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Review for Test #1
For the Chapter 1 material, you need to be able to:
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Explain the significance of any of the seven physical approximations we
made
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Derive the mean free path as the inverse of the macroscopic cross section
-
Expand the directional dimension of the scattering cross section in Legendre
polynomials, using the orthogonality condition to arrive at the coefficients
- Show that the total derivative flux with respect to distance traveled
(d(psi)/ds) is equivalent to the Omega dot Del psi.
I will expect you do expand the total derivative FULLY (in terms of
all of the dependent variables of flux and explain why some of the terms
disappear in Cartesian coordinates.
- List and discuss the explicit and implicit boundary condition types
we studied -- void, surface source, reflected, white, periodic. Be able to show that
the incoming angular flux for the white boundary condition is four times
the outgoing partial current.
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Develop the streaming operator in spherical coordinates as done in the
example in the notes.
- Demonstrate the equivalence of a conservative and non-conservative
version of the streaming operator for any curvilinear coordinate system.
(No need to memorize the versions.)
-
Explain the use of spherical harmonic moments and spherical harmonic distributions
to represent the scattering source term.
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Develop the adjoint of any of the forward Boltzmann sub-operators -- L1,
L2, L3, or L4 -- as was done in class.
-
Explain through use of the definition of the adjoint -- <a,Lb>=<b,L*a>
-- that either the forward or adjoint solution can be used to find a detector
response. Included in this is a description of how it is done (each
way) and examples of when one method would be preferred over the other.
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NE583 Radiation Transport Methods