Eccentricity effects on acoustic radiation from a spherical source suspended within a thermoviscous fluid sphere.

Acoustic radiation from a spherical source undergoing angularly periodic axisymmetric harmonic surface vibrations while eccentrically suspended within a thermoviscous fluid sphere, which is immersed in a viscous thermally conducting unbounded fluid medium, is analyzed in an exact fashion. The formulation uses the appropriate wave-harmonic field expansions along with the translational addition theorem for spherical wave functions and the relevant boundary conditions to develop a closed-form solution in form of infinite series. The analytical results are illustrated with a numerical example in which the vibrating source is eccentrically positioned within a chemical fluid sphere submerged in water. The modal acoustic radiation impedance load on the source and the radiated far-field pressure are evaluated and discussed for representative values of the parameters characterizing the system. The proposed model can lead to a better understanding of dynamic response of an underwater acoustic lens. It is equally applicable in miniature transducer analysis and design with applications in medical ultrasonics.

On the diffraction of acoustic waves by a quarter-plane

This paper follows the work of A.V. Shanin on diffraction by an ideal quarter-plane. Shanin's theory, based on embedding formulae, the acoustic uniqueness theorem and spherical edge Green's functions, leads to three modified Smyshlyaev formulae, which partially solve the far-field problem of scattering of an incident plane wave by a quarter-plane in the Dirichlet case. In this paper, we present similar formulae in the Neumann case, and describe a numerical method allowing a fast computation of the diffraction coefficient using Shanin's third modified Smyshlyaev formula. The method requires knowledge of the eigenvalues of the Laplace-Beltrami operator on the unit sphere with a cut, and we also describe a way of computing these eigenvalues. Numerical results are given for different directions of incident plane wave in the Dirichlet and the Neumann cases, emphasising the superiority of the third modified Smyshlyaev formula over the other two. © 2011 Elsevier B.V.

Imaging the femoral cortex: thickness, density and mass from clinical CT.

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm(2)) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex.

Construction of nonparametric Bayesian models from parametric Bayes equations

We consider the general problem of constructing nonparametric Bayesian models on infinite-dimensional random objects, such as functions, infinite graphs or infinite permutations. The problem has generated much interest in machine learning, where it is treated heuristically, but has not been studied in full generality in non-parametric Bayesian statistics, which tends to focus on models over probability distributions. Our approach applies a standard tool of stochastic process theory, the construction of stochastic processes from their finite-dimensional marginal distributions. The main contribution of the paper is a generalization of the classic Kolmogorov extension theorem to conditional probabilities. This extension allows a rigorous construction of nonparametric Bayesian models from systems of finite-dimensional, parametric Bayes equations. Using this approach, we show (i) how existence of a conjugate posterior for the nonparametric model can be guaranteed by choosing conjugate finite-dimensional models in the construction, (ii) how the mapping to the posterior parameters of the nonparametric model can be explicitly determined, and (iii) that the construction of conjugate models in essence requires the finite-dimensional models to be in the exponential family. As an application of our constructive framework, we derive a model on infinite permutations, the nonparametric Bayesian analogue of a model recently proposed for the analysis of rank data.

The deposition of small particles from a turbulent air flow in a curved duct

The paper describes an experimental and theoretical study of the deposition of small spherical particles from a turbulent air flow in a curved duct. The objective was to investigate the interaction between the streamline curvature of the primary flow and the turbulent deposition mechanisms of diffusion and turbophoresis. The experiments were conducted with particles of uranine (used as a fluorescent tracer) produced by an aerosol generator. The particles were entrained in an air flow which passed vertically downwards through a long straight channel of rectangular cross-section leading to a 90° bend. The inside surfaces of the channel and bend were covered with tape to collect the deposited particles. Following a test run the tape was removed in sections, the uranine was dissolved in sodium hydroxide solution and the deposition rates established by measuring the uranine concentration with a luminescence spectrometer. The experimental results were compared with calculations of particle deposition in a curved duct using a computer program that solved the ensemble-averaged particle mass and momentum conservation equations. A particle density-weighted averaging procedure was used and the equations were expressed in terms of the particle convective, rather than total, velocity. This approach provided a simpler formulation of the particle turbulence correlations generated by the averaging process. The computer program was used to investigate the distance required to achieve a fully-developed particle flow in the straight entry channel as well as the variation of the deposition rate around the bend. The simulations showed good agreement with the experimental results. © 2012 Elsevier Ltd.

Imaging the femoral cortex: Thickness, density and mass from clinical CT

There is growing evidence that focal thinning of cortical bone in the proximal femur may predispose a hip to fracture. Detecting such defects in clinical CT is challenging, since cortices may be significantly thinner than the imaging system's point spread function. We recently proposed a model-fitting technique to measure sub-millimetre cortices, an ill-posed problem which was regularized by assuming a specific, fixed value for the cortical density. In this paper, we develop the work further by proposing and evaluating a more rigorous method for estimating the constant cortical density, and extend the paradigm to encompass the mapping of cortical mass (mineral mg/cm 2) in addition to thickness. Density, thickness and mass estimates are evaluated on sixteen cadaveric femurs, with high resolution measurements from a micro-CT scanner providing the gold standard. The results demonstrate robust, accurate measurement of peak cortical density and cortical mass. Cortical thickness errors are confined to regions of thin cortex and are bounded by the extent to which the local density deviates from the peak, averaging 20% for 0.5mm cortex. © 2012 Elsevier B.V.

Interpreting the input admittance of violins and guitars

The most widespread vibration measurement on musical instrument bodies is of the point mobility at the bridge. Analysis of such measurements is presented, with a view to assessing what range of information could feasibly be extracted from the corpus of data. Analysis approaches include (1) pole-residue extraction; (2) damping trend analysis based on time decay information; (3) statistical estimates based on SEA power-balance and variance theory. Comparative results are shown for some key quantities. Damping trends with frequency are shown to have unexpectedly different forms for violins and for guitars. Linear averaging to estimate the "direct field" component gives a simple and clear visualisation of any local resonance behaviour near the bridge, such as the "bridge hill", and reveals some violins that show a double hill, while viols show only weak hills, and guitars none at all. © S. Hirzel Verlag · EAA.

Effects of multi-scattering on the performance of a single-beam acoustic manipulation device.

The effects of multiple scattering on acoustic manipulation of spherical particles using helicoidal Bessel-beams are discussed. A closed-form analytical solution is developed to calculate the acoustic radiation force resulting from a Bessel-beam on an acoustically reflective sphere, in the presence of an adjacent spherical particle, immersed in an unbounded fluid medium. The solution is based on the standard Fourier decomposition method and the effect of multi-scattering is taken into account using the addition theorem for spherical coordinates. Of particular interest here is the investigation of the effects of multiple scattering on the emergence of negative axial forces. To investigate the effects, the radiation force applied on the target particle resulting from a helicoidal Bessel-beam of different azimuthal indexes (m = 1 to 4), at different conical angles, is computed. Results are presented for soft and rigid spheres of various sizes, separated by a finite distance. Results have shown that the emergence of negative force regions is very sensitive to the level of cross-scattering between the particles. It has also been shown that in multiple scattering media, the negative axial force may occur at much smaller conical angles than previously reported for single particles, and that acoustic manipulation of soft spheres in such media may also become possible.

Decentralised minimal-time dynamic consensus

This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis. © 2012 AACC American Automatic Control Council).

RFID Tag Location Systems

We describe a methods of locating an RFID tag. One method comprises: transmitting tag location signals from a plurality of different transmit antennas, wherein said antennas are spaced apart by more than a near field limit distance at a frequency of a said signal; receiving a corresponding plurality of receiving return signals from said tag; and processing said tag return signals to determine a range to said tag; wherein said transmitting comprises transmitting at a plurality of different frequencies; wherein said processing comprises determining a phase difference at said plurality of different frequencies to determine said range, and wherein said determining of said phase difference determines a phase difference between either i) two or more of said transmit signals resulting in a maxima in the returned signal RSSI or ii) a first transmit signal and its corresponding return signal; and wherein said determining of said range to said tag uses said return signals weighted responsive to a respective received signal strength of the return signal. Further data which may be used for averaging may be generated by using the above techniques along with changes in the polarisation state of the transmit and receive antennas and/or physical reconfiguration of the antennas (e.g. switch the transmit and receive elements).

A neurophysiologically plausible population code model for feature integration explains visual crowding.

An object in the peripheral visual field is more difficult to recognize when surrounded by other objects. This phenomenon is called "crowding". Crowding places a fundamental constraint on human vision that limits performance on numerous tasks. It has been suggested that crowding results from spatial feature integration necessary for object recognition. However, in the absence of convincing models, this theory has remained controversial. Here, we present a quantitative and physiologically plausible model for spatial integration of orientation signals, based on the principles of population coding. Using simulations, we demonstrate that this model coherently accounts for fundamental properties of crowding, including critical spacing, "compulsory averaging", and a foveal-peripheral anisotropy. Moreover, we show that the model predicts increased responses to correlated visual stimuli. Altogether, these results suggest that crowding has little immediate bearing on object recognition but is a by-product of a general, elementary integration mechanism in early vision aimed at improving signal quality.

Lift and the leading edge vortex

Leading edge vortices are considered to be important in generating the high lift coefficients observed in insect flight and may therefore be relevant to micro-air vehicles. A potential flow model of an impulsively started flat plate, featuring a leading edge vortex (LEV) and a trailing edge vortex (TEV) is fitted to experimental data in order to provide insight into the mechanisms that influence the convection of the LEV and to study how the LEV contributes to lift. The potential flow model fits the experimental data best with no bound circulation, which is in accordance with Kelvin's circulation theorem. The lift-to-drag ratio is well approximated by the function 'cot α' for α > 15°, which supports the tentative conclusion that shortly after an impulsive start, at post-stall angles of attack, lift is caused non-circulatory forces and by the action of the LEV as opposed to bound circulation. Copyright © 2012 by C. W. Pitt Ford.

Closely correlating lower and upper bound plastic analysis of real slabs

An engineer assessing the load-carrying capacity of an existing reinforced concrete slab is likely to use elastic analysis to check the load at which the structure might be expected to fail in flexure or in shear. In practice, many reinforced concrete slabs are highly ductile in flexure, so an elastic analysis greatly underestimates the loads at which they fail in this mode. The use of conservative elastic analysis has led engineers to incorrectly condemn many slabs and therefore to specify unnecessary and wasteful flexural strengthening or replacement. The lower bound theorem is based on the same principles as the upper bound theorem used in yield line analysis, but any solution that rigorously satisfies the lower bound theorem is guaranteed to be a safe underestimate of the collapse load. Jackson presented a rigorous lower bound method that obtains very accurate results for complex real slabs.

Lift and the leading-edge vortex

Flapping wings often feature a leading-edge vortex (LEV) that is thought to enhance the lift generated by the wing. Here the lift on a wing featuring a leading-edge vortex is considered by performing experiments on a translating flat-plate aerofoil that is accelerated from rest in a water towing tank at a fixed angle of attack of 15°. The unsteady flow is investigated with dye flow visualization, particle image velocimetry (PIV) and force measurements. Leading-and trailing-edge vortex circulation and position are calculated directly from the velocity vectors obtained using PIV. In order to determine the most appropriate value of bound circulation, a two-dimensional potential flow model is employed and flow fields are calculated for a range of values of bound circulation. In this way, the value of bound circulation is selected to give the best fit between the experimental velocity field and the potential flow field. Early in the trajectory, the value of bound circulation calculated using this potential flow method is in accordance with Kelvin's circulation theorem, but differs from the values predicted by Wagner's growth of bound circulation and the Kutta condition. Later the Kutta condition is established but the bound circulation remains small; most of the circulation is contained instead in the LEVs. The growth of wake circulation can be approximated by Wagner's circulation curve. Superimposing the non-circulatory lift, approximated from the potential flow model, and Wagner's lift curve gives a first-order approximation of the measured lift. Lift is generated by inertial effects and the slow buildup of circulation, which is contained in shed vortices rather than bound circulation. © 2013 Cambridge University Press.

A six sensor method for measuring acoustic properties in ducts.

An accurate description of sound propagation in a duct is important to obtain the sound power radiating from a source in both near and far fields. A technique has been developed and applied to decompose higher-order modes of sound emitted into a duct. Traditional experiments and theory based on two-sensor methods are limited to the plane-wave contribution to the sound field at low frequency. Due to the increase in independent measurements required, a computational method has been developed to simulate sensitivities of real measurements (e.g., noise) and optimize the set-up. An experimental rig has been constructed to decompose the first two modes using six independent measurements from surface, flush-mounted microphones. Experiments were initially performed using a loudspeaker as the source for validation. Subsequently, the sound emitted by a mixed-flow fan has been investigated and compared to measurements made in accordance with the internationally standardized in-duct fan measurement method. This method utilizes large anechoic terminations and a procedure involving averaging over measurements in space and time to account for the contribution from higher-order modes. The new method does not require either of these added complications and gives detail about the underlying modal content of the emitted sound.