r26848 - /trunk/docs/latex/curvefit.tex -- November 29, 2014 - 18:18

Author: bugman
Date: Sat Nov 29 18:18:12 2014
New Revision: 26848

URL: http://svn.gna.org/viewcvs/relax?rev=26848&view=rev
Log:
Expanded the relaxation curve-fitting chapter of the manual to include 
descriptions of the models.

A new section at the start of this chapter has been added to explain the 
different models and their
equations.  This was taken from the script mode section and expanded to 
include the new saturation
recovery experiment.


Modified:
    trunk/docs/latex/curvefit.tex

Modified: trunk/docs/latex/curvefit.tex
URL: 
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/curvefit.tex?rev=26848&r1=26847&r2=26848&view=diff
==============================================================================
--- trunk/docs/latex/curvefit.tex       (original)
+++ trunk/docs/latex/curvefit.tex       Sat Nov 29 18:18:12 2014
@@ -17,6 +17,40 @@
 
 The fitting of exponentials to relaxation curves (relaxation curve-fitting 
or as used throughout this chapter abbreviated simply as relax-fit) involves 
a number of steps including the loading of data, the calculation of both the 
average peak intensity\index{peak!intensity} across replicated spectra and 
the standard deviations\index{standard deviation} of those peak intensities, 
selection of the experiment type, optimisation of the parameters of the 
exponential curves during the fit for each observed spin, Monte Carlo 
simulations\index{Monte Carlo simulation} to find the parameter errors, and 
saving and viewing the results.
 To simplify the process a sample script will be followed step by step as was 
done with the NOE calculation.
+
+
+
+% The models.
+%%%%%%%%%%%%%
+
+\section{The exponential curve models}
+\label{sect: exponential curve models}
+
+A number of different models are supported in this analysis.
+These include the two parameter exponential decay to zero, the inversion 
recovery experiment, and the saturation recovery experiment.
+These can be selected using the 
\uf{relax\ufus{}fit\ufsep{}select\ufus{}model} user function.
+
+The default is the two parameter exponential decay whereby the magnetisation 
starts at $I_0$ and decays to zero.
+It has the parameters \{$\mathrm{R}_x$, $I_0$\}.
+The formula of this function is
+\begin{equation}
+  I(t) = I_0 e^{-\mathrm{R}_x \cdot t} ,
+\end{equation}
+
+\noindent where $I(t)$ is the peak intensity at any time point $t$, $I_0$ is 
the initial intensity, and $\mathrm{R}_x$ is the relaxation rate (either the 
$\Rone$ or $\Rtwo$).
+
+In the inversion recovery experiment, the magnetisation starts at a negative 
value at $-I_0$ and relaxes to a positive $I_{\infty}$ value.
+This curve consists of three parameters \{$\mathrm{R}_x$, $I_0$, 
$I_{\infty}$\}.
+The formula is
+\begin{equation}
+  I(t) = I_{\infty} - I_0 e^{-\mathrm{R}_x \cdot t} .
+\end{equation}
+
+In the saturation recovery experiment, the magnetisation starts at zero and 
relaxes to a positive $I_{\infty}$ value.
+The model consists of the two parameters \{$\mathrm{R}_x$, $I_{\infty}$\} 
and has the formula
+\begin{equation}
+  I(t) = I_{\infty} \left( 1 - e^{-\mathrm{R}_x \cdot t} \right) .
+\end{equation}
 
 
 
@@ -475,18 +509,7 @@
 \end{lstlisting}
 
 The argument \promptstring{exp} sets the relaxation curve to a two parameter 
\{$\mathrm{R}_x$, $I_0$\} exponential which decays to zero.
-The formula of this function is
-\begin{equation}
- I(t) = I_0 e^{-\mathrm{R}_x \cdot t},
-\end{equation}
-
-\noindent where $I(t)$ is the peak intensity at any time point $t$, $I_0$ is 
the initial intensity, and $\mathrm{R}_x$ is the relaxation rate (either the 
$\Rone$ or $\Rtwo$).
-Changing the user function argument to \promptstring{inv} will select the 
inversion recovery experiment.
-This curve consists of three parameters \{$\Rone$, $I_0$, $I_{\infty}$\} and 
does not decay to zero.
-The formula is
-\begin{equation}
- I(t) = I_{\infty} - I_0 e^{-\Rone \cdot t}.
-\end{equation}
+Changing the user function argument to \promptstring{inv} will select the 
inversion recovery experiment, and changing it to \promptstring{sat} will 
select the saturation recovery experiment (see section~\ref{sect: exponential 
curve models} on page~\pageref{sect: exponential curve models}).