Run OpenMC Example Files about mlmc HOT 7 OPEN

set OPENMC_CROSS_SECTIONS environment variable to get cross_sections.xml

e.g.
os.environ['OPENMC_CROSS_SECTIONS']='/Users/wenxin/nndc_hdf5/cross_sections.xml'

Don't use !export in jupyter notebook

from mlmc.

import miniconda path

import sys
sys.executable
sys.path = ['', '/Users/wenxin/miniconda3/lib/python36.zip', '/Users/wenxin/miniconda3/lib/python3.6', '/Users/wenxin/miniconda3/lib/python3.6/lib-dynload', '/Users/wenxin/miniconda3/lib/python3.6/site-packages', '/Users/wenxin/miniconda3/lib/python3.6/site-packages/cycler-0.10.0-py3.6.egg', '/Users/wenxin/miniconda3/lib/python3.6/site-packages/setuptools-27.2.0-py3.6.egg']

from mlmc.

files needed for running openmc
materials.xml: materials of pin-cell
cross_sections.xml: tells OpenMC where it can find nuclide cross sections and S(α,β) tables
geometry.xml: store shape of the containers
settings.xml: specify how many batches and particles we want to run
tallies.xml

output: plots.xml

from mlmc.

After running:

find the statepoint file.
tally.get_values
get pandas dataframs
tally.get_pandas_dataframe
use of pandas
df.boxplot

from mlmc.

./docs/source/io_formats/settings.rst:40:cutoff used below which particles undergo Russian roulette. Surviving particles
./docs/source/io_formats/settings.rst:42:rouletting are not turned on by default. The second is the energy cutoff which
./docs/source/io_formats/settings.rst:48: The weight below which particles undergo Russian roulette.
./docs/source/io_formats/settings.rst:54: roulette.
./docs/source/methods/physics.rst:1621:Russian rouletting. Two user adjustable parameters :math:w_c and :math:w_s
./docs/source/methods/physics.rst:1623:roulette and the weight should they survive Russian roulette. The algorithm for
./docs/source/methods/physics.rst:1624:Russian rouletting is as follows. After a collision if :math:w < w_c, then the
./docs/source/methods/physics.rst:1627:Russian roulette is simply :math:w, so the game can be considered "fair". By
./openmc/settings.py:43: Russian roulette. Value for 'weight_avg' should be a float indicating
./openmc/settings.py:45: roulette. Value of energy should be a float indicating energy in eV
./src/physics.F90:122: ! Play russian roulette if survival biasing is turned on
./src/physics.F90:125: call russian_roulette(p)
./src/physics_common.F90:16: subroutine russian_roulette(p)
./src/physics_common.F90:31: end subroutine russian_roulette
./src/physics_mg.F90:94: ! Play russian roulette if survival biasing is turned on
./src/physics_mg.F90:96: call russian_roulette(p)

From openmc/docs/source/methods/physics.rst
Additionally, since survival biasing can reduce the weight of the neutron to
very low values, it is always used in conjunction with a weight cutoff and
Russian rouletting. Two user adjustable parameters :math:w_c and :math:w_s
are given which are the weight below which neutrons should undergo Russian
roulette and the weight should they survive Russian roulette. The algorithm for
Russian rouletting is as follows. After a collision if :math:w < w_c, then the
neutron is killed with probability :math:1 - w/w_s. If it survives, the weight
is set equal to :math:w_s. One can confirm that the average weight following
Russian roulette is simply :math:w, so the game can be considered "fair". By
default, the cutoff weight in OpenMC is :math:w_c = 0.25 and the survival
weight is :math:w_s = 1.0. These parameters vary from one Monte Carlo code to
another.

from mlmc.

./docs/source/io_formats/settings.rst:582:<survival_biasing> Element
./docs/source/io_formats/settings.rst:585:The <survival_biasing> element has no attributes and has an accepted value
./docs/source/io_formats/settings.rst:587:survival biasing, otherwise known as implicit capture or absorption.
./docs/source/methods/eigenvalue.rst:139:source contained in cell :math:i. To ensure that no bias is introduced, the
./docs/source/methods/parallelization.rst:370:method of successive generations) will be biased from the true fundamental
./docs/source/methods/parallelization.rst:373:per cycle is sufficiently large to neglect this bias.
./docs/source/methods/physics.rst:318:fission. If no survival biasing is being used, then the number of neutrons
./docs/source/methods/physics.rst:328:produced is biased in this manner so that the expected number of fission
./docs/source/methods/physics.rst:1588:biasing* or implicit absorption (or sometimes implicit capture, even though
./docs/source/methods/physics.rst:1591:In survival biasing, absorption reactions are prohibited from occurring and
./docs/source/methods/physics.rst:1596: :label: survival-biasing-weight
./docs/source/methods/physics.rst:1602:handled differently if survival biasing is turned on. Although fission reactions
./docs/source/methods/physics.rst:1603:never actually occur with survival biasing, we still need to create fission
./docs/source/methods/physics.rst:1619:Additionally, since survival biasing can reduce the weight of the neutron to
./docs/source/methods/tallies.rst:95:by the volume of the region of integration. If survival biasing is employed, the
./docs/source/methods/tallies.rst:278::math:x_1, x_2, \dots, x_N, then an unbiased estimator for the population mean
./docs/source/methods/tallies.rst:294:distribution also known as the biased sample variance:
./docs/source/methods/tallies.rst:297: :label: biased-variance
./docs/source/methods/tallies.rst:302:This estimator is biased because its expected value is actually not equal to the
./docs/source/methods/tallies.rst:306: :label: biased-variance-expectation
./docs/source/methods/tallies.rst:312:correction_ to come up with an unbiased sample variance estimator: ./docs/source/methods/tallies.rst:315: :label: unbiased-variance ./docs/source/methods/tallies.rst:321:in equation :eq:unbiased-variance is especially suitable for computation since ./docs/source/methods/tallies.rst:361:We can combine this result with equation :eq:unbiased-variance to come up with ./docs/source/methods/tallies.rst:362:an unbiased estimator for the variance of the sample mean: ./docs/source/methods/tallies.rst:373:population based on equation :eq:unbiased-variance will tend to the true ./docs/source/methods/tallies.rst:404::eq:unbiased-variance. If the random variables :math:X_i` are

From ./docs/source/io_formats/settings.rst
The <survival_biasing> element has no attributes and has an accepted value
of "true" or "false". If set to "true", this option will enable the use of
survival biasing, otherwise known as implicit capture or absorption.

Default: false

• survival_biasing is an element in settings.

From ./docs/source/methods/physics.rst
In problems with highly absorbing materials, a large fraction of neutrons may be
killed through absorption reactions, thus leading to tallies with very few
scoring events. To remedy this situation, an algorithm known as survival
biasing or implicit absorption (or sometimes implicit capture, even though
this is a misnomer) is commonly used.
In survival biasing, absorption reactions are prohibited from occurring and
instead, at every collision, the weight of neutron is reduced by probability of
absorption occurring, i.e.

To be continued

from mlmc.

add openmc to path
export PATH=$PATH:/home/xinwen5/openmc/build/bin
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/home/xinwen5/openmc/build/lib

from mlmc.