r23125 - /trunk/docs/latex/dispersion.tex -- May 09, 2014 - 10:07

Author: bugman
Date: Fri May  9 10:07:24 2014
New Revision: 23125

URL: http://svn.gna.org/viewcvs/relax?rev=23125&view=rev
Log:
Standardised the spacing in the equations for the B14 dispersion model in 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=23125&r1=23124&r2=23125&view=diff
==============================================================================
--- trunk/docs/latex/dispersion.tex     (original)
+++ trunk/docs/latex/dispersion.tex     Fri May  9 10:07:24 2014
@@ -567,9 +567,9 @@
 The equation is
 \begin{subequations}
 \begin{align}
-  \Rtwoeff & = \frac{\RtwozeroA + \RtwozeroB + \kex 
}{2}-\frac{\ncyc}{\Trelax} \cosh{}^{-1}(\nu_{1c}) \nonumber \\
-& \qquad - \frac{1}{\Trelax}\ln{\left(\frac{1+y}{2} + 
\frac{1-y}{2\sqrt{\nu_{1c}^2-1}}(\nu_2 + 2 \kAB p_D)\right)} , \\
-    & = \RtwoeffCR - \frac{1}{\Trelax}\ln{\left( \frac{1+y}{2} + 
\frac{1-y}{2\sqrt{\nu_{1c}^2-1}}(\nu_2 + 2\kAB p_D )\right)} ,
+  \Rtwoeff & = \frac{\RtwozeroA + \RtwozeroB + 
\kex}{2}-\frac{\ncyc}{\Trelax} \cosh{}^{-1}(\nu_{1c}) \nonumber \\
+           & \qquad - \frac{1}{\Trelax}\ln{\left(\frac{1+y}{2} + 
\frac{1-y}{2\sqrt{\nu_{1c}^2-1}}(\nu_2 + 2\kAB p_D)\right)} , \\
+    & = \RtwoeffCR - \frac{1}{\Trelax}\ln{\left(\frac{1+y}{2} + 
\frac{1-y}{2\sqrt{\nu_{1c}^2-1}}(\nu_2 + 2\kAB p_D)\right)} ,
 \end{align}
 \end{subequations}
 
@@ -583,8 +583,8 @@
        \alpha_- & = \Delta \Rtwozero + \kAB - \kBA , \\
        \zeta & = 2 \dw \alpha_- , \\
        \Psi & = \alpha_-^2 + 4 \kAB \kBA - \dw^2 , \\
-       h_3 &= \frac{1}{\sqrt{2}}\sqrt{ \Psi + \sqrt{\zeta^2 + \Psi^2} } , \\
-    h_4 &= \frac{1}{\sqrt{2}}\sqrt{ -\Psi + \sqrt{\zeta^2 + \Psi^2} } .
+       h_3 &= \frac{1}{\sqrt{2}}\sqrt{\Psi + \sqrt{\zeta^2 + \Psi^2} } , \\
+    h_4 &= \frac{1}{\sqrt{2}}\sqrt{-\Psi + \sqrt{\zeta^2 + \Psi^2} } .
 \end{align}
 \end{subequations}
 
@@ -621,9 +621,9 @@
        \nu_{1c} & = F_0  \cosh(E_0) - F_2 \cos(E_2) , \\
        \nu_{1s} & = F_0  \sinh(E_0) - \imath F_2 \sin(E_2), \\
        \nu_3 & = \sqrt{\nu_{1c}^2 - 1} , \\
-       \nu_4 & = F_1^b (-\alpha_- - h_3 ) + \imath F_1^b (\dw - h_4) , \\
-       \nu_5 & =\left(-\Delta \Rtwozero + \kex + \imath \dw\right) \nu_{1s} 
+ 2 \left(\nu_4 + \kAB F_1^{a+b}\right) \sinh(E_1) , \\
-    y & = \left( \frac{\nu_{1c} - \nu_3}{\nu_{1c} + \nu_3} \right) ^ {\ncyc} 
, \\
+       \nu_4 & = F_1^b (-\alpha_- - h_3) + \imath F_1^b (\dw - h_4) , \\
+       \nu_5 & = \left(-\Delta \Rtwozero + \kex + \imath \dw\right) \nu_{1s} 
+ 2 \left(\nu_4 + \kAB F_1^{a+b}\right) \sinh(E_1) , \\
+    y & = \left( \frac{\nu_{1c} - \nu_3}{\nu_{1c} + \nu_3} \right) ^{\ncyc} 
, \\
        T & = \frac{1}{2}(1 + y) + \frac{(1 - y)\nu_5}{2 \nu_3 N} , \\
        \RtwoeffCR & = \frac{\RtwozeroA + \RtwozeroB + \kex}{2} - 
\frac{\ncyc}{\taucpmg} \, \arccosh\left(\Re(\nu_{1c})\right) , \\
        \Rtwoeff & = \RtwoeffCR - \frac{1}{\taucpmg} \log\left(\Re(T)\right) .