From f72469c2b1b5d03ec8e98bb995bb772ef1918af2 Mon Sep 17 00:00:00 2001 From: Paul Romano Date: Thu, 26 Jul 2012 22:56:58 -0400 Subject: [PATCH] Fixed typos in physics section in documentation. --- docs/source/methods/physics.rst | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/docs/source/methods/physics.rst b/docs/source/methods/physics.rst index 27ef40197..aeb4604bc 100644 --- a/docs/source/methods/physics.rst +++ b/docs/source/methods/physics.rst @@ -226,7 +226,7 @@ for the data. ACE Law 1 - Tabular Equiprobable Energy Bins ++++++++++++++++++++++++++++++++++++++++++++ -In the tabular equiprobable bin representation, an array of equiprobably +In the tabular equiprobable bin representation, an array of equiprobable outgoing energy bins is given for a number of incident energies. While the representation itself is simple, the complexity lies in how one interpolates between incident as well as outgoing energies on such a table. If one does @@ -239,7 +239,7 @@ To avoid this situation, the accepted practice is to use a process known as scaled interpolation [Doyas]_. First, we find the tabulated incident energies which bound the actual incoming energy of the particle, i.e. find :math:`i` such that :math:`E_i < E < E_{i+1}` and calculate the interpolation factor :math:`f` -via :eq:`interpolation-factor`. Then, we intepolate between the minimum and +via :eq:`interpolation-factor`. Then, we interpolate between the minimum and maximum energies of the outgoing energy distributions corresponding to :math:`E_i` and :math:`E_{i+1}`: @@ -303,9 +303,9 @@ value in the probability distribution function, :math:`c_{i,j}` the j-th value in the cumulative distribution function, and :math:`E_{i,j}` the j-th outgoing energy. -Weproceed first as we did for ACE Law 1, determining the bounding energies of +We proceed first as we did for ACE Law 1, determining the bounding energies of the particle's incoming energy such that :math:`E_i < E < E_{i+1}` and -calculating an interpolationg factor :math:`f` with equation +calculating an interpolation factor :math:`f` with equation :eq:`interpolation-factor`. Next, statistical interpolation is performed to choose between using the outgoing energy distributions corresponding to energy :math:`E_i` and :math:`E_{i+1}`. Let :math:`\ell` be the chosen table where @@ -319,7 +319,7 @@ choose between using the outgoing energy distributions corresponding to energy c_{\ell,j} < \xi_2 < c_{\ell,j+1} where :math:`\xi_2` is a random number sampled uniformly on :math:`[0,1)`. At -this point, we need to inteporlate between the successive values on the outgoing +this point, we need to interpolate between the successive values on the outgoing energy distribution using either histogram or linear-linear interpolation. The formulas for these can be derived along the same lines as those found in :ref:`angle-tabular`. For histogram interpolation, the interpolated outgoing @@ -462,7 +462,7 @@ ACE Law 44 - Kalbach-Mann Correlated Scattering This law is very similar to ACE Law 4 except now the outgoing angle of the neutron is correlated to the outgoing energy and is not sampled from a separate distribution. For each incident neutron energy :math:`E_i` tabulated, there is -an array of precompoung factors :math:`R_{i,j}` and angular distribution slopes +an array of precompound factors :math:`R_{i,j}` and angular distribution slopes :math:`A_{i,j}` corresponding to each outgoing energy bin :math:`j` in addition to the outgoing energies and distribution functions as in ACE Law 4. @@ -789,7 +789,7 @@ concerns a Monte Carlo simulation it actually bears more similarities to inelastic scattering since fission results in secondary neutrons in the exit channel. Other absorption reactions like :math:`(n,\gamma)` or :math:`(n,\alpha)`, on the contrary, produce no neutrons. There are a few other -idiosyncracies in treating fission. In a criticality calculation, secondary +idiosyncrasies in treating fission. In a criticality calculation, secondary neutrons from fission are only "banked" for use in the next generation rather than being tracked as secondary neutrons from elastic and inelastic scattering would be. On top of this, fission is sometimes broken into first-chance fission, @@ -829,7 +829,7 @@ calculated the delayed neutron fraction \beta = \frac{\nu_d}{\nu_t} We then need to determine how many total neutrons should be emitted from -fission. If no suvival biasing is being used, then the number of neutrons +fission. If no survival biasing is being used, then the number of neutrons emitted is .. math:: @@ -1086,7 +1086,7 @@ Substituting this into equation :eq:`maxwellian-speed`, we get v_T^2 \right ) dv_T Now, changing variables in equation :eq:`target-pdf-2` by using the result from -equation :eq:`maxwellian-speed`, our new probabilty distribution function is +equation :eq:`maxwellian-speed`, our new probability distribution function is .. math:: :label: target-pdf-3 @@ -1177,7 +1177,7 @@ Thus, we need to sample the probability distribution function \frac{4\beta^4 v_T^3}{\sqrt{\pi} \beta v_n + 2} \right ) exp \left ( -\beta^2 v_T^2 \right ) -Now, let us do a change of variables with the following defintions +Now, let us do a change of variables with the following definitions .. math:: :label: beta-to-x