r21544 - /branches/relax_disp/docs/latex/dispersion.tex -- November 20, 2013 - 15:54

Author: bugman
Date: Wed Nov 20 15:54:23 2013
New Revision: 21544

URL: http://svn.gna.org/viewcvs/relax?rev=21544&view=rev
Log:
Fix for the LM63 dispersion model equation in the manual.


Modified:
    branches/relax_disp/docs/latex/dispersion.tex

Modified: branches/relax_disp/docs/latex/dispersion.tex
URL: 
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion.tex?rev=21544&r1=21543&r2=21544&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Wed Nov 20 15:54:23 2013
@@ -233,20 +233,25 @@
 
 This is the original model for 2-site fast exchange for CPMG-type 
experiments.
 It is selected by setting the model to `LM63', here named after 
\citet{LuzMeiboom63}.
-The original $n$-site Equation~(7) from their paper can be written as:
-\begin{equation}
-    \Rex = \left[ 1 - 2\tex\taucpmg \cdot \tanh \left( 2\tex\taucpmg 
\right)^{-1} \right] \cdot \tex \cdot \sum_{i=2}^n p_\textrm{i}\dw_{i} ,
-\end{equation}
-
-or rearranged as:
+The original $n$-site Equation~(7) from their paper can be written as
+\begin{equation}
+    \Rex = \left[ 1 - 2\tex g \cdot \tanh \left( 2\tex g \right)^{-1} 
\right] \cdot \tex \cdot \sum_{i=2}^n p_\textrm{i}\dw_{i},
+\end{equation}
+
+where $g$ is the pulse repetition rate defined as
+\begin{equation}
+    g = 2\nucpmg.
+\end{equation}
+
+It can be rearranged as
 \begin{equation} \label{eq: Luz-Meiboom}
-    \Rex = \sum_{i=2}^n \frac{\Phiexi}{\textrm{k}_\textrm{i}} \cdot \left( 1 
- \frac{4\nucpmg}{\textrm{k}_\textrm{i}} \cdot \tanh \left( 
\frac{\textrm{k}_\textrm{i}}{4\nucpmg} \right) \right) ,
-\end{equation}
-
-
-The equation for the 2-site exchange process can be expressed as:
-\begin{equation}
-    \Rtwoeff = \Rtwozero + \frac{\Phiex}{\kex} \cdot \left( 1 - 
\frac{4\nucpmg}{\kex} \cdot \tanh \left( \frac{\kex}{4\nucpmg} \right) 
\right) .
+    \Rex = \sum_{i=2}^n \frac{\Phiexi}{\textrm{k}_\textrm{i}} \cdot \left( 1 
- \frac{4\nucpmg}{\textrm{k}_\textrm{i}} \cdot \tanh \left( 
\frac{\textrm{k}_\textrm{i}}{4\nucpmg} \right) \right).
+\end{equation}
+
+
+The equation for the 2-site exchange process can be expressed as
+\begin{equation}
+    \Rtwoeff = \Rtwozero + \frac{\Phiex}{\kex} \cdot \left( 1 - 
\frac{4\nucpmg}{\kex} \cdot \tanh \left( \frac{\kex}{4\nucpmg} \right) 
\right).
 \end{equation}
 
 The reference for this equation is: