Aerodynamic noise from rigid trailing edges with finite porous extensions

This paper investigates the effects of finite flat porous extensions to semi-infinite impermeable flat plates in an attempt to control trailing-edge noise through bio-inspired adaptations. Specifically the problem of sound generated by a gust convecting in uniform mean steady flow scattering off the trailing edge and permeable-impermeable junction is considered. This setup supposes that any realistic trailing-edge adaptation to a blade would be sufficiently small so that the turbulent boundary layer encapsulates both the porous edge and the permeable-impermeable junction, and therefore the interaction of acoustics generated at these two discontinuous boundaries is important. The acoustic problem is tackled analytically through use of the Wiener-Hopf method. A two-dimensional matrix Wiener-Hopf problem arises due to the two interaction points (the trailing edge and the permeable-impermeable junction). This paper discusses a new iterative method for solving this matrix Wiener-Hopf equation which extends to further two-dimensional problems in particular those involving analytic terms that exponentially grow in the upper or lower half planes. This method is an extension of the commonly used "pole removal" technique and avoids the needs for full matrix factorisation. Convergence of this iterative method to an exact solution is shown to be particularly fast when terms neglected in the second step are formally smaller than all other terms retained. The final acoustic solution highlights the effects of the permeable-impermeable junction on the generated noise, in particular how this junction affects the far-field noise generated by high-frequency gusts by creating an interference to typical trailing-edge scattering. This effect results in partially porous plates predicting a lower noise reduction than fully porous plates when compared to fully impermeable plates.Comment: LaTeX, 20 pp., 19 graphics in 6 figure

Generalised Fluctuation Formula

We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.Comment: 10 pages, 5 figures, submitted to Procedings of the 3rd Tohwa University International Conference of Statistical Physics, Nov 8-12, 1999 (AIP Conferences Series

Oil price changes and industrial output in the MENA region: nonlinearities and asymmetries

In this paper, we investigate the nature of asymmetry in the influence of oil price changes on output in six MENA countries. To get more observations for our analysis, we proxy GDP with industrial output and hence our inference is based on a relatively larger sample compared to previous studies. The results that we obtain are interesting and intuitive. First, we find that growth in MENA countries is linked to oil in the sense that it benefits from higher oil prices and it gets hurt by a fall in the oil market. Moreover, there are pronounced short- and long-term asymmetries in the influence of oil on output. In particular, the output is faster to respond to increases in the oil price than it responds to decreases. The long-term influence to a rise in oil is also higher, though it is realized over a longer period. These results are important and can be used to guide policies that are concerned with stabilizing the economies of the MENA region against oil price fluctuations

Terrorism, Dread Risk and Bicycle Accidents

Following the airplane attacks of September 11th, 2001 it is claimed that many Americans, dreading a repeat of these events, drove instead of flying, and that, consequently, there were extra car accidents, increasing the number of fatalities directly caused by the attacks by 1,500. After the Madrid train bombings of March 11th, 2004, Spaniards, like Americans, avoided the attacked mode of travel, but no increase in car travel or fatal accidents resulted. Here we analyze behavioral concomitants of the July 7th 2005 bomb attacks on public transport in London. We find reduced underground train travel and an increase in rates of bicycling and, over the 6 months following the attacks, 214 additional bicyclist road casualties - a 15.4% increase. Nevertheless we found no detectable increase in car accidents. We conclude that, while fear caused by terrorism may initiate potentially dangerous behaviors, understanding the secondary effects of terrorism requires consideration of the environmental variables that enable fear to manifest in dangerous behaviors

An analytic solution for the noise generated by gust-aerofoil interaction for plates with serrated leading edges

This paper presents an analytic solution for the sound generated by an unsteady gust interacting with a semi-infinite flat plate with a serrated leading edge in a background steady uniform flow. Viscous and non-linear effects are neglected. The Wiener-Hopf method is used in conjunction with a non-orthogonal coordinate transformation and separation of variables to permit analytical progress. The solution is obtained in terms of a modal expansion in the spanwise coordinate, however for low- and mid-range incident frequencies only the zeroth order mode is seen to contribute to the far-field acoustics, therefore the far-field noise can be quickly evaluated. The solution gives insight into the potential mechanisms behind the reduction of noise for plates with serrated leading edges compared to those with straight edges, and predicts a logarithmic dependence between the tip-to-root serration height and the decrease of far-field noise. The two mechanisms behind the noise reduction are proposed to be an increased destructive interference in the far field, and a redistribution of acoustic energy from low cuton modes to higher cutoff modes as the tip-to-root serration height is increased. The analytic results show good agreement in comparison with experimental measurements. The results are then compared against numerical predictions for the sound generated by a spanwise invariant line vortex interacting with a flat plate with serrated leading edge. Good agreement is also seen between the analytical and numerical results as frequency and tip-to-root ratio are varied

The seductive allure of technical language and its effect on covid-19 vaccine beliefs and intentions

Previous research has demonstrated a ‘seductive allure’ of technical or reductive language such that bad (e.g., circular) explanations are judged better when irrelevant technical terms are included. We aimed to explore if such an effect was observable in relation to a covid-19 vaccinations and if this subsequently affected behavioural intentions to take up a covid-19 vaccine. Using a between subjects design we presented participants (N=996) with one of four possible types of vignette that explained how covid-19 vaccination and herd immunity works. The explanations varied along two factors: (1) Quality, explanations were either good or bad (i.e., tautological); (2) Language, explanations either contained unnecessary technical language or did not. We measured participants’ evaluation of the explanations and intentions to vaccinate. We demonstrate a ‘seductive allure’ effect of technical language on bad vaccine explanations. However, an opposite ‘repellent disdain’ effect occurred for good explanations which were rated worse when they contained technical language. Moreover, we show that evaluations of explanations influence intentions to vaccinate. We suggest that misinformation that includes technical language could be more detrimental to vaccination rates. Importantly, however, clear explanatory public health information that omits technical language will be more effective in increasing intentions to vaccinate

Applying an iterative method numerically to solve n × n matrix Wiener–Hopf equations with exponential factors

This paper presents a generalization of a recent iterative approach to solving a class of 2 × 2 matrix Wiener–Hopf equations involving exponential factors. We extend the method to square matrices of arbitrary dimension n, as arise in mixed boundary value problems with n junctions. To demonstrate the method, we consider the classical problem of scattering a plane wave by a set of collinear plates. The results are compared to other known methods. We describe an effective implementation using a spectral method to compute the required Cauchy transforms. The approach is ideally suited to obtaining far-field directivity patterns of utility to applications. Convergence in iteration is fastest for large wavenumbers, but remains practical at modest wavenumbers to achieve a high degree of accuracy.This work was supported by EPSRC DTP grant no. EP/N509620/1 (M.J.P.), the Sultan Qaboos Research Fellowship at Corpus Christi College at University of Cambridge (A.V.K.) and by EPSRC early career fellowship grant no. EP/P015980/1 (L.J.A.). The authors thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the WHT programme where some work on this paper was undertaken (EPSRC grant no. EP/R014604/1)