The Measurement of Fluctuations of Air Speed by the Hot-Wire Anemometer

The hot-wire anemometer suggests itself as a promising method for measuring the fluctuating air velocities found in turbulent flow. The only obstacle is the presence of a lag due to the limited energy input which makes even a fairly small wire incapable of following rapid fluctuations with accuracy. This paper gives the theory of the lag and describes an experimental arrangement for compensating for the lag for frequencies up to 100 or more per second when the amplitude of the fluctuation is not too great. An experimental test of the accuracy of compensation and some results obtained with the apparatus in a wind-tunnel air stream are described. While the apparatus is very bulky in its present form, it is believed possible to develop a more portable arrangement. (author

Effect of Turbulence in Wind-Tunnel Measurements

This paper gives some quantitative measurements of wind tunnel turbulence and its effect on the air resistance of spheres and airship models, measurements made possible by the hot wire anemometer and associated apparatus in its original form was described in Technical Report no. 320 and some modifications are presented in an appendix to the present paper. One important result of the investigation is a curve by means of which measurements of the air resistance of spheres can be interpreted to give the turbulence quantitatively. Another is the definite proof that the discrepancies in the results on the N. P. L. Standard airship models are due mainly to differences in the turbulences of the wind tunnels in which the tests were made. An attempt is made to interpret the observed results in terms of the boundary layer theory and for this purpose a brief account is given of the physical bases of this theory and of conceptions that have been obtained by analogy with the laws of flow in pipes

Diffusion on random site percolation clusters. Theory and NMR microscopy experiments with model objects

Quasi two-dimensional random site percolation model objects were fabricate based on computer generated templates. Samples consisting of two compartments, a reservoir of H$_2$O gel attached to a percolation model object which was initially filled with D$_2$O, were examined with NMR (nuclear magnetic resonance) microscopy for rendering proton spin density maps. The propagating proton/deuteron inter-diffusion profiles were recorded and evaluated with respect to anomalous diffusion parameters. The deviation of the concentration profiles from those expected for unobstructed diffusion directly reflects the anomaly of the propagator for diffusion on a percolation cluster. The fractal dimension of the random walk, $d_w$, evaluated from the diffusion measurements on the one hand and the fractal dimension, $d_f$, deduced from the spin density map of the percolation object on the other permits one to experimentally compare dynamical and static exponents. Approximate calculations of the propagator are given on the basis of the fractional diffusion equation. Furthermore, the ordinary diffusion equation was solved numerically for the corresponding initial and boundary conditions for comparison. The anomalous diffusion constant was evaluated and is compared to the Brownian case. Some ad hoc correction of the propagator is shown to pay tribute to the finiteness of the system. In this way, anomalous solutions of the fractional diffusion equation could experimentally be verified for the first time.Comment: REVTeX, 12 figures in GIF forma

Short-Run Regional Forecasts: Spatial Models through Varying Cross-Sectional and Temporal Dimensions

In any economic analysis, regions or municipalities should not be regarded as isolated spatial units, but rather as highly interrelated small open economies. These spatial interrelations must be considered also when the aim is to forecast economic variables. For example, policy makers need accurate forecasts of the unemployment evolution in order to design short- or long-run local welfare policies. These predictions should then consider the spatial interrelations and dynamics of regional unemployment. In addition, a number of papers have demonstrated the improvement in the reliability of long-run forecasts when spatial dependence is accounted for. We estimate a heterogeneouscoefficients dynamic panel model employing a spatial filter in order to account for spatial heterogeneity and/or spatial autocorrelation in both the levels and the dynamics of unemployment, as well as a spatial vector-autoregressive (SVAR) model. We compare the short-run forecasting performance of these methods, and in particular, we carry out a sensitivity analysis in order to investigate if different number and size of the administrative regions influence their relative forecasting performance. We compute short-run unemployment forecasts in two countries with different administrative territorial divisions and data frequency: Switzerland (26 regions, monthly data for 34 years) and Spain (47 regions, quarterly data for 32 years)

A note on a matrix criterion for unique colorability of a signed graph

A signed graph, S , is colorable if its point set can be partitioned into subsets such that all positive lines join points of the same subset and all negative lines join points of different subsets. S is uniquely colorable if there is only one such partition. Developed in this note is a new matrix, called the type matrix of S , which provides a classification of the way pairs of points are joined in S . Such a classification yields a criterion for colorability and unique colorability.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45725/1/11336_2005_Article_BF02289592.pd

Theory and Validation of Magnetic Resonance Fluid Motion Estimation Using Intensity Flow Data

15 p.Background Motion tracking based on spatial-temporal radio-frequency signals from the pixel representation of magnetic resonance (MR) imaging of a non-stationary fluid is able to provide two dimensional vector field maps. This supports the underlying fundamentals of magnetic resonance fluid motion estimation and generates a new methodology for flow measurement that is based on registration of nuclear signals from moving hydrogen nuclei in fluid. However, there is a need to validate the computational aspect of the approach by using velocity flow field data that we will assume as the true reference information or ground truth. Methodology/Principal Findings In this study, we create flow vectors based on an ideal analytical vortex, and generate artificial signal-motion image data to verify our computational approach. The analytical and computed flow fields are compared to provide an error estimate of our methodology. The comparison shows that the fluid motion estimation approach using simulated MR data is accurate and robust enough for flow field mapping. To verify our methodology, we have tested the computational configuration on magnetic resonance images of cardiac blood and proved that the theory of magnetic resonance fluid motion estimation can be applicable practically. Conclusions/Significance The results of this work will allow us to progress further in the investigation of fluid motion prediction based on imaging modalities that do not require velocity encoding. This article describes a novel theory of motion estimation based on magnetic resonating blood, which may be directly applied to cardiac flow imaging.Kelvin Kian Loong Wong, Richard Malcolm Kelso, Stephen Grant Worthley, Prashanthan Sanders, Jagannath Mazumdar, Derek Abbot