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in clusters. We also describe the iterative approach for solving the multiple scattering equations. Forward scattering amplitude in conjunction with Foldy's approximation has been used to calculate the extinction rate. It is shown that this is only applicable if the N-particle forward scattering amplitude is calculated to the second order. It is also shown that the coherent wave approaches a delta function in the forward direction in the limit of a large volume and large number of scatterers (large N). Thus, the coherent field intensity has to be subtracted from the total scattered intensity to give (a) the phase matrix which describes the scattering of energy away from the forward direction and (b) the extinction coefficient which describes the wave decay in the forward direction. We perform Monte Carlo simulations by solving the wave equations and averaging over many realizations.

<ObsoleteAttribute( _ "Use the Create(prodName, withComments) instead", False)> _ Public Shared Function Create(ByVal prodName) As Product Return Create(prodID, False) End Function

In this section we redefine the scattering and extinction parameters of radiative transfer theory to include the collective scattering behavior of particles. This distinguishes the definition from the conventional definition of averaged single-particle scattering behavior. In radiative transfer theory we consider a specific intensity incident upon an elemental volume with cross-sectional area A and length ds (Fig. 7.1.1). The cross-sectional shape is arbitrary. It is an elemental test volume in the development of the radiative transfer equation. It is not small in the sense of the wave equation. The elemental volume V = Ads needs to obey the

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ments 1993 1994 to 2001 2002, Science, Innovation and Electronic Information Division, Statistics Canada. Bennof, R. (2002). Half the Nation s R&D Concentrated in Six States, NSF 02-322. Arlington, VA: National Science Foundation, Division of Science Resources Studies. Berg, C., R. Nassr, and K. Pang (2002). The evolution of biotech. Na ture 1(Nov): 845 6. Biomaterials Network. www.biomat.net. BIOTECanada. www.bioech.ca. Biotechnology Australia. www.biotechnology.gov.au. Carr, K. (1999). Science in Latin America. Nature 398(Supplement): 22. Chandler, C. (2003). Coping with China: As China Becomes the Work shop of the World, Where Does That Leave the Rest of Asia Interna tional Fortune(January): 47 9. Charles, D. (2001). Lords of the Harvest: Biotech, Big Money, and the Fu ture of Food. New York: Perseus Publishing. Cliff, R. (2001). The Military Potential of China s Commercial Technol ogy, RAND Corporation. Computational Biology Research Center (CBRC). ww.cbrc.jpI.

following criteria: (i) V ~ >.3 or V~>.3. In other words, V = NV>.3, where N v is a number of moderate size. (ii) There is a large number of particles, N, contained in V. The particles are randomly positioned. Criteria (i) and (ii) are necessary to ensure that the coherent multiple scattering in volume V will include random phase fluctuations so that the energy transfer in and out of volume V can be averaged. Furthermore, if .the particles are of different sizes, shapes, and permittivities in volume V, averaging of particle scattering behavior will also be included in the radiative energy transfer within elemental test volume V. Criteria (i) and (ii) establish a lower limit of volume V. Let E i be the incident field in the direction k = (Oi, <lJi), and let E s be i the scattered field from volume V of N particles.

E i = exp(iki . r) (7.1.1)

The scattered field can be decomposed into coherent field (E s ) and incoherent field Es . (7.1.2) The scattered field E s is a statistical field that contains the coherent multiple scattering within volume V. From one elemental volume V to most other elemental volumes, the far field of E s can be taken. We have

The attribute s name can be de ned with or without the Attribute suf x; either Obsolete or ObsoleteAttribute can be used Your coding standards may de ne that the suf x is included for clarity or not included for brevity Either way, be consistent with all attributes Some attributes, such as the Obsolete attribute, have parameters The rst parameter in this case is a message to any developer using your obsolete method, and the second parameter is an error ag This message appears in the Error List window (see Figure 53) as a warning if the second parameter is False, or as an error if the second parameter is True This gives the developer using the method a warning or error, depending on your standard method obsolescence path

(7.1.3)

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