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Fix omega -> \omega in manual's timescale discussion.
author
W. Trevor King
<wking@drexel.edu>
Tue, 13 Sep 2011 15:15:07 +0000
(11:15 -0400)
committer
W. Trevor King
<wking@drexel.edu>
Tue, 13 Sep 2011 15:15:07 +0000
(11:15 -0400)
src/sawsim.nw
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diff --git
a/src/sawsim.nw
b/src/sawsim.nw
index b83faa5244b194d7200f8c74ed00ed46a1fe5adb..5f89121e6f23443520fdf9bdeabd19a3c47f85c2 100644
(file)
--- a/
src/sawsim.nw
+++ b/
src/sawsim.nw
@@
-685,7
+685,7
@@
along the chain. The quality of this assumption depends on your
particular chain. For example, a damped spring thermalizes on a
timescale of order $\tau = 1/\gamma$ where the damping ratio $\gamma
\equiv \omega_0(-\zeta \pm \sqrt{\zeta^2-1}$, the natural angular
particular chain. For example, a damped spring thermalizes on a
timescale of order $\tau = 1/\gamma$ where the damping ratio $\gamma
\equiv \omega_0(-\zeta \pm \sqrt{\zeta^2-1}$, the natural angular
-frequency $omega_0 \equiv \sqrt{k/m}$, $\zeta \equiv b/2\sqrt{km}$,
+frequency $
\
omega_0 \equiv \sqrt{k/m}$, $\zeta \equiv b/2\sqrt{km}$,
and $b$ sets the drag $F_b = -bv$. For our cantilevers $\tau$ is
on the order of milliseconds, which is longer than a timestep.
However, the approximation is still reasonable, because there is
and $b$ sets the drag $F_b = -bv$. For our cantilevers $\tau$ is
on the order of milliseconds, which is longer than a timestep.
However, the approximation is still reasonable, because there is