Relaxation time for the temperature in a dilute binary mixture from classical kinetic theory

The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the hypothesis of partial local equilibrium for both species. Neither a diffusion force nor mass diffusion appears in the system. We also estimate the time in which the temperatures of the components reach the full local equilibrium. In solving the Boltzmann equation, we imposed no assumptions on the collision term. We work out its solution by using the well known Chapman-Enskog method to first order in the gradients. The time in which the temperatures relax is obtained following Landau's original idea. The result is that the relaxation time for the temperatures is much smaller than the characteristic hydrodynamical times but greater than a collisional time. The main conclusion is that there is no need to study binary mixtures with different temperatures when hydrodynamical properties are sought

On the role of the chaotic velocity in relativistic kinetic theory

In this paper we revisit the concept of chaotic velocity within the context of relativistic kinetic theory. Its importance as the key ingredient which allows to clearly distinguish convective and dissipative effects is discussed to some detail. Also, by addressing the case of the two component mixture, the relevance of the barycentric comoving frame is established and thus the convenience for the introduction of peculiar velocities for each species. The fact that the decomposition of molecular velocity in systematic and peculiar components does not alter the covariance of the theory is emphasized. Moreover, we show that within an equivalent decomposition into space-like and time-like tensors, based on a generalization of the relative velocity concept, the Lorentz factor for the chaotic velocity can be expressed explicitly as an invariant quantity. This idea, based on Ellis' theorem, allows to foresee a natural generalization to the general relativistic case.Comment: 12 pages, 2 figure

Entropy Production in Relativistic Binary Mixtures

In this paper we calculate the entropy production of a relativistic binary mixture of inert dilute gases using kinetic theory. For this purpose we use the covariant form of Boltzmann's equation which, when suitably transformed, yields a formal expression for such quantity. Its physical meaning is extracted when the distribution function is expanded in the gradients using the well-known Chapman-Enskog method. Retaining the terms to first order, consistently with Linear Irreversible Thermodynamics we show that indeed, the entropy production can be expressed as a bilinear form of products between the fluxes and their corresponding forces. The implications of this result are thoroughly discussed

On the validity of the Onsager relations in relativistic binary mixtures

In this work we study the properties of a relativistic mixture of two non-reacting dilute species in thermal local equilibrium. Following the conventional ideas in kinetic theory, we use the concept of chaotic velocity. In particular, we address the nature of the density, or pressure gradient term that arises in the solution of the linearized Boltzmann equation in this context. Such effect, also present for the single component problem, has so far not been analyzed from the point of view of the Onsager resciprocity relations. In order to address this matter, we propose two alternatives for the Onsagerian matrix which comply with the corresponding reciprocity relations and also show that, as in the non-relativistic case, the chemical potential is not an adequate thermodynamic force. The implications of both representations are briefly analyzed

Locating the LCROSS Impact Craters

The Lunar CRater Observations and Sensing Satellite (LCROSS) mission impacted a spent Centaur rocket stage into a permanently shadowed region near the lunar south pole. The Sheperding Spacecraft (SSC) separated \sim9 hours before impact and performed a small braking maneuver in order to observe the Centaur impact plume, looking for evidence of water and other volatiles, before impacting itself. This paper describes the registration of imagery of the LCROSS impact region from the mid- and near-infrared cameras onboard the SSC, as well as from the Goldstone radar. We compare the Centaur impact features, positively identified in the first two, and with a consistent feature in the third, which are interpreted as a 20 m diameter crater surrounded by a 160 m diameter ejecta region. The images are registered to Lunar Reconnaisance Orbiter (LRO) topographical data which allows determination of the impact location. This location is compared with the impact location derived from ground-based tracking and propagation of the spacecraft's trajectory and with locations derived from two hybrid imagery/trajectory methods. The four methods give a weighted average Centaur impact location of -84.6796\circ, -48.7093\circ, with a 1{\sigma} un- certainty of 115 m along latitude, and 44 m along longitude, just 146 m from the target impact site. Meanwhile, the trajectory-derived SSC impact location is -84.719\circ, -49.61\circ, with a 1{\sigma} uncertainty of 3 m along the Earth vector and 75 m orthogonal to that, 766 m from the target location and 2.803 km south-west of the Centaur impact. We also detail the Centaur impact angle and SSC instrument pointing errors. Six high-level LCROSS mission requirements are shown to be met by wide margins. We hope that these results facilitate further analyses of the LCROSS experiment data and follow-up observations of the impact region.Comment: Accepted for publication in Space Science Review. 24 pages, 9 figure

Lunar Terrain and Albedo Reconstruction from Apollo Imagery

Generating accurate three dimensional planetary models and albedo maps is becoming increasingly more important as NASA plans more robotics missions to the Moon in the coming years. This paper describes a novel approach for separation of topography and albedo maps from orbital Lunar images. Our method uses an optimal Bayesian correlator to refine the stereo disparity map and generate a set of accurate digital elevation models (DEM). The albedo maps are obtained using a multi-image formation model that relies on the derived DEMs and the Lunar- Lambert reflectance model. The method is demonstrated on a set of high resolution scanned images from the Apollo era missions