Shock wave structure in highly rarefied flows

The Boltzmann equation is written in terms of two functions associated with the gain and loss of a certain type of molecule due to collisions. Its integral form is then applied to the problem of normal shock structure, and an iteration technique is used to determine the solution. The first approximation to the velocity distribution function of the Chapman-Enskog sequence, which leads to the Navier-Stokes equations, is used to initiate the iteration scheme. Expressions for the distribution function and the flow parameters pertinent to the first iteration are derived and show that the B-G-K model results can be obtained as a special case. This model is found to be valid in the continuum regime only, and is consequently limited to the study of strong shocks. In the present treatment the iteration is carried out on the distribution function and the analysis indicates that the method is equally valid for variations in both Mach and Knudsen numbers. Finally, the results of the first approximation are simplified, and expressed in a form suitable for numerical computation, and the range of their validity is discussed. The method should be equally suitable for other flow problems of linear or nonlinear nature

A non-equilibrium kinetic description of shock wave structure

A formulation for the shock wave structure is devised by viewing the transition as a phenomenon in which non-equilibrium effects play an important role. The essence of the method is the approximation of Boltzmann's equation by a simpler kinetic model. Initially, the distribution function in Boltzmann's collision integral is expressed in terms of a function of deviation from local equilibrium. Then, by suitably transforming the complete collision term, the molecular velocities after collision are eliminated. At this stage the formulation of the method is specialized to hard sphere molecules and the problem of deriving a model equation thus reduces to one of assigning an expression for the deviation function. In the first instance, this function is chosen to be zero and an exploratory model is obtained which, when its variable collision frequency is replaced by its mean value, reduces identically to the Bhatnagar-Gross-Krook model. However, it is found that the exploratory model provides a somewhat crude representation of Boltzmann's equation and is shown to imply a Prandtl number very nearly equal to unity. A more accurate model is then derived by choosing for the deviation function the first order term of Chapman-Enskog’s sequence, leading to the Navier-Stokes equations. Here, the specific form of Boltzmann's collision term is represented more accurately than hitherto and the model is found to possess all the known features of the Boltzmann equation. It is shown that this model contains a description of a gas in non-equilibrium state

Solar system constraints on the Dvali-Gabadadze-Porrati braneworld theory of gravity

A number of proposals have been put forward to account for the observed accelerating expansion of the Universe through modifications of gravity. One specific scenario, Dvali-Gabadadze-Porrati (DGP) gravity, gives rise to a potentially observable anomaly in the solar system: all planets would exhibit a common anomalous precession, dw/dt, in excess of the prediction of General Relativity. We have used the Planetary Ephemeris Program (PEP) along with planetary radar and radio tracking data to set a constraint of |dw/dt| < 0.02 arcseconds per century on the presence of any such common precession. This sensitivity falls short of that needed to detect the estimated universal precession of |dw/dt| = 5e-4 arcseconds per century expected in the DGP scenario. We discuss the fact that ranging data between objects that orbit in a common plane cannot constrain the DGP scenario. It is only through the relative inclinations of the planetary orbital planes that solar system ranging data have sensitivity to the DGP-like effect of universal precession. In addition, we illustrate the importance of performing a numerical evaluation of the sensitivity of the data set and model to any perturbative precession.Comment: 9 pages, 2 figures, accepted for publication in Phys. Rev.

APOLLO: the Apache Point Observatory Lunar Laser-ranging Operation: Instrument Description and First Detections

A next-generation lunar laser ranging apparatus using the 3.5 m telescope at the Apache Point Observatory in southern New Mexico has begun science operation. APOLLO (the Apache Point Observatory Lunar Laser-ranging Operation) has achieved one-millimeter range precision to the moon which should lead to approximately one-order-of-magnitude improvements in the precision of several tests of fundamental properties of gravity. We briefly motivate the scientific goals, and then give a detailed discussion of the APOLLO instrumentation.Comment: 37 pages; 10 figures; 1 table: accepted for publication in PAS

An absolute calibration system for millimeter-accuracy APOLLO measurements

Lunar laser ranging provides a number of leading experimental tests of gravitation -- important in our quest to unify General Relativity and the Standard Model of physics. The Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has for years achieved median range precision at the ~2 mm level. Yet residuals in model-measurement comparisons are an order-of-magnitude larger, raising the question of whether the ranging data are not nearly as accurate as they are precise, or if the models are incomplete or ill-conditioned. This paper describes a new absolute calibration system (ACS) intended both as a tool for exposing and eliminating sources of systematic error, and also as a means to directly calibrate ranging data in-situ. The system consists of a high-repetition-rate (80 MHz) laser emitting short (< 10 ps) pulses that are locked to a cesium clock. In essence, the ACS delivers photons to the APOLLO detector at exquisitely well-defined time intervals as a "truth" input against which APOLLO's timing performance may be judged and corrected. Preliminary analysis indicates no inaccuracies in APOLLO data beyond the ~3 mm level, suggesting that historical APOLLO data are of high quality and motivating continued work on model capabilities. The ACS provides the means to deliver APOLLO data both accurate and precise below the 2 mm level.Comment: 21 pages, 10 figures, submitted to Classical and Quantum Gravit

A map of OMC-1 in CO 9-8

The distribution of 12C16O J=9-8 (1.037 THz) emission has been mapped in OMC-1 at 35 points with 84" resolution. This is the first map of this source in this transition and only the second velocity-resolved ground-based observation of a line in the terahertz frequency band. There is emission present at all points in the map, a region roughly 4' by 6' in size, with peak antenna temperature dropping only near the edges. Away from the Orion KL outflow, the velocity structure suggests that most of the emission comes from the OMC-1 photon-dominated region, with a typical linewidthof 3-6 km/s. Large velocity gradient modeling of the emission in J=9-8 and six lower transitions suggests that the lines originate in regions with temperatures around 120 K and densities of at least 10^(3.5) cm^(-3) near theta^(1) C Ori and at the Orion Bar, and from 70 K gas at around 10^(4) cm^(-3) southeast and west of the bar. These observations are among the first made with the 0.8 m Smithsonian Astrophysical Observatory Receiver Lab Telescope, a new instrument designed to observe at frequencies above 1 THz from an extremely high and dry site in northern Chile.Comment: Minor changes to references, text to match ApJ versio