Question

neutronbalanceequation

Answer 1

\[\newcommand\p\newcommand
\p\dd [1] {\,\mathrm d#1} % infinitesimal
\p\ve [1] {\boldsymbol#1} % vector
\p\ints [3] {\int_{#1}{\dd #3}{#2}} % integral
\p\dif {\operatorname\nabla} % differential operator
\large{\begin{align}
\frac 1{v(E)}&\frac{\dd\Phi(\ve r,E,\ve \Omega,t)}{\dd t}\\=
&-\ve\Omega\cdot\dif\Phi(\ve r,E,\ve\Omega,t)-\Sigma_t(\ve r,E,\ve \Omega)\Phi(\ve r,E,\ve\Omega,t)\\
&+\chi(E)\ints{E'}{}{E}\ints{\Omega'}{\nu\Sigma_f(\ve r,E',\ve\Omega',t)}{\Omega'}\Phi(\ve r,E',\ve\Omega',t)\\
&+\ints{E'}{}{E'}\ints{\Omega'}{\Sigma_s(\ve r;E'\to E;\ve\Omega'\to\ve\Omega)\Phi(\ve r,E',\Omega',t)}{\Omega'}
\end{align}}\]

Answer 2

\[ \LARGE \mathbb{\color{green}{AWESOME} \huge \star}\]