Got the low hanging fruit for implementing MG theory in the theory manual. The majority of work will be in the physics.rst and cross_sections.rst files which I have not attacked yet. I also noticed that the theory wasnt updated for the new secondary particle bank (Ive only seen one place where it needed to be mentioned so far) and for the polar/azimuthal/mu filters. Both have been incorporated.

docs/source/methods/introduction.rst

@@ -8,7 +8,7 @@ The physical process by which a population of particles evolves over time is
 governed by a number of `probability distributions`_. For instance, given a
 particle traveling through some material, there is a probability distribution
 for the distance it will travel until its next collision (an exponential
-distribution). Then, when it collides with a nucleus, there is associated
+distribution). Then, when it collides with a nucleus, there is an associated
 probability of undergoing each possible reaction with that nucleus. While the
 behavior of any single particle is unpredictable, the average behavior of a
 large population of particles originating from the same source is well defined.
@@ -45,10 +45,15 @@ following steps:
 
   - Initialize the pseudorandom number generator.
 
-  - Read ACE format cross sections specified in the problem.
+  - Read the contiuous-energy or multi-group cross section data specified in
+    the problem.
 
   - If using a special energy grid treatment such as a union energy grid or
-    lethargy bins, that must be initialized as well.
+    lethargy bins, that must be initialized as well in a continuous-energy
+    problem.
+
+  - In a multi-group problem, individual nuclide cross section information is
+    combined to produce material-specific cross section data.
 
   - In a fixed source problem, source sites are sampled from the specified
     source. In an eigenvalue problem, source sites are sampled from some initial
@@ -95,6 +100,10 @@ proceed. The life of a single particle will proceed as follows:
 
          P(i) = \frac{\Sigma_{t,i}}{\Sigma_t}.
 
+     Note that the above selection of collided nuclide only applies to
+     continuous-energy simulations as multi-group simulations use nuclide
+     data which has already been combined in to material-specific data.
+
   8. Once the specific nuclide is sampled, the random samples a reaction for
      that nuclide based on the microscopic cross sections. If the microscopic
      cross section for some reaction :math:`x` is :math:`\sigma_x` and the total
@@ -105,13 +114,20 @@ proceed. The life of a single particle will proceed as follows:
 
          P(x) = \frac{\sigma_x}{\sigma_t}.
 
+     Since multi-group simulations use material-specific data, the above is
+     performed with those material multi-group cross sections (i.e.,
+     macroscopic cross sections for the material) instead of microscopic
+     cross sections for the nuclide).
+
   9. If the sampled reaction is elastic or inelastic scattering, the outgoing
-     energy and angle is sampled from the appropriate distribution.  Reactions
-     of type :math:`(n,xn)` are treated as scattering and the weight of the
-     particle is increased by the multiplicity of the reaction. The particle
-     then continues from step 3. If the reaction is absorption or fission, the
-     particle dies and if necessary, fission sites are created and stored in the
-     fission bank.
+     energy and angle is sampled from the appropriate distribution.  In
+     continuous-energy simulation, reactions of type :math:`(n,xn)` are treated
+     as scattering and any additional particles which may be created are added
+     to a secondary particle bank to be tracked later. In a multi-group
+     simulation, this secondary bank is ont used but the particle weight is
+     increased accordingly.  The original particle then continues from step 3.
+     If the reaction is absorption or fission, the particle dies and if
+     necessary, fission sites are created and stored in the fission bank.
 
 After all particles have been simulated, there are a few final tasks that must
 be performed before the run is finished. This include the following:

docs/source/methods/tallies.rst

@@ -32,8 +32,9 @@ OpenMC: flux, total reaction rate, scattering reaction rate, neutron production
 from scattering, higher scattering moments, :math:`(n,xn)` reaction rates,
 absorption reaction rate, fission reaction rate, neutron production rate from
 fission, and surface currents. The following variables can be used as filters:
-universe, material, cell, birth cell, surface, mesh, pre-collision energy, and
-post-collision energy.
+universe, material, cell, birth cell, surface, mesh, pre-collision energy,
+post-collision energy, polar angle, azimuthal angle, and the cosine of the
+change-in-angle due to a scattering event.
 
 With filters for pre- and post-collision energy and scoring functions for
 scattering and fission production, it is possible to use OpenMC to generate
@@ -55,9 +56,9 @@ be scored to for each value of the filter variable. If a particle is in cell
 :math:`n`, the mapping would identify what tally/bin combinations specify cell
 :math:`n` for the cell filter variable. In this manner, it is not necessary to
 check the phase space variables against each tally. Note that this technique
-only applies to discrete filter variables and cannot be applied to energy
-bins. For energy filters, it is necessary to perform a binary search on the
-specified energy grid.
+only applies to discrete filter variables and cannot be applied to energy,
+angle, or change-in-angle bins. For these filters, it is necessary to perform
+a binary search on the specified energy grid.
 
 -----------------------------------------
 Volume-Integrated Flux and Reaction Rates
@@ -196,8 +197,9 @@ One important fact to take into consideration is that the use of a track-length
 estimator precludes us from using any filter that requires knowledge of the
 particle's state following a collision because by definition, it will not have
 had a collision at every event. Thus, for tallies with outgoing-energy filters
-(which require the post-collision energy) or for tallies of scattering moments
-(which require the scattering cosine), we must use an analog estimator.
+(which require the post-collision energy), scattering change-in-angle filters,
+or for tallies of scattering moments (which require the scattering cosine of
+the change-in-angle), we must use an analog estimator.
 
 .. TODO: Add description of surface current tallies
 
@@ -430,7 +432,7 @@ analytically. For one degree of freedom, the t-distribution becomes a standard
 .. math::
     :label: cauchy-cdf
 
-    c(x) = \frac{1}{\pi} \arctan x + \frac{1}{2}. 
+    c(x) = \frac{1}{\pi} \arctan x + \frac{1}{2}.
 
 Thus, inverting the cumulative distribution function, we find the :math:`x`
 percentile of the standard Cauchy distribution to be

docs/source/usersguide/beginners.rst

@@ -65,7 +65,7 @@ Now let's look at the pros and cons of Monte Carlo methods:
 
 - **Pro**: Running simulations in parallel is conceptually very simple.
 
-- **Con**: Because they related on repeated random sampling, they are
+- **Con**: Because they rely on repeated random sampling, they are
   computationally very expensive.
 
 - **Con**: A simulation doesn't automatically give you the global solution