A generalisation of the Delogne-Kasa method for fitting hyperspheres

In this paper, we examine the problem of fitting a hypersphere to a set of noisy measurements of points on its surface. Our work generalises an estimator of Delogne (Proc. IMEKO-Symp. Microwave Measurements 1972,117-123) which he proposed for circles and which has been shown by Kasa (IEEE Trans. Instrum. Meas. 25, 1976, 8-14) to be convenient for its ease of analysis and computation. We also generalise Chan's 'circular functional relationship' to describe the distribution of points. We derive the Cramer-Rao lower bound (CRLB) under this model and we derive approximations for the mean and variance for fixed sample sizes when the noise variance is small. We perform a statistical analysis of the estimate of the hypersphere's centre. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than M + 1, where M is the dimension of the hypersphere. The variance exists when the number of sample points is greater than M + 2. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the CRLB. We provide simulation results to support our findings.

Bed shear stress measurements in dam break and swash flows

A novel shear plate was used to make direct bed shear stress measurements in laboratory dam break and swash flows on smooth, fixed, impermeable beds. The pressure gradient due to the slope of the fluid free-surface across the plate was measured using pressure transducers. Surface elevation was measured at five locations using acoustic displacement sensors. Flow velocity was measured using an Acoustic-Doppler Velocimeter and calculated using the ANUGA inundation model. The measured bed shear stress at the dam break fluid tip for an initially dry, horizontal bed was close to twice that estimated using steady flow theory. The temporal variation of swash bed shear stress showed a large peak in landward directed stress at the uprush tip, followed by a rapid decay throughout the uprush flow interior. The peak seaward directed stress during the backwash phase was less than half that measured in the uprush. Close to the still water line, in the region of bore collapse and at the time of initial uprush, favourable pressure gradients were measured. In the lower swash region predominately weak adverse pressure gradients were measured.

Turbulent Time and Length Scale Measurements in High-Velocity Open Channel Flows

In high-velocity open channel flows, the measurements of air-water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air-water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8 E+5 to 7.1 E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air-water depth Y90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95 to 0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

Incompatibility of Macroscopic Local Realism with Quantum Mechanics in Measurements with Macroscopic Uncertainties

We show that quantum mechanics predicts a contradiction with local hidden variable theories for photon number measurements which have limited resolving power, to the point of imposing an uncertainty in the photon number result which is macroscopic in absolute terms. We show how this can be interpreted as a failure of a new premise, macroscopic local realism.

Continuous high-frequency turbulence and suspended sediment concentration measurements in an upper estuary

The present study details new turbulence field measurements conducted continuously at high frequency for 50 hours in the upper zone of a small subtropical estuary with semi-diurnal tides. Acoustic Doppler velocimetry was used, and the signal was post-processed thoroughly. The suspended sediment concentration wad further deduced from the acoustic backscatter intensity. The field data set demonstrated some unique flow features of the upstream estuarine zone, including some low-frequency longitudinal oscillations induced by internal and external resonance. A striking feature of the data set is the large fluctuations in all turbulence properties and suspended sediment concentration during the tidal cycle. This feature has been rarely documented.

Detailed Measurements during a Transient Front in a Small Subtropical Estuary

High-resolution measurements of velocity and physio-chemistry were conducted before, during and after the passage of a transient front in a small subtropical system about 2.1 km upstream of the river mouth. Detailed acoustic Doppler velocimetry measurements, conducted continuously at 25 Hz, showed the existence of transverse turbulent shear between 300 s prior to the front passage and 1300 s after. This was associated with an increased level of suspended sediment concentration fluctuations, some transverse shear next to the bed and some surface temperature anomaly.

Turbulence in Hydraulic Jumps: Experimental Measurements

A hydraulic jump is the transition from a supercritical open channel flow to a subcritical regime. It is characterised by a highly turbulent flow with macro-scale vortices, some kinetic energy dissipation and a bubbly two-phase flow structure. New air-water flow measurements were performed in hydraulic jump flows for a range of inflow Froude numbers. The experiments were conducted in a large-size facility using two types of phase-detection intrusive probes: i.e., single-tip and double-tip conductivity probes. These were complemented by some measurements of free-surface fluctuations using ultrasonic displacement meters. The present study was focused on the turbulence characteristics of hydraulic jumps with partially-developed inflow conditions. The void fraction measurements showed the presence of an advective diffusion shear layer in which the void fractions profiles matched closely an analytical solution of the advective diffusion equation for air bubbles. The present results highlighted some influence of the inflow Froude number onto the air bubble entrainment process. At the largest Froude numbers, the advected air bubbles were more thoroughly dispersed vertically, and larger amount of air bubbles were detected in the turbulent shear layer. In the air-water mixing layer, the maximum void fraction and bubble count rate data showed some longitudinal decay function in the flow direction. Such trends were previously reported in the literature. The measurements of interfacial velocity and turbulence level distributions provided new information on the turbulent velocity field in the highly-aerated shear region. The present data suggested some longitudinal decay of the turbulence intensity. The velocity profiles tended to follow a wall jet flow pattern. The air–water turbulent time and length scales were deduced from some auto- and cross-correlation analyses based upon the method of CHANSON (2006,2007). The results provided the integral turbulent time and length scales of the eddy structures advecting the air bubbles in the developing shear layer. The experimental data showed that the auto-correlation time scale Txx was larger than the transverse cross-correlation time scale Txz. The integral turbulence length scale Lxz was a function of the inflow conditions, of the streamwise position (x-x1)/d1 and vertical elevation y/d1. Herein the dimensionless integral turbulent length scale Lxz/d1 was closely related to the inflow depth: i.e., Lxz/d1 = 0.2 to 0.8, with Lxz increasing towards the free-surface. The free-surface fluctuations measurements showed large turbulent fluctuations that reflected the dynamic, unsteady structure of the hydraulic jumps. A linear relationship was found between the normalized maximum free-surface fluctuation and the inflow Froude number.

High-Frequency Turbulence and Sediment Flux Measurements in an Upper Estuarine Zone

In natural estuaries, the predictions of scalar dispersion are rarely predicted accurately because of a lack of fundamental understanding of the turbulence structure in estuaries. Herein detailed turbulence field measurements were conducted continuously at high frequency for 50 hours in the upper zone of a small subtropical estuary with semi-diurnal tides. Acoustic Doppler velocimetry was deemed the most appropriate measurement technique for such shallow water depths (less than 0.4 m at low tides), and a thorough post-processing technique was applied. In addition, some experiments were conducted in laboratory under controlled conditions using water and soil samples collected in the estuary to test the relationship between acoustic backscatter strength and suspended sediment load. A striking feature of the field data set was the large fluctuations in all turbulence characteristics during the tidal cycle, including the suspended sediment flux. This feature was rarely documented.

High-Frequency Suspended Sediment Flux Measurements in a Small Estuary

In small estuaries, the predictions of scalar dispersion can rarely be predicted accurately because of a lack of fundamental understanding of the turbulence structure. Herein detailed turbulence measurements and suspended sediment concentrations were conducted simultaneously and continuously at high-frequency for 50 hours per investigation in a small subtropical estuary with semi-diurnal tides. The data analyses provided an unique characterisation of the turbulent mixing processes and suspended sediment fluxes. The turbulence was neither homogeneous nor isotropic, and it was not a Gaussian process. The integral time scales for turbulence and suspended sediment concentration were about equal during flood tides, but differed significantly during ebb tides. The field experiences showed that the turbulence measurements must be conducted at high-frequency to characterise the small eddies and the viscous dissipation process, while a continuous sampling was necessary to characterise the time-variations of the instantaneous velocity field, Reynolds stress tensor and suspended sediment flux during the tidal cycles.

Effect of temperature and sweating on bioimpedance measurements

The effect of skin temperature and hydration status has been suggested by some researchers as a common cause of variation in bioimpedance measurements of the body. This paper details a simple method of measuring the transverse impedance of the skin. The measured resistance and reactance was found to decrease by 35% and 18% for an increase of 20 degrees C. Similarly a decrease in resistance and reactance of 20% and 25% respectively was detected after hydration of the skin. However, the changes in skin temperature and hydration were found to have no significant effect on the whole body bioimpedance measurements using the standard tetra-polar electrode technique. (C) 1998 Elsevier Science Ltd. All rights reserved.

Contradiction of quantum mechanics with local hidden variables for quadrature phase amplitude measurements

We demonstrate a contradiction of quantum mechanics with local hidden variable theories for continuous quadrature phase amplitude (position and momentum) measurements. For any quantum state, this contradiction is lost for situations where the quadrature phase amplitude results are always macroscopically distinct. We show that for optical realizations of this experiment, where one uses homodyne detection techniques to perform the quadrature phase amplitude measurement, one has an amplification prior to detection, so that macroscopic fields are incident on photodiode detectors. The high efficiencies of such detectors may open a way for a loophole-free test of local hidden variable theories.

Emission and holographic interferometry measurements in a superorbital expansion tube

Free-piston-driven expansion tubes are capable of generating flaw conditions over a wide range of enthalpies ranging from orbital up to superorbital velocities. Initial optical measurements aimed at investigating the flow in such a facility are presented. Emission studies were used to identify impurities in the how and to investigate spectral regions that are accessible by optical techniques. At moderate enthalpies, it was found that significant radiation resulted from metallic contaminants. At high enthalpies, the spectrum consisted of a number of atomic lines together with a broadband background component indicative of the presence of electrons. The presence of this radiation may limit the applicability of optical techniques that require spectral regions free from the influence of atomic transitions or background radiation. Emission spectroscopy (through Stark broadened hydrogen lines) and two-wavelength holographic interferometry were used to measure the electron number density behind a bow shock on a blunt body at conditions where significant ionization was observed. They yielded average concentrations of (3 +/- 1) x 10(17) cm(-3) from the emission measurements and (3.8 +/- 0.6) x 10(17) cm(-3) from the interferometry.

Homodyne measurements on a Bose-Einstein condensate

We investigate a nondestructive measurement technique to monitor Josephson-like oscillations between two spatially separated neutral atom Bose-Einstein condensates. One condensate is placed in an optical cavity, which is strongly driven by a coherent optical field. The cavity output field is monitored using a homodyne detection scheme. The cavity field is well detuned from an atomic resonance, and experiences a dispersive phase shift proportional to the number of atoms in the cavity. The detected current is modulated by the coherent tunneling oscillations of the condensate. Even when there is an equal number of atoms in each well initially, a phase is established by the measurement process and Josephson-like oscillations develop due to measurement backaction noise alone.

Characterizing Greenberger-Horne-Zeilinger correlations in nondegenerate parametric oscillation via phase measurements

We present a potential realization of the Greenberger-Horne-Zeilinger all or nothing contradiction of quantum mechanics with local realism using phase measurement techniques in a simple photon number triplet. Such a triplet could be generated using nondegenerate parametric oscillation. [S0031-9007(98)07671-6].

Measurements on trapped laser-cooled ions using quantum computations

There are some interesting connections between the theory of quantum computation and quantum measurement. As an illustration, we present a scheme in which an ion trap quantum computer can be used to make arbitrarily accurate measurements of the quadrature phase variables for the collective vibrational motion of the ion. We also discuss some more general aspects of quantum computation and measurement in terms of the Feynman-Deutsch principle.