Hi, I need to look at the paper more. I can't see where pDN from equation 45 fits into equation 48 or 50, as I only see pD there.
Cheers, Edward On 7 May 2014 10:02, Troels Emtekær Linnet <[email protected]> wrote: > 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
