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.
r23025 - /trunk/docs/latex/dispersion.tex