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boltzmann_equation [2014/03/21 11:11] 127.0.0.1 external edit |
boltzmann_equation [2014/06/26 14:46] nikolaj |
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| | @#DDDDDD: range | @#DDDDDD: $ J[f_i|f_j]({\bf x},{\bf v},t) \equiv \int\int g\ I_{ij}(g,\vartheta,\varphi)\ \left(f_i({\bf x},{\bf v'}({\bf v},{\bf v}_1),t)\cdot f_j({\bf x},{\bf v'}_1({\bf v},{\bf v}_1),t)-f_i({\bf x},{\bf v},t)\cdot f_j({\bf x},{\bf v}_1,t)\right)\ \mathrm d\Omega(\vartheta,\varphi)\ \mathrm d^3v_1 $ | | | @#DDDDDD: range | @#DDDDDD: $ J[f_i|f_j]({\bf x},{\bf v},t) \equiv \int\int g\ I_{ij}(g,\vartheta,\varphi)\ \left(f_i({\bf x},{\bf v'}({\bf v},{\bf v}_1),t)\cdot f_j({\bf x},{\bf v'}_1({\bf v},{\bf v}_1),t)-f_i({\bf x},{\bf v},t)\cdot f_j({\bf x},{\bf v}_1,t)\right)\ \mathrm d\Omega(\vartheta,\varphi)\ \mathrm d^3v_1 $ | | ||
| - | | @#55EE55: postulate | @#55EE55: $ \left(\frac{\mathrm \partial}{\partial t}+{\bf v}\cdot\nabla_{\bf x}+\frac{1}{m_i}{\bf K}\cdot\nabla_{\bf v}\right)f_i = \sum_{k=1}^S J[f_i|f_j]$ | | + | | @#55EE55: postulate | @#55EE55: $ \left(\frac{\mathrm \partial}{\partial t}+{\bf v}\cdot\nabla_{\bf x}+\frac{1}{m_i}{\bf K}\cdot\nabla_{\bf v}\right)f_i = \sum_{j=1}^S J[f_i|f_j]$ | |
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| + | >I'm not sure about the summation $\dots = \sum_{j=1}^S J[f_i|f_j]$ here --- check that. | ||
| ==== Discussion ==== | ==== Discussion ==== | ||
