Changes between Version 183 and Version 184 of FluxLimitedDiffusion

Timestamp:

04/03/13 17:15:35 (12 years ago)

Author:

Jonathan

Comment:

—

FluxLimitedDiffusion

@@ -523 +523 @@
    [[latex(\frac{\partial e}{\partial t} = - \kappa_{0P} \left [ 4 \pi B_0 \left ( 1 + 4\Gamma \frac{e-e_0}{T_0} \right )-cE \right ] + \lambda \left ( 2 \frac{\kappa_{0P}}{\kappa_{0R}}-1 \right ) \mathbf{v} \cdot \nabla E -\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E)]]   
 
-which will be accurate as long as \(4\Gamma \frac{e-e_0}{T_0} < \xi << 1\) or \(\Delta e = e-e_0 < \xi \frac{T_0}{4 \Gamma}\)
+which will be accurate as long as \(4\Gamma \frac{\left | e-e_0 \right | }{T_0} < \xi << 1\) or \(\left | \Delta e \right | = \left | e-e_0 \right | < \xi \frac{T_0}{4 \Gamma}\)
 
 We can calculate the time scale for this to be true using the evolution equation for the energy density
 
-[[latex(e-e_0=\Delta e = -\Delta t \frac{\partial e}{\partial t} < \xi \frac{T_0}{4 \Gamma})]]
+[[latex(\left | e-e_0 \right | = \left | \Delta e \right | = \Delta t \left | \frac{\partial e}{\partial t} \right | < \xi \frac{T_0}{4 \Gamma})]]
 
 which gives [[latex(\Delta t < \xi \frac{T_0}{4 \Gamma \left | \frac{\partial e}{\partial t} \right | } = \xi \frac{T_0}{4 \Gamma \left | - \kappa_{0P} \left [ 4 \pi B_0 \left ( 1 + 4\Gamma \frac{e-e_0}{T_0} \right )-cE \right ] + \lambda \left ( 2 \frac{\kappa_{0P}}{\kappa_{0R}}-1 \right ) \mathbf{v} \cdot \nabla E -\frac{3-R_2}{2}\kappa_{0P}\frac{v^2}{c}E  \right | } )]]