Author: bugman
Date: Thu Aug 21 15:51:49 2014
New Revision: 25172
URL: http://svn.gna.org/viewcvs/relax?rev=25172&view=rev
Log:
LaTeX formatting fixes for the dispersion chapter of the manual.
All sentences are now on new lines and spaces after the terminal full stop have
been removed.
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=25172&r1=25171&r2=25172&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex (original)
+++ trunk/docs/latex/dispersion.tex Thu Aug 21 15:51:49 2014
@@ -659,17 +659,18 @@
\end{align}
\end{subequations}
-The advantage of these equations is that you will always obtain the correct
answer provided you have 2-site exchange, in-phase magnetisation and
on-resonance pulses.
+The advantage of these equations is that you will always obtain the correct
answer provided you have 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, see supplementary Section 3 \citep{Baldwin2014}.
-It is interesting to consider the region of validity of the Carver and
Richards result. The two results are equal when the correction is zero, which
is true when
+It is interesting to consider the region of validity of the Carver and
Richards result.
+The two results are equal when the correction is zero, which is true when
\begin{equation}
\sqrt{\nu_{1c}^2-1} \approx \nu_2 + 2 \kAB p_D .
\end{equation}
This occurs when $\kAB p_D$ tends to zero, and so $\nu_2 = \nu_3$.
-Setting $\kAB p_D$ to zero amounts to neglecting magnetisation that starts on
the ground state ensemble and end on the excited state ensemble and vice versa.
+Setting $\kAB p_D$ 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 $\pA \gg \pB$.
In practise, significant deviations from the Carver and Richards equation can
be incurred if $\pB > 1$\%.
Incorporation of the correction term results in an improved description of the
CPMG experiment over \citet{CarverRichards72}.
@@ -3681,7 +3682,7 @@
From the non-clustered results, it could be argued that all spins in the
entire system experience the same dynamic process, i.e.\ they have the same
$\pA$ and $\kex$ values.
Such an analysis could be performed at a later stage if desired.
-The dispersion curves for the residue :60 could also be inspected to see that
dispersion is likely to be present and another clustered analysis including
this spin performed.
+The dispersion curves for the residue :60 could also be inspected to see that
dispersion is likely to be present and another clustered analysis including
this spin performed.
The number of clustered analyses performed is up to the user -- imagination is
the only limit.
To start the analysis, open the analysis selection wizard as was performed
previously.
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