A note on the Kutta condition in Glauert's solution of the thin aerofoil problem

Glauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the rôle of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied. It is shown here that if Glauert's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series. Furthermore, the present method provides a very direct way to construct other, more singular solutions. A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

The role of impulsivity in the aetiology of drug dependence: reward sensitivity versus automaticity

Journal ArticleResearch Support, Non-U.S. Gov'tCopyright © The Author(s) 2011.RATIONALE: Impulsivity has long been known as a risk factor for drug dependence, but the mechanisms underpinning this association are unclear. Impulsivity may confer hypersensitivity to drug reinforcement which establishes higher rates of instrumental drug-seeking and drug-taking behaviour, or may confer a propensity for automatic (non-intentional) control over drug-seeking/taking and thus intransigence to clinical intervention. METHOD: The current study sought to distinguish these two accounts by measuring Barratt Impulsivity and craving to smoke in 100 smokers prior to their completion of an instrumental concurrent choice task for tobacco (to measure the rate of drug-seeking) and an ad libitum smoking test (to measure the rate of drug-taking-number of puffs consumed). RESULTS: The results showed that impulsivity was not associated with higher rates of drug-seeking/taking, but individual differences in smoking uptake and craving were. Rather, nonplanning impulsivity moderated (decreased) the relationship between craving and drug-taking, but not drug-seeking. CONCLUSIONS: These data suggest that whereas the uptake of drug use is mediated by hypervaluation of the drug as an instrumental goal, the orthogonal trait nonplanning impulsivity confers a propensity for automatic control over well-practiced drug-taking behaviour.MR

Search for neutral MSSM Higgs bosons decaying to a pair of tau leptons in pp collisions

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Measurement of top quark–antiquark pair production in association with a W or Z boson in pp collisions at √s=8 TeV

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Measurement of prompt J/ψ pair production in pp collisions at √s = 7 Tev

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Study of hadronic event-shape variables in multijet final states in pp collisions at √s=7 TeV

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Searches for electroweak production of charginos, neutralinos, and sleptons decaying to leptons and W, Z, and Higgs bosons in pp collisions at 8 TeV

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