Azimuthally symmetric

For the simplest of mirrors, circular apertures, the effects of diffraction cause the diffraction-limited image to be an Airy pattern, and for large distances this pattern falls as 1/0 and will be azimuthally symmetric. 

Figure 7.3 shows the radiated intensity S as a function of the observation angle 0 for a dipole 80 nm from the surface. For simplicity, the azimuthal angle of observation is averaged. (This is equivalent to assuming that the excited dipole distribution is azimuthally symmetric about the surface normal.)... 

It should be noted that for non-isothermal case (and also for isothermal case with autocatalytic kinetics) the local equation may have multiple solutions. When this occurs, the averaged model obtained by the L-S method captures the complete set of solutions of the full CDR equations only within the region of convergence of the local equation. For example, for the wall-catalyzed non-isothermal reaction case, we have shown that the averaged two-mode model can capture only the three azimuthally symmetric solutions of the full CDR equation. The latter has three symmetric solutions (of which two are stable) as... 

Everett, M. E., and A. Schultz, 1996, Geomagnetic induction in a heterogeneous sphere Azimuthally symmetric test computations and the response of an undulating 660-km discontinuity J. Geophys. Res., 101, 2765-2783. 

For numerical computations, an explicit form of the phase function is required. A Legendre polynomial expansion of the phase function is the most common form. For an azimuthally symmetric medium (i.e., one independent of azimuthal angle <(>), the phase function is written as ... 

Isotropic scattering indicates that the radiant energy incident on a volume element is uniformly distributed to all directions. For an isotropically scattering medium, all a, coefficients of the phase function are zero, except a0. If only a0 and the first coefficient a, are considered, then one obtains the linearly anisotropic phase function, which means that the phase function is a linear function of cos 0 (or, in the case of an azimuthally symmetric medium, a linear function of p = cos 9). 

Let us assume that, in a plane-parallel and azimuthally symmetric medium, the intensities in positive and negative z-directions are given as (see Fig. 7.14) ... 

Reacfivify can be controlled by black and gray absorbers arranged in groups or banks of three azimuthally symmetric absorber rods. These penetrate the vertical matrix of fuel channel tubes at an angle to the vertical. The reactivity can also be controlled by boron additions and by varying moderator temperature. 

Equation (5.36) gives the current through unit area normal to the x axis (located at the origin) due to all last scatterings in a cone of width dp about the x axis. This result will be very useful for computing the current in systems in which the neutron density is azimuthally symmetric. 

The velocity vector v is used here to represent the condition on the probability, namely, that the initial coordinates of the neutron be y, /i, and For the present calculation, scattering collisions are assumed to be azimuthally symmetric about That is, it is equally probable that the final vector O will lie in any position on the conical surface which has... 

The solar flux crossing a horizontal plane depends on the Sun s elevation angle but is independent of azimuth. The infrared radiation held is always azimuthally symmetric. Therefore, because only fluxes contribute to heating rates, we are interested solely in azimuth-independent radiation fields in our analysis. By analogy with Eq. (2.5.10), the appropriate equation for describing the transfer of radiation in the visible channel is... 

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