Environmental Engineering Reference
In-Depth Information
where f ( t ) is a suitable function (either deterministic or stochastic) of time, which
determines the interplay between more ordered and more disordered phases required
by the Brownian motor mechanism. These types of Brownian motors are called
fluctuating-potential ratchets ( Wellens et al. , 2004 ) and fall into the more general
family of the pulsating ratchets ( Reimann , 2002 ), which includes also the traveling-
potential ratchets . In this case the potential has the form V [
φ
f ( t )], and an asym-
metry of the potential is not necessary for the occurrence of net transport. Drift is
always in the same direction as the movement of the potential; however, noise is able
to reduce the current
˙
with respect to drift velocity of the potential.
Another important family of Brownian motors are the so-called fluctuating-force
ratchets ( Reimann , 2002 ). In this case a temporal fluctuation y ( t ) is added to the
force F :
φ
d
d t =−
d V
d
+ y ( t )
+ F + ξ gn .
(3.79)
φ
Thus the deterministic dynamics have an effective potential V eff (
φ,
t )
=
V (
φ
)
φ
F .This
type of motors belongs to the class of time-dependent potentials; however, different
from the case of fluctuating ratchets, here the temporal modulation does not affect the
amplitude of the potential but rather the tilt angle, which varies either randomly or
periodically.
[ y ( t )
+
F ], namely the basic potential
v
(
φ
) is tilted with intensity y ( t )
+
 
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