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stress_tensor.tex
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Thu, Nov 28, 01:41
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rLAMMPS lammps
stress_tensor.tex
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\documentclass
[12pt]
{
article
}
\begin
{
document
}
\begin
{
eqnarray*
}
S
_{
ab
}
&
=
&
-
\left
[ m v
_
a v
_
b +
\frac
{
1
}{
2
}
\sum
_{
n = 1
}^{
N
_
p
}
(r
_{
1
_
a
}
F
_{
1
_
b
}
+ r
_{
2
_
a
}
F
_{
2
_
b
}
) +
\frac
{
1
}{
2
}
\sum
_{
n = 1
}^{
N
_
b
}
(r
_{
1
_
a
}
F
_{
1
_
b
}
+ r
_{
2
_
a
}
F
_{
2
_
b
}
) +
\right
.
\\
&&
\left
.
\frac
{
1
}{
3
}
\sum
_{
n = 1
}^{
N
_
a
}
(r
_{
1
_
a
}
F
_{
1
_
b
}
+ r
_{
2
_
a
}
F
_{
2
_
b
}
+
r
_{
3
_
a
}
F
_{
3
_
b
}
) +
\frac
{
1
}{
4
}
\sum
_{
n = 1
}^{
N
_
d
}
(r
_{
1
_
a
}
F
_{
1
_
b
}
+ r
_{
2
_
a
}
F
_{
2
_
b
}
+
r
_{
3
_
a
}
F
_{
3
_
b
}
+ r
_{
4
_
a
}
F
_{
4
_
b
}
) +
\right
.
\\
&&
\left
.
\frac
{
1
}{
4
}
\sum
_{
n = 1
}^{
N
_
i
}
(r
_{
1
_
a
}
F
_{
1
_
b
}
+ r
_{
2
_
a
}
F
_{
2
_
b
}
+
r
_{
3
_
a
}
F
_{
3
_
b
}
+ r
_{
4
_
a
}
F
_{
4
_
b
}
) +
{
\rm
Kspace
}
(r
_{
i
_
a
}
,F
_{
i
_
b
}
) +
\sum
_{
n = 1
}^{
N
_
f
}
r
_{
i
_
a
}
F
_{
i
_
b
}
\right
]
\end
{
eqnarray*
}
\end
{
document
}
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