Point source approximation

Intensity of Irradiation. As discussed below the ionic sample Sriginates from a small volume with a radius of approximately 1 mm., and one can visualize this volume as a sphere placed on top of the leak, oince the distance from the leak to the ion source (R = 3 cm.) is relatively large, we can use a point-source approximation to obtain j, the... 

If the size of the fault is small with respect to distance between the source and the receiver, the representation theorem can be simplified by introducing the point source approximation ... 

The INPAR method for the inversion of moment tensor adopts a point-source approximation. The retrieval of the six components of the moment tensor by waveform inversion is a nonlinear problem anyway linearity can be preserved in the first step of the inversion by considering different time evolutions for each of the six components of the moment tensor, namely, the moment tensor rate functions (MTRFs, Panza and Sarah 2000). The kth component of displacement at the surface is the convolution product of the MTRFs and (medium) Green s function spatial derivatives (hereafter Green s functions) and, using Einstein summation notation, can be written as... 

The initial direction of transport of pollutants from their source is determined by the wind direction at the source. Air pollutant concentrations from point sources are probably more sensitive to wind direction than any other parameter. If the wind is blowing directly toward a receptor (a location receiving transported pollutants), a shift in direction of as little as 5° (the approximate accuracy of a wind direction measurement) causes concentrations at the receptor to drop about 10% under unstable conditions, about 50% under neutral conditions, and about 90% under stable conditions. The direction of plume transport is very important in source impact assessment where there are sensitive receptors or two or more sources and in trying to assess the performance of a model through comparison of measured air quality with model estimates. 

Prevedouros et al (2006) estimate PFCA point source emissions from fluoropolymer manufacturing to contribute with approximately 60 % to the total PFCAs used. The substance distribution upon entry is 23 % to air, 65% to water and 12 % to soils [Prevedouros et al (2006)]. 

The theoretical analysis by Morton, Taylor and Turner (1956) [2] established approximate similarity solutions for an idealized point source in a uniform and stably stratified atmosphere. 

We will derive the governing equations for a buoyant plume with heat added just at its source, approximated here as a point. For a two-dimensional planar plume, this is a line. Either could ideally represent a cigarette tip, electrical resistor, a small fire or the plume far from a big fire where the details of the source are no longer important. We list the following assumptions ... 

From equation (3.13) we can deduct a rough approximation of the location where maximum ground-level concentration occurs. It is argued that the turbulent diffusion acts more and more on the emitted substances, when the distance from the point source increases therefore the downwind distance dependency of the diffusion coefficients is done afterwards. If we drop this dependency, equation (3.13) leads to xmax=34,4 m for AK=I (curve a) and xmax=87,7 m for AK=V (curve b), what is demonstrated in fig n The interpolated ranges of measured values are lined in. Curve a overestimates the nondimensional concentration maximum, but its location seems to be correct. In the case of curve b the situation is inverted. Curve c is calculated with the data of AK=II. The decay of the nondimensional concentration is predicted well behind the maximum. Curve d is produced with F—12,1, f=0,069, G=0,04 and g=l,088. The ascent of concentration is acceptable, but that is all, because there is no explanation of plausibility how to alter the diffusivity parameters. Therefore it must be our aim to find a suitable correction in connection with the meteorological input data. 

We now make two simplifications. One is that the rate of O2 production is uniform over the curved part of the Pt surface, and we ignore the contribution from the end of the rod because it is small in surface area when compared to the rest of the rod. Second, the rod is permeable to O2, with the same diffusion coefficient as in water because the rod is small with respect to the diffusion length in the volume of the solution for the time scale of motion. With these approximations, the problem can be solved by integrating the contributions of a continuum of point sources spread on the cylindrical Pt surface (Eq. (3))... 

Equation (4.22) is the expression for the mean concentration from a continuous point source of strength q at the origin in an infinite fluid when the standard deviations of plume spread are different in the different coordinate directions and when the slender-plume approximation is invoked. 

Trends in air pollutant concentrations can be predicted with simple empirical models based on atmospheric and laboratoiy data. Concentrations of nonreactive pollutants from point sources can be predicted vfith accuracy well within a factor of 2 predictions are more likely to be too high than too low, especially predictions of concentration peaks. Concentrations of reactive pollutants, such as ozone and other photochemical oxidants, can be predicted reasonably well with photochemical-diffusion models when detailed emission, air quality, and meteorolc c measurements are available most such predictions of air pollution in Los Angeles, California, have been accurate to within approximately 50% for ozone. Detailed performance analyses are found elsewhere in this chapter. 

If the effluent discharge is low, compared with the river discharge, we can approach this effluent as a point source, handled as a Dirac delta. As a first approximation, this is not a bad approach. In fact, we will utilize the solution from Example 2.2. 

This op-amp circuit is a Schmitt Trigger with trigger points at approximately 7.5 V. A sinusoidal voltage source will be used to swing the input from +14 V to -14 V and from -14 V to +14 V a few times. The frequency of the source is 1 Hz. This low frequency is chosen to eliminate the effects of the op-amp slew rate on the Schmitt Trigger performance. If you... 

High-pressure mercury lamps operate at pressures about 10 atmospheres and essentially two types are used in industrial applications. The point source lamp focuses on a small-diameter spot, thus delivering an intense radiation to that spot. The capillary lamp is used for narrow webs up to approximately 20 cm (8 in.) wide.4 They are capable of producing a wider spectrum than the medium-pressure lamps and operate with higher power (150-2880 W/cm). Their disadvantage is a relatively short operating life, typically hundreds of hours. 

The difference in efficiency between the large planar 18-cm.3 Ge(Li) detector and the small round 8-cm.3 Ge(Li) detector depends essentially on their cross-sections since they have approximately the same depletion depths. This is apparent in comparing the peaks from 10 pCi of 137Cs generated by the large and small detectors (Figure 9). The geometry of the aluminum can was determined to be less efficient by approximately a factor of 10 than a disc-mounted point source. 

As in Fig. 11.13, the loop can be represented by an array of point sources each of length R0. Using again the spherical-sink approximation of Fig. 11.126 and recalling that d Rl Ro, the quasi-steady-state solution of the diffusion equation in spherical coordinates for a point source at the origin shows that the vacancy diffusion field around each point source must be of the form... 

This approach was employed, since spectra of single spots on the surface might have local variations in composition which would hinder a comparison of the two samples. The spot size at the focal point was approximately 150 microns in diameter. The instrument was operated in dual-cell mode, with ions detected in the analyzer side immediately after the laser was fired, in order to minimize undesirable ion-molecule reactions which might occur at the higher pressures in the source cell. Both positive and negative ion spectra were collected for each sample. 

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