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

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

T-cell intracellular antigens in health and disease

T-cell intracellular antigen 1 (TIA1) and TIA1-related/like protein (TIAR/TIAL1) are 2 proteins discovered in 1991 as components of cytotoxic T lymphocyte granules. They act in the nucleus as regulators of transcription and pre-mRNA splicing. In the cytoplasm, TIA1 and TIAR regulate and/or modulate the location, stability and/or translation of mRNAs. As knowledge of the different genes regulated by these proteins and the cellular/biological programs in which they are involved increases, it is evident that these antigens are key players in human physiology and pathology. This review will discuss the latest developments in the field, with physiopathological relevance, that point to novel roles for these regulators in the molecular and cell biology of higher eukaryotes.Ministry Economic Affairs and Competitiveness through FEDER funds (BFU2008–00354, BFU2011–29653 and BFU2014–57735-R). The CBMSO receives an institutional grant from Fundación Ramón Areces.Peer Reviewe

Photoelectron angular distributions in photodetachment from P-

The angular distributions of electrons ejected in laser photodetachment of the P- ion have been studied in the photon energy range of 0.95-3.28 eV using a photoelectron spectrometer designed to accommodate a source consisting of collinearly overlapping photon and negative ion beams. We observe the value of the asymmetry parameter β starting at zero near the threshold, falling to almost -1 about 0.5 eV above the threshold and eventually rising to a positive value. The experimental data has been fitted to a simplified model of the Cooper-Zare formula which yields a qualitative understanding of the quantum interference between the outgoing s and d waves representing the free electron. The present results are also compared with previous results for other elements involving p-electron photodetachment

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

A Continuum Description of Rarefied Gas Dynamics (I)--- Derivation From Kinetic Theory

We describe an asymptotic procedure for deriving continuum equations from the kinetic theory of a simple gas. As in the works of Hilbert, of Chapman and of Enskog, we expand in the mean flight time of the constituent particles of the gas, but we do not adopt the Chapman-Enskog device of simplifying the formulae at each order by using results from previous orders. In this way, we are able to derive a new set of fluid dynamical equations from kinetic theory, as we illustrate here for the relaxation model for monatomic gases. We obtain a stress tensor that contains a dynamical pressure term (or bulk viscosity) that is process-dependent and our heat current depends on the gradients of both temperature and density. On account of these features, the equations apply to a greater range of Knudsen number (the ratio of mean free path to macroscopic scale) than do the Navier-Stokes equations, as we see in the accompanying paper. In the limit of vanishing Knudsen number, our equations reduce to the usual Navier-Stokes equations with no bulk viscosity.Comment: 16 page