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Building a Class That Uses a DataTable to Support Types Using a DataTable to support types provides a data-centric approach to managing all the types in your application Each valid type is de ned as a row in the DataTable Using a DataTable can provide better performance when there are large numbers of valid types, because it does not require creating individual objects for each type

=w[sin 0 sin 0' cos( - ')

(GDP) for selected industrial countries, 2001.

(10.2.108) (10.2.109)

cos 8 = cos 0 cos 0'

+ sin 0 sin 0' cos(

To build a general class to support types using a DataTable approach: 1 Add a class to the business object Class Library project This is the generalized class that supports any list of types Give it a clear name, such as TypeList

- ')

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Simulations of particle positions by packing several thousands of particles randomly in a box was done in 8. In this section, we solve Maxwell's equations for scattering by these realizations of particle positions. The simulations are performed over many samples (realizations) and the scattering results are averaged over these realizations. The results give information about the collective scattering effects of many particles packed together. In this section, we use volume integral equation to simulate the scattering by densely packed spheres. We still restrict our attention to the case of small particles. In Section 4, we shall use multipole expansions to study scattering by spheres. 3.1 Volume Integral Equation

Consider waves in an inhomogeneous medium with permittivity Ep(r). For the case of N discrete scatterers with permittivity Ep , occupying regions VI, V2 , , VN, we have discontinuous permittivity Ep(r) with

(10.3.1)

NOTE: This approach needs only one class the class that provides the list It does not need a detail item and a detail collection class, as in the prior approach

_ Ep(r) _ x(r) = - - - 1 = Er(r) - 1

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(10.3.2)

where Er (r) is the relative permittivity. The electric field is, from (2.1.37) of 2,

E(r) = Einc(r)

NOTE: This class is given the same name as the detail collection class in the prior example because it performs the same function even though it performs the function very differently If you want to write code for both the collection class approach and this data-centric approach, use a different class name here

dr'g(r, r')x(r')E(r')

(10.3.3)

dr' g(r, r')\7' . (x(r')E(r'))

Note that the integration space of (10.3.3) is over all space. The first integral is over regions where x(r) is nonzero, that is, where Ep(r) i- E. The second integral is over space where 'V. (X(r)E(r)) is nonzero. For the case of discontinuous permittivity like discrete scatterers, the jump of permittivity across the scatterer boundary can have nonzero divergence at the boundary and give rise to a surface integral. Thus 'V. (x(r)E(r)) in (10.3.3) can be both zero outside and inside the scatterer and yet have a surface integral contribution. We can also use polarization density P(r). Let (10.3.4) Then (10.3.3) becomes

E(r) = Einc(r)

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2 Add two read-only properties: one for the name to display in the combo box and one for the associated value Give the properties clear names, such as TypeName and TypeValue The TypeName de nes the information displayed in the combo box, and the TypeValue de nes the value assigned when the user selects the item

dr'g(r, r') P(r')

dr'g(r,r')'V'. (p(r'))

(10.3.5)

dr'g(r,r')'V' (p(r'))

NOTE: These property names must exactly match the names of the fields in the DataTable If the name in the underlying database does not match, use aliases when building the DataTable to change the name to the property name

dr''V' . (g(r, r') p(r')) dS' (g(r, r') p(r'))

('V' g(r, r'))

. P(r')

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. P(r')

Because the data comes from the DataTable, the properties don t need to return any values The properties are de ned only for use in the Data Sources window

('V' g(r, r'))

(10.3.6)

The first term in (10.3.6) vanishes because of radiation condition at infinity. Putting (10.3.6) in (10.3.5) gives

E(r) = Einc(r)

dr'g(r, r') P(r')

7

('V' g(r, r'))

. P(r')

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(10.3.7)

Equation (10.3.7) has an advantage in that one only needs to integrate over regions where P(r) is nonzero (i.e., X(r) nonzero) and does not have surface integral contributions as in (10.3.3).

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