84
6 Ratchet Dimer Brownian Motor with Hydrodynamic Interactions
i, j, k are unit vectors in the direction of the cartesian axis, with
x 12 = x 1 − x 2
y 12 = y 1 − y 2
(6.5)
z 12 = z 1 − z 2
r 12 =
x
2
12 + y
2
12 + z
2
12
1/2
The pair potential V 12 between the two subunit spheres is
V 12 =
kT
2δ 2 (l 0 − r 12 )
2
(6.6)
Then the modulus of the harmonic force is,
F 12 =
kT
δ
(l 0 − r 12 )
(6.7)
where κ = δ −2 is the strength of the harmonic potential and l 0 is the equilibrium
position (Fig. 6.2).
Then the components of the harmonic force are,
Fig. 6.2 The pair potential V 12 versus (l 0 − r 12 ) is ploted. Observe that r 12 are the distances
obtained from the realizations of the stochastic process, l 0 = 8nm, κ = 6.43pN/nm
6 Ratchet Dimer Brownian Motor with Hydrodynamic Interactions
i, j, k are unit vectors in the direction of the cartesian axis, with
x 12 = x 1 − x 2
y 12 = y 1 − y 2
(6.5)
z 12 = z 1 − z 2
r 12 =
x
2
12 + y
2
12 + z
2
12
1/2
The pair potential V 12 between the two subunit spheres is
V 12 =
kT
2δ 2 (l 0 − r 12 )
2
(6.6)
Then the modulus of the harmonic force is,
F 12 =
kT
δ
(l 0 − r 12 )
(6.7)
where κ = δ −2 is the strength of the harmonic potential and l 0 is the equilibrium
position (Fig. 6.2).
Then the components of the harmonic force are,
Fig. 6.2 The pair potential V 12 versus (l 0 − r 12 ) is ploted. Observe that r 12 are the distances
obtained from the realizations of the stochastic process, l 0 = 8nm, κ = 6.43pN/nm