Author: tlinnet
Date: Wed May 7 10:14:09 2014
New Revision: 23030
URL: http://svn.gna.org/viewcvs/relax?rev=23030&view=rev
Log:
Used LaTeX subequations instead, and using R2eff parameter is defined in the
relax.tex
Using the defined \Rtwoeff, \RtwozeroA, \RtwozeroB, \kAB, \kBA, \kex.
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=23030&r1=23029&r2=23030&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Wed May 7 10:14:09 2014
@@ -565,21 +565,26 @@
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{eqnarray}
- 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})
\nonumber \\
- & - & \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)} \nonumber \\
- & = & 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{eqnarray}
+\begin{subequations}
+\begin{align}
+ \Rtwoeff & = \frac{\RtwozeroA + \RtwozeroB + \kex }{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 + 2 \kAB p_D )\right)} \\
+ & = \Rtwoeff^{\textrm{CR72}} - \frac{1}{T_{\textrm{rel}}}\ln{\left(
\frac{1+y}{2} + \frac{1-y}{2\sqrt{v_{1c}^2-1}}(v_2 + 2\kAB p_D )\right)} ,
+\end{align}
+\end{subequations}
+
where
-\begin{eqnarray}
- v_{1c} & = &
F_0\cosh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\cosh{\left(\tau_{\textrm{CP}}E_2\right)}
\nonumber \\
- v_{1s} & = &
F_0\sinh{\left(\tau_{\textrm{CP}}E_0\right)}-F_2\sinh{\left(\tau_{\textrm{CP}}E_2\right)}
\nonumber \\
- v_{2}N & = & v_{1s}\left(O_B-O_A\right)+4O_B F_1^a
\sinh{\left(\tau_{\textrm{CP}}E_1\right)} \nonumber \\
- p_D N & = & v_{1s} +
\left(F_1^a+F_1^b\right)\sinh{\left(\tau_{\textrm{CP}}E_1\right)} \nonumber \\
- v_3 & = & \left( v_2^2 + 4 k_{\textrm{BA}} k_{\textrm{AB}} p_D^2
\right)^{1/2} \nonumber \\
- y & = & \left( \frac{v_{1c}-v_3}{v_{1c}+v_3} \right)^{N_{\textrm{CYC}}}
-\end{eqnarray}
+\begin{subequations}
+\begin{align}
+ 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)} \nonumber \\
+ 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 \kBA \kAB p_D^2 \right)^{1/2} \\
+ y & = \left( \frac{v_{1c}-v_3}{v_{1c}+v_3} \right)^{N_{\textrm{CYC}}}
+\end{align}
+\end{subequations}
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.
r23030 - /trunk/docs/latex/dispersion.tex