Changes between Version 1 and Version 2 of u/johannjc/scratchpad22

Timestamp:

01/12/17 12:38:27 (8 years ago)

Author:

Jonathan

Comment:

—

u/johannjc/scratchpad22

@@ -1 +1 @@
 == Scaling ==
+
+
+The equations in physical units look like
 
 $d\tau = n \sigma dl$
 
 $\frac{dn}{dt} = n \sigma F$
+
+And in computational units
+
+$d\tau = n_c \sigma_c dl_c$
+
+$\frac{dn_c}{dt_c} = n_c \sigma_c F_c$
+
+Dividing the first equation gives $n_c \sigma_c dl_c = n \sigma dl = n_c N_s \sigma dl_c L_s$
+
+where $N_s$ and $L_s$ are the number density and length scales in the code.
+
+This gives $\sigma_c = \sigma N_s L_s$
+
+And dividing the second equation by the first, gives
+
+$N_s/T_s = N_s \frac{1}{N_s L_s} \frac{F}{F_c}$
+
+which gives $F_c=F \frac{T_s}{L_s N_s}$
+
 
 
@@ -26 +48 @@
 
 And with a flux of 2e14, we would expect photo-ionization of the column to take 4.5e4 seconds
+
+
+[[Image(ionization.gif)]]