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solverstack
ScalFMM
Commits
635f5be5
Commit
635f5be5
authored
Jan 14, 2014
by
COULAUD Olivier
Browse files
Add DL_POLY section
parent
ebf2dd3f
Changes
1
Hide whitespace changes
Inline
Side-by-side
Doc/Src_tex/ScalFmm-PeriodicModel/periodicmodel.tex
View file @
635f5be5
...
...
@@ -362,10 +362,10 @@ The kernel should be able to proceed usual FMM operator in a tree of height of s
The energy computed by molecular dynamics codes is given by
$$
U
=
\frac
{
1
}{
4
\pi\epsilon
_
0
}
\sum
_{
i
=
0
}^{
N
}{
\sum
_{
j<i
}{
\frac
{
q
_
i q
_
j
}{
\|
x
_
i
-
x
_
j
\|
}}}
$$
$$
and the force on atom
$
x
_
i
$
$$
f
(
x
_
i
)
=
\frac
{
1
}{
4
\pi\epsilon
_
0
}
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
f
(
x
_
i
)
=
\frac
{
q
_
i
}{
4
\pi\epsilon
_
0
}
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
$$
\subsubsection
{
DL
\_
Poly comparisons
}
DL
\_
POLY
\_
2 uses the following internal molecular units
\\
...
...
@@ -387,8 +387,8 @@ U = \frac{q_0^2}{4 \pi\epsilon_0 l_0}\sum_{i=0}^{N}{\sum_{j<i}{\frac{q_i q_j}{\|
$$
and the forces write
$$
f
(
x
_
i
)
=
-
\frac
{
q
_
0
}{
4
\pi\epsilon
_
0
l
_
0
^
2
}
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
=
-
C
_{
force
}
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
f
(
x
_
i
)
=
-
\frac
{
q
_
0
^
2
}{
4
\pi\epsilon
_
0
l
_
0
^
2
}
q
_
i
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
=
-
C
_{
force
}
q
_
i
\sum
_{
j
=
0
,i
\neq
j
}^{
N
}{
q
_
j
\frac
{
x
_
i
-
x
_
j
}{
\|
x
_
i
-
x
_
j
\|
^
3
}}
$$
The Energy conversion factor is
$
\gamma
_
0
=
\frac
{
q
_
0
^
2
}{
4
\pi\epsilon
_
0
l
_
0
}
/
E
_
0
=
138935
.
4835
$
. The energy unit is in Joules and if you want
$
kcal mol
^{
-
1
}$
unit the the factor becomes
$
\gamma
_
0
/
418
.
400
$
.
...
...
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