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pair_dipole_sf2.tex
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rLAMMPS lammps
pair_dipole_sf2.tex
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\documentclass
[12pt]
{
article
}
\begin
{
document
}
\begin
{
eqnarray*
}
T
_{
pq
}
= T
_{
ij
}
&
=
&
\frac
{
q
_
j
}{
r
^
3
}
\left
[ 1 -
3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
2
}
+
2
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
\right
] (
\vec
{
p
_
i
}
\times\vec
{
r
}
)
\\
T
_{
qp
}
= T
_{
ji
}
&
=
&
-
\frac
{
q
_
i
}{
r
^
3
}
\left
[ 1 -
3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
2
}
+
2
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
\right
] (
\vec
{
p
_
j
}
\times\vec
{
r
}
)
\\
T
_{
pp
}
= T
_{
ij
}
&
=
&
-
\frac
{
1
}{
r
^
3
}
\left
[1-4
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
+
e3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
4
}
\right
] (
\vec
{
p
_
i
}
\times
\vec
{
p
_
j
}
) +
\\
&
&
\frac
{
3
}{
r
^
5
}
\left
[1-4
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
+
3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
4
}
\right
] (
\vec
{
p
_
j
}
\bullet\vec
{
r
}
)
(
\vec
{
p
_
i
}
\times
\vec
{
r
}
)
\\
T
_{
pp
}
= T
_{
ji
}
&
=
&
-
\frac
{
1
}{
r
^
3
}
\left
[1-4
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
+
3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
4
}
\right
](
\vec
{
p
_
j
}
\times
\vec
{
p
_
i
}
) +
\\
&
&
\frac
{
3
}{
r
^
5
}
\left
[1-4
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
3
}
+
3
\left
(
\frac
{
r
}{
r
_
c
}
\right
)
^{
\!
4
}
\right
] (
\vec
{
p
_
i
}
\bullet
\vec
{
r
}
)
(
\vec
{
p
_
j
}
\times
\vec
{
r
}
)
\\
\end
{
eqnarray*
}
\end
{
document
}
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