Changes between Version 6 and Version 7 of u/johannjc/scratchpad7

Timestamp:

10/12/15 14:15:32 (10 years ago)

Author:

Jonathan

Comment:

—

u/johannjc/scratchpad7

@@ -136 +136 @@
 $\frac{\partial T}{\partial t} =  D \nabla^2 T$
 
-where $D$ is the diffusion coefficient.  For uniform density, magnetic field, and for $lambda = 0$, the equations revert to the traditional diffusion equation with 
+where $D$ is the diffusion coefficient.  For uniform density, magnetic field, and for $\lambda = 0$, the equations revert to the traditional diffusion equation with 
 
 $D = \frac{n \chi}{\rho c_v}$
@@ -171 +171 @@
 and it is independent of direction, so it is just a scalar.
 
-|| $E_j$ || $A \left ( \partial_j \kappa \right )$ ||
-|| $F$ || $A \kappa$ ||
-||$\alpha_0 $ ||$ -\frac{2F\delta_{ii} }{\Delta x^2}$ ||
-||$\alpha_{\pm j}$ || $ \pm \frac{E_j }{2 \Delta x} +  \frac{F}{\Delta x^2}$ ||
-||$\alpha_{\pm i, \pm j}$ || $ 0$ ||
-
-Also if $\kappa$ is a constant, the $E_j$ terms drop out.
+
+||$\alpha_0$ || $- \displaystyle \sum_{i} \frac{B_{\hat{i}} + B_{-\hat{i}}}{\Delta x^2}$ ||
+||$\alpha_{\pm i}$ || $ \frac{B_{\pm \hat{i}}}{\Delta x^2}$ ||
+|| $\alpha*_{\pm i \pm j}$ || $ 0$ ||
+
+Also if $\kappa$ is a constant, then we have
+
+||$\alpha_0$ || $- \displaystyle \sum_{i} {2B}{\Delta x^2}$ ||
+||$\alpha_{\pm i}$ || $ \frac{B}{\Delta x^2}$ ||
+|| $\alpha*_{\pm i \pm j}$ || $ 0$ ||
+