r23121 - /trunk/docs/latex/dispersion.tex -- May 09, 2014 - 09:54

Author: bugman
Date: Fri May  9 09:54:09 2014
New Revision: 23121

URL: http://svn.gna.org/viewcvs/relax?rev=23121&view=rev
Log:
More basic editing of the text of the B14 dispersion model section of the 
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=23121&r1=23120&r2=23121&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex     (original)
+++ trunk/docs/latex/dispersion.tex     Fri May  9 09:54:09 2014
@@ -573,7 +573,7 @@
 \end{align}
 \end{subequations}
 
-where Appendix 1 in \citet{Baldwin2014} list the recipe for exact 
calculation of $\Rtwoeff$.
+where Appendix 1 in \citet{Baldwin2014} lists the recipe for the exact 
calculation of $\Rtwoeff$.
 Note that the following definitions are different to those in the original 
publication, but match both the reference implementation and the relax 
implementation.
 The definitions are functionally equivalent.
 First establish the complex free precession eigenfrequency with
@@ -588,7 +588,7 @@
 \end{align}
 \end{subequations}
 
-The ground state ensemble evolution frequency $f_{00}$ expressed in 
separated real and imaginary components, in terms of definitions $\zeta$, 
$\Psi$, and $h_4$ is
+The ground state ensemble evolution frequency $f_{00}$ expressed in 
separated real and imaginary components in terms of definitions $\zeta$, 
$\Psi$, and $h_4$ is
 \begin{equation}
        f_{00} = \frac{1}{2}\left(\RtwozeroA + \RtwozeroB + \kex\right) + 
\frac{\imath}{2}\left(\dw - h_4\right) .
 \end{equation}
@@ -615,7 +615,7 @@
 \end{subequations}
 
 Here $\taucpmg = 1 / 4\nucpmg$.
-The final result, with identities to assist efficient matrix exponentiation 
optimised for numerical calculation is
+The final result, with identities to assist efficient matrix exponentiation 
optimised for numerical calculation, is
 \begin{subequations}
 \begin{align}
        \nu_{1c} & = F_0  \cosh(E_0) - F_2 \cos(E_2) , \\
@@ -630,9 +630,9 @@
 \end{align}
 \end{subequations}
 
-The advantage of this code will be 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, \citet{Baldwin2014}.
+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
 \begin{equation}
@@ -640,10 +640,10 @@
 \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. 
+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 and Richards equation 
can be incurred if $p_B > 1$\%.
-Incorporation of the correction term, results in an improved description of 
the CPMG experiment over \citet{CarverRichards72}.
+Incorporation of the correction term results in an improved description of 
the CPMG experiment over \citet{CarverRichards72}.
 
 The reference for this equation is:
 \begin{itemize}