28
3 Biased Brownian Motion
Fig. 3.2 Results for a simulation corresponding the potential of Fig. 3.1a, see Program 3.1 (Matlab
code) at the end of the chapter, with the parameter: N = 20,000; NR = 1000; dt = 0.01; D = 1.; Vo
= 0.; F = 0.1; r = 1.; x00 = 0
d =
Ddt
2 (dx)
2
1 −
dx
2k B T
dV
dx
(3.12)
The parameters as functions of the dimensionless variables and constants are:
˜
a = 1 −
Dd ˜
t
2 (d ˜
x)
2
V 0
d 2
V
d ˜
x 2 (d ˜
x)
2
− 2
(3.13)
˜
b = 1 +
Dd ˜
t
2 (d ˜
x)
2
V 0
d 2
V
d ˜
x 2 (d ˜
x)
2
− 2
(3.14)
˜
c =
Dd ˜
t
2 (d ˜
x)
2
1 +
d ˜
x
2
V 0
d
V
d ˜
x
(3.15)
˜
d =
Dd ˜
t
2 (d ˜
x)
2
1 −
d ˜
x
2
V 0
d
V
d ˜
x
(3.16)