Author: bugman
Date: Wed Oct 16 16:08:02 2013
New Revision: 21144
URL: http://svn.gna.org/viewcvs/relax?rev=21144&view=rev
Log:
Added the 'MQ CR72' model to the relax user manual.
This is the Carver and Richards (1972) 2-site model expanded for MQ CPMG data
by Korzhnev et al.,
2004.
This follows the tutorial for adding relaxation dispersion models at:
http://wiki.nmr-relax.com/Tutorial_for_adding_relaxation_dispersion_models_to_relax#The_relax_manual.
Modified:
branches/relax_disp/docs/latex/dispersion.tex
branches/relax_disp/docs/latex/dispersion_models.tex
Modified: branches/relax_disp/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion.tex?rev=21144&r1=21143&r2=21144&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Wed Oct 16 16:08:02 2013
@@ -114,6 +114,13 @@
\end{description}
+For the MQ CPMG-type experiments, the analytic models currently supported
are:
+
+\begin{description}
+\item[`MQ CR72':]\index{relaxation dispersion!MQ CR72 model} The Carver and
Richards (1972) 2-site model for all time scales expanded for MQ CPMG data by
\citet{Korzhnev04a}. It has the parameters $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$. See Section~\ref{sect: dispersion: MQ CR72 model} on
page~\pageref{sect: dispersion: MQ CR72 model}.
+\end{description}
+
+
For the MQ CPMG-type experiments, the numeric models currently supported are:
\begin{description}
@@ -566,6 +573,69 @@
This is the numerical model for 2-site exchange using 3D magnetisation
vectors.
It is selected by setting the model to `NS R1rho 2-site'.
The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
+
+
+% The analytic MQ CPMG models.
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{The analytic MQ CPMG models}
+\label{sect: dispersion: analytic MQ CPMG models}
+\index{relaxation dispersion!Analytic MQ CPMG model|textbf}
+
+
+% MQ CR72 model.
+%~~~~~~~~~~~~~~~
+
+\subsection{The MQ CR72 model}
+\label{sect: dispersion: MQ CR72 model}
+\index{relaxation dispersion!MQ CR72 model|textbf}
+
+This is the analytic CR72 model for 2-site exchange on all times scales
(Section~\ref{sect: dispersion: CR72 model} on page~\pageref{sect:
dispersion: CR72 model}) extended for multiple quantum data by
\citet{Korzhnev04a}.
+It is selected by setting the model to `MQ CR72'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+The equation for the exchange process is
+\begin{equation}
+ \Rtwoeff = \Re(\lambda_1) - \frac{\nucpmg}{n}\ln(Q),
+\end{equation}
+
+where
+\begin{align}
+ \lambda_1 &= \RtwozeroMQ + \frac{\kex}{2} - \nucpmg\cosh^{-1} \big(
D_+\cosh(\eta_+) - D_-\cos(\eta_-) \big), \\
+ D_\pm &= \frac{1}{2} \left( \pm1 + \frac{\Psi + 2\dw^2}{\sqrt{\Psi^2
+ \zeta^2}} \right) , \\
+ \eta_\pm &= 2^{\frac{2}{3}}\frac{1}{\nucpmg} \left( \pm\Psi +
\sqrt{\Psi^2 + \zeta^2} \right)^{\frac{1}{2}} , \\
+ \Psi &= \left( \imath \dwH + \pA\kex - \pB\kex \right)^2 - \dw^2 +
4\pA\pB\kex^2 , \\
+ \zeta &= -2\dw \left( \imath \dwH + \pA\kex - \pB\kex \right),
+\end{align}
+
+and where
+\begin{equation}
+ Q = \Re \left( 1 - m_{D+}^2 + m_{D+} m_{Z+} - m_{Z+}^2 + \frac{m_{D+} +
m_{Z+}}{2} \sqrt{\frac{\pB}{\pA}} \right),
+\end{equation}
+
+and
+\begin{align}
+ m_{D\pm} &= \pm \frac{\imath\kex\sqrt{\pA\pB}}{d_\pm z_\pm} \left( z_\pm
+ 2\dw \frac{\sin(z_\pm\delta)}{\sin((d_\pm + z_\pm)\delta)} \right), \\
+ m_{Z\mp} &= \pm \frac{\imath\kex\sqrt{\pA\pB}}{d_\pm z_\pm} \left( d_\pm
- 2\dw \frac{\sin(d_\pm\delta)}{\sin((d_\pm + z_\pm)\delta)} \right),
+\end{align}
+
+and
+\begin{align}
+ d_\pm &= \left( \dwH + \dw \right) \pm \imath\kex, \\
+ z_\pm &= \left( \dwH - \dw \right) \pm \imath\kex.
+\end{align}
+
+The symbol $\delta$ is half of $\taucpmg$ or
+\begin{equation}
+ \delta = \frac{1}{4\nucpmg}.
+\end{equation}
+
+The references for this model are:
+\begin{itemize}
+\item \bibentry{Korzhnev04a}
+\item \bibentry{Korzhnev04b}
+\end{itemize}
+
% The numeric MQ CPMG models.
Modified: branches/relax_disp/docs/latex/dispersion_models.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion_models.tex?rev=21144&r1=21143&r2=21144&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion_models.tex (original)
+++ branches/relax_disp/docs/latex/dispersion_models.tex Wed Oct 16 16:08:02
2013
@@ -58,7 +58,8 @@
MQ CPMG-type \\
\cline{1-1}
\\[-5pt]
-MQ NS CPMG 2-site & Numeric & 2 & $\{\Rtwozero, \dots, \pA, \dw,
\dwH, \kex\}$ & $\pA > \pB$ &
\citet{Korzhnev04a} \\
+MQ CR72 & Analytic & 2 & $\{\Rtwozero, \dots, \pA, \dw, \dwH,
\kex\}$ & $\pA > \pB$ & \citet{Korzhnev04a} \\
+MQ NS CPMG 2-site & Numeric & 2 & $\{\Rtwozero, \dots, \pA, \dw, \dwH,
\kex\}$ & $\pA > \pB$ & \citet{Korzhnev04a} \\
\bottomrule
r21144 - in /branches/relax_disp/docs/latex: dispersion.tex dispersion_models.tex