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The permittivity Eg is chosen such that the effective permittivity calculated by the bilocal approximation differs from f g by a term that is required to be small. That small difference is dependent on particle size. The particle-size-



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dependent term vanishes as k o ---. 0 so that Eg is the effective permittivity at the verylow frequency limit. Let Gg(r, r') be the dyadic Green's function that satisfies a vector wave equation with wavenumber kg with (4.3.3) Thus, (4.3.4) Note that both Eg and Gg are non-random quantities and are chosen to approximate well the effective background through conditions that are to be imposed later. Using (4.3.4) in (4.3.2), we have

E(r) = Eo(r)

E(r')

(4.3.5)

where Eo(r) is the field that satisfies the homogeneous wave equation with wavenumber kg. We note that in (4.3.5) both r, the observation point, and





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r', the source point of the dyadic Green's function Gg(r, r'), are inside the random medium. The two points can coincide with each other within the domain of integration of dr'. The singular nature of the dyadic Green's function at r = r' must be taken into consideration. The singularity of the dyadic Green's function depends on the shape of the infinitesimal exclusion volume as discussed in 2, Section 1.3 of Volume II. For permittivity fluctuations with spherical symmetric correlation functions, a spherical exclusion volume is chosen for the singularity of Gg

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We decompose the dyadic Green's function Gg(r, r') as follows:

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The opposite of a price breakout is a price failure, or breakdown. The rules are very similar to what you ve learned about price breakouts, except that instead of prices moving above resistance, prices are moving below support. If they do so, it is likely they will continue moving substantially lower as the mass of buyers at the former price range loses hope and sells off the stock. Monsanto (Figure 9.7) provides a clear example of this. The price of the stock had a range of about $27 to $36. Holders of the stock were surely getting anxious and frustrated that their investment wasn t really doing anything. The psychology of stockholders when a stock dips below support is quite different from when it pushes above resistance instead of greed and excitement (which drives more buying and higher prices), there is fear and panic (which compels selling and lower prices). Just as buying at higher prices can feed on itself, selling at lower prices can too. As with price breakouts, the power of a price breakdown is partly based on the amount of time that the stock has been trapped within a certain range. If a person has been holding onto a security for years, and when that security nally does make a move, it s a losing move, the typical holder will vow enough is enough and simply sell the stock out of frustration and despair. Figure 9.8 shows the chart of a company called Hop-

Gg(r,r') = P8Gg(r,r') - 3k2t5(r-r')

(4.3.6)

where P S stands for principal value. For nonspherical correlation functions, other shapes of exclusion volumes are to be chosen. Substituting (4.3.6) into (4.3.5) gives (4.3.7) where (4.3.8) (4.3.9)

The diagrammatic method of random medium 01Section 1 can be applied to (4.3.7) using F(r) as the field quantity, PSGg(r,f') as the propagator, and k5~(f) as the "scatterer." The expression E(r) = f. ('~~/2 f!J P(r) can be understood from electrostat1 ics. If E is the incident field for a spherical particle with permittivity E(r) embedded in a background medium of permittivity E , then 3E g /(E(r) + 2E g ) g is the factor that relates the internal field to the incident field. Thus F(f) and E(f) play, respectively, the roles of external and internal fields. For the required small corrections in the bilocal approxiniation, we choose Eg such that

(~(r)) = 0

(4.3.10)

Then, applying the bilocal approximation to (4.3.7) gives an equation that is analogous to (4.1.26), (F(r)) = Eo(r) with

d:f"

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