Loaded Sullivan's Perfect Ratchet
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Show that in the case of zero external force the equation v=(fL/kT)^2 D/L (e^(fL/kT) - 1 - fL/kT)^-1 reduces to 2D/L. Then show that at high force (but still smaller than (epsilon/L)) the equation reduces to v=(fL/kT)^2 D/L (e^(-fL/kT)).
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Solution Summary
This solution includes multiple calculations proving the equation reduces. The loaded Sullivan's perfect ratchet is analyzed.
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Part 1:
v=(fL/kT)^2 D/L (e^(fL/kT) - 1 - fL/kT)^-1
=> v = (fL/kT)^2 (D/L)/ (e^(fL/kT) - 1 - fL/kT)
=> v = (fL/kT)^2 (D/L)/ (1 + (fL/kT) + (fL/kT)^2/2! + ... - 1 - ...
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- BEng, Allahabad University, India
- MSc , Pune University, India
- PhD (IP), Pune University, India
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