Directional distribution

For opaque materials, the reflectance p is the complement of the absorptance. The directional distribution of the reflected radiation depends on the material, its degree of roughness or grain size, and, if a metal, its state of oxidation. Polished surfaces of homogeneous materials reflect speciilarly. In contrast, the intensity of the radiation reflected from a perfectly diffuse, or Lambert, surface is independent of direction. The directional distribution of reflectance of many oxidized metals, refractoiy materials, and natural products approximates that of a perfectly diffuse reflector. A better model, adequate for many calculational purposes, is achieved by assuming that the total reflectance p is the sum of diffuse and specular components p i and p. ... 

By adopting the basic assumption that the probability density of the direction distribution of particle velocity vector is uniform in the whole space, i.e., 0(0,jS) =sin 0/4tt, the probability of collision between the wall and a particle located S away from the wall (see Fig. 7) can be expressed as the following equation ... 

Acute effects often involve the central nervous system, because of the rapid absorption of the solvent from the lungs and direct distribution to the brain. The immediate effects may result in mild impairment of judgment or drowsiness. In most situations these effects are not serious and will end quickly once exposure stops. In some circumstances a slight lapse of judgment could be disastrous. A person responding to a hazardous material spill or perhaps a fire must take appropriate precautions to limit exposure to any solvents that could impair judgment and thus increase risk of injury. 

The directional distribution of the scattering intensity can be described by phase functions. A phase function is defined as the ratio of scattering intensity in a direction to the scattering intensity in the same direction if the scattering is isotropic. Thus, it is a normalized function and is defined over all directions. Typical phase functions for small, intermediate, and large values of f and n, are illustrated in Fig. 4.4, with the spheres assumed to be nonabsorbing [Tien and Drolen, 1987]. It is shown that the phase functions mainly vary... 

The directional distribution of scaffering is given by the phase function (s s ). This function depends on the angle between the incident s and scattered directions s, cos 9g = s s. The determination of the phase function requires elaborate experiments. It is common to use approximate phase functions, like the Henyey-Greenstein phase function "Thg.a (see, for instance. Modest, 2003), which can be used to approximate the real phase function for many t)pies of particles... 

Radiation is emitted by all parts of a plane surface in a)t directions into the hemisphere above llte surface, and the directional distribution of emitted (or incident) radiation is usually not uniform. Therefore, we need a quantity that describes the magnitude of radiation emitted (or incident) in a specified direction in space. This quatuity i.s radialion intensity, denoted by/. Before we can describe a directional quantity, we need to specify direction in space. The direction of radiation passing through a point is best described in spherical coordinates in terms of the zenith angle 6 and the azimuth angle , as shown in... 

M. Schiitz and R. Lindh, An integral direct, distributed-data, parallel MP2 algorithm, Theor. Chim. Acta, 95 (1997), 13-34. 

Table II gives values of Jx for an intermediate set of conditions details are in Leighton s report (18). This equation uses the weak absorption approximation it neglects surface reflection, and it takes no account of the effects of diffusion within the absorbing layer. The weak absorption approximation will make the calculated rates too high, and neglecting the surface reflection will make them too low as a result these two errors partially cancel each other. Any accounting of internal diffusion on absorption rates will depend on the directional distribution of the diffused radiation and on whether the rate near the surface on the average rate throughout the layer is the more important. Until more is known of these factors, the effects of diffusion within the layer must be regarded as indeterminate.

The directional distribution of the emission integrated over all the wave lengths is described by the total intensity L(f3,(p,T). This is found by integrating (5.4) over A, yielding... 

The distribution function Kx(X,/3,incident spectral intensity, is defined by this. It describes the wavelength and directional distribution of the radiation flow falling onto the irradiated surface element. Like the corresponding quantity Lx for the emission of radiation, Kx is defined with the projection d 4p = cos/SdAl of the irradiated surface element perpendicular to the direction of the incident radiation, Fig. 5.12. The SI units of Kx are W/(m2pmsr) the relationship to the wavelength interval dA and the solid angle element dw is also clear from this. 

The spectral irradiance Ex describes the distribution of the incident energy over the spectrum, whereby the radiation from all directions in the hemisphere is combined. If, on the contrary, the directional distribution of the radiation... 

The incident intensity K(f3,(p) describes the directional distribution of the incident radiation flow (directional total quantity). 

However, this is valid with the restriction that the bidirectional reflectivities are not covered, which describe the directional distribution of the reflected radiation see for this the comments in 5.1.5 as well as [5.4], p. 71 ff. 

TABLE 7.14 Directional Distribution of Significant Wave Heights off Warnemunde in Approx, d = 10 m Water Depth (Frohle et al., 2006)... 

The given concepts also apply to incident radiation. Such radiation originates from emission and reflection occuring at other surfaces and have spectral and directional distributions determined by the spectral intensity Ix,i X, 9, (p). 

FIGURE 7.5 Directional distributions of the total directional emissivity for conductors (metals) and nonconductors (dielectrics). 

Sometimes it is important to consider the direction of reflected irradiation exitent from a surface. A property called the bidirectional reflectance distribution function (BRDF) is used to specify the directional distribution of the reflected intensity for a specified direction of incident radiation [2-4]. A specular surface is a mirrorlike surface for which the incidence angle is equal to the reflection angle. For a diffusely reflecting surface, the reflected intensity is the same in all directions, and if perfectly reflective, the BRDF is l/n sr. ... 

It was found that the z-directional distribution of magnetic field strength can be satisfactorily approximated by the following forms ... 

The five d and seven/orbitals are also unsymmetrical figures. Their exact form is a matter of less immediate concern to us than the fact that, in common with the p orbitals, they represent a directed distribution of electron density. As we shall shortly see, this spatial direction of the orbitals plays a very important part when we come to consider the interatomic binding forces between atoms, and we must remember that it is determined by the subsidiary quantum number l. 

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