Changes between Version 2 and Version 3 of u/ticket

Timestamp:

11/18/14 15:15:17 (10 years ago)

Author:

Erica Kaminski

Comment:

—

u/ticket

@@ -30 +30 @@
 '''2.5 D'''
 
-This is cylindrical geometry with axial symmetry. Therefore we begin with the Laplacian in cylindrical, throwing out the theta derivetive: 
+This is cylindrical geometry with axial symmetry. Therefore we begin with the Laplacian in cylindrical coordinates, throwing out the theta derivative: 
 
+[[latex($ \triangledown ^2_{(2.5D)} = \frac{1}{r}\frac{\partial }{\partial r}(r\frac{\partial}{\partial r}) + \frac {\partial ^2}{\partial z ^2} = \frac{1}{r} [\frac{\partial}{\partial r} + r \frac{\partial^2}{\partial r ^2}] + \frac{\partial ^2}{\partial z^2}$)]]
+
+Expanding out and putting into Poisson equation, 
+
+[[latex($  \frac{1}{r}\frac{D }{Dr} \phi_{r,z} + \frac{D^2}{D r^2}\phi_{r,z} + \frac{D^2}{Dz^2} \phi_{r,z} = \rho_{r,z}$)]]
+
+
+