilbert-Chapman-Enskog expansion of the kinetic equations in mean flight times is believed to be asymptotic rather than convergent. It is therefore inadvisable to use lower order results to simplify the current approximation as is done in the traditional Chapman-Enskog procedure, since that is an iterative method. By avoiding such recycling of lower order results, one obtains macroscopic equations that are asymptotically equivalent to the ones found in the Chapman-Enskog approach. The new equations contain higher order terms that are discarded in the Chapman-Enskog method. These make a significant impact on the results for such problems as ultrasound propagation. In this paper, it is shown that these results turn out well with relatively little complication when the expansions are carried to second order in the mean free time, for the example of the relaxation or BGK model of kinetic theory.Comment: 20 pages, 2 figures, RevTeX 4 macro

Instability and multiple steady states in a meridional-plane model of the thermohaline circulation

A meridional-plane model of the thermohaline circulation with a simple friction force and advection and vertical diffusion of the T-S field has been used to demonstrate the instability and existence of multiple steady states associated with “mixed” T-S boundary conditions (specified temperature, flux condition for salinity). With forcing and geometry symmetric to the equator, the symmetric solution was found to be unstable to infinitesimal perturbations, and an asymmetric pole-to-pole circulation was the end-result in all cases. The structure obtained for the meridional-plane stream function and for the poleward heat flux are in qualitative agreement with those obtained by Bryan (1986). Convective overturning caused by static instability was not found to be essential for the transition to the asymmetric steady state. The study suggests that certain aspects of the ocean circulation, in particular those related to the ocean climate, may be profitably explored by use of two-dimensional, zonally averaged models

Granular mixtures modeled as elastic hard spheres subject to a drag force

Granular gaseous mixtures under rapid flow conditions are usually modeled by a multicomponent system of smooth inelastic hard spheres with constant coefficients of normal restitution. In the low density regime an adequate framework is provided by the set of coupled inelastic Boltzmann equations. Due to the intricacy of the inelastic Boltzmann collision operator, in this paper we propose a simpler model of elastic hard spheres subject to the action of an effective drag force, which mimics the effect of dissipation present in the original granular gas. The Navier--Stokes transport coefficients for a binary mixture are obtained from the model by application of the Chapman--Enskog method. The three coefficients associated with the mass flux are the same as those obtained from the inelastic Boltzmann equation, while the remaining four transport coefficients show a general good agreement, especially in the case of the thermal conductivity. Finally, the approximate decomposition of the inelastic Boltzmann collision operator is exploited to construct a model kinetic equation for granular mixtures as a direct extension of a known kinetic model for elastic collisions.Comment: The title has been changed, 4 figures, and to be published in Phys. Rev.

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

Radiographic viewing conditions at Johannesburg Hospital

Purpose: To measure the luminance level of X-ray viewing boxes and ambient lighting levels in reporting rooms as a quality assurance procedure, and to compare the results with those recommended by the Directorate of Radiatio

Identification and characterization of Rhodopseudomonas palustris TIE-1 hopanoid biosynthesis mutants

Hopanes preserved in both modern and ancient sediments are recognized as the molecular fossils of bacteriohopanepolyols, pentacyclic hopanoid lipids. Based on the phylogenetic distribution of hopanoid production by extant bacteria, hopanes have been used as indicators of specific bacterial groups and/or their metabolisms. However, our ability to interpret them ultimately depends on understanding the physiological roles of hopanoids in modern bacteria. Toward this end, we set out to identify genes required for hopanoid biosynthesis in the anoxygenic phototroph Rhodopseudomonas palustris TIE-1 to enable selective control of hopanoid production. We attempted to delete 17 genes within a putative hopanoid biosynthetic gene cluster to determine their role, if any, in hopanoid biosynthesis. Two genes, hpnH and hpnG, are required to produce both bacteriohopanetetrol and aminobacteriohopanetriol, whereas a third gene, hpnO, is required only for aminobacteriohopanetriol production. None of the genes in this cluster are required to exclusively synthesize bacteriohopanetetrol, indicating that at least one other hopanoid biosynthesis gene is located elsewhere on the chromosome. Physiological studies with the different deletion mutants demonstrated that unmethylated and C_30 hopanoids are sufficient to maintain cytoplasmic but not outer membrane integrity. These results imply that hopanoid modifications, including methylation of the A-ring and the addition of a polar head group, may have biologic functions beyond playing a role in membrane permeability

Causal Relativistic Fluid Dynamics

We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and avoiding the iterative steps of the conventional Chapman-Enskog --- CE---method, we are able to derive causal equations in the first order of the expansion in terms of the mean flight time of the particles. This is in contrast to what is found using the CE approach. We illustrate the general results with the example of a gas of identical ultrarelativistic particles such as photons under the assumptions of homogeneity and isotropy. When we couple the fluid dynamical equations to Einstein's equation we find, in addition to the geometry-driven expanding solution of the FRW model, a second, matter-driven nonequilibrium solution to the equations. In only the second solution, entropy is produced at a significant rate.Comment: 23 pages (CQG, in press