Wykład 10.pdf

(602 KB) Pobierz
Molecular Dynamics
Lecture 10: MD algorithms - part 3
D
M
A
T
y
b
-
3
1
0
2
Periodic boundary conditions
In small systems surface effects can dominate
The number of particles close to the surface is ca. 6N
2/3
and the ratio of surface particles to bulk particles is 6N
−1/3
for a system conisisting of 1000 water molecules ca. 60% of
them will be at the surface (even for 10
6
water molecules
surface effects are still non-negligible with a surface fraction
of 6%)
This will introduce artifacts
D
M
A
T
y
b
-
3
1
0
2
Periodic boundary conditions
It is not possible to simulate the number of atoms contained
in macroscopic samples of substances (of the order of 10
23
particles)
In simulations the ratio between the boundary atoms and the
total number of atoms will always be much larger than in
reality resulting in much more pronounced surface effects
A solution to the boundary effects caused by finite-size is to
use periodic boundary conditions
D
M
A
T
y
b
-
3
1
0
2
Issues with periodic boundary conditions
Upon introducing periodic boundary conditions particles are
placed in a box
The box is replicated throughout space by translations in all
directions
The central box is surrounded by 26 copies of the original
box, which are again surrounded by 98 boxes etc.
When a particle leaves the central box its image (from the
neighboring box) will simultaneously enter the central box
from the other side
D
M
The number of particles in the central box and thus in the
entire system is conserved
A
T
y
b
-
3
1
0
2
PBC
D
M
A
T
y
b
-
3
1
0
2
http://www.cse/scitech.ac.uk/ccg/software/Democritus

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika:

Zgłoś jeśli naruszono regulamin