git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@6695 f3b2605a-c512-4ea7-a41b-209d697bcdaa

doc/Eqs/pair_dipole_sf.tex

@@ -3,51 +3,49 @@
 \begin{document}
 
 \begin{eqnarray*}
-E_{LJ} & = &  4\epsilon \left\{\left[ \left( \frac{\sigma}{r} \right)^{12} -  \left( \frac{\sigma}{r} \right)^6  \right]
- + \left[ 6\left( \frac{\sigma}{r_c} \right)^{12} -  3\left( \frac{\sigma}{r_c} \right)^6  \right] \left(\frac{r}{r_c}\right)^2
--7\left( \frac{\sigma}{r_c} \right)^{12} +4\left( \frac{\sigma}{r_c} \right)^6\right\}\\
-E_{qq} & = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^2 \\
-E_{pq} & = & E_{ji} = -\frac{q}{r^3} \left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right](\vec{p} \bullet \vec{r})
- \\
-E_{qp} & = & E_{ij} = \frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] (\vec{p} \bullet \vec{r})
- \\
-E_{pp} & = & \left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right]\left[\frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right]
+E_{LJ} & = &  4\epsilon \left\{ \left[ \left( \frac{\sigma}{r} \right)^{\!12} -
+  \left( \frac{\sigma}{r} \right)^{\!6}  \right] +
+  \left[ 6\left( \frac{\sigma}{r_c} \right)^{\!12} - 
+  3\left(\frac{\sigma}{r_c}\right)^{\!6}\right]\left(\frac{r}{r_c}\right)^{\!2}
+  - 7\left( \frac{\sigma}{r_c} \right)^{\!12} +
+  4\left( \frac{\sigma}{r_c} \right)^{\!6}\right\} \\
+E_{qq} & = & \frac{q_i q_j}{r}\left(1-\frac{r}{r_c}\right)^{\!2} \\
+E_{pq} & = & E_{ji} = -\frac{q}{r^3} \left[ 1 -
+  3\left(\frac{r}{r_c}\right)^{\!2} +
+  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
+E_{qp} & = & E_{ij} = \frac{q}{r^3} \left[ 1 -
+  3\left(\frac{r}{r_c}\right)^{\!2} +
+  2\left(\frac{r}{r_c}\right)^{\!3}\right] (\vec{p}\bullet\vec{r}) \\
+E_{pp} & = & \left[1-4\left(\frac{r}{r_c}\right)^{\!3} +
+  3\left(\frac{r}{r_c}\right)^{\!4}\right]\left[\frac{1}{r^3} 
+  (\vec{p_i} \bullet \vec{p_j}) - \frac{3}{r^5} 
+  (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})\right] \\
 \end{eqnarray*}                           
 
 \begin{eqnarray*}
-F_{LJ} & = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{12} - 
-         24\epsilon \left(\frac{\sigma}{r}\right)^6 \right]\frac{1}{r^2} - 
-\left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{12} - 
-         24\epsilon \left(\frac{\sigma}{r_c}\right)^6 \right]\frac{1}{r_c^2}
-\right\}\vec{r}\\
-F_{qq} & = & \frac{q_i q_j}{r}\left(\frac{1}{r^2}-\frac{1}{r_c^2}\right) 
-\vec{r} \\
-F_{pq} &=& F_{ij } =  -\frac{3q}{r^5}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2\right] (\vec{p} \bullet \vec{r}) \vec{r}+\frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] \vec{p}   \\
-F_{qp} &=& F_{ij}  = \frac{3q}{r^5}\left[1-\left(\frac{r}{r_\mathrm{c}}\right)^2\right] (\vec{p} \bullet \vec{r}) \vec{r}-\frac{q}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{c}}\right)^3\right] \vec{p}   \\
-F_{pp} & = & \frac{3}{r^5} \left\{\left[1-\left(\frac{r}{r_c}\right)^4\right]
-\left[(\vec{p_i} \bullet \vec{p_j}) -
-             \frac{3}{r^2} (\vec{p_i} \bullet \vec{r}) 
-	     (\vec{p_j} \bullet \vec{r})\right]
- \vec{r} \right\\&&
-+ \left\left[1-4\left(\frac{r}{r_c}\right)^3+3\left(\frac{r}{r_c}\right)^4\right]
-             \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + 
-             (\vec{p_i} \bullet \vec{r}) \vec{p_j} -\frac{2}{r^2}
-	       (\vec{p_i} \bullet \vec{r}) 
-	     (\vec{p_j} \bullet \vec{r})\vec{r}\right]
-	     \right\}\\
-\end{eqnarray*}                           
-
-\begin{eqnarray*}
-T_{pq} = T_{ij} & = & \frac{q_j}{r^3}\left[1-3\left(\frac{r}{r_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{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_\mathrm{c}}\right)^2+2\left(\frac{r}{r_\mathrm{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+3\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}) \\
+F_{LJ} & = & \left\{\left[48\epsilon \left(\frac{\sigma}{r}\right)^{\!12} - 
+  24\epsilon \left(\frac{\sigma}{r}\right)^{\!6} \right]\frac{1}{r^2} - 
+  \left[48\epsilon \left(\frac{\sigma}{r_c}\right)^{\!12} - 24\epsilon 
+  \left(\frac{\sigma}{r_c}\right)^{\!6} \right]\frac{1}{r_c^2}\right\}\vec{r}\\
+F_{qq} & = & \frac{q_i q_j}{r}\left(\frac{1}{r^2} -
+  \frac{1}{r_c^2}\right)\vec{r} \\
+F_{pq} &=& F_{ij } =  -\frac{3q}{r^5} \left[ 1 -
+  \left(\frac{r}{r_c}\right)^{\!2}\right](\vec{p}\bullet\vec{r})\vec{r} +
+  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
+  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
+F_{qp} &=& F_{ij}  = \frac{3q}{r^5} \left[ 1 - 
+  \left(\frac{r}{r_c}\right)^{\!2}\right] (\vec{p}\bullet\vec{r})\vec{r} -
+  \frac{q}{r^3}\left[1-3\left(\frac{r}{r_c}\right)^{\!2} +
+  2\left(\frac{r}{r_c}\right)^{\!3}\right] \vec{p} \\
+F_{pp} & = &\frac{3}{r^5}\Bigg\{\left[1-\left(\frac{r}{r_c}\right)^{\!4}\right]
+  \left[(\vec{p_i}\bullet\vec{p_j}) - \frac{3}{r^2} (\vec{p_i}\bullet\vec{r}) 
+  (\vec{p_j} \bullet \vec{r})\right] \vec{r} + \\
+  & & \left[1 -
+  4\left(\frac{r}{r_c}\right)^{\!3}+3\left(\frac{r}{r_c}\right)^{\!4}\right]
+  \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + (\vec{p_i} \bullet \vec{r}) 
+  \vec{p_j} -\frac{2}{r^2} (\vec{p_i} \bullet \vec{r})
+  (\vec{p_j} \bullet \vec{r})\vec{r}\right] \Bigg\} \\
 \end{eqnarray*}                           
 
 \end{document}
 
-

doc/Eqs/pair_dipole_sf2.tex

@@ -0,0 +1,24 @@
+\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}

doc/pair_dipole.html

@@ -65,7 +65,10 @@ particles I and J:
 </P>
 <CENTER><IMG SRC = "Eqs/pair_dipole_sf.jpg">
 </CENTER>
-<P>where qi and qj are the charges on the two particles, pi and pj are
+<CENTER><IMG SRC = "Eqs/pair_dipole_sf2.jpg">
+</CENTER>
+<P>where epsilon and sigma are the standard LJ parameters, r_c is the
+cutoff, qi and qj are the charges on the two particles, pi and pj are
 the dipole moment vectors of the two particles, r is their separation
 distance, and the vector r = Ri - Rj is the separation vector between
 the two particles.  Note that Eqq and Fqq are simply Coulombic energy

doc/pair_dipole.txt

@@ -59,8 +59,10 @@ these formulas for the energy (E), force (F), and torque (T) between
 particles I and J:
 
 :c,image(Eqs/pair_dipole_sf.jpg)
+:c,image(Eqs/pair_dipole_sf2.jpg)
 
-where qi and qj are the charges on the two particles, pi and pj are
+where epsilon and sigma are the standard LJ parameters, r_c is the
+cutoff, qi and qj are the charges on the two particles, pi and pj are
 the dipole moment vectors of the two particles, r is their separation
 distance, and the vector r = Ri - Rj is the separation vector between
 the two particles.  Note that Eqq and Fqq are simply Coulombic energy