Molecular Dynamics Simulations 2011
Exercise 6: Suggested solutions
Eero Holmstr¨
om
October 19, 2011
1.
The code was modified to create and output the distribution of velocities.
The implementation in
main.f90/c
is such that after 15 ps of running, we
start to create a histogram of velocities.
The distribution is cumulatively
updated at each time step after 15 ps until the run ends at 100 ps. Finally
we output the collected distribution. To compare with the analytical distri
bution, we calculate the average temperature in the interval 15 ps to 100 ps.
The analytical distribution can be created with an
awk
one liner such as this:
awk ’BEGIN
{m=1.0552067484e25; k=1.38e23; T=303.272; pi=3.1416;
for(v=0.0; v<=1267; v=v+1.0)
{print v, 4*pi*v^2*(m/(2*pi*k*T))^(3./2.)*exp(1.0*m*v^2/(2*k*T))}}’
> mb_analytical.dat
Results are plotted in Figs 1 and 2. It is seen that generally the simulated
distribution follows the analytical one very nicely.
However, from Fig.
2
with the logarithmic
y
axis we see that there is noise in the higher part of
the simulated distribution.
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 Winter '12
 Kotakoski
 Entropy, TI, Molecular dynamics, molecular dynamics simulations, Eero Holmstrom

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