Source function

If the light-source function is "tuned" to peak near co = cof i, and if g(co) is much broader (in... 

The main functions of soil [3] within a river basin are its sink and source functions, which can be described by filtering, buffering and transformation activities between the atmosphere and the underground, thus protecting sediments, groundwater and surface water against contamination. 

Consider continuous radiation with specific intensity I incident normally on a uniform slab with a source function 5 = Bv(Tex) unit volume per unit solid angle to the volume absorption coefficient Kp and is equal to the Planck function Bv of an excitation temperature Tcx obtained by force-fitting the ratio of upper to lower state atomic level populations to the Boltzmann formula, Eq. (3.4). For the interstellar medium at optical and UV wavelengths, effectively S = 0. 

A form of the curve of growth more relevant to stellar (as opposed to interstellar) absorption lines is derived from work by E. A. Milne, A. S. Eddington, M. Min-naert, D. H. Menzel and A. Unsold. In the Milne-Eddington model of a stellar photosphere, the continuum source function (equated to the Planck function in the LTE approximation) increases linearly with continuum optical depth rA and there is a selective absorption i]K, in the line, where rj(Av), the ratio of selective to continuous absorption, is a constant independent of depth given by... 

In other cases the scalar field is affected by a source function q(x, y, z) according to... 

The integral true fluorescence intensity is obtained again by Eq. (8.15). Also the partial intensities emerging from the front and back surface are accessible with the Kubelka-Munk formalism in closed analytical form. In order to solve the system of coupled differential equations, the source function... 

Measurements of radionuclides in seawater have been used to study a variety of processes, including ocean mixing, cycling of materials, and carbon flux (by proxy). These measurements provide information on both process rates and mechanisms. Because of the unique and well-understood source functions of these elements, models of radionuclide behavior have often led to new understanding of the behavior of other chemically similar elements in the ocean. 

The rate of heat generation per unit volume, the heat source function, of a sphere is given by... 

Note that the heat source function is proportional to the imaginary... 

Sitarski (1987) computed heat source functions for layered spheres consisting of a core of coal surrounded by a layer of water. One of these source functions is shown in Fig. 24 as a slice through the equatorial plane of the composite sphere. The anisotropy is quite significant with a source spike at the front of the sphere. There is relatively little heat generated in the core, for the electrical field is strongest near the surface. That is quite typical of a strongly absorbing sphere, and Allen and her coworkers showed similar results for a carbonaceous microsphere illuminated by visible and by infrared sources. 

Fig. 24. The heat source function for concentric spheres with an outer diameter of 10.08 laa. The core, consisting of coal, has a diameter of 9.24 pm, and the outer layer is water. The incident wavelength is 1,450 nm. (From Sitarski, 1987.)...

As indicated by Fig. 23 and Fig. 24, the source function can be highly asymmetrical. For the liquid droplet corresponding to Fig. 23, one would expect the internal temperature to be higher near the back and front of the sphere because of the spikes in the source function in those regions. As a result, the evaporation rate should be enhanced at the rear stagnation point and the front of the sphere. To calculate the evaporation rate when internal heating occurs, one must solve the full problem of conduction within the sphere coupled with convective heat and mass transport in the surrounding gas. 

Table III shows that the experimental and predicted evaporation rates are in good agreement at all beam intensities. There is some inconsistency at the highest power levels. It was difficult to maintain the droplet in the center of the laser beam at the highest power level, and the measured evaporation rate is somewhat low as a result of that problem. Additional computations demonstrate that the predicted evaporation rate is quite sensitive to the choice of the imaginary component of N, so the results suggest that this evaporation method is suitable for the determination of the complex refractive index of weakly absorbing liquids. For strong absorbers, the linearizations of the Clausius-Clapeyron equation and of the radiation energy loss term in the interfacial boundary condition may not be valid. In this event, a numerical solution of the governing equations is required. The structure of the source function, however, makes this a rather tedious task.

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