Note on the limits to the local Mach number on an aerofoil in subsonic flow

It has been noted in some experiments that the local Mach number just ahead of a shock wave on an aerofoil in subsonic flow is limited, values of the limit of the order of 1.4 are usually quoted. This note presents two lines of thought indicating how such a limit may arise. The first starts with the observation that the pressure after the shock will not be higher than the rain stream pressure. Fig.1 shows the calculated relation between local Mach number ahead of the shock (M„ 1 ), shock inclination (S), mainstream Mach number (M1) and pressure coefficient just aft of the shock. • (Cp) It is noted that, for given M1 , Cp and .5 ,two shocks are possible in general, a strong one for which Ms , > 1.48, and a weak one for which MS1 < 1.48, and it is argued that the latter is the more likely. The second approach is based on the fact that a relation between stream deflection (8) and Mach number for the flow in the limited supersonics regions on a number of aerofoils has been derived from some. experimental data. Further analysis of experimental data is required before this relation can be accepted as general. If it is accepted, however, then it indicates that the Mach numbers increase above unity for a given deflection is about one-third of that given by simple wave theory (Fig.2). An analysis of the possible deflections on aerofoils of various thicknesses (Fig.3) then indicates that deflections corresponding to local Mach numbers of the order of 1,5 or higher are unlikely except at incidences of the order of5 ° or more, and may then be more likely for thick wings than for thin wings. Flow breakaway will make the attainment of such high local Mach numbers less likely

Extrapolation of lattice QCD results beyond the power-counting regime

Resummation of the chiral expansion is necessary to make accurate contact with current lattice simulation results of full QCD. Resummation techniques including relativistic formulations of chiral effective field theory and finite-range regularization (FRR) techniques are reviewed, with an emphasis on using lattice simulation results to constrain the parameters of the chiral expansion. We illustrate how the chiral extrapolation problem has been solved and use FRR techniques to identify the power-counting regime (PCR) of chiral perturbation theory. To fourth-order in the expansion at the 1% tolerance level, we find 0 \le m_pi \le 0.18 GeV for the PCR, extending only a small distance beyond the physical pion mass.Comment: 12 pages, 5 figures, plenary talk at BARYONS 2004, Paris, Oct. 25-2

Hadron structure on the back of an envelope

In order to remove a little of the mysticism surrounding the issue of strangeness in the nucleon, we present simple, physically transparent estimates of both the strange magnetic moment and charge radius of the proton. Although simple, the estimates are in quite good agreement with sophisticated calculations using the latest input from lattice QCD. We further explore the possible size of systematic uncertainties associated with charge symmetry violation (CSV) in the recent precise determination of the strange magnetic moment of the proton. We find that CSV acts to increase the error estimate by 0.003 \mu_N such that G_M^s = -0.046 +/- 0.022 \mu_N.Comment: 9 pages, 1 figure, Invited talk at First Workshop on Quark-Hadron Duality and the Transition to pQCD, Frascati, June 6-8 200

Chiral extrapolation and physical insights

It has recently been established that finite-range regularisation in chiral effective field theory enables the accurate extrapolation of modern lattice QCD results to the chiral regime. We review some of the highlights of extrapolations of quenched lattice QCD results, including spectroscopy and magnetic moments. The $\Delta$ resonance displays peculiar chiral features in the quenched theory which can be exploited to demonstrate the presence of significant chiral corrections.Comment: 6 pages, 5 figures, presented at LHP2003, Cairns, Australi

Integrability and maximally helicity violating diagrams in n=4 supersymmetric yang-mills theory.

We apply maximally helicity violating (MHV) diagrams to the derivation of the one-loop dilatation operator of N=4 supersymmetric Yang-Mills theory in the SO(6) sector. We find that in this approach the calculation reduces to the evaluation of a single MHV diagram in dimensional regularization. This provides the first application of MHV diagrams to an off-shell quantity. We also discuss other applications of the method and future directions