A sufficient condition related to mistaken intuition about adjusted sums-of-squares in linear regression

We consider a misconception common among students of statistics involving "adjusted" and "unadjusted" sums-of-squares. While the presence of misconception has been noted before (e.g. Hamilton (1986)), we argue that it may be related to the language we use in describing the meaning of sums-of-squares. For linear regression with two independent variables, we then present a sufficient condition for SSR( X1 | X2 ) > SSR( X1 ) in terms of the signs of the sample correlations between pairs of predictor and response variables, and note how this sufficient condition may also be related to misconceptions held by some students of statistics. --

Visual attitude orientation and alignment system

Active vehicle optical alignment aid and a passive vehicle three-dimensional alignment target ensure proper orientation and alignment plus control of the closure range and rate between two bodies, one in controlled motion and one at rest

Far Field Deposition Of Scoured Regolith Resulting From Lunar Landings

As a lunar lander approaches a dusty surface, the plume from the descent engine impinges on the ground, entraining loose regolith into a high velocity dust spray. Without the inhibition of a background atmosphere, the entrained regolith can travel many kilometers from the landing site. In this work, we simulate the flow field from the throat of the descent engine nozzle to where the dust grains impact the surface many kilometers away. The near field is either continuum or marginally rarefied and is simulated via a loosely coupled hybrid DSMC - Navier Stokes (DPLR) solver. Regions of two-phase and polydisperse granular flows are solved via DSMC. The far field deposition is obtained by using a staged calculation, where the first stages are in the near field where the flow is quasi-steady and the outer stages are unsteady. A realistic landing trajectory is approximated by a set of discrete hovering altitudes which range from 20m to 3m. The dust and gas motions are fully coupled using an interaction model that conserves mass, momentum, and energy statistically and inelastic collisions between dust particles are also accounted for. Simulations of a 4 engine configuration are also examined, and the erosion rates as well as near field particle fluxes are discussed.Astronom

Variance Reduction For A Discrete Velocity Gas

We extend a variance reduction technique developed by Baker and Hadjiconstantinou [1] to a discrete velocity gas. In our previous work, the collision integral was evaluated by importance sampling of collision partners [2]. Significant computational effort may be wasted by evaluating the collision integral in regions where the flow is in equilibrium. In the current approach, substantial computational savings are obtained by only solving for the deviations from equilibrium. In the near continuum regime, the deviations from equilibrium are small and low noise evaluation of the collision integral can be achieved with very coarse statistical sampling. Spatially homogenous relaxation of the Bobylev-Krook-Wu distribution [3,4], was used as a test case to verify that the method predicts the correct evolution of a highly non-equilibrium distribution to equilibrium. When variance reduction is not used, the noise causes the entropy to undershoot, but the method with variance reduction matches the analytic curve for the same number of collisions. We then extend the work to travelling shock waves and compare the accuracy and computational savings of the variance reduction method to DSMC over Mach numbers ranging from 1.2 to 10.Aerospace Engineering and Engineering Mechanic

Charged Vacuum Bubble Stability

A type of scenario is considered where electrically charged vacuum bubbles, formed from degenerate or nearly degenerate vacuua separated by a thin domain wall, are cosmologically produced due to the breaking of a discrete symmetry, with the bubble charge arising from fermions residing within the domain wall. Stability issues associated with wall tension, fermion gas, and Coulombic effects for such configurations are examined. The stability of a bubble depends upon parameters such as the symmetry breaking scale and the fermion coupling. A dominance of either the Fermi gas or the Coulomb contribution may be realized under certain conditions, depending upon parameter values.Comment: 16 pages,revtex; accepted for publication in Phys.Rev.

Electrically driven convection in a thin annular film undergoing circular Couette flow

We investigate the linear stability of a thin, suspended, annular film of conducting fluid with a voltage difference applied between its inner and outer edges. For a sufficiently large voltage, such a film is unstable to radially-driven electroconvection due to charges which develop on its free surfaces. The film can also be subjected to a Couette shear by rotating its inner edge. This combination is experimentally realized using films of smectic A liquid crystals. In the absence of shear, the convective flow consists of a stationary, azimuthally one-dimensional pattern of symmetric, counter-rotating vortex pairs. When Couette flow is applied, an azimuthally traveling pattern results. When viewed in a co-rotating frame, the traveling pattern consists of pairs of asymmetric vortices. We calculate the neutral stability boundary for arbitrary radius ratio $\alpha$ and Reynolds number ${{\cal R} e}$ of the shear flow, and obtain the critical control parameter ${\cal R}_c (\alpha, {{\cal R} e})$ and the critical azimuthal mode number ${m_c (\alpha, {{\cal R} e})}$. The Couette flow suppresses the onset of electroconvection, so that ${\cal R}_c (\alpha, {{\cal R} e}) > {\cal R}_c (\alpha,0)$. The calculated suppression is compared with experiments performed at $\alpha = 0.56$ and $0 \leq {{\cal R} e} \leq 0.22$.Comment: 17 pages, 2 column with 9 included eps figures. See also http://mobydick.physics.utoronto.c

An experimental and theoretical investigation of deposition patterns from an agricultural airplane

A flight test program has been conducted with a representative agricultural airplane to provide data for validating a computer program model which predicts aerially applied particle deposition. Test procedures and the data from this test are presented and discussed. The computer program features are summarized, and comparisons of predicted and measured particle deposition are presented. Applications of the computer program for spray pattern improvement are illustrated

A sufficient condition related to mistaken intuition about adjusted sums-of-squares in linear regression

We consider a misconception common among students of statistics involving "adjusted" and "unadjusted" sums-of-squares. While the presence of misconception has been noted before (e.g. Hamilton (1986)), we argue that it may be related to the language we use in describing the meaning of sums-of-squares. For linear regression with two independent variables, we then present a sufficient condition for SSR( X1 | X2 ) > SSR( X1 ) in terms of the signs of the sample correlations between pairs of predictor and response variables, and note how this sufficient condition may also be related to misconceptions held by some students of statistics

QSO hosts and environments at z=0.9 to 4.2: JHK images with adaptive optics

We have observed nine QSOs with redshifts 0.85 to 4.16 at near-IR wavelengths with the adaptive optics bonnette of the Canada-France-Hawaii telescope. Exposure times ranged from 1500 to 24000s (mostly near 7000s) in J, H, or K bands, with pixels 0.035 arcsec on the sky. The FWHM of the co-added images at the location of the quasars are typically 0.16 arcsec. Including another QSO published previously, we find associated QSO structure in at least eight of ten objects, including the QSO at z = 4.16. The structures seen in all cases include long faint features which appear to be tidal tails. In four cases we have also resolved the QSO host galaxy, but find them to be smooth and symmetrical: future PSF removal may expand this result. Including one object previously reported, of the nine objects with more extended structure, five are radio-loud, and all but one of these appear to be in a dense small group of compact galaxy companions. The radio-quiet objects do not occupy the same dense environments, as seen in the NIR. In this small sample we do not find any apparent trends of these properties with redshift, over the range 0.8 < z < 2.4. The colors of the host galaxies and companions are consistent with young stellar populations at the QSO redshift. Our observations suggest that adaptive optic observations in the visible region will exhibit luminous signatures of the substantial star-formation activity that must be occurring.Comment: 22 pages including 10 tables, plus 11 figures. To appear in A

Excitation and abundance of C_3 in star forming cores: Herschel/HIFI observations of the sight-lines to W31C and W49N

We present spectrally resolved observations of triatomic carbon (C_3) in several ro-vibrational transitions between the vibrational ground state and the low-energy ν_2 bending mode at frequencies between 1654−1897 GHz along the sight-lines to the submillimeter continuum sources W31C and W49N, using Herschel’s HIFI instrument. We detect C_3 in absorption arising from the warm envelope surrounding the hot core, as indicated by the velocity peak position and shape of the line profile. The sensitivity does not allow to detect C_3 absorption due to diffuse foreground clouds. From the column densities of the rotational levels in the vibrational ground state probed by the absorption we derive a rotation temperature (T_(rot)) of ~50−70 K, which is a good measure of the kinetic temperature of the absorbing gas, as radiative transitions within the vibrational ground state are forbidden. It is also in good agreement with the dust temperatures for W31C and W49N. Applying the partition function correction based on the derived T_(rot), we get column densities N(C_3) ~ 7−9 × 10^(14) cm^(−2) and abundance x(C_3) ~ 10^(−8) with respect to H_2. For W31C, using a radiative transfer model including far-infrared pumping by the dust continuum and a temperature gradient within the source along the line of sight we find that a model with x(C_3) = 10^(−8), T_(kin) = 30−50 K, N(C_3) = 1.5 × 10^(15) cm^(−2) fits the observations reasonably well and provides parameters in very good agreement with the simple excitation analysis