Blowtorch Effect on the Escape and Equilibration Rates for the Hopping Model
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Date
2003-06
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Addis Ababa University
Abstract
In bistable systems the transition kinetics between two locally stable states can be altered
by heating locally one of the stable states (using blow-torch). As a model for diffusion in
a non-homogeneous medium, we consider the hopping model. The kinetic aspect of blowtorch
effect is investigated for a model double-well potential with localized heating. That is,
we analyze the relaxation behavior of a bistable system when the background temperature
profile is non-homogeneous. Using Brinkman’s method, we derive the general and analytic
expressions for the escape and equilibration rates of the system as a function of the strength,
width, and the position of the hot locality, the barrier height and the pit potential of traps
for the model that we consider.
Our result shows that the presence of the hot locality enhances the escape rate from the
well where it is placed and retards the escape rate from the other well. Our work also shows
a remarkable result in relation to the position of the hot locality in that placing the hot
locality mid way between the top and bottom of the well has the largest enhancing effect on
the escape rate from the hot zone than any other position. This result is similar to the work
of Solomon Fekade and Mulugeta Bekele for the case of Landauer’s heated pipe model[1].
Moreover, the escape and equilibration rates of the system become decreasing functions of
the barrier height and the pit potential of traps
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Blowtorch Effect on the Escape