With velocity correlation measurements

Mayevskii, N.V. (1823—1892), eminent Russian ballistician and originator of the science of Exterior Ballistics. He was equally known for work in the field of Interior Ballistics. In 1856 he designed a method of measuring the pressures in various sections of a gun barrel on firing. In 1867 he conducted expts to detn projectile velocity and correlated press with velocity Refs 1) Hayes, Elements of Ordnance , J. Wiley, NY, 437 (1938) 2) A.D. Blinov, Kurs-... 

Radial velocities were measured by cross-correlation, using a synthetic spectrum as template. Individual spectra were shifted to rest wavelength and coadded. Effective temperatures were derived from the (V — I)o colours by means of the Alonso calibration [8], We assumed log g = 2.0 for all stars (estimated from isochrones) and with these parameters we fed the spectra to our automatic procedure for the determination of abundances [9], We found that the S/N ratio was too low to be able to determine reliably the microturbulent velocities, the weak Fe I lines could not be measured on many spectra. This resulted in a marked dependence of derived abundances on microturbulent velocities. It is well known that microturbulence is not a truly independent parameter but correlates with surface gravity and, more mildly also with effective temperature. By considering the large sample of stars studied by [10] one can be convinced that for all stars with 1.5 < logg < 3.0 (20 stars) there is no marked dependence from either Tefi or log g, and the mean value of the microturbulent velocity is 1.6 kms 1. For this reason we fixed the microturbulent velocity at 1.6 kms-1. 

Since the complications due to solvent structure have already been discussed, the remainder of this chapter is mainly devoted to a discussion of the complications introduced into the theory of reaction rates when the collision of solvent molecules does not lead to a complete loss of memory of the molecules about their former velocity. Nevertheless, while such effects are undoubtedly important over some time scale, the differences noted by Kapral and co-workers [37, 285, 286] between the rate kernel for reaction estimated from the diffusion and reaction Green s function and their extended analysis were rather small over times of 10 ps or more (see Chap. 8, Sect. 3.3 and Fig. 40). At this stage, it is a moot point whether the correlation of solvent velocity before collision with that after collision has a significant and experimentally measurable effect on the rate of reaction. The time scale of the loss of velocity correlation is typically less than 1 ps, while even rapid recombination of radicals formed in close proximity to each other occurs over times of 10 ps or more (see Chap. 6, Sect. 3.3). 

Velocity mapping has been employed in studies of 02 photophysics taking place at the one-photon [64,65], two-photon [66], and higher photon [24,25] levels. A short summary of the studies of one-photon dissociation that illustrates the importance of three-vector correlation measurements in photofragmentation of molecular oxygen will be given. Processes resulting from absorption of three or more photons will be described in more detail here since they have aspects in common with the D2 studies. 

The most convenient of these methods is viscosity measurement of a liquid in which particles coated with a polymer are dispersed, or measurement of the flow rate of a liquid through a capillary coated with a polymer. Measurement of diffusion coefficients by photon correlation spectroscopy as well as measurement of sedimentation velocity have also been used. Hydrodynamically estimated thicknesses are usually considered to represent the correct thicknesses of the adsorbed polymer layers, but it is worth noting that recent theoretical calculations52, have shown that the hydrodynamic thickness is much greater than the average thickness of loops. 

Earlier studies (ref. 440-442) with ordinary air microbubbles (without any synthetic surfactant coating) have already shown that echocardiographic contrast produced by microbubbles is useful in the qualitative analysis of blood flow and valvular regurgitation. In addition, quantitative studies (ref. 440) have shown a correlation between individual contrast trajectories on M-mode echocardiography and invasive velocity measurements in human beings. Meltzer et al. (ref. 441) have shown that velocities derived from the slopes of contrast trajectories seen on M-mode echocardiography correlate with simultaneous velocities obtained by Doppler techniques. (This correlation is expected because both measures represent the same projection of the microbubble velocity vector, that is, in the direction of the sound beam.) More detailed studies (ref. 442) confirmed that microbubble velocity obtained from either Doppler echocardiography or M-mode contrast trajectory slope analysis correlates well with actual (Doppler-measured) red blood cell velocity. Thus, these early studies have shown that microbubbles travel with intracardiac velocities similar to those of red blood cells. 

Nerve conduction velocities were measured in 55 employees of a 2,4,5-T and 2,4-D manufacturing facility in Jacksonville, Arkansas (Singer et al. 1982). Statistically significant decreases in median motor nerve and sural nerve conduction velocities were observed, as compared to a control group of workers not exposed to phenoxy herbicides. No effect on median sensory nerve conduction velocity was found. Sural nerve conduction velocity was significantly inversely correlated with duration of employment. 

Also described in Ref. k is a new optical layout for LV data acquisition which permits a significant increase in the overlap between the Raman and LV probe test volumes. The worth of the various correlations of density and temperature with velocity is critically dependent upon the accuracy of this overlap at all flame measurement positions. Thus, one must either lock the Raman and LV probes together in a precise but movable fashion -a rather difficult procedure for the precision required for bench scale" laboratory flames - or else translate the flame. 

The effects of liquid velocity (at least at low velocities), direction of flow and liquid properties are only minor for Newtonian fluids. Correlations on gas-liquid columns are given by Joshi [63], Field and Davidson [64] measured the dispersion in a large industrial column (de - 3.2 m, H — 19 m) and found agreement with the correlations of Dcckwer et al. [65] and Joshi [63] (Tabic 3). The influence of particles can be expected to be small, at least for low concentrations and small particles. This is confirmed by the early experiments of Kato et al. [15, 69], For particle sizes ranging from 63... 

Das and Bhattacharjee236 derive the frequency and shear dependent viscosity of a simple fluid at the critical point and find good agreement with recent experimental measurements of Berg et al.237 Ernst238 calculates universal power law tails for single and multi-particle time correlation functions and finds that the collisional transfer component of the stress autocorrelation function in a classical dense fluid has the same long-time behaviour as the velocity autocorrelation function for the Lorentz gas, i.e. 

In the case of microelectrophoresis, the migration of the particles is determined optically. The velocity is measured by timing individual particles between marks on a grid placed in the microscope eyepiece. The sample has to be highly diluted, so that individual particles can be observed. Progress in microscopy and the combination with photon correlation spectroscopy opened the possibility for determining particles in the range between 3 nm and 5 m [3],... 

In principle, the ultrasonic techniques described for solid-liquid flow measurement can be applied to measure air flow rate and particle velocity. Direct measurement of air flow rate by measuring upstream and downstream transit times has been demonstrated. But, the Doppler and cross-correlation techniques have never been applied to solid/gas flow because the attenuation of ultrasound in the air is high. Recent developments have shown that high-frequency (0.5-MHz) air-coupled transducers can be built and 0.5-MI Iz ultrasound can be transmitted through air for a distance of at least 1 in. Thus, the cross-correlation technique should be applicable to monitoring of solid/gas flow. Here, we present a new cross-correlation technique that does not require transmission of ultrasonic waves through the solid/gas flow. The new technique detects chiefly the noise that interacts with the acoustic field established within the pipe wall. Because noise may be related to particle concentration, as we discussed earlier, the noise-modulated sound field in the pipe wall may contain flow information that is related to the variation in particle concentration. Therefore, crosscorrelation of the noise modulation may yield a velocity-dependent correlation function. 

Once the optical constant was known, the turbidity of the flocculated suspension calculated from Equation 11, using the known particle size distribution, could be compared with the experimentally measured turbidity. Correlations were made between particle size distributions and turbidity readings as the PEI molecular weight and dose were varied. The velocity gradient in the stirrer-reactor was held constant at G = 20 sec Other experiments indicate that the influence of varying the velocity gradient in the range G = 20 to 60 sec" on either turbidity or particle size distribution was minor. 

Small amounts of surface damage are found to produce a marked change in the most probable value of the static friction of monofilament contacts. This frictional force or critical junction rupture stress decreases with time often in a linear manner. The rate of change is a function of the normal load and becomes pronounced above a critical load which is about one tenth of the calculated plastic flow stress in normal loading. There is an empirical correlation between this rate of friction change and the extent of microslip detected in the contact prior to the initiation of the rapid slip phase. At a constant normal load the observed rate increases with velocity. It is not yet possible to identify the processes responsible for the type of damage produced in these fibre systems but it has been demonstrated that frictional measurements can provide a very sensitive means of detecting low levels of wear which may ultimately lead to a severe deterioration in physical properties. 

A reference beam with forward scatter method has been used with a TPD rotating grating preshift and tracking system ( 6) for the 16.4 mm tube. An average volt meter and a correlator HP 3720 with a spectrum analyser were used to interpret the tracker output. Complementary velocity field measurements were carried out in a 44 mm diameter tube. 

The parameter reflects interactions of the cation-constituent with the solvent and with itself. 1 likewise for the anion-constituent, while 1 is a measure of the degree of coupling between the motions of cation- and anion-constituent. The 1 approach has been most actively fostered by Don Miller (TtO 111. 115). An alternative method of representation, introduced by Gerhard Hertz (116.1171, is based on velocity correlation coefficients. There are six of these for a binary electrolyte with self-diffusion coefficients being required to evaluate them. Sets of vcc values have recently been published for concentrated solutions of electrolytes which exhibit strong complexation like Cdl (118). The main problem in calculating these turned out to be a deficiency in suitable transference number information ... 

Figure 11 Comparison of predicted elutriation rate constants with measurements by Colakyan and Levenspiel (1984), Choi et al. (1998), and George and Grace (1981). Sand, =90 pm, for correlation 13 D = 0.6 m was assumed, and the terminal velocity was calculated with the correlation for the drag coefficient by Kaskas and Brauer as cited by Brauer (1971). The numbers denote the various correlations in Table 1. 

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