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41 (uniform random N = 500) and the lc = 02)" of Fig 742 are presented, respectively Both the incoherent phase function Pine (dotted line) and the combined phase function Pine + Peoherent (solid line) are given The results are averaged over 100 realizations In the polar plots, the top half-plane gives <Ps = 10 and (}s ranges from 0 ----t 180 going clockwise In the bottom half-plane <Ps = 190 and (}s ranges from 0 ----t 180 going counterclockwise Comparing Figs 743 and 744, we see that the clustered scattering case gives a larger incoherent contribution than does the uniform case, while the opposite is true for the coherent contribution In both figures, the coherent part has a sharp peak of large amplitude (many decibels larger) in the forward direction (()s = 170 , <Ps = 10 ).

Note that the polar plot is in the decibel scale, so that the coherent forward peak has much larger amplitude than that of the other directions As V approaches infinity,.

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0 1985 1990 1995 50 75 100

polar plot (dB)

Figure 7.4.3 Polar plot (dB) of the phase function of Fig. 7.4.1 of the uniform random case for N = 500 and L = 50A with the geometry given as in Fig. 7.3.1. Upper half-plane shows s = 10 and Os is 0 -+ 180 going clockwise. Lower half-plane shows s = 190 and Os is 0 -+ 180 going counterclockwise. Incident angles are 0i = 10 and i = 10 .

polar plot (dB)

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Figure 7.4.4 Polar plot (dB) of the phase function of Fig. 7.4.2 of the clustered random case for N = 500, le = 0.2A, and L = 50A with incident angles at 0i = 10 and i = 10 . Upper half-plane shows s = 10 and Os is 0 -+ 180 going clockwise. Lower half-plane shows s = 190 and Os is 0 -+ 180 going counterclockwise.

The Class Details window displays all the properties and methods for a class and allows you to add or edit properties and methods

c: c:

4.0 3.0 2.0

....

. .... .

You can add properties, methods, elds, or events to the class from this window or from Class Designer directly There are many ways to add these class members For example, use one of the following techniques to add a property to a class:

s (K)

0.0 -t---..-.,..._-,................,.-~c..,....&...4

40 80 80 100 120 140 180 180

scattering angle (degree)

Figure 7.4.5 Comparison test between the second-order approach and the exact solution. Phase function of Fig. 7.4.2 with Ie = 0.35'\, N = 500 and L = 50,\ for 1 realization ( i = 10 , 0i = 10 , s = 20 and Os ranges from 0 to 180 ).

Right-click the class in Class Designer and select Add | Property from the context menu Right-click the Properties node for the class in Class Designer, and select Add | Property from the context menu Select the class in Class Designer, and then select Class Diagram | Add | Property from the main menu bar Type in the Class Details window in the Properties node containing the text <add property> Select New Property from the New Member drop-down list on the Class Details toolbar shown to the left of the Class Details window

the coherent wave will approach a Dirac delta function. Thus, the coherent peak has to be excluded from the phase matrix and extinction coefficient calculations. All the Monte Carlo results given so far are obtained by solving the multiple scattering equation (7.4.3) exactly. To compare the iterative method solution and the exact solution, we compare the incoherent phase functions for a single realization using the second-order approximation and the exact method. The comparison is shown in Fig. 7.4.5. In the figure, le = 0.35>', N = 500, cPs = 20 , and es is varied from 0 to 180 . For one realization, the second-order solution shows significant differences from the exact solution for most scattering angles. However, when 100 realizations are averaged, the second-order solution agrees with the exact method (Fig. 7.4.6). This shows that for a single realization, higher-order scattering effects are important. However, these higher-order scattering effects tend to cancel out on averaging over realizations, and the second-order theory gives a quite accurate average. The iteration approach can be very attractive for more complicated problems of vector electromagnetic scattering by a large number of dielectric scatterers of arbitrary size. In Fig. 7.4.7 the comparison between the analytic collective scattering theory of (7.3.46), the independent scattering of (7.3.4), and the Monte Carlo simulation of Fig. 7.4.6 with

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databases from 1980 through 2003 is indicative of the research and development in biotech over the same period.

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