Author: bugman
Date: Tue Sep 29 18:26:10 2015
New Revision: 27895
URL: http://svn.gna.org/viewcvs/relax?rev=27895&view=rev
Log:
Removed lots of useless comments about book references.
Modified:
branches/frame_order_cleanup/docs/latex/frame_order/modelling.tex
branches/frame_order_cleanup/docs/latex/frame_order/models.tex
branches/frame_order_cleanup/docs/latex/frame_order/pcs_numerical_integration.tex
branches/frame_order_cleanup/docs/latex/frame_order/theory.tex
Modified: branches/frame_order_cleanup/docs/latex/frame_order/modelling.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/frame_order_cleanup/docs/latex/frame_order/modelling.tex?rev=27895&r1=27894&r2=27895&view=diff
==============================================================================
--- branches/frame_order_cleanup/docs/latex/frame_order/modelling.tex
(original)
+++ branches/frame_order_cleanup/docs/latex/frame_order/modelling.tex Tue
Sep 29 18:26:10 2015
@@ -29,7 +29,6 @@
% Tilt and torsion angles.
%-------------------------
-% From pages 138-142, book 4.
\subsubsection{Tilt and torsion angles from robotics}
To describe the motional mechanics of a ball and socket joint, the Euler
angle system is a poor representation as the angles do not correspond to the
mechanical modes of motion.
@@ -82,7 +81,7 @@
The angle can be completely restricted as $\conesmax = 0$ to create
torsionless models.
In this case, the tilt and torsion rotation matrix simplifies to
-\begin{subequations} % From page 120, book 5.
+\begin{subequations}
\begin{align}
R(\theta, \phi, 0)
&= R_z(\phi)R_y(\theta)R_z(-\phi) , \\
@@ -134,7 +133,6 @@
% Frame order axis permutations.
-% From pages 53-54 and 71-81, book 7.
\subsection{Frame order axis permutations}
\label{sect: axis permutations}
\index{Frame order!axis permutations}
@@ -250,7 +248,6 @@
% Frame order linear constraints.
-% From pages 48-50, book 7.
\subsection{Linear constraints for the frame order models}
\index{Frame order!linear constraints|textbf}
Modified: branches/frame_order_cleanup/docs/latex/frame_order/models.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/frame_order_cleanup/docs/latex/frame_order/models.tex?rev=27895&r1=27894&r2=27895&view=diff
==============================================================================
--- branches/frame_order_cleanup/docs/latex/frame_order/models.tex
(original)
+++ branches/frame_order_cleanup/docs/latex/frame_order/models.tex Tue
Sep 29 18:26:10 2015
@@ -52,7 +52,6 @@
% Tilt and torsion angles.
%-------------------------
-% From pages 138-142, book 4.
\subsection{Tilt and torsion angles from robotics}
To describe the motional mechanics of a ball and socket joint, the Euler
angle system is a poor representation as the angles do not correspond to the
mechanical modes of motion.
@@ -105,7 +104,7 @@
The angle can be completely restricted as $\conesmax = 0$ to create
torsionless models.
In this case, the tilt and torsion rotation matrix simplifies to
-\begin{subequations} % From page 120, book 5.
+\begin{subequations}
\begin{align}
R(\theta, \phi, 0)
&= R_z(\phi)R_y(\theta)R_z(-\phi) , \\
@@ -257,7 +256,6 @@
% Rotor model parameterisation.
-% From pages 44-47, book 7.
\subsection{Rotor parameterisation}
The natural way to parameterise the rotation axis of rotor frame order model
is to use a 3D point, the pivot point, and a unit vector using the spherical
angle basis set.
@@ -306,7 +304,6 @@
% Rotor model equations.
-% This is from page 147, book 5.
\subsection{Rotor equations}
The only motion is in the torsion angle about the rotation axis.
@@ -477,7 +474,6 @@
% Free rotor model equations.
-% This is from page 148, book 5.
\subsection{Free rotor equations}
\begin{figure}
@@ -595,7 +591,6 @@
% Isotropic cone model parameterisation.
%---------------------------------------
-% From page 116, book 3.
\subsection{Isotropic cone parameterisation}
In this model, the tilt component of the tilt and torsion angle system is
modelled simply as
@@ -621,7 +616,6 @@
% Isotropic cone model equations.
-% From pages 124 and 135-137, book 5.
\subsection{Isotropic cone equations}
\begin{figure}
@@ -800,7 +794,6 @@
% Torsionless isotropic cone model equations.
-% This is from page 146, book 5.
\subsection{Torsionless isotropic cone equations}
\begin{figure}
@@ -967,7 +960,6 @@
% Free rotor isotropic cone model equations.
-% This is from page 138, book 5.
\subsection{Free rotor isotropic cone equations}
\begin{figure}
@@ -1102,7 +1094,6 @@
% Pseudo-ellipse model parameterisation.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 14 and 62, book 5.
\subsection{Pseudo-ellipse parameterisation}
To extend to the next level of motional complexity above the isotropic cone
models, an anisotropic cone can be modelled.
@@ -1152,7 +1143,6 @@
% Pseudo-elliptic cosine 2D trigonometric function.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 63-73, book 5.
\subsection{Derivation of a 2D trigonometric function - the pseudo-elliptic
cosine}
For the surface normalisation factor of the pseudo-elliptic cone, the
integral from equation~\ref{eq: pseudo-ellipse surface norm non-integratable}
on page~\pageref{eq: pseudo-ellipse surface norm non-integratable} is
@@ -1250,7 +1240,6 @@
% Pseudo-ellipse model equations.
%--------------------------------
-% This is from page 139-144, book 5.
\subsection{Pseudo-ellipse equations}
\begin{figure}
@@ -1343,7 +1332,6 @@
-% From page 78, book 5.
\subsubsection{Pseudo-ellipse rotation matrices}
For the pseudo-ellipse model, the full torsion-tilt system is used.
@@ -1587,7 +1575,6 @@
% The torsionless pseudo-ellipse model.
-% This is from pages 120-121 and 131-133, book 5.
\section{Torsionless pseudo-ellipse frame order model}
\index{Frame order!model!pseudo-ellipse, torsionless|textbf}
@@ -1689,7 +1676,6 @@
\end{figure}
-% From page 120, book 5.
\subsubsection{Torsionless pseudo-ellipse rotation matrices}
Setting the torsion angle $\sigma$ to zero in the full torsion-tilt rotation
matrix of equation~\ref{eq: R torsion-tilt}, the matrix becomes
@@ -1909,7 +1895,6 @@
% Free rotor pseudo-ellipse model equations.
-% From pages 123 and 133-134, book 5.
\subsection{Free rotor pseudo-ellipse equations}
\begin{figure}
@@ -2158,7 +2143,6 @@
% Double rotor parameterisation.
-% From pages 55-56, book 7.
\subsection{Double rotor parameterisation}
Assuming the axes are orthogonal for the model, the size of the set of
non-redundant parameters is 15.
@@ -2187,7 +2171,6 @@
% Double rotor equations.
-% From pages 58-64, book 7.
\subsection{Double rotor equations}
The double rotor model consists of two standard rotations, the first about
the x-axis and the second about the y-axis.
Modified:
branches/frame_order_cleanup/docs/latex/frame_order/pcs_numerical_integration.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/frame_order_cleanup/docs/latex/frame_order/pcs_numerical_integration.tex?rev=27895&r1=27894&r2=27895&view=diff
==============================================================================
---
branches/frame_order_cleanup/docs/latex/frame_order/pcs_numerical_integration.tex
(original)
+++
branches/frame_order_cleanup/docs/latex/frame_order/pcs_numerical_integration.tex
Tue Sep 29 18:26:10 2015
@@ -1,7 +1,6 @@
% The PCS.
%%%%%%%%%%
-% From pages 151-156, book 6.
\section{Computation time and the numerical integration of the PCS}
The numerical integration of the PCS using standard quadratic integration
for the frame order models is impractical and cannot be used.
@@ -13,7 +12,6 @@
% Numerical integration techniques.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 102-106, book 6.
\subsection{Numerical integration techniques}
The numerical integration is approximated as
@@ -44,7 +42,6 @@
% Monte Carlo numerical integration.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 102-106, book 6.
\subsubsection{Monte Carlo numerical integration}
As the convergence properties are better than that of a uniform
distribution, the Monte Carlo integration algorithm is a viable option for
using the PCS in the frame order analysis.
@@ -57,7 +54,6 @@
% Numerical integration using quasi-random Sobol' points.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From page 152, book 6.
\subsubsection{Quasi-random numerical integration -- Sobol' point sequence}
Although the Monte Carlo numerical integration algorithm is a huge
improvement on both the quadratic integration and the uniform distribution
numerical integration techniques, it was nevertheless still too slow for
optimising the frame order models.
@@ -83,7 +79,6 @@
% Sobol' oversampling.
%~~~~~~~~~~~~~~~~~~~~~
-% From pages 82-84, book 7.
\subsubsection{Oversampling the Sobol' sequence points}
As generating Sobol' points is computationally expensive, for speed this
operation occurs during target function initialisation prior to optimisation.
@@ -115,7 +110,6 @@
% Parallelization and running on a cluster.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From page 153, book 6.
\subsection{Parallelization and running on a cluster}
Four different attempts at parallelizing the calculations using the MPI 2
protocol resulted in no speeds up.
@@ -129,7 +123,6 @@
% Frame order model nesting.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 66-69, book 7.
\subsection{Frame order model nesting}
\index{Frame order!model nesting}
@@ -250,7 +243,6 @@
% PCS subset.
%~~~~~~~~~~~~
-% From page 155, book 6.
\subsection{PCS subset}
Another trick that can be used to speed up the optimisation is to use a
subset of all PCS values.
@@ -282,7 +274,6 @@
%---------------------------
-% From page 155, book 6.
\subsubsection{Low precision grid search}
\index{optimisation!algorithm!grid search!low precision|textbf}
@@ -297,7 +288,6 @@
%-------------------------
-% From page 70, book 7.
\subsubsection{The zooming grid search}
\index{optimisation!algorithm!grid search!zooming|textbf}
@@ -313,7 +303,6 @@
%-----------------------------
-% From page 70, book 7.
\subsubsection{The alternating grid search}
\index{optimisation!algorithm!grid search!alternating|textbf}
@@ -330,7 +319,6 @@
%--------------------------------
-% From page 154, book 6.
\subsubsection{Zooming precision optimisation}
\index{optimisation!algorithm!precision!zooming|textbf}
@@ -357,7 +345,6 @@
%---------------------------------------
-% From page 156, book 6.
\subsubsection{Low precision Monte Carlo simulations}
\index{Monte Carlo simulations|textbf}
Modified: branches/frame_order_cleanup/docs/latex/frame_order/theory.tex
URL:
http://svn.gna.org/viewcvs/relax/branches/frame_order_cleanup/docs/latex/frame_order/theory.tex?rev=27895&r1=27894&r2=27895&view=diff
==============================================================================
--- branches/frame_order_cleanup/docs/latex/frame_order/theory.tex
(original)
+++ branches/frame_order_cleanup/docs/latex/frame_order/theory.tex Tue
Sep 29 18:26:10 2015
@@ -17,7 +17,6 @@
% The ordering of a vector.
%--------------------------
-% From page 139-140, book 1.
\subsubsection{The ordering of a vector}
Let $\mu(t)$ be a time dependent vector defined within an arbitrary fixed
frame $F$ as
@@ -79,7 +78,6 @@
% The ordering of a frame.
%--------------------------
-% From page 141, book 1.
\subsubsection{The ordering of a frame}
Let the frame $C(t)$ be time dependent within an arbitrary fixed frame $F$.
@@ -107,7 +105,7 @@
This is the definition of the second degree frame order tensor.
The matrix form of the second degree frame order tensor in rank-2, 9D
Kronecker product notation is
-\begin{equation} \label{eq: frame order matrix 9D} % From page 127, book
5.
+\begin{equation} \label{eq: frame order matrix 9D}
\FOtwo(t) =
\overline{\left[
\begin{array}{@{}ccc;{2pt/4pt}ccc;{2pt/4pt}ccc@{}}
@@ -132,7 +130,7 @@
This is a rank-2, 3D order matrix of rank-2, 3D order matrices.
To see this, the $T_{14}$ rank-4 matrix transpose of $\FOtwo$ in Kronecker
product notation is
-\begin{equation} \label{eq: frame order matrix 9D T14} % From page 127,
book 5.
+\begin{equation} \label{eq: frame order matrix 9D T14}
\FO^{T_{14}}(t) =
\overline{\left[
\begin{array}{@{}ccc;{2pt/4pt}ccc;{2pt/4pt}ccc@{}}
@@ -153,7 +151,7 @@
The 3D matrix in the top left corner is the ordering of the x-axis with
itself, the central matrix is the ordering of the y-axis with itself, and the
bottom right is the ordering of the z-axis with itself.
The off-diagonal 3D matrices are the cross-correlations between the three
axes.
Using the notation $e_x$, $e_y$ and $e_z$ for the orthogonal axis system of
the time dependent frame $C(t)$, the second degree frame order matrix can be
written as
-\begin{equation} % From page 50, book 4.
+\begin{equation}
\FO^{T_{14}}(t) =
\begin{bmatrix}
\overline{e_x \otimes e_x} & \overline{e_x \otimes e_y} &
\overline{e_x \otimes e_z} \\
@@ -163,12 +161,12 @@
\end{equation}
If the rank-2, 3D order matrix between the axes A and B is denoted as
-\begin{equation} % From page 127, book 5.
+\begin{equation}
S_\textrm{AB}(t) = \overline{e_A \otimes e_B},
\end{equation}
then the frame order matrix is
-\begin{equation} % From page 127, book 5.
+\begin{equation}
\FO^{T_{14}}(t) =
\begin{bmatrix}
S_\textrm{XX}(t) & S_\textrm{XY}(t) & S_\textrm{XZ}(t) \\
@@ -181,7 +179,6 @@
The frame order matrix is diagonally symmetric, as can be seen in the
$T_{14}$ transpose of the matrix in rank-2, 9D Kronecker product form
(equation~\ref{eq: frame order matrix 9D T14}, hence for the second degree
frame order matrix there are 45 unique elements.
For the 9D Kronecker product notation of equation~\ref{eq: frame order
matrix 9D}, this transformed diagonal symmetry can be schematically
represented as
-% From page 162, book 1.
\setlength{\unitlength}{0.5cm}
\begin{picture}(19,9)
% Frame order symbol.
@@ -267,7 +264,7 @@
When rotational symmetries are present in the time modulation of the frame
$C(t)$ then, according to \citet{Perrin36}, the averages of the double
products $\overline{c_{ij}c_{kl}}$ where an index appears only once is zero.
In this case, the active frame order matrix elements are
-\begin{equation} \label{eq: frame order matrix 9D symmetry} % From page
144, book 1.
+\begin{equation} \label{eq: frame order matrix 9D symmetry}
\FOtwo(t) =
\left[
\begin{array}{@{}ccc;{2pt/4pt}ccc;{2pt/4pt}ccc@{}}
@@ -293,7 +290,6 @@
% The fourth rank identity matrices.
%-----------------------------------
-% From pages 3-4, book 4.
\subsubsection{The fourth rank identity matrices}
According to \citet{Spencer80}, the rank-4 identity matrices are defined as
@@ -383,7 +379,6 @@
% Tensor power of the frame order.
%---------------------------------
-% From pages 39, 41-42, book 3.
\subsubsection{Tensor power of the frame order}
The rank-4, 3D frame order tensor of equation~\ref{eq: 2nd degree frame
order definition} on page~\pageref{eq: 2nd degree frame order definition} was
derived for second order rotational physical processes.
@@ -469,14 +464,13 @@
% Rotation to the average position frame of the rigid body.
%----------------------------------------------------------
-% From page 42, book 3, page 41, book 4 and page 93&96, book 6.
\subsubsection{Rotation to the average position frame of the rigid body}
For the modelling aspect of the frame order theory, one more rotation is
required.
In equation~\ref{eq: frame order equation, arbitrary frame}, it is assumed
that the starting position for the moving rigid body is that of its motional
average.
However in the initial 3D structure, this is not the case and an additional
rotation to the average position $R_\textrm{ave}$ is required.
Taking this into account, the generalised frame order tensor is defined as
-\begin{equation} % From page 41, book 4.
+\begin{equation}
\FOn(t) = R_\textrm{eigen}^{\otimes n} \cdot \overline{R^{\otimes n}(t)}
\cdot R_\textrm{eigen}^{T \otimes n} \cdot R_\textrm{ave}^{T \otimes n} ,
\end{equation}
@@ -507,7 +501,6 @@
% Frame order and the alignment tensor.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From pages 103-106, 114-115, book 3 and pages 128-129, book 5.
\subsection{Frame order and the alignment tensor}
@@ -523,7 +516,6 @@
% The RDC.
-% From page 106, book 1.
\paragraph{The RDC}
The residual dipolar coupling is given by
@@ -546,7 +538,6 @@
% The PCS.
-% From page 88, book 6.
\paragraph{The PCS}
The pseudo-contact shift equation is simply
@@ -709,7 +700,6 @@
% The alignment tensor is the anisotropic part of a frame order matrix.
%~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-% From page 174, book 3.
\subsubsection{The alignment tensor is the anisotropic part of a frame order
matrix}
The alignment tensor is related to the orientational probability tensor by
@@ -745,7 +735,6 @@
% Ball-and-socket joint.
%-----------------------
-% From page 88-95, book 6.
\subsubsection{Atomic level mechanics of the single pivot}
For the PCS, the lanthanide ion to nuclear vector is
@@ -804,7 +793,6 @@
% Pivoted PCS.
%-------------
-% From page 95-96, book 6.
\subsubsection{PCS and single pivoted motions}
For a single state $i$, the PCS value when substituting~\ref{eq: pivoted
rotation vector i} into~\ref{eq: PCS equation} is
@@ -841,7 +829,6 @@
% Double pivot.
%~~~~~~~~~~~~~~
-% From pages 41-43, book 7.
\subsection{Double pivoted motions}
When the motion of a multiple rigid body system can be described as two
rotations about two different pivots, the modulation of the PCS becomes more
complicated.
@@ -952,7 +939,6 @@
% Free ellipsoidal Brownian diffusion.
%-------------------------------------
-% From pages 131-132, 148, book 3.
\subsubsection{Free ellipsoidal Brownian diffusion}
\label{sect: Free ellipsoidal Brownian diffusion}
r27895 - /branches/frame_order_cleanup/docs/latex/frame_order/