Author: bugman
Date: Fri May 9 09:57:41 2014
New Revision: 23122
URL: http://svn.gna.org/viewcvs/relax?rev=23122&view=rev
Log:
The T_relax symbol is now defined in the preamble of the manual.
This is to standardise its usage in the dispersion chapter.
Modified:
trunk/docs/latex/dispersion.tex
trunk/docs/latex/relax.tex
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=23122&r1=23121&r2=23122&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Fri May 9 09:57:41 2014
@@ -220,24 +220,24 @@
For the fixed relaxation time period CPMG-type experiments, the
$\Rtwoeff$/$\Ronerho$ values are determined by direct calculation using the
formula
\begin{equation}
- \Rtwoeff(\nucpmg) = - \frac{1}{T_\textrm{relax}} \cdot \ln \left(
\frac{I_1(\nucpmg)}{I_0} \right) .
+ \Rtwoeff(\nucpmg) = - \frac{1}{\Trelax} \cdot \ln \left(
\frac{I_1(\nucpmg)}{I_0} \right) .
\end{equation}
The values and errors are determined with a single call of the \uf{calc}
user function.
The $\Ronerho$ version of the equation is essentially the same:
\begin{equation}
- \Ronerho(\omega_1) = - \frac{1}{T_\textrm{relax}} \cdot \ln \left(
\frac{I_1(\omega_1)}{I_0} \right) .
+ \Ronerho(\omega_1) = - \frac{1}{\Trelax} \cdot \ln \left(
\frac{I_1(\omega_1)}{I_0} \right) .
\end{equation}
Errors are calculated using the formula
\begin{equation} \label{eq: dispersion error}
- \sigma_{\Rtwo} = \frac{1}{T_\textrm{relax}} \sqrt{ \left(
\frac{\sigma_{I_1}}{I_1(\omega_1)} \right)^2 + \left(
\frac{\sigma_{I_0}}{I_0} \right)^2 } .
+ \sigma_{\Rtwo} = \frac{1}{\Trelax} \sqrt{ \left(
\frac{\sigma_{I_1}}{I_1(\omega_1)} \right)^2 + \left(
\frac{\sigma_{I_0}}{I_0} \right)^2 } .
\end{equation}
In a number of publications, the error formula from \citet{IshimaTorchia05}
has been used.
This is the collapse of Equation~\ref{eq: dispersion error} by setting
$\sigma_{I_0}$ to zero:
\begin{equation} \label{eq: IT05 dispersion error}
- \sigma_{\Rtwo} = \frac{\sigma_{I_1}}{T_\textrm{relax} I_1(\omega_1)} .
+ \sigma_{\Rtwo} = \frac{\sigma_{I_1}}{\Trelax I_1(\omega_1)} .
\end{equation}
This is not implemented in relax as it can be shown by simple simulation
that the formula is incorrect (see Figure~\ref{fig: dispersion error
comparison}).
@@ -772,9 +772,9 @@
\begin{subequations}
\begin{align}
I_0 &= \pA, \\
- I_1 &= \Re(t_{139}) \exp(-T_\textrm{relax} \Rtwozero), \\
+ I_1 &= \Re(t_{139}) \exp(-\Trelax \Rtwozero), \\
M_x &= I_1 / I_0, \\
- \Rtwoeff &= -\frac{1}{T_\textrm{relax}} \cdot \ln \left( M_x \right).
\label{eq: R2eff NS CPMG 2-site expanded}
+ \Rtwoeff &= -\frac{1}{\Trelax} \cdot \ln \left( M_x \right). \label{eq:
R2eff NS CPMG 2-site expanded}
\end{align}
\end{subequations}
@@ -894,7 +894,7 @@
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{1}{T_\textrm{relax}}\ln(Q),
+ \Rtwoeff = \Re(\lambda_1) - \frac{1}{\Trelax}\ln(Q),
\end{equation}
where
@@ -973,12 +973,12 @@
The basic evolution matrices for single, zero and double quantum CPMG-type
data for this model are
\begin{equation}
- \Rtwoeff = - \frac{1}{T_\textrm{relax}} \log
\frac{\mathbf{M}_A(T_\textrm{relax})}{\mathbf{M}_A(0)},
+ \Rtwoeff = - \frac{1}{\Trelax} \log
\frac{\mathbf{M}_A(\Trelax)}{\mathbf{M}_A(0)},
\end{equation}
where $\mathbf{M}_A(0)$ is proportional to the vector $[\pA, \pB]^T$ and
\begin{equation}
- \mathbf{M}_A(T_\textrm{relax}) = \left(
\mathbf{A_\pm}\mathbf{A_\mp}\mathbf{A_\mp}\mathbf{A_\pm} \right)^n
\mathbf{M}_A(0)
+ \mathbf{M}_A(\Trelax) = \left(
\mathbf{A_\pm}\mathbf{A_\mp}\mathbf{A_\mp}\mathbf{A_\pm} \right)^n
\mathbf{M}_A(0)
\end{equation}
The evolution matrix $\mathbf{A}$ is defined as
@@ -1468,7 +1468,7 @@
For this model, the equations from \citet{Korzhnev05a} have been used.
The $\Ronerho$ value for state A magnetisation is defined as
\begin{equation}
- \Ronerho = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot
e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
+ \Ronerho = - \frac{1}{\Trelax} \cdot \ln \left( M_0^T \cdot e^{R \cdot
\Trelax} \cdot M_0 \right),
\end{equation}
where
@@ -1514,7 +1514,7 @@
These have been however rearranged to match the notation in
\citet{PalmerMassi06}.
The $\Ronerho$ value for state A magnetisation is defined as
\begin{equation}
- \Ronerho = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot
e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
+ \Ronerho = - \frac{1}{\Trelax} \cdot \ln \left( M_0^T \cdot e^{R \cdot
\Trelax} \cdot M_0 \right),
\end{equation}
where
@@ -2139,7 +2139,7 @@
\item The van't Hoff analysis of multi-temperature dispersion data (see
\url{https://en.wikipedia.org/wiki/Van\_\%27t\_Hoff\_equation}).
\item ZZ exchange.
\item HD exchange.
- \item The \citet{Korzhnev05a} correction for constant-time $\Ronerho$
experiments for the analytic models ($\Ronerho$ = $-\lambda_1
-1/T_\textrm{relax}\log{a_1}$, where $a_1$ = $1 - \pB\cos^2(\theta_A -
\theta_B)$, and $\theta_A$ = $\arctan(\omegaone/\omegaA)$ and $\theta_B$ =
$\arctan(\omegaone/\omegaB)$.
+ \item The \citet{Korzhnev05a} correction for constant-time $\Ronerho$
experiments for the analytic models ($\Ronerho$ = $-\lambda_1
-1/\Trelax\log{a_1}$, where $a_1$ = $1 - \pB\cos^2(\theta_A - \theta_B)$, and
$\theta_A$ = $\arctan(\omegaone/\omegaA)$ and $\theta_B$ =
$\arctan(\omegaone/\omegaB)$.
\end{itemize}
If you would like one of these features, please contact the ``relax-devel at
gna.org''\index{mailing list!relax-devel} mailing list.
Modified: trunk/docs/latex/relax.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/relax.tex?rev=23122&r1=23121&r2=23122&view=diff
==============================================================================
--- trunk/docs/latex/relax.tex (original)
+++ trunk/docs/latex/relax.tex Fri May 9 09:57:41 2014
@@ -215,6 +215,7 @@
\newcommand{\RtwoZQC}{\mathrm{R}_\mathrm{2,ZQ}^\mathrm{C}}
\newcommand{\tex}{\tau_\textrm{ex}}
\newcommand{\taucpmg}{\tau_\textrm{CPMG}}
+\newcommand{\Trelax}{T_\textrm{relax}}
% Natbib Citation format.
\bibpunct{(}{)}{;}{a}{,}{,}
r23122 - in /trunk/docs/latex: dispersion.tex relax.tex