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Latest updates to documentation.

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This commit is contained in:
Paul Romano 2012-08-20 22:18:48 -04:00
parent 3b0a50e6fc
commit e21e92ccc5
57 changed files with 1174 additions and 395 deletions
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@ -1,327 +0,0 @@
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17733 7201 17630 7123 17513 7054 ct 17526 7032 l 17539 7010 l p ef
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17978 7474 17907 7377 17820 7289 ct 17838 7271 l 17856 7253 l p ef
10525 4809 m 10513 5411 l 10877 5298 l 10525 4809 l p ef
18145 7986 m 18171 7384 l 17804 7489 l 18145 7986 l p ef
0 6988 t
pom
count op_count sub {pop} repeat countdictstack dict_count sub {end} repeat b4_inc_state restore
%%PageTrailer
%%Trailer
%%EOF

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1
_sources/devguide/index.txt
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@ -14,3 +14,4 @@ as debugging.
structures
xml-fortran
statepoint

205
_sources/devguide/statepoint.txt Normal file
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@ -0,0 +1,205 @@
.. _devguide_statepoint:
======================================
State Point Binary File Specifications
======================================
----------
Revision 2
----------
**integer(4) REVISION_STATEPOINT**
Revision of the binary state point file. Any time a change is made in the
format of the state-point file, this integer is incremented.
**integer(4) VERSION_MAJOR**
Major version number for OpenMC
**integer(4) VERSION_MINOR**
Minor version number for OpenMC
**integer(4) VERSION_RELEASE**
Release version number for OpenMC
**integer(4) run_mode**
run mode used. The modes are described in constants.F90.
**integer(8) n_particles**
Number of particles used per generation.
**integer(4) n_batches**
Total number of batches (active + inactive).
**integer(4) n_inactive**
Number of inactive batches
**integer(4) gen_per_batch**
Number of generations per batch for criticality calculations
**integer(4) current_batch**
The number of batches already simulated.
*do i = 1, current_batch*
**real(8) k_batch(i)**
k-effective for the i-th batch
if (entropy_on)
**real(8) entropy for the i-th batch**
**integer(4) N_GLOBAL_TALLIES**
Number of global tally scores
*do i = 1, N_GLOBAL_TALLIES*
**real(8) global_tallies(i) % sum**
Accumulated sum for the i-th global tally
*do i = 1, N_GLOBAL_TALLIES*
**real(8) global_tallies(i) % sum_sq**
Accumulated sum of squares for the i-th global tally
**integer(4) n_tallies**
*do i = 1, n_tallies*
**integer(4) size(tallies(i) % scores, 1)**
Total number of score bins for the i-th tally
**integer(4) size(tallies(i) % scores, 2)**
Total number of filter bins for the i-th tally
*do i = 1, n_tallies*
*do k = 1, size(tallies(i) % scores, 2)*
*do j = 1, size(tallies(i) % scores, 1)*
**real(8) tallies(i) % scores(j,k) % sum**
Accumulated sum for the j-th score and k-th filter of the i-th
tally
**real(8) tallies(i) % scores(j,k) % sum_sq**
Accumulated sum of squares for the j-th score and k-th filter of
the i-th tally
----------
Revision 1
----------
**integer(4) REVISION_STATEPOINT**
Revision of the binary state point file. Any time a change is made in the
format of the state-point file, this integer is incremented.
**integer(4) VERSION_MAJOR**
Major version number for OpenMC
**integer(4) VERSION_MINOR**
Minor version number for OpenMC
**integer(4) VERSION_RELEASE**
Release version number for OpenMC
**integer(4) run_mode**
run mode used. The modes are described in constants.F90.
**integer(8) n_particles**
Number of particles used per generation.
**integer(4) n_batches**
Total number of batches (active + inactive).
**integer(4) n_inactive**
Number of inactive batches
**integer(4) gen_per_batch**
Number of generations per batch for criticality calculations
**integer(4) current_batch**
The number of batches already simulated.
*do i = 1, current_batch*
**real(8) k_batch(i)**
k-effective for the i-th batch
if (entropy_on)
**real(8) entropy for the i-th batch**
**integer(4) N_GLOBAL_TALLIES**
Number of global tally scores
*do i = 1, N_GLOBAL_TALLIES*
**real(8) global_tallies(i) % sum**
Accumulated sum for the i-th global tally
*do i = 1, N_GLOBAL_TALLIES*
**real(8) global_tallies(i) % sum_sq**
Accumulated sum of squares for the i-th global tally
**integer(4) n_tallies**
*do i = 1, n_tallies*
**integer(4) size(tallies(i) % scores, 1)**
Total number of score bins for the i-th tally
**integer(4) size(tallies(i) % scores, 2)**
Total number of filter bins for the i-th tally
*do k = 1, size(tallies(i) % scores, 2)*
*do j = 1, size(tallies(i) % scores, 1)*
**real(8) tallies(i) % scores(j,k) % sum**
Accumulated sum for the j-th score and k-th filter of the i-th
tally
*do k = 1, size(tallies(i) % scores, 2)*
*do j = 1, size(tallies(i) % scores, 1)*
**real(8) tallies(i) % scores(j,k) % sum_sq**
Accumulated sum of squares for the j-th score and k-th filter of
the i-th tally

37
_sources/devguide/statepointtable.txt Normal file
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@ -0,0 +1,37 @@
============ ====================== =============================================
Type Variable Description
============ ====================== =============================================
integer(4) REVISION_STATEPOINT Revision of the binary state point file. Any
time a change is made in the format of the
state-point file, this integer is
incremented.
integer(4) VERSION_MAJOR Major version number for OpenMC
integer(4) VERSION_MINOR Minor version number for OpenMC
integer(4) VERSION_RELEASE Release version number for OpenMC
integer(4) run_mode Run mode used. 1 = criticality, 2 = fixed
source
integer(8) n_particles Number of particles used per generation.
integer(4) n_batches Total number of batches (active + inactive).
integer(4) n_inactive Number of inactive batches
integer(4) gen_per_batch Number of generations per batch for
criticality calculations
integer(4) current_batch Number of batches already simulated.
============ ====================== =============================================
The next variable appears only for a criticality calculation (run_mode =
MODE_CRITICALITY = 1).
============ ====================== =============================================
real(8) k_batch(i), i = 1, k-effective for the i-th batch
current_batch
============ ====================== =============================================
The next variable appears only for a criticality calculation where Shannon
entropy has been turned on.
============ ====================== =============================================
real(8) entropy(i), i = 1, Shannon entropy for the i-th batch
current_batch
============ ====================== =============================================

120
_sources/methods/statistics.txt
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@ -173,6 +173,110 @@ of this is that the longer you run a simulation, the better you know your
results. Therefore, by running a simulation long enough, it is possible to
reduce the stochastic uncertainty to arbitrarily low levels.
Confidence Intervals
--------------------
While the sample variance and standard deviation gives us some idea about the
variability of the estimate of the mean of whatever quantities we've tallied, it
does not help us interpret how confidence we should be in the results. To
quantity the reliability of our estimates, we can use `confidence intervals`_
based on the calculated sample variance.
A :math:`1-\alpha` confidence interval for a population parameter is defined as
such: if we repeat the same experiment many times and calculate the confidence
interval for each experiment, then :math:`1 - \alpha` percent of the calculated
intervals would encompass the true population parameter. Let :math:`x_1, x_2,
\dots, x_N` be samples from a set of independent, identically-distributed random
variables each with population mean :math:`\mu` and variance
:math:`\sigma^2`. The t-statistic is defined as
.. math::
:label: t-statistic
t = \frac{\bar{x} - \mu}{s/\sqrt{N}}
where :math:`\bar{x}` is the sample mean from equation :eq:`sample-mean` and
:math:`s` is the standard deviation based on equation
:eq:`unbiased-variance`. If the random variables :math:`X_i` are
normally-distributed, then the t-statistic has a `Student's t-distribution`_
with :math:`N-1` degrees of freedom. This implies that
.. math::
:label: t-probability
Pr \left ( -t_{1 - \alpha/2, N - 1} \le \frac{\bar{x} - \mu}{s/\sqrt{N}} \le
t_{1 - \alpha/2, N - 1} \right ) = 1 - \alpha
where :math:`t_{1-\alpha/2, N-1}` is the :math:`1 - \alpha/2` percentile of a
t-distribution with :math:`N-1` degrees of freedom. Thus, the :math:`1 - \alpha`
two sided confidence interval for the sample mean is
.. math::
:label: two-sided-ci
\bar{x} \pm t_{1 - \alpha/2, N-1} \frac{s}{\sqrt{N}}.
One should be cautioned that equation :eq:`two-sided-ci` **only applies if the
underlying random variables are normally-distributed!** In general, this may not
be true for a tally random variable -- the central limit theorem guarantees only
that the sample mean is normally distributed, not the underlying random
variable. If batching is used, then the underlying random variable, which would
then be the averages from each batch, will be normally distributed as long as
the conditions of the central limit theorem are met.
Let us now outline the method used to calculate the percentile of the Student's
t-distribution. For one or two degrees of freedom, the percentile can be written
analytically. For one degree of freedom, the t-distribution becomes a standard
`Cauchy distribution`_ whose cumulative distribution function is
.. math::
:label: cauchy-cdf
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
.. math::
:label: percentile-1
t_{x,1} = \tan \left ( \pi \left ( x - \frac{1}{2} \right ) \right ).
For two degrees of freedom, the cumulative distribution function is the
second-degree polynomial
.. math::
:label: t-2-polynomial
c(x) = \frac{1}{2} + \frac{x}{2\sqrt{x^2 + 2}}
Solving for :math:`x`, we find the :math:`x` percentile to be
.. math::
:label: percentile-2
t_{x,2} = \frac{2\sqrt{2} (x - 1/2)}{\sqrt{1 - 4 (x - 1/2)^2}}
For degrees of freedom greater than two, it is not possible to obtain an
analytical formula for the inverse of the cumulative distribution function. We
must resort to either numerically solving for the inverse or to an
approximation. Approximations for percentiles of the t-distribution have been
found with high levels of accuracy. OpenMC uses the approximation from
[George]_:
.. math::
:label: percentile-n
t_{x,n} = \sqrt{\frac{n}{n-2}} \left ( z_x + \frac{1}{4} \frac{z_x^3 -
3z_x}{n-2} + \frac{1}{96} \frac{5z_x^5 - 56z_x^3 + 75z_x}{(n-2)^2} +
\frac{1}{384} \frac{3z_x^7 - 81z_x^5 + 417z_x^3 - 315z_x}{(n-2)^3} \right )
where :math:`z_x` is the :math:`x` percentile of the standard normal
distribution. In order to determine an arbitrary percentile of the standard
normal distribution, we use an `unpublished rational approximation`_. After
using the rational approximation, one iteration of Newton's method is applied to
improve the estimate of the percentile.
------------------------
Random Number Generation
------------------------
@ -226,6 +330,14 @@ Note that equation :eq:`lcg-skipahead` has the same form as equation :eq:`lcg`
so the idea is to determine the new multiplicative and additive constants in
:math:`O(\log N)` operations.
----------
References
----------
.. [George] E. E. Olusegun George and Meenakshi Sivaram, "A modification of the
Fisher-Cornish approximation for the student t percentiles," Communication
in Statistics - Simulation and Computation, 16 (4), pp. 1123-1132 (1987).
.. _linear congruential generator: http://en.wikipedia.org/wiki/Linear_congruential_generator
.. _Brown: https://laws.lanl.gov/vhosts/mcnp.lanl.gov/pdf_files/anl_rn_arb-strides_1994.pdf
@ -247,3 +359,11 @@ so the idea is to determine the new multiplicative and additive constants in
.. _normal distribution: http://en.wikipedia.org/wiki/Normal_distribution
.. _converges in distribution: http://en.wikipedia.org/wiki/Convergence_of_random_variables#Convergence_in_distribution
.. _confidence intervals: http://en.wikipedia.org/wiki/Confidence_interval
.. _Student's t-distribution: http://en.wikipedia.org/wiki/Student%27s_t-distribution
.. _Cauchy distribution: http://en.wikipedia.org/wiki/Cauchy_distribution
.. _unpublished rational approximation: http://home.online.no/~pjacklam/notes/invnorm/

1
_sources/releasenotes/index.txt
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@ -10,6 +10,7 @@ bugs fixed, and known issues for each successive release.
.. toctree::
:maxdepth: 1
notes_0.4.4
notes_0.4.3
notes_0.4.2
notes_0.4.1

8
_sources/releasenotes/notes_0.4.3.txt
View file

@ -4,10 +4,6 @@
Release Notes for OpenMC 0.4.3
==============================
.. note::
These release notes are for an upcoming release of OpenMC and are still
subject to change.
-------------------
System Requirements
-------------------
@ -21,7 +17,9 @@ the problem at hand (mostly on the number of nuclides in the problem).
New Features
------------
- Option to report confidence intervals for tally results.
- Rotation and translation for filled cells.
- Ability to explicitly specify <estimator> for tallies.
- Ability to store state points and use them to restart runs.
- Fixed source calculations (no subcritical multiplication however).
- Expanded options for external source distribution.
@ -34,6 +32,7 @@ New Features
Bug Fixes
---------
- 33f29a_: Handle negative values in probability table.
- 1c472d_: Fixed survival biasing with probability tables.
- 3c6e80_: Fixed writing tallies with no filters.
- 460ef1_: Invalid results for duplicate tallies.
@ -43,6 +42,7 @@ Bug Fixes
- 3212f5_: Fixed issue with blank line at beginning of XML files.
.. _nelsonag: https://github.com/nelsonag
.. _33f29a: https://github.com/mit-crpg/openmc/commit/33f29a
.. _1c472d: https://github.com/mit-crpg/openmc/commit/1c472d
.. _3c6e80: https://github.com/mit-crpg/openmc/commit/3c6e80
.. _3bd35b: https://github.com/mit-crpg/openmc/commit/3bd35b

28
_sources/releasenotes/notes_0.4.4.txt Normal file
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@ -0,0 +1,28 @@
.. _notes_0.4.4:
==============================
Release Notes for OpenMC 0.4.4
==============================
.. note::
These release notes are for an upcoming release of OpenMC and are still
subject to change.
-------------------
System Requirements
-------------------
There are no special requirements for running the OpenMC code. As of this
release, OpenMC has been tested on a variety of Linux distributions, Mac OS X,
and Microsoft Windows 7. Memory requirements will vary depending on the size of
the problem at hand (mostly on the number of nuclides in the problem).
------------
New Features
------------
- Option to specify <upper_right> for tally meshes.
---------
Bug Fixes
---------

47
_sources/usersguide/input.txt
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@ -55,6 +55,17 @@ Settings Specification -- settings.xml
All simulation parameters and miscellaneous options are specified in the
settings.xml file.
``<confidence_intervals>`` Element
----------------------------------
The ``<confidence_intervals>`` element has no attributes and has an accepted
value of "on" or "off". If set to "on", uncertainties on tally results will be
reported as the half-width of the 95% two-sided confidence interval. If set to
"off", uncertainties on tally results will be reported as the sample standard
deviation.
*Default*: off
``<criticality>`` Element
-------------------------
@ -344,8 +355,21 @@ displayed. This element takes the following attributes:
*Default*: 5
``<write_state_point>`` Element
-------------------------------
The ``<write_state_point>`` element is used to indicate batches at which the
user wishes to have a binary state point file written to disk. The state point
file can be used to restart a run or to get tally results at an intermediate
stage. This element has no attributes and should consist of a list of integers
corresponding to batches at which a binary state point file should be written to
disk.
*Default*: None
``<write_source>`` Element
------------------------------
--------------------------
The ``<write_source>`` element has no attributes and has an accepted value of
"on" or "off". If set to "on", a binary source file will be written to disk at
@ -512,9 +536,9 @@ Each ``<cell>`` element can have the following attributes or sub-elements:
:rotation:
If the cell is filled with a universe, this element specifies the angles in
degrees about the x, y, and z axes that the filled universe should be
rotated. Should be given as three real numbers.For example, if you wanted to
rotate the filled universe by 90 degrees about the z-axis, the cell element
would look something like:
rotated. Should be given as three real numbers. For example, if you wanted
to rotate the filled universe by 90 degrees about the z-axis, the cell
element would look something like:
.. code-block:: xml
@ -669,6 +693,21 @@ The ``<tally>`` element accepts the following sub-elements:
A list of filters to specify what region of phase space should contribute to
the tally. See below for full details on what filters are available.
:nuclides:
If specified, the scores listed will be for particular nuclides, not the
summation of reactions from all nuclides. The format for nuclides should be
[Atomic symbol]-[Mass number], e.g. "U-235". The reaction rate for all
nuclides can be obtained with "total". For example, to obtain the reaction
rates for U-235, Pu-239, and all nuclides in a material, this element should
be:
.. code-block:: xml
<nuclides>U-235 Pu-239 total</nuclides>
*Default*: total
:scores:
The desired responses to be accumulated. See below for full details on what
responses can be tallied.

5
devguide/index.html
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@ -60,6 +60,11 @@ as debugging.</p>
<ul>
<li class="toctree-l1"><a class="reference internal" href="structures.html">1. Data Structures</a></li>
<li class="toctree-l1"><a class="reference internal" href="xml-fortran.html">2. xml-fortran Input Parsing</a></li>
<li class="toctree-l1"><a class="reference internal" href="statepoint.html">3. State Point Binary File Specifications</a><ul>
<li class="toctree-l2"><a class="reference internal" href="statepoint.html#revision-2">3.1. Revision 2</a></li>
<li class="toctree-l2"><a class="reference internal" href="statepoint.html#revision-1">3.2. Revision 1</a></li>
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<div class="content">
<div class="section" id="state-point-binary-file-specifications">
<span id="devguide-statepoint"></span><h1>3. State Point Binary File Specifications<a class="headerlink" href="#state-point-binary-file-specifications" title="Permalink to this headline"></a></h1>
<div class="section" id="revision-2">
<h2>3.1. Revision 2<a class="headerlink" href="#revision-2" title="Permalink to this headline"></a></h2>
<p><strong>integer(4) REVISION_STATEPOINT</strong></p>
<blockquote>
<div>Revision of the binary state point file. Any time a change is made in the
format of the state-point file, this integer is incremented.</div></blockquote>
<p><strong>integer(4) VERSION_MAJOR</strong></p>
<blockquote>
<div>Major version number for OpenMC</div></blockquote>
<p><strong>integer(4) VERSION_MINOR</strong></p>
<blockquote>
<div>Minor version number for OpenMC</div></blockquote>
<p><strong>integer(4) VERSION_RELEASE</strong></p>
<blockquote>
<div>Release version number for OpenMC</div></blockquote>
<p><strong>integer(4) run_mode</strong></p>
<blockquote>
<div>run mode used. The modes are described in constants.F90.</div></blockquote>
<p><strong>integer(8) n_particles</strong></p>
<blockquote>
<div>Number of particles used per generation.</div></blockquote>
<p><strong>integer(4) n_batches</strong></p>
<blockquote>
<div>Total number of batches (active + inactive).</div></blockquote>
<p><strong>integer(4) n_inactive</strong></p>
<blockquote>
<div>Number of inactive batches</div></blockquote>
<p><strong>integer(4) gen_per_batch</strong></p>
<blockquote>
<div>Number of generations per batch for criticality calculations</div></blockquote>
<p><strong>integer(4) current_batch</strong></p>
<blockquote>
<div>The number of batches already simulated.</div></blockquote>
<p><em>do i = 1, current_batch</em></p>
<blockquote>
<div><p><strong>real(8) k_batch(i)</strong></p>
<blockquote>
<div>k-effective for the i-th batch</div></blockquote>
<p>if (entropy_on)</p>
<blockquote>
<div><strong>real(8) entropy for the i-th batch</strong></div></blockquote>
</div></blockquote>
<p><strong>integer(4) N_GLOBAL_TALLIES</strong></p>
<blockquote>
<div>Number of global tally scores</div></blockquote>
<p><em>do i = 1, N_GLOBAL_TALLIES</em></p>
<blockquote>
<div><p><strong>real(8) global_tallies(i) % sum</strong></p>
<blockquote>
<div>Accumulated sum for the i-th global tally</div></blockquote>
</div></blockquote>
<p><em>do i = 1, N_GLOBAL_TALLIES</em></p>
<blockquote>
<div><p><strong>real(8) global_tallies(i) % sum_sq</strong></p>
<blockquote>
<div>Accumulated sum of squares for the i-th global tally</div></blockquote>
</div></blockquote>
<p><strong>integer(4) n_tallies</strong></p>
<p><em>do i = 1, n_tallies</em></p>
<blockquote>
<div><p><strong>integer(4) size(tallies(i) % scores, 1)</strong></p>
<blockquote>
<div>Total number of score bins for the i-th tally</div></blockquote>
<p><strong>integer(4) size(tallies(i) % scores, 2)</strong></p>
<blockquote>
<div>Total number of filter bins for the i-th tally</div></blockquote>
</div></blockquote>
<p><em>do i = 1, n_tallies</em></p>
<blockquote>
<div><p><em>do k = 1, size(tallies(i) % scores, 2)</em></p>
<blockquote>
<div><p><em>do j = 1, size(tallies(i) % scores, 1)</em></p>
<blockquote>
<div><p><strong>real(8) tallies(i) % scores(j,k) % sum</strong></p>
<blockquote>
<div>Accumulated sum for the j-th score and k-th filter of the i-th
tally</div></blockquote>
<p><strong>real(8) tallies(i) % scores(j,k) % sum_sq</strong></p>
<blockquote>
<div>Accumulated sum of squares for the j-th score and k-th filter of
the i-th tally</div></blockquote>
</div></blockquote>
</div></blockquote>
</div></blockquote>
</div>
<div class="section" id="revision-1">
<h2>3.2. Revision 1<a class="headerlink" href="#revision-1" title="Permalink to this headline"></a></h2>
<p><strong>integer(4) REVISION_STATEPOINT</strong></p>
<blockquote>
<div>Revision of the binary state point file. Any time a change is made in the
format of the state-point file, this integer is incremented.</div></blockquote>
<p><strong>integer(4) VERSION_MAJOR</strong></p>
<blockquote>
<div>Major version number for OpenMC</div></blockquote>
<p><strong>integer(4) VERSION_MINOR</strong></p>
<blockquote>
<div>Minor version number for OpenMC</div></blockquote>
<p><strong>integer(4) VERSION_RELEASE</strong></p>
<blockquote>
<div>Release version number for OpenMC</div></blockquote>
<p><strong>integer(4) run_mode</strong></p>
<blockquote>
<div>run mode used. The modes are described in constants.F90.</div></blockquote>
<p><strong>integer(8) n_particles</strong></p>
<blockquote>
<div>Number of particles used per generation.</div></blockquote>
<p><strong>integer(4) n_batches</strong></p>
<blockquote>
<div>Total number of batches (active + inactive).</div></blockquote>
<p><strong>integer(4) n_inactive</strong></p>
<blockquote>
<div>Number of inactive batches</div></blockquote>
<p><strong>integer(4) gen_per_batch</strong></p>
<blockquote>
<div>Number of generations per batch for criticality calculations</div></blockquote>
<p><strong>integer(4) current_batch</strong></p>
<blockquote>
<div>The number of batches already simulated.</div></blockquote>
<p><em>do i = 1, current_batch</em></p>
<blockquote>
<div><p><strong>real(8) k_batch(i)</strong></p>
<blockquote>
<div>k-effective for the i-th batch</div></blockquote>
<p>if (entropy_on)</p>
<blockquote>
<div><strong>real(8) entropy for the i-th batch</strong></div></blockquote>
</div></blockquote>
<p><strong>integer(4) N_GLOBAL_TALLIES</strong></p>
<blockquote>
<div>Number of global tally scores</div></blockquote>
<p><em>do i = 1, N_GLOBAL_TALLIES</em></p>
<blockquote>
<div><p><strong>real(8) global_tallies(i) % sum</strong></p>
<blockquote>
<div>Accumulated sum for the i-th global tally</div></blockquote>
</div></blockquote>
<p><em>do i = 1, N_GLOBAL_TALLIES</em></p>
<blockquote>
<div><p><strong>real(8) global_tallies(i) % sum_sq</strong></p>
<blockquote>
<div>Accumulated sum of squares for the i-th global tally</div></blockquote>
</div></blockquote>
<p><strong>integer(4) n_tallies</strong></p>
<p><em>do i = 1, n_tallies</em></p>
<blockquote>
<div><p><strong>integer(4) size(tallies(i) % scores, 1)</strong></p>
<blockquote>
<div>Total number of score bins for the i-th tally</div></blockquote>
<p><strong>integer(4) size(tallies(i) % scores, 2)</strong></p>
<blockquote>
<div>Total number of filter bins for the i-th tally</div></blockquote>
<p><em>do k = 1, size(tallies(i) % scores, 2)</em></p>
<blockquote>
<div><p><em>do j = 1, size(tallies(i) % scores, 1)</em></p>
<blockquote>
<div><p><strong>real(8) tallies(i) % scores(j,k) % sum</strong></p>
<blockquote>
<div>Accumulated sum for the j-th score and k-th filter of the i-th
tally</div></blockquote>
</div></blockquote>
</div></blockquote>
<p><em>do k = 1, size(tallies(i) % scores, 2)</em></p>
<blockquote>
<div><p><em>do j = 1, size(tallies(i) % scores, 1)</em></p>
<blockquote>
<div><p><strong>real(8) tallies(i) % scores(j,k) % sum_sq</strong></p>
<blockquote>
<div>Accumulated sum of squares for the j-th score and k-th filter of
the i-th tally</div></blockquote>
</div></blockquote>
</div></blockquote>
</div></blockquote>
</div>
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<div class="content">
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="28%" />
<col width="57%" />
</colgroup>
<thead valign="bottom">
<tr class="row-odd"><th class="head">Type</th>
<th class="head">Variable</th>
<th class="head">Description</th>
</tr>
</thead>
<tbody valign="top">
<tr class="row-even"><td>integer(4)</td>
<td>REVISION_STATEPOINT</td>
<td>Revision of the binary state point file. Any
time a change is made in the format of the
state-point file, this integer is
incremented.</td>
</tr>
<tr class="row-odd"><td>integer(4)</td>
<td>VERSION_MAJOR</td>
<td>Major version number for OpenMC</td>
</tr>
<tr class="row-even"><td>integer(4)</td>
<td>VERSION_MINOR</td>
<td>Minor version number for OpenMC</td>
</tr>
<tr class="row-odd"><td>integer(4)</td>
<td>VERSION_RELEASE</td>
<td>Release version number for OpenMC</td>
</tr>
<tr class="row-even"><td>integer(4)</td>
<td>run_mode</td>
<td>Run mode used. 1 = criticality, 2 = fixed
source</td>
</tr>
<tr class="row-odd"><td>integer(8)</td>
<td>n_particles</td>
<td>Number of particles used per generation.</td>
</tr>
<tr class="row-even"><td>integer(4)</td>
<td>n_batches</td>
<td>Total number of batches (active + inactive).</td>
</tr>
<tr class="row-odd"><td>integer(4)</td>
<td>n_inactive</td>
<td>Number of inactive batches</td>
</tr>
<tr class="row-even"><td>integer(4)</td>
<td>gen_per_batch</td>
<td>Number of generations per batch for
criticality calculations</td>
</tr>
<tr class="row-odd"><td>integer(4)</td>
<td>current_batch</td>
<td>Number of batches already simulated.</td>
</tr>
</tbody>
</table>
<p>The next variable appears only for a criticality calculation (run_mode =
MODE_CRITICALITY = 1).</p>
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="28%" />
<col width="57%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>real(8)</td>
<td>k_batch(i), i = 1,
current_batch</td>
<td>k-effective for the i-th batch</td>
</tr>
</tbody>
</table>
<p>The next variable appears only for a criticality calculation where Shannon
entropy has been turned on.</p>
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="28%" />
<col width="57%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>real(8)</td>
<td>entropy(i), i = 1,
current_batch</td>
<td>Shannon entropy for the i-th batch</td>
</tr>
</tbody>
</table>
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<li class="toctree-l3"><a class="reference internal" href="statistics.html#mean">3.3.1. Mean</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#variance">3.3.2. Variance</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#variance-of-the-mean">3.3.3. Variance of the Mean</a></li>
<li class="toctree-l3"><a class="reference internal" href="statistics.html#confidence-intervals">3.3.4. Confidence Intervals</a></li>
</ul>
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<li class="toctree-l2"><a class="reference internal" href="statistics.html#random-number-generation">3.4. Random Number Generation</a></li>
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@ -178,6 +178,75 @@ of this is that the longer you run a simulation, the better you know your
results. Therefore, by running a simulation long enough, it is possible to
reduce the stochastic uncertainty to arbitrarily low levels.</p>
</div>
<div class="section" id="confidence-intervals">
<h3>3.3.4. Confidence Intervals<a class="headerlink" href="#confidence-intervals" title="Permalink to this headline"></a></h3>
<p>While the sample variance and standard deviation gives us some idea about the
variability of the estimate of the mean of whatever quantities we&#8217;ve tallied, it
does not help us interpret how confidence we should be in the results. To
quantity the reliability of our estimates, we can use <a class="reference external" href="http://en.wikipedia.org/wiki/Confidence_interval">confidence intervals</a>
based on the calculated sample variance.</p>
<p>A <img class="math" src="../_images/math/feea5c83d5de074b138327d3617c30402fdd9768.png" alt="1-\alpha"/> confidence interval for a population parameter is defined as
such: if we repeat the same experiment many times and calculate the confidence
interval for each experiment, then <img class="math" src="../_images/math/e63009dbf6176a47dc83a6c06dd5ce224d6e57d4.png" alt="1 - \alpha"/> percent of the calculated
intervals would encompass the true population parameter. Let <img class="math" src="../_images/math/d0c7c0908f2b24307dd8c0d64e8082efd5872155.png" alt="x_1, x_2,
\dots, x_N"/> be samples from a set of independent, identically-distributed random
variables each with population mean <img class="math" src="../_images/math/2d8c833ed800824727cd7bd2fb9de1a12ad7e674.png" alt="\mu"/> and variance
<img class="math" src="../_images/math/741fb9098efcb98055f467f87630a5d0ca599b6b.png" alt="\sigma^2"/>. The t-statistic is defined as</p>
<div class="math" id="equation-t-statistic">
<p><span class="eqno">(9)</span><img src="../_images/math/7a8fa6d18fdddd436cd3c52612a3372897f7c5c0.png" alt="t = \frac{\bar{x} - \mu}{s/\sqrt{N}}"/></p>
</div><p>where <img class="math" src="../_images/math/f06e84fe84a6c63a9c2c392af11652f6e0d72cf4.png" alt="\bar{x}"/> is the sample mean from equation <a href="#equation-sample-mean">(2)</a> and
<img class="math" src="../_images/math/f37bba504894945c07a32f5496d74299a37aa51c.png" alt="s"/> is the standard deviation based on equation
<a href="#equation-unbiased-variance">(5)</a>. If the random variables <img class="math" src="../_images/math/5f8e5cbb6204882df1cf17cfe4b308d485af8056.png" alt="X_i"/> are
normally-distributed, then the t-statistic has a <a class="reference external" href="http://en.wikipedia.org/wiki/Student%27s_t-distribution">Student&#8217;s t-distribution</a>
with <img class="math" src="../_images/math/a256c70ad4c46ec1127c5be68f8bb3075e9ced31.png" alt="N-1"/> degrees of freedom. This implies that</p>
<div class="math" id="equation-t-probability">
<p><span class="eqno">(10)</span><img src="../_images/math/4a210f77a1c79011bdc5ac4f2cac91a4c5a08959.png" alt="Pr \left ( -t_{1 - \alpha/2, N - 1} \le \frac{\bar{x} - \mu}{s/\sqrt{N}} \le
t_{1 - \alpha/2, N - 1} \right ) = 1 - \alpha"/></p>
</div><p>where <img class="math" src="../_images/math/1bc7ce223ddb22edcd126ed8d841b796f2f337d9.png" alt="t_{1-\alpha/2, N-1}"/> is the <img class="math" src="../_images/math/f3f0133f5afb7e759a00024c929a5f273f316403.png" alt="1 - \alpha/2"/> percentile of a
t-distribution with <img class="math" src="../_images/math/a256c70ad4c46ec1127c5be68f8bb3075e9ced31.png" alt="N-1"/> degrees of freedom. Thus, the <img class="math" src="../_images/math/e63009dbf6176a47dc83a6c06dd5ce224d6e57d4.png" alt="1 - \alpha"/>
two sided confidence interval for the sample mean is</p>
<div class="math" id="equation-two-sided-ci">
<p><span class="eqno">(11)</span><img src="../_images/math/80bc7504239295d322d8606b71adc1190e09a896.png" alt="\bar{x} \pm t_{1 - \alpha/2, N-1} \frac{s}{\sqrt{N}}."/></p>
</div><p>One should be cautioned that equation <a href="#equation-two-sided-ci">(11)</a> <strong>only applies if the
underlying random variables are normally-distributed!</strong> In general, this may not
be true for a tally random variable &#8211; the central limit theorem guarantees only
that the sample mean is normally distributed, not the underlying random
variable. If batching is used, then the underlying random variable, which would
then be the averages from each batch, will be normally distributed as long as
the conditions of the central limit theorem are met.</p>
<p>Let us now outline the method used to calculate the percentile of the Student&#8217;s
t-distribution. For one or two degrees of freedom, the percentile can be written
analytically. For one degree of freedom, the t-distribution becomes a standard
<a class="reference external" href="http://en.wikipedia.org/wiki/Cauchy_distribution">Cauchy distribution</a> whose cumulative distribution function is</p>
<div class="math" id="equation-cauchy-cdf">
<p><span class="eqno">(12)</span><img src="../_images/math/436e8db97463066d1a7386a95b10ac520bbe8b3a.png" alt="c(x) = \frac{1}{\pi} \arctan x + \frac{1}{2}."/></p>
</div><p>Thus, inverting the cumulative distribution function, we find the <img class="math" src="../_images/math/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" alt="x"/>
percentile of the standard Cauchy distribution to be</p>
<div class="math" id="equation-percentile-1">
<p><span class="eqno">(13)</span><img src="../_images/math/fa2f03813f247d34e237d7d4f70aad833a23ac36.png" alt="t_{x,1} = \tan \left ( \pi \left ( x - \frac{1}{2} \right ) \right )."/></p>
</div><p>For two degrees of freedom, the cumulative distribution function is the
second-degree polynomial</p>
<div class="math" id="equation-t-2-polynomial">
<p><span class="eqno">(14)</span><img src="../_images/math/6951671d483dd1a00fdbf1c2a63f822d8a5dfb0f.png" alt="c(x) = \frac{1}{2} + \frac{x}{2\sqrt{x^2 + 2}}"/></p>
</div><p>Solving for <img class="math" src="../_images/math/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" alt="x"/>, we find the <img class="math" src="../_images/math/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" alt="x"/> percentile to be</p>
<div class="math" id="equation-percentile-2">
<p><span class="eqno">(15)</span><img src="../_images/math/9bc6d41e157898a5956cd9c4ccf338dea7050d12.png" alt="t_{x,2} = \frac{2\sqrt{2} (x - 1/2)}{\sqrt{1 - 4 (x - 1/2)^2}}"/></p>
</div><p>For degrees of freedom greater than two, it is not possible to obtain an
analytical formula for the inverse of the cumulative distribution function. We
must resort to either numerically solving for the inverse or to an
approximation. Approximations for percentiles of the t-distribution have been
found with high levels of accuracy. OpenMC uses the approximation from
<a class="reference internal" href="#george">[George]</a>:</p>
<div class="math" id="equation-percentile-n">
<p><span class="eqno">(16)</span><img src="../_images/math/5ba93ef9c5f2963c0b31e884c59317c780965345.png" alt="t_{x,n} = \sqrt{\frac{n}{n-2}} \left ( z_x + \frac{1}{4} \frac{z_x^3 -
3z_x}{n-2} + \frac{1}{96} \frac{5z_x^5 - 56z_x^3 + 75z_x}{(n-2)^2} +
\frac{1}{384} \frac{3z_x^7 - 81z_x^5 + 417z_x^3 - 315z_x}{(n-2)^3} \right )"/></p>
</div><p>where <img class="math" src="../_images/math/13ec3386d628b5ca8d96ff83af9b240831084348.png" alt="z_x"/> is the <img class="math" src="../_images/math/26eeb5258ca5099acf8fe96b2a1049c48c89a5e6.png" alt="x"/> percentile of the standard normal
distribution. In order to determine an arbitrary percentile of the standard
normal distribution, we use an <a class="reference external" href="http://home.online.no/~pjacklam/notes/invnorm/">unpublished rational approximation</a>. After
using the rational approximation, one iteration of Newton&#8217;s method is applied to
improve the estimate of the percentile.</p>
</div>
</div>
<div class="section" id="random-number-generation">
<h2>3.4. Random Number Generation<a class="headerlink" href="#random-number-generation" title="Permalink to this headline"></a></h2>
@ -195,7 +264,7 @@ simplest and commonly used algorithms is called a <a class="reference external"
generator</a>. We start with some random number seed <img class="math" src="../_images/math/da04290a79211712a58bf7241c9fb64251e000c3.png" alt="\xi_0"/> and a sequence
of random numbers is generated using the following recurrence relation:</p>
<div class="math" id="equation-lcg">
<p><span class="eqno">(9)</span><img src="../_images/math/838ea831f2458960d581811d15ea37bae3f20014.png" alt="\xi_{i+1} = g \xi_i + c \mod M"/></p>
<p><span class="eqno">(17)</span><img src="../_images/math/838ea831f2458960d581811d15ea37bae3f20014.png" alt="\xi_{i+1} = g \xi_i + c \mod M"/></p>
</div><p>where <img class="math" src="../_images/math/311cabda3a9b09f0dde217303ca9d1cd9201dcf6.png" alt="g"/>, <img class="math" src="../_images/math/3372c1cb6d68cf97c2d231acc0b47b95a9ed04cc.png" alt="c"/>, and <img class="math" src="../_images/math/5d1e4485dc90c450e8c76826516c1b2ccb8fce16.png" alt="M"/> are constants. The choice of these
constants will have a profound effect on the quality and performance of the
generator, so they should not be chosen arbitrarily. As Donald Knuth said in his
@ -215,11 +284,22 @@ us to skip ahead in <img class="math" src="../_images/math/c0db20de736ea9b9091c5
algorithm to do so is described in a paper by <a class="reference external" href="https://laws.lanl.gov/vhosts/mcnp.lanl.gov/pdf_files/anl_rn_arb-strides_1994.pdf">Brown</a>. This algorithm relies on
the following relationship:</p>
<div class="math" id="equation-lcg-skipahead">
<p><span class="eqno">(10)</span><img src="../_images/math/29e04a6d8160c6dd91ec828d9133bcdeff0f1fdc.png" alt="\xi_{i+k} = g^k \xi_i + c \frac{g^k - 1}{g - 1} \mod M"/></p>
</div><p>Note that equation <a href="#equation-lcg-skipahead">(10)</a> has the same form as equation <a href="#equation-lcg">(9)</a>
<p><span class="eqno">(18)</span><img src="../_images/math/29e04a6d8160c6dd91ec828d9133bcdeff0f1fdc.png" alt="\xi_{i+k} = g^k \xi_i + c \frac{g^k - 1}{g - 1} \mod M"/></p>
</div><p>Note that equation <a href="#equation-lcg-skipahead">(18)</a> has the same form as equation <a href="#equation-lcg">(17)</a>
so the idea is to determine the new multiplicative and additive constants in
<img class="math" src="../_images/math/c0db20de736ea9b9091c56adbd1e4111cc026472.png" alt="O(\log N)"/> operations.</p>
</div>
<div class="section" id="references">
<h2>3.5. References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
<table class="docutils citation" frame="void" id="george" rules="none">
<colgroup><col class="label" /><col /></colgroup>
<tbody valign="top">
<tr><td class="label"><a class="fn-backref" href="#id2">[George]</a></td><td>E. E. Olusegun George and Meenakshi Sivaram, &#8220;A modification of the
Fisher-Cornish approximation for the student t percentiles,&#8221; Communication
in Statistics - Simulation and Computation, 16 (4), pp. 1123-1132 (1987).</td></tr>
</tbody>
</table>
</div>
</div>

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@ -29,7 +29,7 @@
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@ -40,7 +40,7 @@
<div class="topnav">
<p>
«&#160;&#160;<a href="devguide/xml-fortran.html">2. xml-fortran Input Parsing</a>
«&#160;&#160;<a href="devguide/statepoint.html">3. State Point Binary File Specifications</a>
&#160;&#160;::&#160;&#160;
<a class="uplink" href="index.html">Contents</a>
&#160;&#160;::&#160;&#160;
@ -74,7 +74,7 @@ pp. 125&#8211;135 (2012). [<a class="reference external" href="http://web.mit.ed
<div class="bottomnav">
<p>
«&#160;&#160;<a href="devguide/xml-fortran.html">2. xml-fortran Input Parsing</a>
«&#160;&#160;<a href="devguide/statepoint.html">3. State Point Binary File Specifications</a>
&#160;&#160;::&#160;&#160;
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@ -28,7 +28,7 @@
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@ -44,7 +44,7 @@
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&#160;&#160;::&#160;&#160;
<a href="notes_0.4.3.html">Release Notes for OpenMC 0.4.3</a>&#160;&#160;»
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@ -57,6 +57,7 @@
bugs fixed, and known issues for each successive release.</p>
<div class="toctree-wrapper compound">
<ul>
<li class="toctree-l1"><a class="reference internal" href="notes_0.4.4.html">Release Notes for OpenMC 0.4.4</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes_0.4.3.html">Release Notes for OpenMC 0.4.3</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes_0.4.2.html">Release Notes for OpenMC 0.4.2</a></li>
<li class="toctree-l1"><a class="reference internal" href="notes_0.4.1.html">Release Notes for OpenMC 0.4.1</a></li>
@ -74,7 +75,7 @@ bugs fixed, and known issues for each successive release.</p>
&#160;&#160;::&#160;&#160;
<a class="uplink" href="../index.html">Contents</a>
&#160;&#160;::&#160;&#160;
<a href="notes_0.4.3.html">Release Notes for OpenMC 0.4.3</a>&#160;&#160;»
<a href="notes_0.4.4.html">Release Notes for OpenMC 0.4.4</a>&#160;&#160;»
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@ -30,7 +30,7 @@
<link rel="top" title="OpenMC Documentation" href="../index.html" />
<link rel="up" title="Release Notes" href="index.html" />
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@ -41,7 +41,7 @@
<div class="topnav">
<p>
«&#160;&#160;<a href="index.html">Release Notes</a>
«&#160;&#160;<a href="notes_0.4.4.html">Release Notes for OpenMC 0.4.4</a>
&#160;&#160;::&#160;&#160;
<a class="uplink" href="../index.html">Contents</a>
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@ -54,11 +54,6 @@
<div class="section" id="release-notes-for-openmc-0-4-3">
<span id="notes-0-4-3"></span><h1>Release Notes for OpenMC 0.4.3<a class="headerlink" href="#release-notes-for-openmc-0-4-3" title="Permalink to this headline"></a></h1>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">These release notes are for an upcoming release of OpenMC and are still
subject to change.</p>
</div>
<div class="section" id="system-requirements">
<h2>System Requirements<a class="headerlink" href="#system-requirements" title="Permalink to this headline"></a></h2>
<p>There are no special requirements for running the OpenMC code. As of this
@ -69,7 +64,9 @@ the problem at hand (mostly on the number of nuclides in the problem).</p>
<div class="section" id="new-features">
<h2>New Features<a class="headerlink" href="#new-features" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li>Option to report confidence intervals for tally results.</li>
<li>Rotation and translation for filled cells.</li>
<li>Ability to explicitly specify &lt;estimator&gt; for tallies.</li>
<li>Ability to store state points and use them to restart runs.</li>
<li>Fixed source calculations (no subcritical multiplication however).</li>
<li>Expanded options for external source distribution.</li>
@ -82,6 +79,7 @@ the problem at hand (mostly on the number of nuclides in the problem).</p>
<div class="section" id="bug-fixes">
<h2>Bug Fixes<a class="headerlink" href="#bug-fixes" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li><a class="reference external" href="https://github.com/mit-crpg/openmc/commit/33f29a">33f29a</a>: Handle negative values in probability table.</li>
<li><a class="reference external" href="https://github.com/mit-crpg/openmc/commit/1c472d">1c472d</a>: Fixed survival biasing with probability tables.</li>
<li><a class="reference external" href="https://github.com/mit-crpg/openmc/commit/3c6e80">3c6e80</a>: Fixed writing tallies with no filters.</li>
<li><a class="reference external" href="https://github.com/mit-crpg/openmc/commit/460ef1">460ef1</a>: Invalid results for duplicate tallies.</li>
@ -98,7 +96,7 @@ the problem at hand (mostly on the number of nuclides in the problem).</p>
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<div class="section" id="release-notes-for-openmc-0-4-4">
<span id="notes-0-4-4"></span><h1>Release Notes for OpenMC 0.4.4<a class="headerlink" href="#release-notes-for-openmc-0-4-4" title="Permalink to this headline"></a></h1>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">These release notes are for an upcoming release of OpenMC and are still
subject to change.</p>
</div>
<div class="section" id="system-requirements">
<h2>System Requirements<a class="headerlink" href="#system-requirements" title="Permalink to this headline"></a></h2>
<p>There are no special requirements for running the OpenMC code. As of this
release, OpenMC has been tested on a variety of Linux distributions, Mac OS X,
and Microsoft Windows 7. Memory requirements will vary depending on the size of
the problem at hand (mostly on the number of nuclides in the problem).</p>
</div>
<div class="section" id="new-features">
<h2>New Features<a class="headerlink" href="#new-features" title="Permalink to this headline"></a></h2>
<ul class="simple">
<li>Option to specify &lt;upper_right&gt; for tally meshes.</li>
</ul>
</div>
<div class="section" id="bug-fixes">
<h2>Bug Fixes<a class="headerlink" href="#bug-fixes" title="Permalink to this headline"></a></h2>
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@ -76,21 +76,23 @@ essential aspects of using OpenMC to perform neutronic simulations.</p>
<li class="toctree-l1"><a class="reference internal" href="input.html">3. Writing XML Input Files</a><ul>
<li class="toctree-l2"><a class="reference internal" href="input.html#overview-of-files">3.1. Overview of Files</a></li>
<li class="toctree-l2"><a class="reference internal" href="input.html#settings-specification-settings-xml">3.2. Settings Specification &#8211; settings.xml</a><ul>
<li class="toctree-l3"><a class="reference internal" href="input.html#criticality-element">3.2.1. <tt class="docutils literal"><span class="pre">&lt;criticality&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#cross-sections-element">3.2.2. <tt class="docutils literal"><span class="pre">&lt;cross_sections&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#cutoff-element">3.2.3. <tt class="docutils literal"><span class="pre">&lt;cutoff&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#energy-grid-element">3.2.4. <tt class="docutils literal"><span class="pre">&lt;energy_grid&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#entropy-element">3.2.5. <tt class="docutils literal"><span class="pre">&lt;entropy&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#fixed-source-element">3.2.6. <tt class="docutils literal"><span class="pre">&lt;fixed_source&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#no-reduce-element">3.2.7. <tt class="docutils literal"><span class="pre">&lt;no_reduce&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#ptables-element">3.2.8. <tt class="docutils literal"><span class="pre">&lt;ptables&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#seed-element">3.2.9. <tt class="docutils literal"><span class="pre">&lt;seed&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#source-element">3.2.10. <tt class="docutils literal"><span class="pre">&lt;source&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#survival-biasing-element">3.2.11. <tt class="docutils literal"><span class="pre">&lt;survival_biasing&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#trace-element">3.2.12. <tt class="docutils literal"><span class="pre">&lt;trace&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#uniform-fs-element">3.2.13. <tt class="docutils literal"><span class="pre">&lt;uniform_fs&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#verbosity-element">3.2.14. <tt class="docutils literal"><span class="pre">&lt;verbosity&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#write-source-element">3.2.15. <tt class="docutils literal"><span class="pre">&lt;write_source&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#confidence-intervals-element">3.2.1. <tt class="docutils literal"><span class="pre">&lt;confidence_intervals&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#criticality-element">3.2.2. <tt class="docutils literal"><span class="pre">&lt;criticality&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#cross-sections-element">3.2.3. <tt class="docutils literal"><span class="pre">&lt;cross_sections&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#cutoff-element">3.2.4. <tt class="docutils literal"><span class="pre">&lt;cutoff&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#energy-grid-element">3.2.5. <tt class="docutils literal"><span class="pre">&lt;energy_grid&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#entropy-element">3.2.6. <tt class="docutils literal"><span class="pre">&lt;entropy&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#fixed-source-element">3.2.7. <tt class="docutils literal"><span class="pre">&lt;fixed_source&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#no-reduce-element">3.2.8. <tt class="docutils literal"><span class="pre">&lt;no_reduce&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#ptables-element">3.2.9. <tt class="docutils literal"><span class="pre">&lt;ptables&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#seed-element">3.2.10. <tt class="docutils literal"><span class="pre">&lt;seed&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#source-element">3.2.11. <tt class="docutils literal"><span class="pre">&lt;source&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#survival-biasing-element">3.2.12. <tt class="docutils literal"><span class="pre">&lt;survival_biasing&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#trace-element">3.2.13. <tt class="docutils literal"><span class="pre">&lt;trace&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#uniform-fs-element">3.2.14. <tt class="docutils literal"><span class="pre">&lt;uniform_fs&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#verbosity-element">3.2.15. <tt class="docutils literal"><span class="pre">&lt;verbosity&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#write-state-point-element">3.2.16. <tt class="docutils literal"><span class="pre">&lt;write_state_point&gt;</span></tt> Element</a></li>
<li class="toctree-l3"><a class="reference internal" href="input.html#write-source-element">3.2.17. <tt class="docutils literal"><span class="pre">&lt;write_source&gt;</span></tt> Element</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="input.html#geometry-specification-geometry-xml">3.3. Geometry Specification &#8211; geometry.xml</a><ul>

84
usersguide/input.html
View file

@ -94,8 +94,18 @@ which should be plotted. OpenMC expects that these files are called:</p>
<h2>3.2. Settings Specification &#8211; settings.xml<a class="headerlink" href="#settings-specification-settings-xml" title="Permalink to this headline"></a></h2>
<p>All simulation parameters and miscellaneous options are specified in the
settings.xml file.</p>
<div class="section" id="confidence-intervals-element">
<h3>3.2.1. <tt class="docutils literal"><span class="pre">&lt;confidence_intervals&gt;</span></tt> Element<a class="headerlink" href="#confidence-intervals-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;confidence_intervals&gt;</span></tt> element has no attributes and has an accepted
value of &#8220;on&#8221; or &#8220;off&#8221;. If set to &#8220;on&#8221;, uncertainties on tally results will be
reported as the half-width of the 95% two-sided confidence interval. If set to
&#8220;off&#8221;, uncertainties on tally results will be reported as the sample standard
deviation.</p>
<blockquote>
<div><em>Default</em>: off</div></blockquote>
</div>
<div class="section" id="criticality-element">
<h3>3.2.1. <tt class="docutils literal"><span class="pre">&lt;criticality&gt;</span></tt> Element<a class="headerlink" href="#criticality-element" title="Permalink to this headline"></a></h3>
<h3>3.2.2. <tt class="docutils literal"><span class="pre">&lt;criticality&gt;</span></tt> Element<a class="headerlink" href="#criticality-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;criticality&gt;</span></tt> element indicates that a criticality calculation should be
performed. It has the following attributes/sub-elements:</p>
<blockquote>
@ -130,7 +140,7 @@ immediately.</p>
</div></blockquote>
</div>
<div class="section" id="cross-sections-element">
<span id="cross-sections"></span><h3>3.2.2. <tt class="docutils literal"><span class="pre">&lt;cross_sections&gt;</span></tt> Element<a class="headerlink" href="#cross-sections-element" title="Permalink to this headline"></a></h3>
<span id="cross-sections"></span><h3>3.2.3. <tt class="docutils literal"><span class="pre">&lt;cross_sections&gt;</span></tt> Element<a class="headerlink" href="#cross-sections-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;cross_sections&gt;</span></tt> element has no attributes and simply indicates the path
to an XML cross section listing file (usually named cross_sections.xml). If this
element is absent from the settings.xml file, the <span class="target" id="index-0"></span><tt class="xref std std-envvar docutils literal"><span class="pre">CROSS_SECTIONS</span></tt>
@ -138,7 +148,7 @@ environment variable will be used to find the path to the XML cross section
listing.</p>
</div>
<div class="section" id="cutoff-element">
<h3>3.2.3. <tt class="docutils literal"><span class="pre">&lt;cutoff&gt;</span></tt> Element<a class="headerlink" href="#cutoff-element" title="Permalink to this headline"></a></h3>
<h3>3.2.4. <tt class="docutils literal"><span class="pre">&lt;cutoff&gt;</span></tt> Element<a class="headerlink" href="#cutoff-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;cutoff&gt;</span></tt> element indicates the weight cutoff used below which particles
undergo Russian roulette. Surviving particles are assigned a user-determined
weight. Note that weight cutoffs and Russian rouletting are not turned on by
@ -162,7 +172,7 @@ roulette.</p>
</div></blockquote>
</div>
<div class="section" id="energy-grid-element">
<h3>3.2.4. <tt class="docutils literal"><span class="pre">&lt;energy_grid&gt;</span></tt> Element<a class="headerlink" href="#energy-grid-element" title="Permalink to this headline"></a></h3>
<h3>3.2.5. <tt class="docutils literal"><span class="pre">&lt;energy_grid&gt;</span></tt> Element<a class="headerlink" href="#energy-grid-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;energy_grid&gt;</span></tt> element determines the treatment of the energy grid during
a simulation. Setting this element to &#8220;nuclide&#8221; will cause OpenMC to use a
nuclide&#8217;s energy grid when determining what points to interpolate between for
@ -173,7 +183,7 @@ treatment is slightly different than that employed in Serpent.</p>
<div><em>Default</em>: union</div></blockquote>
</div>
<div class="section" id="entropy-element">
<h3>3.2.5. <tt class="docutils literal"><span class="pre">&lt;entropy&gt;</span></tt> Element<a class="headerlink" href="#entropy-element" title="Permalink to this headline"></a></h3>
<h3>3.2.6. <tt class="docutils literal"><span class="pre">&lt;entropy&gt;</span></tt> Element<a class="headerlink" href="#entropy-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;entropy&gt;</span></tt> element describes a mesh that is used for calculating Shannon
entropy. This mesh should cover all possible fissionable materials in the
problem. It has the following attributes/sub-elements:</p>
@ -203,7 +213,7 @@ problem. It has the following attributes/sub-elements:</p>
</div></blockquote>
</div>
<div class="section" id="fixed-source-element">
<h3>3.2.6. <tt class="docutils literal"><span class="pre">&lt;fixed_source&gt;</span></tt> Element<a class="headerlink" href="#fixed-source-element" title="Permalink to this headline"></a></h3>
<h3>3.2.7. <tt class="docutils literal"><span class="pre">&lt;fixed_source&gt;</span></tt> Element<a class="headerlink" href="#fixed-source-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;fixed_source&gt;</span></tt> element indicates that a fixed source calculation should be
performed. It has the following attributes/sub-elements:</p>
<blockquote>
@ -225,7 +235,7 @@ represents a realization of random variables for tallies.</p>
</div></blockquote>
</div>
<div class="section" id="no-reduce-element">
<h3>3.2.7. <tt class="docutils literal"><span class="pre">&lt;no_reduce&gt;</span></tt> Element<a class="headerlink" href="#no-reduce-element" title="Permalink to this headline"></a></h3>
<h3>3.2.8. <tt class="docutils literal"><span class="pre">&lt;no_reduce&gt;</span></tt> Element<a class="headerlink" href="#no-reduce-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;no_reduce&gt;</span></tt> element has no attributes and has an accepted value of &#8220;on&#8221;
or &#8220;off&#8221;. If set to &#8220;on&#8221;, all user-defined tallies and global tallies will not
be reduced across processors in a parallel calculation. This means that the
@ -236,7 +246,7 @@ tally data, this option can significantly improve the parallel efficiency.</p>
<div><em>Default</em>: off</div></blockquote>
</div>
<div class="section" id="ptables-element">
<h3>3.2.8. <tt class="docutils literal"><span class="pre">&lt;ptables&gt;</span></tt> Element<a class="headerlink" href="#ptables-element" title="Permalink to this headline"></a></h3>
<h3>3.2.9. <tt class="docutils literal"><span class="pre">&lt;ptables&gt;</span></tt> Element<a class="headerlink" href="#ptables-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;ptables&gt;</span></tt> element determines whether probability tables should be used
in the unresolved resonance range if available. This element has no attributes
or sub-elements and can be set to either &#8220;off&#8221; or &#8220;on&#8221;.</p>
@ -244,14 +254,14 @@ or sub-elements and can be set to either &#8220;off&#8221; or &#8220;on&#8221;.<
<div><em>Default</em>: on</div></blockquote>
</div>
<div class="section" id="seed-element">
<h3>3.2.9. <tt class="docutils literal"><span class="pre">&lt;seed&gt;</span></tt> Element<a class="headerlink" href="#seed-element" title="Permalink to this headline"></a></h3>
<h3>3.2.10. <tt class="docutils literal"><span class="pre">&lt;seed&gt;</span></tt> Element<a class="headerlink" href="#seed-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">seed</span></tt> element is used to set the seed used for the linear congruential
pseudo-random number generator.</p>
<blockquote>
<div><em>Default</em>: 1</div></blockquote>
</div>
<div class="section" id="source-element">
<h3>3.2.10. <tt class="docutils literal"><span class="pre">&lt;source&gt;</span></tt> Element<a class="headerlink" href="#source-element" title="Permalink to this headline"></a></h3>
<h3>3.2.11. <tt class="docutils literal"><span class="pre">&lt;source&gt;</span></tt> Element<a class="headerlink" href="#source-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">source</span></tt> element gives information on an external source distribution to
be used either as the source for a fixed source calculation or the initial
source guess for criticality calculations. It takes the following
@ -353,7 +363,7 @@ c E e^{-E/a} dE"/>.</p>
</div></blockquote>
</div>
<div class="section" id="survival-biasing-element">
<h3>3.2.11. <tt class="docutils literal"><span class="pre">&lt;survival_biasing&gt;</span></tt> Element<a class="headerlink" href="#survival-biasing-element" title="Permalink to this headline"></a></h3>
<h3>3.2.12. <tt class="docutils literal"><span class="pre">&lt;survival_biasing&gt;</span></tt> Element<a class="headerlink" href="#survival-biasing-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;survival_biasing&gt;</span></tt> element has no attributes and has an accepted value
of &#8220;on&#8221; or &#8220;off&#8221;. If set to &#8220;on&#8221;, this option will enable the use of survival
biasing, otherwise known as implicit capture or absorption.</p>
@ -361,7 +371,7 @@ biasing, otherwise known as implicit capture or absorption.</p>
<div><em>Default</em>: off</div></blockquote>
</div>
<div class="section" id="trace-element">
<span id="trace"></span><h3>3.2.12. <tt class="docutils literal"><span class="pre">&lt;trace&gt;</span></tt> Element<a class="headerlink" href="#trace-element" title="Permalink to this headline"></a></h3>
<span id="trace"></span><h3>3.2.13. <tt class="docutils literal"><span class="pre">&lt;trace&gt;</span></tt> Element<a class="headerlink" href="#trace-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;trace&gt;</span></tt> element can be used to print out detailed information about a
single particle during a simulation. This element should be followed by three
integers: the batch number, generation number, and particle number.</p>
@ -369,7 +379,7 @@ integers: the batch number, generation number, and particle number.</p>
<div><em>Default</em>: None</div></blockquote>
</div>
<div class="section" id="uniform-fs-element">
<h3>3.2.13. <tt class="docutils literal"><span class="pre">&lt;uniform_fs&gt;</span></tt> Element<a class="headerlink" href="#uniform-fs-element" title="Permalink to this headline"></a></h3>
<h3>3.2.14. <tt class="docutils literal"><span class="pre">&lt;uniform_fs&gt;</span></tt> Element<a class="headerlink" href="#uniform-fs-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;uniform_fs&gt;</span></tt> element describes a mesh that is used for re-weighting
source sites at every generation based on the uniform fission site methodology
described in Kelly et al., &#8220;MC21 Analysis of the Nuclear Energy Agency Monte
@ -398,7 +408,7 @@ problem. It has the following attributes/sub-elements:</p>
</div></blockquote>
</div>
<div class="section" id="verbosity-element">
<h3>3.2.14. <tt class="docutils literal"><span class="pre">&lt;verbosity&gt;</span></tt> Element<a class="headerlink" href="#verbosity-element" title="Permalink to this headline"></a></h3>
<h3>3.2.15. <tt class="docutils literal"><span class="pre">&lt;verbosity&gt;</span></tt> Element<a class="headerlink" href="#verbosity-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;verbosity&gt;</span></tt> element tells the code how much information to display to
the standard output. A higher verbosity corresponds to more information being
displayed. This element takes the following attributes:</p>
@ -415,8 +425,19 @@ displayed. This element takes the following attributes:</p>
</table>
</div></blockquote>
</div>
<div class="section" id="write-state-point-element">
<h3>3.2.16. <tt class="docutils literal"><span class="pre">&lt;write_state_point&gt;</span></tt> Element<a class="headerlink" href="#write-state-point-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;write_state_point&gt;</span></tt> element is used to indicate batches at which the
user wishes to have a binary state point file written to disk. The state point
file can be used to restart a run or to get tally results at an intermediate
stage. This element has no attributes and should consist of a list of integers
corresponding to batches at which a binary state point file should be written to
disk.</p>
<blockquote>
<div><em>Default</em>: None</div></blockquote>
</div>
<div class="section" id="write-source-element">
<h3>3.2.15. <tt class="docutils literal"><span class="pre">&lt;write_source&gt;</span></tt> Element<a class="headerlink" href="#write-source-element" title="Permalink to this headline"></a></h3>
<h3>3.2.17. <tt class="docutils literal"><span class="pre">&lt;write_source&gt;</span></tt> Element<a class="headerlink" href="#write-source-element" title="Permalink to this headline"></a></h3>
<p>The <tt class="docutils literal"><span class="pre">&lt;write_source&gt;</span></tt> element has no attributes and has an accepted value of
&#8220;on&#8221; or &#8220;off&#8221;. If set to &#8220;on&#8221;, a binary source file will be written to disk at
the end of the run that can be used as a starting source for another run.</p>
@ -579,9 +600,9 @@ bounding surfaces would be given as &#8220;-3 5&#8221;.</p>
</tr>
<tr class="field-even field"><th class="field-name">rotation:</th><td class="field-body"><p class="first">If the cell is filled with a universe, this element specifies the angles in
degrees about the x, y, and z axes that the filled universe should be
rotated. Should be given as three real numbers.For example, if you wanted to
rotate the filled universe by 90 degrees about the z-axis, the cell element
would look something like:</p>
rotated. Should be given as three real numbers. For example, if you wanted
to rotate the filled universe by 90 degrees about the z-axis, the cell
element would look something like:</p>
<div class="highlight-xml"><div class="highlight"><pre><span class="nt">&lt;cell</span> <span class="na">fill=</span><span class="s">&quot;...&quot;</span> <span class="na">rotation=</span><span class="s">&quot;0 0 90&quot;</span> <span class="nt">/&gt;</span>
</pre></div>
</div>
@ -730,15 +751,30 @@ post-collision energy, and an arbitrary structured mesh.</p>
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">label:</th><td class="field-body">This is an optional sub-element specifying the name of this tally to be used
<tr class="field-odd field"><th class="field-name">label:</th><td class="field-body"><p class="first">This is an optional sub-element specifying the name of this tally to be used
for output purposes. This string is limited to 52 characters for formatting
purposes.</td>
purposes.</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">filters:</th><td class="field-body">A list of filters to specify what region of phase space should contribute to
the tally. See below for full details on what filters are available.</td>
<tr class="field-even field"><th class="field-name">filters:</th><td class="field-body"><p class="first">A list of filters to specify what region of phase space should contribute to
the tally. See below for full details on what filters are available.</p>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">scores:</th><td class="field-body">The desired responses to be accumulated. See below for full details on what
responses can be tallied.</td>
<tr class="field-odd field"><th class="field-name">nuclides:</th><td class="field-body"><p class="first">If specified, the scores listed will be for particular nuclides, not the
summation of reactions from all nuclides. The format for nuclides should be
[Atomic symbol]-[Mass number], e.g. &#8220;U-235&#8221;. The reaction rate for all
nuclides can be obtained with &#8220;total&#8221;. For example, to obtain the reaction
rates for U-235, Pu-239, and all nuclides in a material, this element should
be:</p>
<div class="highlight-xml"><div class="highlight"><pre><span class="nt">&lt;nuclides&gt;</span>U-235 Pu-239 total<span class="nt">&lt;/nuclides&gt;</span>
</pre></div>
</div>
<p><em>Default</em>: total</p>
</td>
</tr>
<tr class="field-even field"><th class="field-name">scores:</th><td class="field-body"><p class="first last">The desired responses to be accumulated. See below for full details on what
responses can be tallied.</p>
</td>
</tr>
</tbody>
</table>