3.5 Fluctuating Potential, or “Flashing” Ratchet
35
3.5 Fluctuating Potential, or “Flashing” Ratchet
The flashing ratchet model was introduced by Ajdari and Prost [4].
The corresponding Euler equation for the fluctuating potential is given by (Figs. 3.8
and 3.9),
˜
x
t n+1
= ˜
x
t n
−
1
2
1 + η
t n
D
V 0
V
˜
x
t n
˜ t +
D
F F˜ t +
2DD˜ t
1/2 rand n
(3.37)
with
V
˜
x
˜
t n
=
cos
2π ˜
x
˜
t n
−
1
2
cos
4π ˜
x
˜
t n
(3.38)
Fig. 3.8 Representation of a
Flashing Ratchet
ON
OFF
ON
Fig. 3.9 Fluctuating Potential:The potential switches between the linear, −F.x and the tilted
periodic potential: −F.x + V (x) where V (x) is given by any of the curves Fig. 3.3a or b
35
3.5 Fluctuating Potential, or “Flashing” Ratchet
The flashing ratchet model was introduced by Ajdari and Prost [4].
The corresponding Euler equation for the fluctuating potential is given by (Figs. 3.8
and 3.9),
˜
x
t n+1
= ˜
x
t n
−
1
2
1 + η
t n
D
V 0
V
˜
x
t n
˜ t +
D
F F˜ t +
2DD˜ t
1/2 rand n
(3.37)
with
V
˜
x
˜
t n
=
cos
2π ˜
x
˜
t n
−
1
2
cos
4π ˜
x
˜
t n
(3.38)
Fig. 3.8 Representation of a
Flashing Ratchet
ON
OFF
ON
Fig. 3.9 Fluctuating Potential:The potential switches between the linear, −F.x and the tilted
periodic potential: −F.x + V (x) where V (x) is given by any of the curves Fig. 3.3a or b