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Documentation typo (#2561)
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* A small typo

* A small typo

* Mailmap

* A small typo

* A small typo

* Typo

* Update basicprinciples.rst

Removed the subscript as it was evident from the expression which variable the distribution is referred to.
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Sumit112192 authored May 3, 2024
1 parent ea5a1bf commit b4d3568
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10 changes: 5 additions & 5 deletions docs/physics/montecarlo/basicprinciples.rst
Original file line number Diff line number Diff line change
Expand Up @@ -95,8 +95,8 @@ Here, all scattering angles are equally likely. Thus, the corresponding

.. math::
\rho_{\mu}(\mu) &= \frac{1}{2}\\
f_{\mu}(\mu) &= \frac{1}{2} (\mu - 1).
\rho(\mu) &= \frac{1}{2}\\
f(\mu) &= \frac{1}{2} (\mu + 1).
This leads to the sampling rule

Expand All @@ -112,8 +112,8 @@ The probability of a photon interacting after covering an optical depth

.. math::
\rho_{\tau}(\tau) &= \exp(-\tau)\\
f_{\tau}(\tau) &= 1 - \exp(-\tau).
\rho(\tau) &= \exp(-\tau)\\
f(\tau) &= 1 - \exp(-\tau).
With the inverse transformation method, the optical depth to the next interaction location may then be sampled by
Expand All @@ -127,4 +127,4 @@ which is equivalent to

.. math::
\tau = - \mathrm{ln}z.
\tau = - \mathrm{ln}z.
4 changes: 2 additions & 2 deletions docs/physics/montecarlo/propagation.rst
Original file line number Diff line number Diff line change
Expand Up @@ -186,9 +186,9 @@ Thomson scattering is calculated by the formula
\Delta \tau = \sigma_{\mathrm{T}} n_e l.
The Thomson cross section :math:`\sigma_{\mathrm{T}}`, which is a constant,
appears here. This corresponds to the fact that a packet has a probability of :math:`1-e^{\sigma_{\mathrm{T}} n_e l}`
appears here. This corresponds to the fact that a packet has a probability of :math:`1-e^{-\sigma_{\mathrm{T}} n_e l}`
of going through a Thomson scattering prior to traveling a distance :math:`l` (in other words, the probability of the
packet making it across a distance :math:`l` without scattering is :math:`e^{\sigma_{\mathrm{T}} n_e l}`).
packet making it across a distance :math:`l` without scattering is :math:`e^{-\sigma_{\mathrm{T}} n_e l}`).

The situation is complicated by the inclusion of frequency-dependent
bound-bound interactions, i.e. interactions with atomic line transitions.
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