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fix the some math rendering in docs
this seems to be a sphinx 9 issue
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Docs/source/networks.rst

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@@ -559,10 +559,8 @@ X_a / (A_a m_u)`, our rate equation is
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.. math::
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\begin{align}
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\frac{dX_f}{dt} &= - \frac{r_0}{m_u} \rho X_f^2 \frac{1}{A_f} \left (\frac{T}{T_0}\right)^\nu \equiv \omegadot_f \\
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\frac{dX_a}{dt} &= \frac{1}{2}\frac{r_0}{m_u} \rho X_f^2 \frac{A_a}{A_f^2} \left (\frac{T}{T_0}\right)^\nu = \frac{r_0}{m_u} \rho X_f^2 \frac{1}{A_f} \left (\frac{T}{T_0}\right)^\nu
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\end{align}
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We define a new rate constant, :math:`\rt` with units of :math:`[\mathrm{s^{-1}}]` as
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Docs/source/ode_integrators.rst

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@@ -231,7 +231,7 @@ Some suggestions when setting tolerances:
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* The VODE integrator has additional logic meant to ensure that
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species don't change too much per timestep. This is controlled by
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``integrator.X_reject_buffer``. If a species $k$, has a mass
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fraction $X_k > \mbox{X_reject_buffer} \cdot \mbox{atol_spec}$ then
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fraction $X_k > \mathrm{X_reject_buffer} \cdot \mathrm{atol_spec}$ then
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we reject a VODE timestep if the mass fraction changes by more than
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a factor of 4 in a single VODE timestep and we try again. This is
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all done internally to VODE. Making ``X_reject_buffer`` larger will

Docs/source/sdc.rst

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@@ -58,12 +58,10 @@ $k+1$ appears as:
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.. math::
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\begin{align*}
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\Uc^{m+1,(k+1)} = \Uc^{m,(k+1)}
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&+ \delta t_m\left[\Advs{\Uc^{m,(k+1)}} - \Advs{\Uc^{m,(k)}}\right] \\
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&+ \delta t_m\left[\Rbs{\Uc^{m+1,(k+1)}} - \Rbs{\Uc^{m+1,(k)}}\right]\\
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&+ \int_{t^m}^{t^{m+1}}\Advs{\Uc^{(k)}} + \Rbs{\Uc^{(k)}}d\tau.
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\end{align*}
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Solving this requires a nonlinear solve of:
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@@ -76,11 +74,9 @@ define ${\bf C}$ for convenience as:
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.. math::
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\begin{align}
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{\bf C} &= \left [ {\Advs{\Uc}}^{m,(k+1)} - {\Advs{\Uc}}^{m,(k)} \right ]
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- {\Rbs{\Uc}}^{{m+1},(k)} \nonumber \\
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&+ \frac{1}{\delta t_m} \int_{t^m}^{t^{m+1}} \left ( {\Advs{\Uc}}^{(k)} + {\Rbs{\Uc}}^{(k)}\right ) d\tau
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\end{align}
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&+ \frac{1}{\delta t_m} \int_{t^m}^{t^{m+1}} \left ( {\Advs{\Uc}}^{(k)} + {\Rbs{\Uc}}^{(k)}\right ) d\tau
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This can be cast as an ODE system as:
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