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Subsections

4 Double-integral Kramers' theory

The double-integral form of overdamped Kramers' theory may be too complex for analytical predictions of unfolding-force histograms. Rather than testing the entire sawsim simulation, we will focus on demonstrating that the Kramers' $ k(F)$ evaluations are working properly. If the Bell modeled histograms check out, that gives reasonable support for the $ k(F) \rightarrow$   histogram portion of the simulation.

Looking for analytic solutions to Kramers' $ k(F)$, we find that there are not many floating around in a finished form. However, we do have analytic solutions for unforced $ k$ for cusp-like and quartic potentials.

4.1 Cusp-like potentials

4.2 Quartic potentials


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4 Double-integral Kramers' theory
Copyright © 2009-10-12, W. Trevor King (contact)
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Drexel Physics