sawsim/discussion.tex: Remove cusp section and others I don't have time for

The following are theoretically tractable, but I don't have time to
write them up:

* Inverse power law potentials
* Cusp potentials
* Cusp-like potentials
* Quartic potentials

See evans97 if you're interested.

diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex
index 053bce91af0deb1cc66188c5aeeb5fc59d8a0e74..e0c17e85ff48c334a019e82bb7fb075bf2faf81c 100644 (file)
--- a/src/sawsim/discussion.tex
+++ b/src/sawsim/discussion.tex
@@ -822,27 +822,6 @@ $l_{ts}$ is the characteristic length of the transition state
 
 \citet{evans97} solved this unfolding rate for both inverse power law potentials and cusp potentials.
 
-\subsubsection{Inverse power law potentials}
-
-\begin{equation}
-  E(x) = \frac{-A}{x^n}
-\end{equation}
-(e.g. $n=6$ for a van der Waals interaction, see \citet{evans97} in
-the text on page 1544, in the first paragraph of the section
-\emph{Dissociation under force from an inverse power law attraction}).
-Evans then goes into diffusion constants that depend on the
-protein's end to end distance, and I haven't worked out the math
-yet.  TODO: clean up.
-
-
-\subsubsection{Cusp potentials}
-
-\begin{equation}
-  E(x) = \frac{1}{2}\kappa_a \p({\frac{x}{x_a}})^2
-\end{equation}
-(see \citet{evans97} in the text on page 1545, in the first paragraph
-of the section \emph{Dissociation under force from a deep harmonic well}).
-
 \section{Double-integral Kramers' theory}
 
 The double-integral form of overdamped Kramers' theory may be too
@@ -856,8 +835,3 @@ portion of the simulation.
 Looking for analytic solutions to Kramers' $k(F)$, we find that there
 are not many available in a closed form.  However, we do have analytic
 solutions for unforced $k$ for cusp-like and quartic potentials.
-
-\subsection{Cusp-like potentials}
-
-
-\subsection{Quartic potentials}