1549380323-Statistical Mechanics Theory and Molecular Simulation

Problems 527

Uwf(x,y) =ǫ

{[

σ

y−f(l)(x)

] 12

+

[

σ

Ly−y−f(u)(x)

] 12 }

, (13.5.27)

whereLyis the length of the box in theydirection, andf(l)(x) =f(u)(x) =acos(kx)
characterizes the corrugation of the lower and upper walls, respectively. In Fig. 13.9,
a corrugation amplitude ofa= 0. 02 σis used with a corrugation period of 1.0 ̊A, and
the zero of the shear field occurs aty 0 =− 26. 6 ̊A. The shear rate isγ=0.05 ps−^1. The
massive thermostatting scheme of Section 4.10 is used in order to stabilize the linear
profile. Because moving boundaries are absent, the quality of the simulation can be
monitored by using the conservation law in eqn. (13.5.23).

-40 -20 0 20 40

y (Å)

0

1

2

3

vx

(y

) (Å/ps)

Fig. 13.9Velocity profile at regularly spaced slabs in theydirection of a soft-sphere fluid
confined between corrugated plates (Fig. 13.8) atT= 480 K.

13.6 Problems

13.1. Consider two models of a velocity autocorrelation function:

C 1 (t) =〈v^2 〉e−γt, C 2 (t) =〈v^2 〉e−γtcos(αt).

a. Calculate the diffusion constantsD 1 andD 2 for each model. Which one

is larger?