Abstract
The random-walk problem is modified by letting the length d and the duration τ of the walker's step change as a function of the distance r from the origin. The theory is developed by taking into consideration the variation of both d and τ with r. This is accomplished by replacing d and τ with their respective Gaussian averages over r. A situation like this arises in the problem of the unwinding of DNA, when the problem is considered as one of rotational Brownian motion. In that case, the angular velocity increases as the DNA rod shortens because of unwinding. The effect of this variation is to reduce the unwinding time by a factor of 4/9 from that calculated previously on the basis of a constant angular velocity. Other improvements on previous calculations are made.
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