Hi Edward.
What is the equation inconsistency with pD and pDN. ? I cant see it? I look at eq: 45 in the paper. Best Troels 2014-05-06 18:19 GMT+02:00 Edward d'Auvergne <[email protected]>: > 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, <[email protected]> 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. >> >> >> _______________________________________________ >> relax (http://www.nmr-relax.com) >> >> This is the relax-commits mailing list >> [email protected] >> >> To unsubscribe from this list, get a password >> reminder, or change your subscription options, >> visit the list information page at >> https://mail.gna.org/listinfo/relax-commits > > _______________________________________________ > relax (http://www.nmr-relax.com) > > This is the relax-devel mailing list > [email protected] > > To unsubscribe from this list, get a password > reminder, or change your subscription options, > visit the list information page at > https://mail.gna.org/listinfo/relax-devel _______________________________________________ relax (http://www.nmr-relax.com) This is the relax-devel mailing list [email protected] To unsubscribe from this list, get a password reminder, or change your subscription options, visit the list information page at https://mail.gna.org/listinfo/relax-devel
