Author: bugman
Date: Mon Dec 9 16:05:35 2013
New Revision: 21909
URL: http://svn.gna.org/viewcvs/relax?rev=21909&view=rev
Log:
Added the 'NS R1rho 3-site' models to the relax user manual.
This is for the 'NS R1rho 3-site' and 'NS R1rho 3-site linear' dispersion
models.
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
trunk/docs/latex/dispersion_models.tex
trunk/docs/latex/dispersion_software.tex
trunk/docs/latex/relax.tex
Modified: trunk/docs/latex/dispersion.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion.tex?rev=21909&r1=21908&r2=21909&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Mon Dec 9 16:05:35 2013
@@ -127,6 +127,8 @@
\begin{description}
\item[`NS R1rho 2-site':]\index{relaxation dispersion!NS R1rho 2-site model}
The model for 2-site exchange using 3D magnetisation vectors. It has the
parameters $\{\Ronerhoprime, \dots, \pA, \dw, \kex\}$. See
Section~\ref{sect: dispersion: NS R1rho 2-site model} on page~\pageref{sect:
dispersion: NS R1rho 2-site model}.
+\item[`NS $\Ronerho$ 3-site linear':]\index{relaxation dispersion!NS R1rho
3-site linear model} The model for 3-site exchange linearised with
$\kAC=\kCA=0$ whereby the simplification $\RonerhoprimeA = \RonerhoprimeB =
\RonerhoprimeC$ is assumed. It has the parameters \{$\Ronerhoprime$,
$\dots$, $\pA$, $\pB$, $\dwAB$, $\dwBC$, $\kexAB$, $\kexBC$\}. See
Section~\ref{sect: dispersion: NS R1rho 3-site linear model} on
page~\pageref{sect: dispersion: NS R1rho 3-site linear model}.
+\item[`NS $\Ronerho$ 3-site':]\index{relaxation dispersion!NS R1rho 3-site
model} The model for 3-site exchange whereby the simplification
$\RonerhoprimeA = \RonerhoprimeB = \RonerhoprimeC$ is assumed. It has the
parameters \{$\Ronerhoprime$, $\dots$, $\pA$, $\pB$, $\dwAB$, $\dwBC$,
$\kexAB$, $\kexBC$, $\kexAC$\}. See Section~\ref{sect: dispersion: NS R1rho
3-site model} on page~\pageref{sect: dispersion: NS R1rho 3-site model}.
\end{description}
@@ -1128,6 +1130,143 @@
where $\delta_{A,B}$ is defined in Equations~\ref{eq: deltaA} and~\ref{eq:
deltaB}.
+% NS R1rho 3-site model.
+%~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The NS 3-site $\Ronerho$ model}
+\label{sect: dispersion: NS R1rho 3-site model}
+\index{relaxation dispersion!NS R1rho 3-site model|textbf}
+
+This is the numerical model for 3-site exchange using 3D magnetisation
vectors.
+It is selected by setting the model to `NS R1rho 3-site'.
+The constraints $\pA > \pB$ and $\pA > \pC$ is used to decrease the size of
the optimisation space, as both sides of the limit are mirror image spaces.
+
+For this model, as for the 2-site model above, the equations from
\citet{Korzhnev05a} have been used.
+These have been however rearranged to match the notation in
\citet{PalmerMassi06}.
+The $\Ronerho$ value for state A magnetisation is defined as
+\begin{equation}
+ \Ronerho = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot
e^{R \cdot T_\textrm{relax}} \cdot M_0 \right),
+\end{equation}
+
+where
+\begin{align}
+ M_0 &= \begin{pmatrix} \sin{\theta} \\ 0 \\ \cos{\theta} \\ 0 \\ 0 \\
0 \\ 0 \\ 0 \\ 0 \end{pmatrix}, \\
+ \theta &= \arctan \left( \frac{\omegaone}{\aveoffset} \right).
+\end{align}
+
+This assumes that the starting magnetisation has an X and Z component only
for the A state.
+The relaxation evolution matrix is defined as
+\begin{align}
+ R &= \begin{pmatrix}
+ -\RonerhoprimeA-\kAB-\kAC & -\delta_A & 0
& \cdots \\
+ \delta_A & -\RonerhoprimeA-\kAB-\kAC &
-\omegaone & \cdots \\
+ 0 & \omegaone &
-\RoneA-\kAB-\kAC & \cdots \\
+ \vdots & \vdots & \vdots
& \ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & \vdots & \vdots &
\vdots & \iddots \\
+ \cdots & -\RonerhoprimeB-\kBA-\kBC & -\delta_B &
0 & \cdots \\
+ \cdots & \delta_B & -\RonerhoprimeB-\kBA-\kBC &
-\omegaone & \cdots \\
+ \cdots & 0 & \omegaone &
-\RoneB-\kBA-\kBC & \cdots \\
+ \iddots & \vdots & \vdots &
\vdots & \ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & \vdots & \vdots &
\vdots \\
+ \cdots & -\RonerhoprimeC-\kCA-\kCB & -\delta_C &
0 \\
+ \cdots & \delta_C & -\RonerhoprimeC-\kCA-\kCB &
-\omegaone \\
+ \cdots & 0 & \omegaone &
-\RoneC-\kCA-\kCB \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ & & & \kAB & 0 & 0 &
\cdots \\
+ & \ddots & & 0 & \kAB & 0 &
\cdots \\
+ & & & 0 & 0 & \kAB &
\cdots \\
+ \kBA & 0 & 0 & & & & \\
+ 0 & \kBA & 0 & & \ddots & &
\cdots\\
+ 0 & 0 & \kBA & & & & \\
+ \vdots & \vdots & \vdots & & \vdots & &
\ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ & & & \cdots & \kAC & 0 & 0 \\
+ & \ddots & & \cdots & 0 & \kAC & 0 \\
+ & & & \cdots & 0 & 0 & \kAC
\\
+ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots &
\vdots \\
+ \kCA & 0 & 0 & \cdots & & & \\
+ 0 & \kCA & 0 & \cdots & & \ddots & \\
+ 0 & 0 & \kCA & \cdots & & & \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & & \vdots & & \vdots & \vdots &
\vdots \\
+ & & & & \kBC & 0 & 0 \\
+ \cdots & & \ddots & & 0 & \kBC & 0 \\
+ & & & & 0 & 0 & \kBC
\\
+ \cdots & \kCB & 0 & 0 & & & \\
+ \cdots & 0 & \kCB & 0 & & \ddots & \\
+ \cdots & 0 & 0 & \kCB & & & \\
+ \end{pmatrix},
+\end{align}
+
+where $\delta_{A,B,C}$ are defined as in Equations~\ref{eq: deltaA}
and~\ref{eq: deltaB}.
+For the model, the assumptions $\RonerhoprimeA$ = $\RonerhoprimeB$ =
$\RonerhoprimeC$ = $\Ronerhoprime$ and $\RoneA$ = $\RoneB$ = $\RoneC$ =
$\Rone$ have been made.
+
+
+% NS R1rho 3-site linear model.
+%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
+
+\subsection{The NS 3-site linear $\Ronerho$ model}
+\label{sect: dispersion: NS R1rho 3-site linear model}
+\index{relaxation dispersion!NS R1rho 3-site linear model|textbf}
+
+This is the numerical model for 3-site linear exchange using 3D
magnetisation vectors.
+The assumption that $\kAC$~= $\kCA$~= 0 has been made to linearise this
model.
+It is selected by setting the model to `NS R1rho 3-site linear'.
+The constraints $\pA > \pB$ and $\pA > \pC$ is used to decrease the size of
the optimisation space, as both sides of the limit are mirror image spaces.
+To simplify the optimisation space for the model as in the `NS $\Ronerho$
3-site' model, the assumptions $\RtwozeroA$~= $\RtwozeroB$~= $\RtwozeroC$~=
$\Rtwozero$ and $\RoneA$ = $\RoneB$ = $\RoneC$ = $\Rone$ have been made.
+
+The equations are the same as for the `NS R1rho 3-site' model except for the
relaxation evolution matrix which simplifies to
+\begin{align}
+ R &= \begin{pmatrix}
+ -\RonerhoprimeA-\kAB & -\delta_A & 0 &
\cdots \\
+ \delta_A & -\RonerhoprimeA-\kAB & -\omegaone &
\cdots \\
+ 0 & \omegaone & -\RoneA-\kAB &
\cdots \\
+ \vdots & \vdots & \vdots &
\ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & \vdots & \vdots &
\vdots & \iddots \\
+ \cdots & -\RonerhoprimeB-\kBA-\kBC & -\delta_B &
0 & \cdots \\
+ \cdots & \delta_B & -\RonerhoprimeB-\kBA-\kBC &
-\omegaone & \cdots \\
+ \cdots & 0 & \omegaone &
-\RoneB-\kBA-\kBC & \cdots \\
+ \iddots & \vdots & \vdots &
\vdots & \ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & \vdots & \vdots & \vdots \\
+ \cdots & -\RonerhoprimeC-\kCB & -\delta_C & 0 \\
+ \cdots & \delta_C & -\RonerhoprimeC-\kCB & -\omegaone
\\
+ \cdots & 0 & \omegaone &
-\RoneC-\kCB \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ & & & \kAB & 0 & 0 &
\cdots \\
+ & \ddots & & 0 & \kAB & 0 &
\cdots \\
+ & & & 0 & 0 & \kAB &
\cdots \\
+ \kBA & 0 & 0 & & & & \\
+ 0 & \kBA & 0 & & \ddots & &
\cdots\\
+ 0 & 0 & \kBA & & & & \\
+ \vdots & \vdots & \vdots & & \vdots & &
\ddots \\
+ \end{pmatrix} \nonumber \\
+ &+ \begin{pmatrix}
+ \ddots & & \vdots & & \vdots & \vdots &
\vdots \\
+ & & & & \kBC & 0 & 0 \\
+ \cdots & & \ddots & & 0 & \kBC & 0 \\
+ & & & & 0 & 0 & \kBC
\\
+ \cdots & \kCB & 0 & 0 & & & \\
+ \cdots & 0 & \kCB & 0 & & \ddots & \\
+ \cdots & 0 & 0 & \kCB & & & \\
+ \end{pmatrix},
+\end{align}
+
+where $\delta_{A,B,C}$ are defined as in Equations~\ref{eq: deltaA}
and~\ref{eq: deltaB}.
+For the model, the assumptions $\RonerhoprimeA$ = $\RonerhoprimeB$ =
$\RonerhoprimeC$ = $\Ronerhoprime$ and $\RoneA$ = $\RoneB$ = $\RoneC$ =
$\Rone$ have been made.
+
+
% Relaxation dispersion optimisation theory.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1596,8 +1735,6 @@
Some of the missing models include:
\begin{description}
\item[`TP04':]\index{relaxation dispersion!TP04 model} The $\Ronerho$-type
data \citet{TrottPalmer04} N-site analytic equation for all time scales with
parameters $\{\Ronerhoprime, \dots, \pone, \dots, \pN, \aveomega, \konetwo,
\dots\, \koneN\}$.
-\item[`NS $\Ronerho$ 3-site linear':]\index{relaxation dispersion!NS R1rho
3-site linear model} The model of the numeric solution for linear 3-site
exchange for $\Ronerho$-type data.
-\item[`NS $\Ronerho$ 3-site':]\index{relaxation dispersion!NS R1rho 3-site
model} Similar to the `NS $\Ronerho$ 3-site linear' model but with one of
the $\kex$ parameters not set to zero.
\item[`* $\Ronerho$':] All of the 3-site and N-site models as summarised in
Table~1 of \citet{PalmerMassi06}.
\end{description}
Modified: trunk/docs/latex/dispersion_models.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion_models.tex?rev=21909&r1=21908&r2=21909&view=diff
==============================================================================
--- trunk/docs/latex/dispersion_models.tex (original)
+++ trunk/docs/latex/dispersion_models.tex Mon Dec 9 16:05:35 2013
@@ -75,10 +75,10 @@
TP04\footnotemark[1] & Analytic & N & $\{\Ronerhoprime, \dots,
\pone, \dots, \pN, \aveomega, \konetwo, \dots\, \koneN\}$ & One site
dominant & \citet{TrottPalmer04} \\
MP05 & Analytic & 2 & $\{\Ronerhoprime, \dots, \pA,
\dw, \kex\}$ & $\pA > \pB$ &
\citet{MiloushevPalmer05} \\
NS R1rho 2-site & Numeric & 2 & $\{\Ronerhoprime, \dots, \pA,
\dw, \kex\}$ & $\pA > \pB$ & - \\
-NS R1rho 3-site linear\footnotemark[1] & Numeric & 3 & $\{\Ronerhoprime,
\dots, \pA, \pB, \dwAB, \dwBC,$ & $\pA > \pB$ and $\pA > \pC$ & - \\
- & & & $\dwHAB, \dwHBC, \kexAB,
\kexBC\}$ \\
-NS R1rho 3-site\footnotemark[1] & Numeric & 3 & $\{\Ronerhoprime,
\dots, \pA, \pB, \dwAB, \dwBC,$ & $\pA > \pB$ and $\pA > \pC$ & - \\
- & & & $\dwHAB, \dwHBC, \kexAB,
\kexBC, \kexAC\}$ \\
+NS R1rho 3-site linear & Numeric & 3 & $\{\Ronerhoprime, \dots, \pA,
\pB, \dwAB, \dwBC,$ & $\pA > \pB$ and $\pA > \pC$ & - \\
+ & & & $\kexAB, \kexBC\}$ \\
+NS R1rho 3-site & Numeric & 3 & $\{\Ronerhoprime, \dots, \pA,
\pB, \dwAB, \dwBC,$ & $\pA > \pB$ and $\pA > \pC$ & - \\
+ & & & $\kexAB, \kexBC, \kexAC\}$ \\
\footnotetext[1]{Not implemented yet}
Modified: trunk/docs/latex/dispersion_software.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/dispersion_software.tex?rev=21909&r1=21908&r2=21909&view=diff
==============================================================================
--- trunk/docs/latex/dispersion_software.tex (original)
+++ trunk/docs/latex/dispersion_software.tex Mon Dec 9 16:05:35 2013
@@ -67,8 +67,8 @@
TP04 & \no & \no & \no & \no & \no & \no & \no
& \no & \no \\
MP05 & \no & \no & \no & \no & \no & \no & \no
& \no & \yes \\
NS $\Ronerho$ 2-site & \no & \yes & \no & \no & \no & \no & ?
& \no & \yes \\
-NS $\Ronerho$ 3-site linear & \no & \yes & \no & \no & \no & \no & \no
& \no & \no \\
-NS $\Ronerho$ 3-site & \no & \yes & \no & \no & \no & \no & \no
& \no & \no \\
+NS $\Ronerho$ 3-site linear & \no & \yes & \no & \no & \no & \no & \no
& \no & \yes \\
+NS $\Ronerho$ 3-site & \no & \yes & \no & \no & \no & \no & \no
& \no & \yes \\
\midrule
\vspace{-5pt} \\
Modified: trunk/docs/latex/relax.tex
URL:
http://svn.gna.org/viewcvs/relax/trunk/docs/latex/relax.tex?rev=21909&r1=21908&r2=21909&view=diff
==============================================================================
--- trunk/docs/latex/relax.tex (original)
+++ trunk/docs/latex/relax.tex Mon Dec 9 16:05:35 2013
@@ -40,6 +40,7 @@
% Better maths.
\usepackage{amsmath}
\usepackage{amssymb}
+\usepackage{mathdots}
% Source code and scripts.
\usepackage[procnames]{listings}
@@ -181,7 +182,13 @@
\newcommand{\PhiexC}{\Phi_\textrm{ex,C}}
\newcommand{\Phiexi}{\Phi_\textrm{ex,i}}
\newcommand{\Rex}{\mathrm{R}_\textrm{ex}}
+\newcommand{\RoneA}{\mathrm{R}_\textrm{1A}}
+\newcommand{\RoneB}{\mathrm{R}_\textrm{1B}}
+\newcommand{\RoneC}{\mathrm{R}_\textrm{1C}}
\newcommand{\Ronerhoprime}{\mathrm{R}_{1\rho}'}
+\newcommand{\RonerhoprimeA}{\mathrm{R}_{1\rho A}'}
+\newcommand{\RonerhoprimeB}{\mathrm{R}_{1\rho B}'}
+\newcommand{\RonerhoprimeC}{\mathrm{R}_{1\rho C}'}
\newcommand{\Rtwoeff}{\mathrm{R}_\textrm{2eff}}
\newcommand{\Rtwozero}{\mathrm{R}_2^0}
\newcommand{\RtwozeroA}{\mathrm{R}_\mathrm{2A}^0}
r21909 - in /trunk/docs/latex: dispersion.tex dispersion_models.tex dispersion_software.tex relax.tex