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Tweaked the triclinic text 

git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@8013 f3b2605a-c512-4ea7-a41b-209d697bcdaa
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athomps 2012-04-10 19:36:03 +00:00
parent c4fc0d38a6
commit 039ebfbdbe
4 changed files with 35 additions and 25 deletions
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doc/Eqs/transform.tex
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@ -20,7 +20,7 @@ a_x &=& A \\
b_x &=& \mathbf{B} \cdot \mathbf{\hat{A}} \quad = \quad B \cos{\gamma} \\
b_y &=& |\mathbf{\hat{A}} \times \mathbf{B}| \quad = \quad B \sin{\gamma} \quad = \quad \sqrt{B^2 - {b_x}^2} \\
c_x &=& \mathbf{C} \cdot \mathbf{\hat{A}} \quad = \quad C \cos{\beta} \\
c_y &=& \mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})} \times \mathbf{\hat{A}} \quad = \quad \frac{B C - b_x c_x}{b_y} \\
c_y &=& \mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})} \times \mathbf{\hat{A}} \quad = \quad \frac{\mathbf{B} \cdot \mathbf{C} - b_x c_x}{b_y} \\
c_z &=& |\mathbf{C} \cdot \widehat{(\mathbf{A} \times \mathbf{B})}|\quad = \quad \sqrt{C^2 - {c_x}^2 - {c_y}^2} \\
\end{eqnarray*}

31
doc/Section_howto.html
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@ -811,22 +811,27 @@ The equivalent LAMMPS <B>a</B>,<B>b</B>,<B>c</B> are a linear rotation of <B>A</
<CENTER><IMG SRC = "Eqs/transform.jpg">
</CENTER>
<P>where A = |<B>A</B>| indicates the scalar length of <B>A</B>. The ^ hat symbol
indicates the corresponding unit vector. beta and gamma are angles
between the vectors described below. The same rotation must also
be applied to atom positions, velocities, and any other vector quantities.
This can be done by first converting to fractional coordinates in the
indicates the corresponding unit vector. <I>beta</I> and <I>gamma</I> are angles
between the vectors described below. Note that by construction,
<B>a</B>, <B>b</B>, and <B>c</B> have strictly positive x, y, and z components, respectively.
If it should happen that
<B>A</B>, <B>B</B>, and <B>C</B> form a left-handed basis, then the above equations
are not valid for <B>c</B>. In this case, it is necessary
to first apply an inversion. This can be achieved
by interchanging two basis vectors or by changing the sign of one of them.
</P>
<P>For consistency, the same rotation/inversion appied to the basis vectors
must also be applied to atom positions, velocities,
and any other vector quantities.
This can be conveniently achieved by first converting to
fractional coordinates in the
old basis and then converting to distance coordinates in the new basis.
The transformation is given by the following equation:
</P>
<CENTER><IMG SRC = "Eqs/rotate.jpg">
</CENTER>
<P>where V is the volume of the box, <B>X</B> is the original vector quantity and
<B>x</B> is the vector in the LAMMPS basis.
</P>
<P>If it should happen that
<B>A</B>, <B>B</B>, and <B>C</B> form a left-handed basis, then it is necessary
to first apply an inversion in addition to rotation. This can be achieved
by interchanging two of the basis vectors or changing the sign of one of them.
<P>where <I>V</I> is the volume of the box, <B>X</B> is the original vector quantity and
<B>x</B> is the vector in the LAMMPS basis.
</P>
<P>There is no requirement that a triclinic box be periodic in any
dimension, though it typically should be in at least the 2nd dimension
@ -1237,7 +1242,7 @@ discussed below, it can be referenced via the following bracket
notation, where ID in this case is the ID of a compute. The leading
"c_" would be replaced by "f_" for a fix, or "v_" for a variable:
</P>
<DIV ALIGN=center><TABLE BORDER=1 >
<DIV ALIGN=center><TABLE WIDTH="0%" BORDER=1 >
<TR><TD >c_ID </TD><TD > entire scalar, vector, or array</TD></TR>
<TR><TD >c_ID[I] </TD><TD > one element of vector, one column of array</TD></TR>
<TR><TD >c_ID[I][J] </TD><TD > one element of array
@ -1436,7 +1441,7 @@ data and scalar/vector/array data.
input, that could be an element of a vector or array. Likewise a
vector input could be a column of an array.
</P>
<DIV ALIGN=center><TABLE BORDER=1 >
<DIV ALIGN=center><TABLE WIDTH="0%" BORDER=1 >
<TR><TD >Command</TD><TD > Input</TD><TD > Output</TD><TD ></TD></TR>
<TR><TD ><A HREF = "thermo_style.html">thermo_style custom</A></TD><TD > global scalars</TD><TD > screen, log file</TD><TD ></TD></TR>
<TR><TD ><A HREF = "dump.html">dump custom</A></TD><TD > per-atom vectors</TD><TD > dump file</TD><TD ></TD></TR>

27
doc/Section_howto.txt
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@ -802,22 +802,27 @@ The equivalent LAMMPS [a],[b],[c] are a linear rotation of [A], [B], and
:c,image(Eqs/transform.jpg)
where A = |[A]| indicates the scalar length of [A]. The ^ hat symbol
indicates the corresponding unit vector. beta and gamma are angles
between the vectors described below. The same rotation must also
be applied to atom positions, velocities, and any other vector quantities.
This can be done by first converting to fractional coordinates in the
indicates the corresponding unit vector. {beta} and {gamma} are angles
between the vectors described below. Note that by construction,
[a], [b], and [c] have strictly positive x, y, and z components, respectively.
If it should happen that
[A], [B], and [C] form a left-handed basis, then the above equations
are not valid for [c]. In this case, it is necessary
to first apply an inversion. This can be achieved
by interchanging two basis vectors or by changing the sign of one of them.
For consistency, the same rotation/inversion applied to the basis vectors
must also be applied to atom positions, velocities,
and any other vector quantities.
This can be conveniently achieved by first converting to
fractional coordinates in the
old basis and then converting to distance coordinates in the new basis.
The transformation is given by the following equation:
:c,image(Eqs/rotate.jpg)
where V is the volume of the box, [X] is the original vector quantity and
[x] is the vector in the LAMMPS basis.
If it should happen that
[A], [B], and [C] form a left-handed basis, then it is necessary
to first apply an inversion in addition to rotation. This can be achieved
by interchanging two of the basis vectors or changing the sign of one of them.
where {V} is the volume of the box, [X] is the original vector quantity and
[x] is the vector in the LAMMPS basis.
There is no requirement that a triclinic box be periodic in any
dimension, though it typically should be in at least the 2nd dimension