sawsim/discussion.tex: Normalize to k_u and U for eq:kramers-saddle

Also add U_b(F), l_b, \rho_b, and l_{ts} to the nomenclature.  Thanks
Mom!

diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex
index 713f1fc144ba1e8f9760cd2d54cbb1e21a2eb703..053bce91af0deb1cc66188c5aeeb5fc59d8a0e74 100644 (file)
--- a/src/sawsim/discussion.tex
+++ b/src/sawsim/discussion.tex
@@ -799,9 +799,10 @@ constant loading does indeed follow the Gumbel distribution.
 For the saddle-point approximation for Kramers' model for unfolding
 (\citet{evans97} Eqn.~3, \citet{hanggi90} Eqn. 4.56c, \citet{vanKampen07} Eqn. XIII.2.2).
 \begin{equation}
-  \kappa = \frac{D}{l_b l_{ts}} \cdot \exp\p({\frac{-E_b(F)}{k_B T}}) \;,
+  k_u = \frac{D}{l_b l_{ts}} \cdot \exp\p({\frac{-U_b(F)}{k_B T}}) \;,
+    \label{eq:kramers-saddle}
 \end{equation}
-where $E_b(F)$ is the barrier height under an external force $F$,
+where $U_b(F)$ is the barrier height under an external force $F$,
 $D$ is the diffusion constant of the protein conformation along the reaction coordinate,
 $l_b$ is the characteristic length of the bound state $l_b \equiv 1/\rho_b$,
 $\rho_b$ is the density of states in the bound state, and
@@ -809,6 +810,15 @@ $l_{ts}$ is the characteristic length of the transition state
 \begin{equation}
   l_{ts} = TODO
 \end{equation} 
+%
+\nomenclature{$U_b(F)$}{The barrier energy as a function of force
+  (\cref{eq:kramers-saddle}).}
+\nomenclature{$l_b$}{The charicteristic length of the bound state $l_b
+  \equiv 1/\rho_b$ (\cref{eq:kramers-saddle}).}
+\nomenclature{$\rho_b$}{The density of states in the bound state
+  (\cref{eq:kramers-saddle}).}
+\nomenclature{$l_{ts}$}{The charicteristic length of the transition
+  state (\cref{eq:kramers-saddle}).}
 
 \citet{evans97} solved this unfolding rate for both inverse power law potentials and cusp potentials.