Some examples of
application
How to analyse the errors of simulation results?
Systematic errors:
Possible sources:
poor equilibration;
bad random number generator;
system size effect.
Practical method for detecting systematic errors:
longer simulation,different initial configurations;
test random number generator,use different generators;
simulation with larger systems.
Statistical errors:
Statistical errors can be reduced by longer simulations but can not
be eliminated completely.
Practical method for estimating statistical errors - block average
method:
Let <A>run be the mean value of a property A calculated from a
sample of size N,i.e.,
Ni ir un ANA 11
Separate N into n blocks,each of the size Nb=N/n and calculate the
block average,
NA b
i ibb AN 1
1
and

n
b r unb
AAn
1
22 1?
gives an estimation of the statistical error.
Example 1:
Diffusion-controlled reactions
Reference:
W,Dong,F,Baros and J.C,André,J,Chem,Phys,91,4643,
(1989).
Diffusion-controlled reactions,I,Molecular dynamics simulations
of a noncontinuum model.
Example 2:
Fluid diffusion through a porous solid
Reference:
W,Dong and H,Luo,Phys,Rev,E 52,801,(1995).
Fluid diffusion through a porous solid,Nonequilibrium molecular-
dynamics simulations.