Fiber-optic vibration sensing of cantilevers immersed in fluids

An all fiber-optical method to monitor densities and viscosities of liquids utilizing a steel cantilever (4 x 0.3 x 0.08 cm3) is presented. The actuation is performed by photothermally heating the cantilever at its base with an intensity-modulated 808 nm diode laser. The cantilever vibrations are picked up by an in-fiber Fabry Perot cavity sensor attached along the length of the cantilever. The fluid properties can be related to the resonance characteristics of the cantilever, e.g. a shift in the resonance frequency corresponds to a change in fluid density, and the width of the resonance peak gives information on the dynamic viscosity after calibration of the system. Aqueous glycerol, sucrose and ethanol samples in the range of 0.79–1.32 gcm−3 (density) and 0.89–702 mPas (viscosity) were used to investigate the limits of the sensor. A good agreement with literature values could be found with an average deviation of around 10 % for the dynamic viscosities, and 5–16 % for the mass densities. A variety of clear and opaque commercial spirits and an unknown viscous sample, e.g. home-made maple syrup, were analyzed and compared to literature values. The unique detection mechanism allows for the characterization of opaque samples and is superior to conventional microcantilever sensors. The method is expected to be beneficial in various industrial sectors such as quality control of food samples.

Shear-free perfect fluids with a γ-law equation of state

 We investigate all shear-free perfect fluid solutions of the Einstein field equations where the pressure and energy density satisfy a (Formula presented.)-law equation of state with (Formula presented.). We prove that such a fluid is either non rotating or non expanding. As a consequence, it follows by combining our result with those of Collins and Wainwright that any such shear-free perfect fluid which models either an expand universe or a collapsing star must in fact be a Friedmann–Robertson–Walker spacetime.

Correcting for bias when estimating the cost of hospital-acquired infection : an analysis of lower respiratory tract infections in non-surgical patients

Hospital acquired infections (HAI) are costly but many are avoidable. Evaluating prevention programmes requires data on their costs and benefits. Estimating the actual costs of HAI (a measure of the cost savings due to prevention) is difficult as HAI changes cost by extending patient length of stay, yet, length of stay is a major risk factor for HAI. This endogeneity bias can confound attempts to measure accurately the cost of HAI. We propose a two-stage instrumental variables estimation strategy that explicitly controls for the endogeneity between risk of HAI and length of stay. We find that a 10% reduction in ex ante risk of HAI results in an expected savings of £693 ($US 984).

A Petrov-Galerkin method for a singularly perturbed ordinary differential equation with non-smooth data

In this paper, a singularly perturbed ordinary differential equation with non-smooth data is considered. The numerical method is generated by means of a Petrov-Galerkin finite element method with the piecewise-exponential test function and the piecewise-linear trial function. At the discontinuous point of the coefficient, a special technique is used. The method is shown to be first-order accurate and singular perturbation parameter uniform convergence. Finally, numerical results are presented, which are in agreement with theoretical results.