r20485 - /branches/relax_disp/docs/latex/dispersion.tex -- July 31, 2013 - 16:56

Author: bugman
Date: Wed Jul 31 16:56:27 2013
New Revision: 20485

URL: http://svn.gna.org/viewcvs/relax?rev=20485&view=rev
Log:
Added the 'TP02' model to relaxation dispersion chapter of the relax user 
manual.

This is the Trott and Palmer 2002 R1rho analytic model for 2-site exchange.

This commit follows step 2 of the relaxation dispersion model addition 
tutorial
(http://thread.gmane.org/gmane.science.nmr.relax.devel/3907).

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=20485&r1=20484&r2=20485&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Wed Jul 31 16:56:27 2013
@@ -85,6 +85,7 @@
 \item[`M61':]\index{relaxation dispersion!M61 model}  The \citet{Meiboom61} 
2-site fast exchange equation for on-resonance data with parameters 
$\{\Ronerhoprime, \dots, \Phiex, \kex\}$.  See Section~\ref{sect: dispersion: 
M61 model} on page~\pageref{sect: dispersion: M61 model}.
 \item[`DPL94':]\index{relaxation dispersion!DPL94 model}  The 
\citet{Davis94} 2-site fast exchange equation for off-resonance data with 
parameters $\{\Ronerhoprime, \dots, \Phiex, \kex\}$.  See Section~\ref{sect: 
dispersion: DPL94 model} on page~\pageref{sect: dispersion: DPL94 model}.
 \item[`M61 skew':]\index{relaxation dispersion!M61 skew model}  The 
\citet{Meiboom61} 2-site equation for all time scales with $\pA \gg \pB$ and 
with parameters $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$.  This model is 
disabled by default in the dispersion auto-analysis.  See Section~\ref{sect: 
dispersion: M61 skew model} on page~\pageref{sect: dispersion: M61 skew 
model}.
+\item[`TP02':]\index{relaxation dispersion!TP02 model}  The 
\citet{TrottPalmer02} 2-site equation for all time scales with parameters 
$\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$.  See Section~\ref{sect: 
dispersion: TP02 model} on page~\pageref{sect: dispersion: TP02 model}.
 \end{description}
 
 
@@ -201,6 +202,7 @@
 M61        & Analytic & 2     & $\{\Ronerhoprime, \dots, \Phiex, \kex\}$     
     & Fast exchange, on-resonance       & \citet{Meiboom61} \\
 DPL94      & Analytic & 2     & $\{\Ronerhoprime, \dots, \Phiex, \kex\}$     
     & Fast exchange                     & \citet{Davis94} \\
 M61 skew   & Analytic & 2     & $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$   
     & $\pA \gg \pB$, on-resonance       & \citet{Meiboom61} \\
+TP02       & Analytic & 2     & $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$   
     & -                                 & \citet{TrottPalmer02} \\
 \bottomrule
 \label{table: R1rho dispersion models}
 \end{tabular}
@@ -502,6 +504,19 @@
 \end{equation}
 
 Care must be taken as this model appears to have infinite lines of solutions 
-- $\pA$ and $\dw$ are convoluted.  Hence this model is disabled in the 
dispersion auto-analysis.
+
+
+% TP02 model.
+%~~~~~~~~~~~~
+
+\subsection{The TP02 2-site fast exchange $\Ronerho$ model}
+\label{sect: dispersion: TP02 model}
+\index{relaxation dispersion!TP02 model|textbf}
+
+This is the model for 2-site fast exchange for off-resonance $\Ronerho$-type 
experiments from \citet{TrottPalmer02}.  It is selected by setting the model 
to `TP02'.  The equation for the exchange process is:
+\begin{equation}
+    \Ronerho = \Rone\cos^2(\theta) + \Ronerhoprime\sin^2(\theta) + 
\frac{\sin^2(\theta)\pA\pB\dw^2\kex}{\kex^2 + \omgea_{beff}^2} .
+\end{equation}