Author: bugman
Date: Thu Aug 29 18:28:00 2013
New Revision: 20713
URL: http://svn.gna.org/viewcvs/relax?rev=20713&view=rev
Log:
Many fixes and improvements for all of the R1rho dispersion models in the
user manual.
The equations are now correct and the parameter table updated with new
parameters and equations.
Modified:
branches/relax_disp/docs/latex/dispersion.tex
branches/relax_disp/docs/latex/relax.tex
Modified: branches/relax_disp/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/dispersion.tex?rev=20713&r1=20712&r2=20713&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/dispersion.tex (original)
+++ branches/relax_disp/docs/latex/dispersion.tex Thu Aug 29 18:28:00 2013
@@ -127,7 +127,7 @@
\begin{sidewaystable}
\begin{center}
\caption{The parameters of relaxation dispersion.}
-\begin{tabular}{llll}
+\begin{longtable}{llll}
\toprule
Parameter & Equation & Description
& Units \\
\midrule
@@ -140,9 +140,14 @@
$\RtwozeroA$ & - & $\Rtwo$ relaxation
rate for state A in the absence of exchange & rad.s$^{-1}$ \\
$\RtwozeroB$ & - & $\Rtwo$ relaxation
rate for state B in the absence of exchange & rad.s$^{-1}$ \\
$\Ronerhoprime$ & - & $\Ronerho$ relaxation
rate in the absence of exchange & rad.s$^{-1}$ \\
-$\theta$ & - & Rotating frame tilt
angle & rad \\
-$\omegaone$ & - & Spin-lock field
strength & rad.s$^{-1}$
\\
-$\omegae$ & - & Effective field in the
rotating frame & rad.s$^{-1}$ \\
+$\aveoffset$ & $\aveomega - \omegarf$ & The average resonance
offset in the rotating frame & rad.s$^{-1}$ \\
+$\omegaA$ & - & The Larmor frequency
of the spin in state A & rad.s$^{-1}$ \\
+$\omegaB$ & - & The Larmor frequency
of the spin in state B & rad.s$^{-1}$ \\
+$\aveomega$ & $\pA\omegaA + \pB\omegaB$ & The population
averaged Larmor frequency of the spin & rad.s$^{-1}$
\\
+$\omegaone$ & - & Spin-lock field
strength, i.e. the amplitude of the rf field & rad.s$^{-1}$
\\
+$\omegae$ & $\sqrt(\aveoffset^2 + \omegaone^2)$ & Effective field
in the rotating frame & rad.s$^{-1}$ \\
+$\omegarf$ & - & Spin-lock offset, i.e.
the frequency of the rf field & rad.s$^{-1}$ \\
+$\theta$ & $\arctan \left( \frac{\omegaone}{\aveoffset} \right)$
& Rotating frame tilt angle & rad \\
$\kex$ & $1 / (2 \tex)$ & Chemical exchange rate
constant & rad.s$^{-1}$ \\
$\kexB$ & $\kAB + \kBA$ & Chemical exchange rate
constant between sites A and B & rad.s$^{-1}$ \\
$\kexC$ & $\kAC + \kCA$ & Chemical exchange rate
constant between sites A and C & rad.s$^{-1}$ \\
@@ -151,13 +156,13 @@
$\tex$ & $1 / (2 \kex)$ & Time of exchange
& s.rad$^{-1}$ \\
$\pA$ & - & Population of state A
& - \\
$\pB$ & - & Population of state B
& - \\
-$\dw$ & - & Chemical shift
difference between the two states & ppm \\
+$\dw$ & - & Chemical shift
difference between the two states & ppm (or
rad.s$^{-1}$) \\
$\Phiex$ & $\pA\pB\dw^2$ & Fast exchange factor
& rad$^2$.s$^{-2}$ \\
$\PhiexB$ & See \ref{eq: disp phiexB} on page \pageref{eq: disp
phiexB} & Fast exchange factor between sites A and B & rad$^2$.s$^{-2}$
\\
$\PhiexC$ & See \ref{eq: disp phiexC} on page \pageref{eq: disp
phiexC} & Fast exchange factor between sites A and C & rad$^2$.s$^{-2}$
\\
\bottomrule
\label{table: dispersion parameters}
-\end{tabular}
+\end{longtable}
\end{center}
\end{sidewaystable}
@@ -464,7 +469,7 @@
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} .
+ \Ronerho = \Ronerhoprime + \frac{\Phiex\kex}{\kex^2 + \omegae^2} .
\end{equation}
The reference for this equation is:
@@ -482,10 +487,10 @@
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}
-
-The reference for this equation is:
+ \Ronerho = \Rone \cos^2\theta + \left( \Ronerhoprime +
\frac{\Phiex\kex}{\kex^2 + \omegae^2} \right) \sin^2\theta ,
+\end{equation}
+
+where $\theta$ is the rotating frame tilt angle. The reference for this
equation is:
\begin{itemize}
\item \bibentry{Davis94}
\end{itemize}
@@ -515,7 +520,7 @@
This is the model for 2-site 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{\pA\pB\dw^2\kex}{\omega_\textrm{Aeff}^2\omega_\textrm{Beff}^2/\omega_\textrm{eff}^2
+ \kex^2} \sin^2(\theta).
+ \Ronerho = \Rone\cos^2\theta + \left( \Ronerhoprime +
\frac{\pA\pB\dw^2\kex}{\omega_\textrm{Aeff}^2\omega_\textrm{Beff}^2/\omega_\textrm{eff}^2
+ \kex^2} \right) \sin^2\theta.
\end{equation}
Modified: branches/relax_disp/docs/latex/relax.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/relax_disp/docs/latex/relax.tex?rev=20713&r1=20712&r2=20713&view=diff
==============================================================================
--- branches/relax_disp/docs/latex/relax.tex (original)
+++ branches/relax_disp/docs/latex/relax.tex Thu Aug 29 18:28:00 2013
@@ -128,6 +128,8 @@
\newcommand{\Localset}{\mathfrak{T}}
\newcommand{\KL}{\Delta_{\scriptscriptstyle \text{K-L}}}
+\newcommand{\aveoffset}{\bar\Omega}
+\newcommand{\aveomega}{\bar\omega}
\newcommand{\dw}{\Delta\omega}
\newcommand{\dwAB}{\Delta\omega_\textrm{AB}}
\newcommand{\dwAC}{\Delta\omega_\textrm{AC}}
@@ -144,8 +146,11 @@
\newcommand{\kBC}{\textrm{k}_\textrm{BC}}
\newcommand{\kCB}{\textrm{k}_\textrm{CB}}
\newcommand{\nucpmg}{\nu_\textrm{CPMG}}
+\newcommand{\omegaA}{\omega_\textrm{A}}
+\newcommand{\omegaB}{\omega_\textrm{B}}
\newcommand{\omegae}{\omega_\textrm{e}}
\newcommand{\omegaone}{\omega_1}
+\newcommand{\omegarf}{\omega_\textrm{rf}}
\newcommand{\pA}{p_\textrm{A}}
\newcommand{\pB}{p_\textrm{B}}
\newcommand{\pC}{p_\textrm{C}}
r20713 - in /branches/relax_disp/docs/latex: dispersion.tex relax.tex