From 9a1a4a42499db7f7a2180c1b6ebf5e74bed269e9 Mon Sep 17 00:00:00 2001
From: sjplimp <sjplimp@f3b2605a-c512-4ea7-a41b-209d697bcdaa>
Date: Mon, 8 Aug 2011 22:40:13 +0000
Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@6644
 f3b2605a-c512-4ea7-a41b-209d697bcdaa

---
 doc/Eqs/angle_cosine_shift.jpg        | Bin 0 -> 2435 bytes
 doc/Eqs/angle_cosine_shift.tex        |   9 +++++++++
 doc/Eqs/angle_cosine_shift_exp.tex    |  10 ++++++++++
 doc/Eqs/bond_harmonic_shift.jpg       | Bin 0 -> 3087 bytes
 doc/Eqs/bond_harmonic_shift.tex       |   9 +++++++++
 doc/Eqs/bond_harmonic_shift_cut.jpg   | Bin 0 -> 2947 bytes
 doc/Eqs/bond_harmonic_shift_cut.tex   |   9 +++++++++
 doc/Eqs/dihedral_cosine_shift_exp.tex |  10 ++++++++++
 8 files changed, 47 insertions(+)
 create mode 100644 doc/Eqs/angle_cosine_shift.jpg
 create mode 100644 doc/Eqs/angle_cosine_shift.tex
 create mode 100644 doc/Eqs/angle_cosine_shift_exp.tex
 create mode 100644 doc/Eqs/bond_harmonic_shift.jpg
 create mode 100644 doc/Eqs/bond_harmonic_shift.tex
 create mode 100644 doc/Eqs/bond_harmonic_shift_cut.jpg
 create mode 100644 doc/Eqs/bond_harmonic_shift_cut.tex
 create mode 100644 doc/Eqs/dihedral_cosine_shift_exp.tex

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diff --git a/doc/Eqs/angle_cosine_shift.tex b/doc/Eqs/angle_cosine_shift.tex
new file mode 100644
index 0000000000..e795d6beff
--- /dev/null
+++ b/doc/Eqs/angle_cosine_shift.tex
@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]
+$$
+
+\end{document}
diff --git a/doc/Eqs/angle_cosine_shift_exp.tex b/doc/Eqs/angle_cosine_shift_exp.tex
new file mode 100644
index 0000000000..c66017e717
--- /dev/null
+++ b/doc/Eqs/angle_cosine_shift_exp.tex
@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=-Umin \frac{Exp(-a U(\theta,\theta_0))-1\right}{Exp(a)-1}\quad\mbox{with}\quad
+U(\theta,\theta_0)=0.5 \left(-cos[\theta-\theta_0]-1 \right)
+$$
+
+\end{document}
diff --git a/doc/Eqs/bond_harmonic_shift.jpg b/doc/Eqs/bond_harmonic_shift.jpg
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diff --git a/doc/Eqs/bond_harmonic_shift.tex b/doc/Eqs/bond_harmonic_shift.tex
new file mode 100644
index 0000000000..3daa16724f
--- /dev/null
+++ b/doc/Eqs/bond_harmonic_shift.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right] 
+$$
+
+\end{document}
\ No newline at end of file
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diff --git a/doc/Eqs/bond_harmonic_shift_cut.tex b/doc/Eqs/bond_harmonic_shift_cut.tex
new file mode 100644
index 0000000000..3daa16724f
--- /dev/null
+++ b/doc/Eqs/bond_harmonic_shift_cut.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right] 
+$$
+
+\end{document}
\ No newline at end of file
diff --git a/doc/Eqs/dihedral_cosine_shift_exp.tex b/doc/Eqs/dihedral_cosine_shift_exp.tex
new file mode 100644
index 0000000000..d9657a351a
--- /dev/null
+++ b/doc/Eqs/dihedral_cosine_shift_exp.tex
@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=-Umin \frac{Exp(-a U(\theta,\theta_0))-1\right}{Exp(a)-1}\quad\mbox{with}\quad 
+U(\theta,\theta_0)=0.5 \left(-cos[\theta-\theta_0]-1 \right)
+$$
+
+\end{document}