On Affine Normal Forms and a Classification of Homogeneous Surfaces in Affine Three-Space

We classify homogeneous surfaces in real and complex affine three-space. This is achieved by choosing affine coordinates so that the surface is defined by a function whose Taylor series is in a preferred normal form.     

Gas-phase and catalytic combustion in heat-recirculating burners

An experimental study of a spiral counterflow “Swiss roll” burner was conducted, with emphasis on the determination of extinction limits and comparison of results with and without bare-metal Pt catalyst. A wide range of Reynolds numbers (Re) were tested using propane–air mixtures. Both lean and rich extinction limits were extended with the catalyst, though rich limits were extended much further. With the catalyst, combustion could be sustained at Re as low as 1.2 with peak temperatures as low as 350 K. A heat transfer parameter characterizing the thermal performance of both gas-phase and catalytic combustion at all Re was identified. At low Re, the “lean” extinction limit was actually rich of stoichiometric, and rich-limit had equivalence ratios exceeded 40 in some cases. No corresponding behavior was observed without the catalyst. Gas-phase combustion, in general, occurred in a “flameless” mode near the burner center. With or without catalyst, for sufficiently robust conditions (high Re, near-stoichiometric) not requiring heat recirculation, a visible flame would propagate out of the center, but this flame could only be re-centered if the catalyst were present. Gas chromatography indicated that at low Re, even in extremely rich mixtures, CO and non-propane hydrocarbons did not form. For higher Re, where both gas-phase and catalytic combustion could occur, catalytic limits were slightly broader but had much lower limit temperatures. At sufficiently high Re, catalytic and gas-phase limits merged. It is concluded that combustion at low Re in heat-recirculating burners greatly benefits from catalytic combustion with the proper choice of mixtures that are different from those preferred for gas-phase combustion. In particular, the importance of providing a reducing environment for the catalyst to enhance O₂ desorption, especially at low Re where heat losses are severe thus peak temperatures are low, is noted.     

Conformally invariant differential operators on Minkowski space and their curved analogues

This article describes the construction of a natural family of conformally invariant differential operators on a four-dimensional (pseudo-)Riemannian manifold. Included in this family are the usual massless field equations for arbitrary helicity but there are many more besides. The article begins by classifying the invariant operators on flat space. This is a fairly straightforward task in representation theory best solved through the theory of Verma modules. The method generates conformally invariant operators in the curved case by means of Penrose's local twistor transport.S.E.R.C. Advanced Fellow and Flinders University Visiting Research Fellow     

Extreme Value Asymptotics for Multivariate Renewal Processes

For a sequence of partial sums ofd-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for thed-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.     

Experimental comparison of Jψ production by π±, K±, p and p̄ beams at 39.5 GeV/c

Measurements have been made of relative production cross sections of the $\text{J}\text{ψ}$ by π^±, K^±, p and p? at 39.5 GeV/c incident on copper. $\text{J}\text{ψ}$ production rates from π^?, K^? and p? are similar. The $\text{J}\text{ψ}$ relative particle/anti-particle production cross sections for x>0 are $\text{σ(π}{}^{\mathrm{+}}\text{)}\text{σ(π}{}^{\mathrm{?}}\text{)=(0.87±0.14)}$, σ(K⁺)/σ(K^?)=(0.85±0.5) and $\text{σ(}\text{p}\text{)}\text{σ(}\text{p}\text{?}\text{)=(0.15 ±0.08)}$. The small p/p? cross section ratio disagrees with models of J/ψ production by gluon amalgamation.     

Large-eddy simulations of chevron jet flows with noise predictions

Hybrid large-eddy type simulations for chevron nozzle jet flows are performed at Mach 0.9 and Re = 1.03 × 10⁶. Without using any subgrid scale model (SGS), the numerical approach applied in the present study is essentially implicit large-eddy simulation (ILES). However, a Reynolds-averaged Navier–Stokes (RANS) solution is patched into the near wall region. This makes the overall solution strategy hybrid RANS–ILES. The disparate turbulence length scales, implied by these different modeling approaches, are matched using a Hamilton–Jacobi equation. The complex geometry features of the chevron nozzles are fully meshed. With numerical fidelity in mind, high quality, hexahedral multi-block meshes of 12.5 × 10⁶ cells are used. Despite the modest meshes, the novel RANS–ILES approach shows encouraging performance. Computed mean and second-order fluctuating quantities of the turbulent near field compare favorably with measurements. The radiated far-field sound is predicted using the Ffowcs Williams and Hawkings (FW–H) surface integral method. Encouraging agreement of the predicted far-field sound directivity and spectra with measurements is obtained.