Hi Troels,
These are just a few LaTeX tips. But first, do you think it's worth
putting simplified equations into the 'B14' model section? And what
do you think about including the comparison to the CR72 model at
http://wiki.nmr-relax.com/B14?
For the tips:
1) For the R2eff equation, you could wrap this all in a block:
\begin{subequations}
\begin{align}
R2eff ...
\end{align}
\end{subequations}
This will give numbers to both parts. Search
docs/latex/dispersion.tex for examples. The multi-line part can be
made prettier by using a \qquad.
2) The align environment is much nicer than eqnarray.
3) For consistency, the R2eff parameter is defined in the relax.tex
file with \Rtwoeff. Also see \RtwozeroA, \RtwozeroB, \kAB, \kBA,
\kex, etc. Most dispersion parameters are defined in a consistent way
- just have a look at the relax.tex file.
One last thing, there appears to be an equation inconsistency with pD and pDN.
Cheers!
Edward
On 6 May 2014 17:35, <tlinnet@xxxxxxxxxxxxx> wrote:
Author: tlinnet
Date: Tue May 6 17:35:00 2014
New Revision: 23025
URL: http://svn.gna.org/viewcvs/relax?rev=23025&view=rev
Log:
Added model B14 description in the manual.
sr #3154: (https://gna.org/support/?3154) Implementation of Baldwin (2014)
B14 model - 2-site exact solution model for all time scales.
This follows the tutorial for adding relaxation dispersion models at:
http://wiki.nmr-relax.com/Tutorial_for_adding_relaxation_dispersion_models_to_relax#The_relax_manual
Modified:
trunk/docs/latex/dispersion.tex
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=23025&r1=23024&r2=23025&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Tue May 6 17:35:00 2014
@@ -102,6 +102,11 @@
$2*\taucpmg$ is the time between successive 180 degree pulses.
Parameters are $\{\RtwozeroA, \dots, \dw, \kAB\}$.
See Section~\ref{sect: dispersion: TSMFK01 model} on
page~\pageref{sect: dispersion: TSMFK01 model}.
+ \item[`B14':]\index{relaxation dispersion!B14 model} The reduced
\citet{Baldwin2014} 2-site exact solution equation for all time scales
whereby the simplification $\RtwozeroA = \RtwozeroB$ is assumed.
+ It has the parameters $\{\Rtwozero, \dots, \pA, \dw, \kex\}$.
+ See Section~\ref{sect: dispersion: B14 model} on page~\pageref{sect:
dispersion: B14 model}.
+ \item[`B14 full':]\index{relaxation dispersion!B14 full model} The full
\citet{Baldwin2014} 2-site exact equation for all time scales with parameters
$\{\RtwozeroA, \RtwozeroB, \dots, \pA, \dw, \kex\}$.
+ See Section~\ref{sect: dispersion: B14 full model} on
page~\pageref{sect: dispersion: B14 full model}.
\end{description}
For the SQ CPMG-type experiments, the numeric models currently supported
are:
@@ -549,6 +554,78 @@
\item the relaxation dispersion page of the relax website at
\url{http://www.nmr-relax.com/analyses/relaxation\_dispersion.html#TSMFK01}.
\end{itemize}
+
+% Full B14 model.
+%~~~~~~~~~~~~~~~~~
+
+\subsection{The full B14 2-site CPMG model}
+\label{sect: dispersion: B14 full model}
+\index{relaxation dispersion!B14 full model|textbf}
+
+This is the model for 2-site exchange exact analytical derivation on all time
scales (with the constraint that $\pA > \pB$), named after
\citet{Baldwin2014}.
+It is selected by setting the model to `B14 full'.
+The equation is
+\begin{equation}
+ R_{2,\textrm{eff}} =
\frac{R_2^A+R_2^B+k_{\textrm{EX}}}{2}-\frac{N_{\textrm{CYC}}}{T_{\textrm{rel}}}\cosh{}^{-1}(v_{1c})
- \frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} +
\frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D )\right)} \\
+ = R_{2,\textrm{eff}}^{\textrm{CR72}} -
\frac{1}{T_{\textrm{rel}}}\ln{\left( \frac{1+y}{2} +
\frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2k_{\textrm{AB}}p_D )\right)} ,
+\end{equation}
+
+where
+\begin{equation}
+ v_{1c} =
F_0\cosh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\cosh{\left(\tau_{\textrm{CP}}E_2\right)}
\\
+ v_{1s} =
F_0\sinh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\sinh{\left(\tau_{\textrm{CP}}E_2\right)}
\\
+ v_{2}N = v_{1s}\left(O_B-O_A\right)+4O_B F_1^a
\sinh{\left(\tau_{\textrm{CP}}E_1\right)} \\
+ p_D N = v_{1s} +
\left(F_1^a+F_1^b\right)\sinh{\left(\tau_{\textrm{CP}}E_1\right)}\\
+ v_3 = \left( v_2^2 + 4 k_{\textrm{BA}} k_{\textrm{AB}} p_D^2
\right)^{1/2} \\
+ y = \left( \frac{v_{1c}-v_3}{v_{1c}+v_3} \right)^{N_{\textrm{CYC}}}
+\end{equation}
+
+The advantage of this code will be that you will always get the right answer
provided you got 2-site exchange, in-phase magnetisation and on-resonance
pulses.
+
+The term $$p_D$$ is based on product of the off diagonal elements in the
CPMG propagator (Supplementary Section 3, \citet{Baldwin2014}).
+
+It is interesting to consider the region of validity of the Carver Richards
result. The two results are equal when the correction is zero, which is true
when
+
+\begin{equation}
+ \sqrt{v_{1c}^2-1} \approx v_2 + 2k_{\textrm{AB}}p_D
+\end{equation}
+
+This occurs when $$k_{\textrm{AB}}p_D$$ tends to zero, and so $$v_2=v_3$$.
+Setting $$k_{\textrm{AB}}p_D$$ to zero, amounts to neglecting magnetisation
that starts on the ground state ensemble and end on the excited state
ensemble and vice versa.
+This will be a good approximation when $$p_A \gg p_B$$.
+In practise, significant deviations from the Carver Richards equation can be
incurred if $$p_B > 1\%$$.
+Incorporation of the correction term, results in an improved description of
the CPMG experiment over the Carver Richards equation
\citet{CarverRichards72}.
+
+The reference for this equation is:
+\begin{itemize}
+ \item \bibentry{Baldwin2014}
+\end{itemize}
+
+More information about the B14 full model is available from:
+\begin{itemize}
+ \item the relax wiki at \url{http://wiki.nmr-relax.com/B14\_full},
+ \item the API documentation at
\url{http://www.nmr-relax.com/api/3.1/lib.dispersion.B14-module.html},
+ \item the relaxation dispersion page of the relax website at
\url{http://www.nmr-relax.com/analyses/relaxation\_dispersion.html#B14\_full}.
+\end{itemize}
+
+
+% B14 model.
+%~~~~~~~~~~~~
+
+\subsection{The reduced B14 2-site CPMG model}
+\label{sect: dispersion: B14 model}
+\index{relaxation dispersion!B14 model|textbf}
+
+This is the model for 2-site exchange exact analytical derivation on all time
scales (with the constraint that $\pA > \pB$), named after
\citet{Baldwin2014}.
+It is selected by setting the model to `B14'.
+It is the same as the full B14 model described above, but with the
simplification that $\RtwozeroA = \RtwozeroB$.
+
+More information about the B14 model is available from:
+\begin{itemize}
+ \item the relax wiki at \url{http://wiki.nmr-relax.com/B14},
+ \item the API documentation at
\url{http://www.nmr-relax.com/api/3.1/lib.dispersion.B14-module.html},
+ \item the relaxation dispersion page of the relax website at
\url{http://www.nmr-relax.com/analyses/relaxation\_dispersion.html#B14}.
+\end{itemize}
% The numeric CPMG models.
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Re: r23025 - /trunk/docs/latex/dispersion.tex