Commit 3018795e by Tianbai Xiao

### Fix physics.rst

parent 7d1e77c0
Pipeline #138012 passed with stage
in 19 minutes and 2 seconds
 ... ... @@ -119,10 +119,11 @@ Then, we substitute .. math:: \widehat{\psi}(E,x,\Omega):= S(E)\rho(x)\psi(E,x,\Omega) into \eqref{eq:CSD3}, which yields into :eq:CSD3, which yields .. math:: :label: CSD4 -S(E)\partial_E\widehat{\psi}(E,x,\Omega)+\Omega\cdot\nabla_x \frac{\widehat{\psi}(E,x,\Omega)}{\rho}+\Sigma_t(E)\widehat{\psi}(E,x,\Omega) = \int_{\mathbb{S}^2}\Sigma_s(E,\Omega\cdot\Omega')\widehat{\psi}(E,x,\Omega')d\Omega'. Now, to get rid of the stopping power in front of the energy derivative, we make use of the transformation ... ... @@ -140,7 +141,7 @@ Now let us change to In this case, the energy derivative becomes .. math:: \partial_{\widetilde{E}}\widetilde{\widehat{\psi}}(\widetilde E,x,\Omega) = \partial_{E}\widetilde{\widehat{\psi}}( E,x,\Omega)\partial_{\widetlde E }E(\widetilde E(\widetilde E) = \partial_{ E}\widetilde{\widehat{\psi}}(\widetilde E,x,\Omega){S(E(\widetilde E))}. \partial_{\widetilde{E}}\widetilde{\widehat{\psi}}(\widetilde E,x,\Omega) = \partial_{E}\widetilde{\widehat{\psi}}( E,x,\Omega)\partial_{\widetilde E }E(\widetilde E(\widetilde E) = \partial_{ E}\widetilde{\widehat{\psi}}(\widetilde E,x,\Omega){S(E(\widetilde E))}. And by rearranging the terms, we finally get ... ... @@ -161,7 +162,7 @@ Here, we define :math:\widetilde\Sigma_{t}(\widetilde E):=\Sigma_t(E(\widetilde .. math:: \bar{E}(\widetilde{E}) = \widetilde{E}_{\text{max}}-\widetilde{E}. Then, with :math:\bar{\psi}(\bar{E},x,\Omega):=\widetilde{\widehat{\psi}}(\widetilde{E}(\bar{E}),x,\Omega), :math:\bar\Sigma_{t}(\bar E):=\widetilde{\Sigma}_t(\widetilde{E}(\bar{E})) as well as :math:\bar\Sigma_{s}(\bar E,\Omega\cdot\Omega'):=\widetilde{\Sigma}_s(\widetilde{E}(\bar{E}),\Omega\cdot\Omega') equation \eqref{eq:CSD4} becomes Then, with :math:\bar{\psi}(\bar{E},x,\Omega):=\widetilde{\widehat{\psi}}(\widetilde{E}(\bar{E}),x,\Omega), :math:\bar\Sigma_{t}(\bar E):=\widetilde{\Sigma}_t(\widetilde{E}(\bar{E})) as well as :math:\bar\Sigma_{s}(\bar E,\Omega\cdot\Omega'):=\widetilde{\Sigma}_s(\widetilde{E}(\bar{E}),\Omega\cdot\Omega') equation :eq:CSD4` becomes .. math:: :label: CSD6 ... ...
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