Changes between Version 22 and Version 23 of u/ehansen/RT

Timestamp:

09/14/11 12:41:23 (13 years ago)

Author:

ehansen

Comment:

—

u/ehansen/RT

@@ -23 +23 @@
 == Calculating the Growth Rate ==
 With the accuracy of the tracking confirmed, the next step was to calculate the growth rate.
+
 For small perturbations, a linear analysis is used to show that the position of the interface at x = 0 rises exponentially as:
-[[latex($y(t)=y_o e^{\gamma t}$)]].  Taking the log of both sides yields: [[latex($\log{y(t)}=\log{y_o}+\gamma t$)]].  Therefore, the slope of a [[latex($\log{y(t)} vs. t$)]] plot would yield the growth rate [[latex($\gamma$)]].
+[[latex($y(t)=y_o e^{\gamma t}$)]].
+
+Taking the log of both sides yields: [[latex($\log{y(t)}=\log{y_o}+\gamma t$)]].  
+
+Therefore, the slope of a [[latex($\log{y(t)}$)]] vs. [[latex($t$)]] plot would yield the growth rate [[latex($\gamma$)]].
 * [attachment:snapshot1.png Log(interface_position) Plot]
 == Results ==