Author: bugman
Date: Fri Jul 19 10:38:31 2013
New Revision: 20405
URL: http://svn.gna.org/viewcvs/relax?rev=20405&view=rev
Log:
Sectioning improvements for the relaxation dispersion chapter of the relax
user 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=20405&r1=20404&r2=20405&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Fri Jul 19 10:38:31 2013
@@ -50,18 +50,17 @@
The modelling of relaxation dispersion data can hence be catergorised into
these two distinct methodologies:
\begin{description}
-\item[Analytical models:]\index{relaxation dispersion!Analytical model}
Optimisation of models based on analytical, closed-form expressions derived
from the Bloch-McConnell equations subject to certain conditions (see
Section~\ref{sect: dispersion: analytic models} on page~\pageref{sect:
dispersion: analytic models}).
+\item[Analytical models:]\index{relaxation dispersion!Analytical model}
Optimisation of models based on analytical, closed-form expressions derived
from the Bloch-McConnell equations subject to certain conditions (see
Section~\ref{sect: dispersion: analytical models} on page~\pageref{sect:
dispersion: analytical models}).
\item[Numerical models:]\index{relaxation dispersion!Numerical model}
Optimisation of models based on numerically solving the Bloch-McConnell
equations (see Section~\ref{sect: dispersion: numerical models} on
page~\pageref{sect: dispersion: numerical models}).
\end{description}
-% Analytic models.
-%~~~~~~~~~~~~~~~~~
-
-\subsection{Analytic models}
-\label{sect: dispersion: analytic models}
-\index{relaxation dispersion!Analytical model|textbf}
+% Implemented models.
+%~~~~~~~~~~~~~~~~~~~~
+
+\subsection{Implemented models}
+\label{sect: dispersion: implemented models}
A number of analytic models are supported within relax.
If the model you are interested in is not available, see Section~\ref{sect:
dispersion: model tutorial} on page~\pageref{sect: dispersion: model
tutorial} for how new models can be added to relax.
@@ -87,14 +86,6 @@
\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}.
\end{description}
-
-
-% Numerical models.
-%~~~~~~~~~~~~~~~~~~
-
-\subsection{Numerical models}
-\label{sect: dispersion: numerical models}
-\index{relaxation dispersion!Numerical model|textbf}
Like the analytic models, a number of numerical models are supported within
relax.
These models are also dependant upon whether the data originates from a
CPMG-type or $\Ronerho$-type experiment.
@@ -209,10 +200,19 @@
\end{sidewaystable}
+
+% The base models.
+%%%%%%%%%%%%%%%%%%
+
+\clearpage
+
+\section{The base dispersion models}
+\label{sect: dispersion: base models}
+\index{relaxation dispersion!Base model|textbf}
+
+
% R2eff model.
%~~~~~~~~~~~~~
-
-\clearpage
\subsection{The R2eff model}
\label{sect: dispersion: R2eff model}
@@ -269,6 +269,14 @@
This model is provided for model selection purposes. In combination with
frequentist methods, such as AIC\index{model selection!AIC}, or Bayesian
methods\index{model selection!Bayesian} it can show if the presence of
chemical exchange is statistically significant. Optimisation is still
required as one $\Rtwozero$ value per magnetic field strength will be fit to
the measured data for each spin system. It is selected by setting the model
to `No Rex'.
+
+
+% The analytical models.
+%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{The analytical dispersion models}
+\label{sect: dispersion: analytical models}
+\index{relaxation dispersion!Analytical model|textbf}
% LM63 model.
@@ -372,66 +380,6 @@
\end{itemize}
-% Full NS 2-site 3D model.
-%~~~~~~~~~~~~~~~~~~~~~~~~~
-
-\subsection{The full NS 2-site 3D CPMG model}
-\label{sect: dispersion: NS 2-site 3D full model}
-\index{relaxation dispersion!NS 2-site 3D full model|textbf}
-
-This is the numerical model for 2-site exchange using 3D magnetisation
vectors.
-Is it selected by setting the model to `NS 2-site 3D full'.
-The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
-
-
-% Reduced NS 2-site 3D model.
-%~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-\subsection{The reduced NS 2-site 3D CPMG model}
-\label{sect: dispersion: NS 2-site 3D model}
-\index{relaxation dispersion!NS 2-site 3D model|textbf}
-
-This is the numerical model for 2-site exchange using 3D magnetisation
vectors, whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed.
-Is it selected by setting the model to `NS 2-site 3D'.
-The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
-
-
-% Full NS 2-site star model.
-%~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-\subsection{The full NS 2-site star CPMG model}
-\label{sect: dispersion: NS 2-site star full model}
-\index{relaxation dispersion!NS 2-site star full model|textbf}
-
-This is the numerical model for 2-site exchange using complex conjugate
matrices.
-Is it selected by setting the model to `NS 2-site star full'.
-The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
-
-
-% Reduced NS 2-site star model.
-%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-\subsection{The reduced NS 2-site star CPMG model}
-\label{sect: dispersion: NS 2-site star model}
-\index{relaxation dispersion!NS 2-site star model|textbf}
-
-This is the numerical model for 2-site exchange using complex conjugate
matrices, whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed.
-Is it selected by setting the model to `NS 2-site star'.
-The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
-
-
-% NS 2-site expanded model.
-%~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-\subsection{The NS 2-site expanded CPMG model}
-\label{sect: dispersion: NS 2-site expanded model}
-\index{relaxation dispersion!NS 2-site expanded model|textbf}
-
-This is the numerical model for 2-site exchange expanded using Maple by
Nikolai Skrynnikov.
-Is it selected by setting the model to `NS 2-site expanded'.
-The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
-
-
% M61 model.
%~~~~~~~~~~~
@@ -481,6 +429,76 @@
\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.
+
+
+
+% The numerical models.
+%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{The numerical dispersion models}
+\label{sect: dispersion: numerical models}
+\index{relaxation dispersion!Numerical model|textbf}
+
+
+% Full NS 2-site 3D model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The full NS 2-site 3D CPMG model}
+\label{sect: dispersion: NS 2-site 3D full model}
+\index{relaxation dispersion!NS 2-site 3D full model|textbf}
+
+This is the numerical model for 2-site exchange using 3D magnetisation
vectors.
+Is it selected by setting the model to `NS 2-site 3D full'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
+
+% Reduced NS 2-site 3D model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The reduced NS 2-site 3D CPMG model}
+\label{sect: dispersion: NS 2-site 3D model}
+\index{relaxation dispersion!NS 2-site 3D model|textbf}
+
+This is the numerical model for 2-site exchange using 3D magnetisation
vectors, whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed.
+Is it selected by setting the model to `NS 2-site 3D'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
+
+% Full NS 2-site star model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The full NS 2-site star CPMG model}
+\label{sect: dispersion: NS 2-site star full model}
+\index{relaxation dispersion!NS 2-site star full model|textbf}
+
+This is the numerical model for 2-site exchange using complex conjugate
matrices.
+Is it selected by setting the model to `NS 2-site star full'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
+
+% Reduced NS 2-site star model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The reduced NS 2-site star CPMG model}
+\label{sect: dispersion: NS 2-site star model}
+\index{relaxation dispersion!NS 2-site star model|textbf}
+
+This is the numerical model for 2-site exchange using complex conjugate
matrices, whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed.
+Is it selected by setting the model to `NS 2-site star'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
+
+% NS 2-site expanded model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The NS 2-site expanded CPMG model}
+\label{sect: dispersion: NS 2-site expanded model}
+\index{relaxation dispersion!NS 2-site expanded model|textbf}
+
+This is the numerical model for 2-site exchange expanded using Maple by
Nikolai Skrynnikov.
+Is it selected by setting the model to `NS 2-site expanded'.
+The simple constraint $\pA > \pB$ is used to halve the optimisation space,
as both sides of the limit are mirror image spaces.
+
% Script UI.
r20405 - /branches/relax_disp/docs/latex/dispersion.tex