Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.Comment: 7 pages, 4 figure

On unbounded bodies with finite mass: asymptotic behaviour

There is introduced a class of barotropic equations of state (EOS) which become polytropic of index $n = 5$ at low pressure. One then studies asymptotically flat solutions of the static Einstein equations coupled to perfect fluids having such an EOS. It is shown that such solutions, in the same manner as the vacuum ones, are conformally smooth or analytic at infinity, when the EOS is smooth or analytic, respectively.Comment: 6 page

Improved diamond coring bits developed for dry and chip-flush drilling

Two rotary diamond bit designs, one operating with a chip-flushing fluid, the second including auger section to remove drilled chips, enhance usefulness of tool for exploratory and industrial core-drilling of hard, abrasive mineral deposits and structural masonry

A survey of oscillating flow in Stirling engine heat exchangers

Similarity parameters for characterizing the effect of flow oscillation on wall shear stress, viscous dissipation, pressure drop and heat transfer rates are proposed. They are based on physical agruments and are derived by normalizing the governing equations. The literature on oscillating duct flows, regenerator and porous media flows is surveyed. The operating characteristics of the heat exchanger of eleven Stirling engines are discribed in terms of the similarity parameters. Previous experimental and analytical results are discussed in terms of these parameters and used to estimate the nature of the oscillating flow under engine operating conditions. The operating points for many of the modern Stirling engines are in or near the laminar to turbulent transition region. In several engines, working fluid does not pass entirely through heat exchangers during a cycle. Questions that need to be addressed by further research are identified

Flat plate collector performance determined experimentally with a solar simulator

The NASA is constructing a new office building at Langley Research Center that will utilize solar energy for heating and cooling. A collector technology program being conducted at Lewis will provide the basis for selecting collectors for use at Langley. The technology program includes testing collectors in an indoor facility under simulated solar radiation. Tests have been conducted on five collectors to date and performance data are presented herein

Bypass transition in boundary layers including curvature and favorable pressure gradient effects

Recent studies of 2-D boundary layers undergoing bypass transition were reviewed. Bypass transition is characterized by the sudden appearance of turbulent spots in boundary layer without first the regular, observable growth of disturbances predicted by linear stability theory. There are no standard criteria or parameters for defining bypass transition, but it is known to be the mode of transition when the flow is disturbed by perturbations of sufficient amplitude

Current-induced metallic behavior in Pr0.5_{0.5}Ca0.5_{0.5}MnO3_3 thin films: competition between Joule heating and nonlinear conduction mechanism

Thin films of Pr0.5Ca0.5MnO3 manganites exhibiting charge/orbital-ordered properties with colossal magnetoresistance have been synthesized by the pulsed laser deposition technique on both (100)-SrTiO3 and (100)-LaAlO3 substrates. The effects of current-induced metallic-behavior of the films are investigated as a function of the temperature and the magnetic field. Calculations based on a heat transfer model across the substrate, and our resistivity measurements reveal effects of Joule heating on charge transport over certain ranges of temperatures and magnetic fields. Our results also indicate that a nonlinear conduction, which cannot be explained by homogeneous Joule heating of the film, is observed when the material is less resistive (10-2 W.cm). The origin of this behavior is explained with a model based on local thermal instabilities associated with phase-separation mechanism and a change in the long range charge-ordered state.Comment: To be published in Phys. Rev.

Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Minimal data at a given point of space for solutions to certain geometric systems

We consider a geometrical system of equations for a three dimensional Riemannian manifold. This system of equations has been constructed as to include several physically interesting systems of equations, such as the stationary Einstein vacuum field equations or harmonic maps coupled to gravity in three dimensions. We give a characterization of its solutions in a neighbourhood of a given point through sequences of symmetric trace free tensors (referred to as `null data'). We show that the null data determine a formal expansion of the solution and we obtain necessary and sufficient growth estimates on the null data for the formal expansion to be absolutely convergent in a neighbourhood of the given point. This provides a complete characterization of all the solutions to the given system of equations around that point.Comment: 26 pages, no figure

Turbulent boundary layer heat transfer experiments: Convex curvature effects, including introduction and recovery

Heat transfer rates were measured through turbulent and transitional boundary layers on an isothermal, convexly curved wall and downstream flat plate. The effect of convex curvature on the fully turbulent boundary layer was a reduction of the local Stanton numbers 20-50% below those predicted for a flat wall under the same circumstances. The recovery of the heat transfer rates on the downstream flat wall was extremely slow. After 60 cm of recovery length, the Stanton number was still typically 15-20% below the flat wall predicted value. Various effects important in the modeling of curved flows were studied separately. These are: (1) the effect of initial boundary layer thickness; (2) the effect of freestream velocity; (3) the effect of freestream acceleration; (4) the effect of unheated starting length; and (5) the effect of the maturity of the boundary layer. Regardless of the initial state, curvature eventually forced the boundary layer into an asymptotic curved condition. The slope, minus one, is believed to be significant