From 4bdbd9008447f7c537a520b4a3c67e5bcdb1e17d Mon Sep 17 00:00:00 2001 From: "W. Trevor King" Date: Thu, 2 Feb 2012 10:27:35 -0500 Subject: [PATCH] Add comments referenceing Brockwell's 2002 paper with respect to Gumbel dist. --- src/sawsim/discussion.tex | 2 ++ src/unfolding/distributions-single_domain-constant_loading.tex | 2 ++ 2 files changed, 4 insertions(+) diff --git a/src/sawsim/discussion.tex b/src/sawsim/discussion.tex index 777e50c..ec276e8 100644 --- a/src/sawsim/discussion.tex +++ b/src/sawsim/discussion.tex @@ -118,6 +118,8 @@ and and average \p[{-\ln\p({\frac{N_fk_{u0}k_BT}{\kappa v\Delta x_u}}) -\gamma_e}] \;, \label{eq:sawsim:order-dep} \end{equation} +% This is discussed in brockwell02, p465 +% consolidate with src/unfolding/distributions-single_domain-constant_loading.tex where $N_f$ and $\kappa$ depend on the domain index $i=N_u$. Curves based on this formula fit the simulated data remarkably well considering the effective WLC\index{WLC} stiffness $\kappa_\text{WLC}$ is the only fitted diff --git a/src/unfolding/distributions-single_domain-constant_loading.tex b/src/unfolding/distributions-single_domain-constant_loading.tex index 902896e..d9456e8 100644 --- a/src/unfolding/distributions-single_domain-constant_loading.tex +++ b/src/unfolding/distributions-single_domain-constant_loading.tex @@ -129,6 +129,8 @@ $\alpha=-\beta\ln(\kappa\beta/kv)$, and $F=x$ we have So our unfolding force histogram for a single Bell domain under constant loading does indeed follow the Gumbel distribution. +% Consolidate with src/sawsim/discussion.tex + \subsection{Saddle-point Kramers' model} For the saddle-point approximation for Kramers' model for unfolding -- 2.26.2