The Dirichlet Problem for Einstein Metrics on Cohomogeneity One Manifolds

Let $G/H$ be a compact homogeneous space, and let $\hat{g}_0$ and $\hat{g}_1$ be $G$-invariant Riemannian metrics on $G/H$. We consider the problem of finding a $G$-invariant Einstein metric $g$ on the manifold $G/H\times [0,1]$ subject to the constraint that $g$ restricted to $G/H\times \{0\}$ and $G/H\times \{1\}$ coincides with $\hat{g}_0$ and $\hat{g}_1$, respectively. By assuming that the isotropy representation of $G/H$ consists of pairwise inequivalent irreducible summands, we show that we can always find such an Einstein metric.Comment: 16 pages, no figure

Deduction of temperature fluctuations in transient compression wind tunnels using incompressible turbulent flow data

Wind tunnels and other aero-thermal experimental facilities are likely to make a contribution to the optimisation of energy and propulsion systems for the foreseeable future. Short duration wind tunnels such as shock tunnels and gun tunnels rely on a transient compression rocess and are likely to generate significant turbulent fluctuations in the nozzle reservoir region. In the present study, the magnitude of likely stagnation temperature fluctuations in two such facilities is inferred from incompressible temperature fluctuations data obtained by other workers. The friction velocity Reynolds numbers for the gun tunnel and shock tunnel cases considered presently were ReT= 31,579 and 24,975 respectively. The RMS stagnation temperature fluctuations, when averaged over the pipe flow diameter, are estimated to be 15.3 and 291 K for the gun tunnel and shock tunnel cases respectively. The estimated RMS value in the case of the gun tunnel is significantly larger than the experimental value previously measured on the centre line of the gun tunnel nozzle of 2.3 K. The difference observed between the inferred and measured temperature fluctuations in the gun tunnel case may be related to spatial variations in the temperature fluctuations. In the case of the shock tunnel, the magnitude of the fluctuations is demonstrated to be significant for supersonic combustion experiments. The present approach for estimating the magnitude temperature fluctuations should be refined, but more detailed measurements of temperature fluctuations in such facilities are also required

A new internal combustion engine configuration: opposed pistons with crank offset

[Abstract]: Theoretical and experimental performance results for a new internal combustion engine configuration are presented in this paper. The engine is a piston ported, spark ignition petrol engine which consists of two opposed pistons in a single cylinder controlled by two synchronously timed crankshafts at opposite ends of the cylinder. It makes use of crank offset to create the required piston motion aimed at engine efficiency improvements through thermodynamic performance gains. In particular, the engine employs full expansion in which the power stroke displaces a larger volume than the compression stroke, thereby allowing the expanding gas to reach near atmospheric pressure before the exhaust port opens. This allows more work to be done by each thermodynamic cycle. It also features a greater rate of volume change after combustion than a convention 4-stroke engine for the same crank speed. This reduces the time that the temperature difference between the gas and the cylinder is high relative to a conventional engine which in turn, should reduce the heat lost from the combustion products. Thermodynamic and friction modelling of the engine indicated that efficiencies around 38% might be achieved. However, experiments with a prototype engine demonstrated that friction losses in the engine exceeded that predicted in the original modelling

Impact on a water filled cylinder

The computational and experimental results of impact loading a water filled cylinder with a high speed piston are presented. Computational simulation of the impact process is performed by means of DIANA, a commercial finite element software package. In this simulation, water is modeled as a solid with very small shear modulus compared to the bulk modulus of water. The efficiency of the simulated impact is evaluated by the time dependent water pressure in the vicinity of the cylinder. Also, the shock pressure resulting from impact is detected by using a pressure transducer located in the middle of the water tube. Comparison of the computational and experimental results shows that the impact process on a water filled cylinder is well modeled. It is shown that the best way to increase the pressure peaks of the pressure profile curve is to increase the piston’s impact velocity

Eroding ribbon thermocouples: impulse response and transient heat flux analysis

We have investigated a particular type of fast-response surface thermocouple to determine if it is appropriate to use a one dimensional transient heat conduction model to derive the transient surface heat flux from the measurements of surface temperature. With these sensors, low thermal inertia thermocouple junctions are formed near the surface by abrasive wear. Using laser excitation, we obtained the impulse response of these commercially available devices. The response of particular sensors can vary if new junctions are created by abrasive wear. Furthermore, the response of these sensors was found to deviate substantially from the one dimensional model and varied from sensor to sensor. The impulse response was simulated with greater fidelity using a two dimensional finite element model, but three dimensional effects also appear to be significant. The impact of these variations on the derived heat flux is assessed for the case of measurements in an internal combustion engine. When the measured impulse response is used to derive the surface heat flux, the apparent reversal of heat flux during the expansion stroke does not occur

Assessing intonation skills in a tertiary music training programme

[Abstract]: Buttsworth, Fogarty, and Rorke (1993) reported the construction of a battery of tonal tests designed to assess intonation abilities. A subset of the tests in the battery predicted 36 per cent of final scores in an aural training subject in a tertiary music course. In the current study, the original battery of fourteen tests was reduced to six tests and administered three times throughout the academic year to a new sample (N = 87) of tertiary music students. Three research questions were investigated. Firstly, it was hypothesised that tests in the battery would discriminate among the different aural classes at USQ, which were grouped according to ability level. The results from discriminant function analyses provided strong support for this hypothesis. Secondly, it was hypothesised that students should improve their performance on the pitch battery across the three administrations. A repeated measures analysis of variance failed to find evidence of overall improvement. Finally, it was hypothesised that there would be significant differences on the intonation tests between musicians of different instrumental families. Again, no overall differences were found. The results indicated that intonation tests appear to tap an ability that (a) is not significantly modified by training, (b) is more or less the same across different instrument families, and (c) is related to success in music training programmes

The Prescribed Ricci Curvature Problem for Homogeneous Metrics

The prescribed Ricci curvature problem consists in finding a Riemannian metric $g$ on a manifold $M$ such that the Ricci curvature of $g$ equals a given $(0,2)$-tensor field $T$. We survey the recent progress on this problem in the case where $M$ is a homogeneous space.Comment: 16 pages, 2 tables. Version 2: omission in Table 1 corrected; other minor change

A Robust Method for Tuning Photoacoustic Gas Detectors

Detection of gases in industrial contexts is of great importance for ensuring safety in storage and transport, so as to limit atmospheric pollution and precisely control industrial and agricultural processes. Although chemical sensors are in widespread use, solid-state infrared detectors for gas sensing promise numerous advantages over conventional catalytic detectors in terms of sensitivity, calibration requirements, and lifetime. The laser-modulation photoacoustic approach is an alternative. Compared to other approaches, it provides more precise measurements with a stable zero baseline, as well as having significantly less complicated optics than cavity ringdown approaches. One enduring problem, though, is the relatively long time required to make photoacoustic measurements. The key contribution of this paper to the industrial context is twofold: first, we show how a sensitive dual-buffer acoustic resonator may be fabricated using 3D printing, and secondly we describe a method for localizing the peak absorption more rapidly than stepping a laser through the gas absorption profile. Modelling of the proposed approach demonstrates its potential, and the expected results are confirmed using an extensive experimental setup for the detection of methane in air