Author: bugman
Date: Mon Jun 17 15:00:36 2013
New Revision: 20175
URL: http://svn.gna.org/viewcvs/relax?rev=20175&view=rev
Log:
Expansion of the modelling of dispersion data section of the relax user
manual.
Modified:
branches/relax_disp/docs/latex/relax_disp.tex
Modified: branches/relax_disp/docs/latex/relax_disp.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/relax_disp.tex?rev=20175&r1=20174&r2=20175&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/relax_disp.tex (original)
+++ branches/relax_disp/docs/latex/relax_disp.tex Mon Jun 17 15:00:36 2013
@@ -61,9 +61,9 @@
\begin{description}
\item[`R2eff':]\index{relaxation dispersion!R2eff model} This is the model
used to determine the $\Rtwoeff$ values and errors required as the base data
for all other models,
\item[`No Rex':]\index{relaxation dispersion!No Rex model} This is the
model for no chemical exchange being present,
-\item[`LM63':]\index{relaxation dispersion!LM63 model} The original
\citet{LuzMeiboom63} 2-site fast exchange equation with parameters
\{$\Rtwozero$, $\dots$, $\Phiex$, $\kex$\},
-\item[`CR72':]\index{relaxation dispersion!CR72 model} The
\citet{CarverRichards72} 2-site equation for all time scales with parameters
\{$\Rtwozero$, $\dots$, $\pA$, $\dw$, $\kex$\}.
-\item[`IT99':]\index{relaxation dispersion!IT99 model} The
\citet{IshimaTorchia99} 2-site model for all time scales with $\pA \gg \pB$
and with parameters \{$\Rtwozero$, $\dots$, $\Phiex$, $\pA.\dw^2$,
k$_\textrm{ex}$\}.
+\item[`LM63':]\index{relaxation dispersion!LM63 model} The original
\citet{LuzMeiboom63} 2-site fast exchange equation with parameters
$\{\Rtwozero, \dots, \Phiex, \kex\}$,
+\item[`CR72':]\index{relaxation dispersion!CR72 model} The
\citet{CarverRichards72} 2-site equation for all time scales with parameters
$\{\Rtwozero, \dots, \pA, \dw, \kex\}$.
+\item[`IT99':]\index{relaxation dispersion!IT99 model} The
\citet{IshimaTorchia99} 2-site model for all time scales with $\pA \gg \pB$
and with parameters $\{\Rtwozero, \dots, \Phiex, \pA.\dw^2, \kex\}$.
\end{description}
For the $\Ronerho$-type experiment, the currently supported models are:
@@ -71,18 +71,18 @@
\begin{description}
\item[`R2eff':]\index{relaxation dispersion!R2eff model} This is the same
model model as for the CPMG-type experiments except that the $\Ronerho$ and
not $\Rtwoeff$ values are determined.
\item[`No Rex':]\index{relaxation dispersion!No Rex model} This is the
model for no chemical exchange being present,
-\item[`M61':]\index{relaxation dispersion!M61 model} The \citet{Meiboom61}
2-site fast exchange equation with parameters \{$\mathrm{R}_{1\rho}'$,
$\dots$, $\Phiex$, $\kex$\},
-\item[`DPL94':]\index{relaxation dispersion!DPL94 model} The
\citet{Davis94} 2-site fast exchange equation with parameters
\{$\mathrm{R}_{1\rho}'$, $\dots$, $\Phiex$, $\kex$\},
-\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 \{$\mathrm{R}_{1\rho}'$, $\dots$, $\pA$, $\dw$,
k$_\textrm{ex}$\},
+\item[`M61':]\index{relaxation dispersion!M61 model} The \citet{Meiboom61}
2-site fast exchange equation for on-resonance data with parameters
$\{\Ronerhoprime, \dots, \Phiex, \kex\}$,
+\item[`DPL94':]\index{relaxation dispersion!DPL94 model} The
\citet{Davis94} 2-site fast exchange equation for off-resonance data with
parameters $\{\Ronerhoprime, \dots, \Phiex, \kex\}$,
+\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.
\end{description}
-Except for `R2eff' and `No Rex', these CPMG and $\Ronerho$ models can be fit
to clusterings of spins, or spin blocks.
-The models are described in more detail below.
+Except for `R2eff' and `No Rex', these models can be fit to clusterings of
spins, or spin blocks.
+The models are described in more detail below and summarised in
Table~\ref{table: CPMG dispersion models} for CPMG-type experiments and
Table~\ref{table: R1rho dispersion models} for $\Ronerho$-type experiments.
The parameters are given in Table~\ref{table: dispersion parameters}.
\begin{sidewaystable}
\begin{center}
-\caption{The parameters of relaxation dispersion}
+\caption{The parameters of relaxation dispersion.}
\begin{tabular}{llll}
\toprule
Parameter & Equation & Description
& Units \\
@@ -110,6 +110,45 @@
\end{sidewaystable}
+\begin{sidewaystable}
+\begin{center}
+\caption{The analytic models for CPMG-type experiments currently supported
within relax}
+\begin{tabular}{llcll}
+\toprule
+Model code & Parameters
& Number of sites & Restriction & Reference \\
+\midrule
+R2eff & $\{\Rtwoeff, \cdots\}$
& - & Fixed relaxation time period & - \\
+R2eff & $\{\Rtwoeff, I_0, \cdots\}$
& - & Variable relaxation time period & - \\
+No Rex & $\{\Rtwozero, \cdots\}$
& 0 & - & - \\
+LM63 & $\{\Rtwozero, \dots, \Phiex, \kex\}$
& 2 & Fast exchange &
\citet{LuzMeiboom63} \\
+CR72 & $\{\Rtwozero, \dots, \pA, \dw, \kex\}$
& 2 & $\pA > \pB$ &
\citet{CarverRichards72} \\
+IT99 & $\{\Rtwozero, \dots, \Phiex, \pA.\dw^2, \kex\}$
& 2 & $\pA \gg \pB$ &
\citet{IshimaTorchia99} \\
+\bottomrule
+\label{table: CPMG dispersion models}
+\end{tabular}
+\end{center}
+\end{sidewaystable}
+
+
+\begin{sidewaystable}
+\begin{center}
+\caption{The analytic models for $\Ronerho$-type experiments currently
supported within relax.}
+\begin{tabular}{llcll}
+\toprule
+Model code & Parameters
& Number of sites & Restriction & Reference \\
+\midrule
+R2eff & $\{\Ronerho, \cdots\}$
& - & Fixed relaxation time period & - \\
+R2eff & $\{\Ronerho, I_0, \cdots\}$
& - & Variable relaxation time period & - \\
+No Rex & $\{\Ronerhoprime, \cdots\}$
& 0 & - & - \\
+M61 & $\{\Ronerhoprime, \dots, \Phiex, \kex\}$
& 2 & Fast exchange, on-resonance & \citet{Meiboom61} \\
+DPL94 & $\{\Ronerhoprime, \dots, \Phiex, \kex\}$
& 2 & Fast exchange & \citet{Davis94} \\
+M61 skew & $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$
& 2 & $\pA \gg \pB$, on-resonance & \citet{Meiboom61} \\
+\bottomrule
+\label{table: R1rho dispersion models}
+\end{tabular}
+\end{center}
+\end{sidewaystable}
+
% R2eff model.
%~~~~~~~~~~~~~
@@ -241,12 +280,12 @@
% M61 model.
-%~~~~~~~~~~~~
+%~~~~~~~~~~~
\subsection{The M61 2-site fast exchange $\Ronerho$ model}
\index{relaxation dispersion!M61 model|textbf}
-This is the model for 2-site fast exchange for $\Ronerho$-type experiments.
It is selected by setting the model to `M61', here named after
\citet{Meiboom61}. The equation for the exchange process is:
+This is the model for 2-site fast exchange for on-resonance $\Ronerho$-type
experiments. It is selected by setting the model to `M61', here named after
\citet{Meiboom61}. The equation for the exchange process is:
\begin{equation}
\Ronerho = \Ronerhoprime + \sin^2(\theta) \frac{\Phiex\kex}{\kex^2 +
\omegae^2} .
\end{equation}
@@ -263,7 +302,7 @@
\subsection{The DPL94 2-site fast exchange $\Ronerho$ model}
\index{relaxation dispersion!DPL94 model|textbf}
-This is the model for 2-site fast exchange for $\Ronerho$-type experiments.
It is selected by setting the model to `DPL94', here named after
\citet{Davis94}. The equation for the exchange process is:
+This is the model for 2-site fast exchange for $\Ronerho$-type experiments.
It is selected by setting the model to `DPL94', here named after
\citet{Davis94}. It extends the \citet{Meiboom61} model to off-resonance
data. The model collapses to the M61 model for on-resonance data. The
equation for the exchange process is:
\begin{equation}
\Ronerho = \Ronerhoprime + \sin^2(\theta) \frac{\Phiex\kex}{\kex^2 +
\omegae^2} .
\end{equation}
@@ -272,6 +311,20 @@
\begin{itemize}
\item \bibentry{Davis94}
\end{itemize}
+
+
+% M61 skew model.
+%~~~~~~~~~~~~~~~~
+
+\subsection{The M61 skew 2-site fast exchange $\Ronerho$ model}
+\index{relaxation dispersion!M61 model|textbf}
+
+This is the second model for 2-site fast exchange for on-resonance
$\Ronerho$-type experiments from \citet{Meiboom61}. It is selected by
setting the model to `M61 skew'. The equation for the exchange process is:
+\begin{equation}
+ \Ronerho = \Ronerhoprime + \frac{\pA^2\pB\dw^2\kex}{\kex^2 + \pA^2\dw^2
+ \omegaone^2} .
+\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.
% Script UI.
r20175 - /branches/relax_disp/docs/latex/relax_disp.tex