From: W. Trevor King <wking@tremily.us>
Date: Mon, 20 May 2013 17:23:20 +0000 (-0400)
Subject: sawsim/methods.tex: Add WLC and FJC params to the nomenclature
X-Git-Tag: v1.0~153
X-Git-Url: http://git.tremily.us/?a=commitdiff_plain;h=555fd0bb17d5256282f049dcd62092d1696fb8d1;p=thesis.git

sawsim/methods.tex: Add WLC and FJC params to the nomenclature

Also the hyperbolic cotangent.  Thanks Mom!
---

diff --git a/src/sawsim/methods.tex b/src/sawsim/methods.tex
index cd8fd9b..3ea714d 100644
--- a/src/sawsim/methods.tex
+++ b/src/sawsim/methods.tex
@@ -120,6 +120,10 @@ $L$ (\cref{fig:wlc}).  The relationship between tension $F$ and
 extension (end-to-end distance) $x$ is given by Bustamante's
 interpolation formula\citep{marko95,bustamante94}.
 \nomenclature{WLC}{Wormlike chain, an entropic spring model}
+\nomenclature{$p$}{Persistence length of a wormlike chain
+  (\cref{eq:sawsim:wlc})).}
+\nomenclature{$L$}{Contour length in a polymer tension model
+  (\cref{eq:sawsim:wlc,eq:sawsim:fjc})}
 \begin{equation}
   F_\text{WLC}(x,p,L) = \frac{k_B T}{p}
       \p[{  \frac{1}{4}\p({ \frac{1}{(1-x/L)^2} - 1 })
@@ -222,9 +226,6 @@ the polymer as a series of $N$ rigid links, each of length $l$ (the
 Kuhn length), which are free to rotate about their joints
 (\cref{fig:fjc}).
 \index{Langevin function}
-\nomenclature{FJC}{Freely-jointed chain, an entropic spring model}
-\nomenclature{$\Langevin$}{The Langevin function,
-  $\Langevin(\alpha)\equiv\coth{\alpha}-\frac{1}{\alpha}$}
 \begin{equation}
   F_\text{FJC}(x,l,L) = \frac{k_B T}{l} \Langevin^{-1}\p({\frac{x}{L}}) \;,
   \label{eq:sawsim:fjc}
@@ -232,6 +233,18 @@ Kuhn length), which are free to rotate about their joints
 where $L=Nl$ is the total length of the chain, and
 $\Langevin(\alpha)\equiv\coth{\alpha}-\frac{1}{\alpha}$ is the
 Langevin function\citep{hatfield99}.
+%
+\nomenclature{FJC}{Freely-jointed chain, an entropic spring model
+  (\cref{eq:sawsim:fjc}).}
+\nomenclature{$\Langevin$}{The Langevin function,
+  $\Langevin(\alpha)\equiv\coth{\alpha}-\frac{1}{\alpha}$}
+\nomenclature{$\coth$}{Hyperbolic cotangent,
+  \begin{equation}
+    \coth(x) = \frac{\exp{x} + \exp{-x}}{\exp{x} - \exp{-x}} \;.
+  \end{equation}
+}
+\nomenclature{$l$}{Kuhn length in the freely-jointed chain
+  (\cref{fig:fjc-model,eq:sawsim:fjc}).}
 
 \begin{figure}
   \begin{center}