Started intro in theory/methods documentation.

docs/source/methods/introduction.rst

@@ -4,7 +4,37 @@
 Introduction
 ============
 
+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
+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.
+
+If the probability distributions that govern the transport of a particle are
+known, the process of single particles randomly streaming and colliding with
+nuclei can be simulated directly with computers using a technique known as
+`Monte Carlo`_ simulation. If enough particles are simulated this way, the
+average behavior can be determined to within arbitrarily small statistical
+error, a fact guaranteed by the `central limit theorem`_. To be more precise,
+the central limit theorem tells us that the variance of the sample mean of some
+physical parameter being estimated with Monte Carlo will be inversely
+proportional to the number of realizations, i.e. the number of particles we
+simulate:
+
+.. math::
+
+    \sigma^2 \propto \frac{1}{N}.
+
+where :math:`\sigma^2` is the variance of the sample mean and :math:`N` is the
+number of realizations.
+
 ---------------------
 Criticality Algorithm
 ---------------------
 
+.. _probability distributions: http://en.wikipedia.org/wiki/Probability_distribution
+.. _Monte Carlo: http://en.wikipedia.org/wiki/Monte_Carlo_method
+.. _central limit theorem: http://en.wikipedia.org/wiki/Central_limit_theorem

docs/source/publications.rst

@@ -4,7 +4,11 @@
 Publications
 ============
 
-- Paul K. Romano and Beonit Forget, "The OpenMC Monte Carlo Particle Transport
+- Paul K. Romano and Benoit Forget, "Reducing Parallel Communication in Monte
+  Carlo Simulations via Batch Statistics," *Trans. Am. Nucl. Soc.*, Submitted
+  (2012).
+
+- Paul K. Romano and Benoit Forget, "The OpenMC Monte Carlo Particle Transport
   Code," *Annals of Nuclear Energy*, Submitted (2012).
 
 - Andrew R. Siegel, Kord Smith, Paul K. Romano, Benoit Forget, and Kyle Felker,

docs/source/usersguide/beginners.rst

@@ -22,7 +22,7 @@ quantity one is interested in) very accurately.
 Using Monte Carlo methods to determine the average behavior of various physical
 quantities in a nuclear reactor is quite different from other means of solving
 the same problem. The other class of methods for determining the behavior of
-neutrons and reactions rates in a reactor is so-called `determinstic`_
+neutrons and reactions rates in a reactor is so-called `deterministic`_
 methods. In these methods, the starting point is not randomly simulating
 particles but rather writing an equation that describes the average behavior of
 the particles. The equation that describes the average behavior of neutrons is
@@ -138,7 +138,7 @@ and `Volume II`_. You may also find it helpful to review the following terms:
 .. _nuclear reactor: http://en.wikipedia.org/wiki/Nuclear_reactor
 .. _Monte Carlo: http://en.wikipedia.org/wiki/Monte_Carlo_method
 .. _fission: http://en.wikipedia.org/wiki/Nuclear_fission
-.. _determinstic: http://en.wikipedia.org/wiki/Deterministic_algorithm
+.. _deterministic: http://en.wikipedia.org/wiki/Deterministic_algorithm
 .. _neutron transport: http://en.wikipedia.org/wiki/Neutron_transport
 .. _discretization: http://en.wikipedia.org/wiki/Discretization
 .. _constructive solid geometry: http://en.wikipedia.org/wiki/Constructive_solid_geometry