University of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Pressure in Molecular Dynamics I
where
r
i
is the position of atom
i
,
F
i
Tot
is the total force acting on atom
i
.
Tot
i
N
i
i
N
Tot
F
r
r
r
W
r
r
v
r
⋅
=
∑
=
1
1
)
,...,
(
(t)dt
r
m
(t)
r
τ
1
lim
W
i
i
τ
0
N
1
i
i
τ
Tot
r
&
&
r
⋅
=
∫
∑
=
∞
→
Averaging over the MD trajectory and using Newton’s law, we obtain
In order to introduce pressure, let us consider a system of N atoms that is developing in
a finite space and let us introduce a function that is called
Clausius virial function
:
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View Full DocumentUniversity of Virginia, MSE 4270/6270: Introduction to Atomistic Simulations, Leonid Zhigilei
Pressure in Molecular Dynamics II
Integrating by parts
(t)dt
r
m
(t)
r
τ
1
lim
W
i
i
τ
0
N
1
i
i
τ
Tot
r
&
&
r
⋅
=
∫
∑
=
∞
→
T
Nk
3
.
E
.
K
2
dt
)
t
(
r
m
1
lim
W
B
0
N
1
i
2
i
i
Tot
−
=
−
=
τ
−
=
∫
∑
τ
=
∞
→
τ
r
&
dt
)
t
(
r
m
1
lim
)
0
(
r
)
0
(
r
)
(
r
)
(
r
m
lim
W
0
N
1
i
2
i
i
N
1
i
i
i
i
i
i
Tot
∫
∑
∑
τ
=
∞
→
τ
=
∞
→
τ
τ
−
τ
⋅
−
τ
⋅
τ
=
r
&
r
r
&
r
r
&
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 Fall '11
 Zhigilei
 Atom, Trigraph, Ri, Molecular dynamics, Atomistic Simulations, ri ⋅ Fi

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