From 315cc6011e700bb645fa89b9966634bc75f6b9bb Mon Sep 17 00:00:00 2001
From: sjplimp <sjplimp@f3b2605a-c512-4ea7-a41b-209d697bcdaa>
Date: Mon, 4 Nov 2013 20:51:55 +0000
Subject: [PATCH] git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@10954
 f3b2605a-c512-4ea7-a41b-209d697bcdaa

---
 doc/Eqs/fix_ti_rs_force.jpg          | Bin 0 -> 1777 bytes
 doc/Eqs/fix_ti_rs_force.tex          |  11 +++++++++++
 doc/Eqs/fix_ti_rs_function_1.jpg     | Bin 0 -> 2534 bytes
 doc/Eqs/fix_ti_rs_function_1.tex     |   9 +++++++++
 doc/Eqs/fix_ti_rs_function_2.jpg     | Bin 0 -> 3233 bytes
 doc/Eqs/fix_ti_rs_function_2.tex     |   9 +++++++++
 doc/Eqs/fix_ti_rs_function_3.jpg     | Bin 0 -> 4801 bytes
 doc/Eqs/fix_ti_rs_function_3.tex     |   9 +++++++++
 doc/Eqs/fix_ti_spring_force.jpg      | Bin 0 -> 3627 bytes
 doc/Eqs/fix_ti_spring_force.tex      |  11 +++++++++++
 doc/Eqs/fix_ti_spring_function_1.jpg | Bin 0 -> 1040 bytes
 doc/Eqs/fix_ti_spring_function_1.tex |   9 +++++++++
 doc/Eqs/fix_ti_spring_function_2.jpg | Bin 0 -> 5753 bytes
 doc/Eqs/fix_ti_spring_function_2.tex |   9 +++++++++
 doc/compute_ti.html                  |  10 +++++++---
 doc/compute_ti.txt                   |  10 +++++++---
 16 files changed, 81 insertions(+), 6 deletions(-)
 create mode 100644 doc/Eqs/fix_ti_rs_force.jpg
 create mode 100644 doc/Eqs/fix_ti_rs_force.tex
 create mode 100644 doc/Eqs/fix_ti_rs_function_1.jpg
 create mode 100644 doc/Eqs/fix_ti_rs_function_1.tex
 create mode 100644 doc/Eqs/fix_ti_rs_function_2.jpg
 create mode 100644 doc/Eqs/fix_ti_rs_function_2.tex
 create mode 100644 doc/Eqs/fix_ti_rs_function_3.jpg
 create mode 100644 doc/Eqs/fix_ti_rs_function_3.tex
 create mode 100644 doc/Eqs/fix_ti_spring_force.jpg
 create mode 100644 doc/Eqs/fix_ti_spring_force.tex
 create mode 100644 doc/Eqs/fix_ti_spring_function_1.jpg
 create mode 100644 doc/Eqs/fix_ti_spring_function_1.tex
 create mode 100644 doc/Eqs/fix_ti_spring_function_2.jpg
 create mode 100644 doc/Eqs/fix_ti_spring_function_2.tex

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diff --git a/doc/Eqs/fix_ti_rs_force.tex b/doc/Eqs/fix_ti_rs_force.tex
new file mode 100644
index 0000000000..849c0ccc97
--- /dev/null
+++ b/doc/Eqs/fix_ti_rs_force.tex
@@ -0,0 +1,11 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+
+\begin{document}
+
+$$
+  F_{\text{total}} = \lambda F_{\text{int}}
+$$
+
+\end{document}
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diff --git a/doc/Eqs/fix_ti_rs_function_1.tex b/doc/Eqs/fix_ti_rs_function_1.tex
new file mode 100644
index 0000000000..033d8d7559
--- /dev/null
+++ b/doc/Eqs/fix_ti_rs_function_1.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  \lambda(\tau) = \lambda_i + \tau \left( \lambda_f - \lambda_i \right)
+$$
+
+\end{document}
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diff --git a/doc/Eqs/fix_ti_rs_function_2.tex b/doc/Eqs/fix_ti_rs_function_2.tex
new file mode 100644
index 0000000000..a1dd377dcc
--- /dev/null
+++ b/doc/Eqs/fix_ti_rs_function_2.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  \lambda(\tau) = \frac{\lambda_i}{1 + \tau \left( \frac{\lambda_i}{\lambda_f} - 1 \right)}
+$$
+
+\end{document}
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diff --git a/doc/Eqs/fix_ti_rs_function_3.tex b/doc/Eqs/fix_ti_rs_function_3.tex
new file mode 100644
index 0000000000..2d2790fa97
--- /dev/null
+++ b/doc/Eqs/fix_ti_rs_function_3.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  \lambda(\tau) = \frac{\lambda_i}{ 1 + \log_2(1+\tau) \left( \frac{\lambda_i}{\lambda_f} - 1 \right)}
+$$
+
+\end{document}
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diff --git a/doc/Eqs/fix_ti_spring_force.tex b/doc/Eqs/fix_ti_spring_force.tex
new file mode 100644
index 0000000000..0acd0e54ae
--- /dev/null
+++ b/doc/Eqs/fix_ti_spring_force.tex
@@ -0,0 +1,11 @@
+\documentclass[12pt]{article}
+
+\usepackage{amsmath}
+
+\begin{document}
+
+$$
+  F_{\text{total}} = \left( 1-\lambda \right) F_{\text{solid}} + \lambda F_{\text{harm}}
+$$
+
+\end{document}
diff --git a/doc/Eqs/fix_ti_spring_function_1.jpg b/doc/Eqs/fix_ti_spring_function_1.jpg
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diff --git a/doc/Eqs/fix_ti_spring_function_1.tex b/doc/Eqs/fix_ti_spring_function_1.tex
new file mode 100644
index 0000000000..0673410b00
--- /dev/null
+++ b/doc/Eqs/fix_ti_spring_function_1.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  \lambda(\tau) = \tau
+$$
+
+\end{document}
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diff --git a/doc/Eqs/fix_ti_spring_function_2.tex b/doc/Eqs/fix_ti_spring_function_2.tex
new file mode 100644
index 0000000000..f2cb51e47d
--- /dev/null
+++ b/doc/Eqs/fix_ti_spring_function_2.tex
@@ -0,0 +1,9 @@
+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  \lambda(\tau) = \tau^5 \left( 70 \tau^4 - 315 \tau^3 + 540 \tau^2 - 420 \tau + 126 \right)
+$$
+
+\end{document}
diff --git a/doc/compute_ti.html b/doc/compute_ti.html
index ae98598362..5a7ef6e1ed 100644
--- a/doc/compute_ti.html
+++ b/doc/compute_ti.html
@@ -84,7 +84,7 @@ wildcard asterisk can be used in place of or in conjunction with the
 an asterisk with no numeric values means all types from 1 to N.  A
 leading asterisk means all types from 1 to n (inclusive).  A trailing
 asterisk means all types from n to N (inclusive).  A middle asterisk
-means all types from m to n (inclusive). 
+means all types from m to n (inclusive).
 </P>
 <P>You also specify two functions, as <A HREF = "variable.html">equal-style
 variables</A>.  The first is specified as <I>v_name1</I>, where
@@ -113,6 +113,8 @@ command.
 <P>More details about the exact functional forms for the computation of
 du/dl can be found in the paper by <A HREF = "#Eike">Eike</A>.
 </P>
+<HR>
+
 <P><B>Output info:</B> 
 </P>
 <P>This compute calculates a global scalar, namely dUs/dlambda.  This
@@ -127,8 +129,8 @@ options.
 </P>
 <P><B>Restrictions:</B>
 </P>
-<P>This compute is part of the MISC package.  It is only enabled if LAMMPS
-was built with that package.  See the <A HREF = "Section_start.html#start_3">Making
+<P>This compute is part of the MISC package.  It is only enabled if
+LAMMPS was built with that package.  See the <A HREF = "Section_start.html#start_3">Making
 LAMMPS</A> section for more info.
 </P>
 <P><B>Related commands:</B>
@@ -137,6 +139,8 @@ LAMMPS</A> section for more info.
 </P>
 <P><B>Default:</B> none
 </P>
+<HR>
+
 <A NAME = "Eike"></A>
 
 <P><B>(Eike)</B> Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).
diff --git a/doc/compute_ti.txt b/doc/compute_ti.txt
index 1ab13e5a97..8ba147e50c 100644
--- a/doc/compute_ti.txt
+++ b/doc/compute_ti.txt
@@ -76,7 +76,7 @@ wildcard asterisk can be used in place of or in conjunction with the
 an asterisk with no numeric values means all types from 1 to N.  A
 leading asterisk means all types from 1 to n (inclusive).  A trailing
 asterisk means all types from n to N (inclusive).  A middle asterisk
-means all types from m to n (inclusive). 
+means all types from m to n (inclusive).
 
 You also specify two functions, as "equal-style
 variables"_variable.html.  The first is specified as {v_name1}, where
@@ -105,6 +105,8 @@ command.
 More details about the exact functional forms for the computation of
 du/dl can be found in the paper by "Eike"_#Eike.
 
+:line
+
 [Output info:] 
 
 This compute calculates a global scalar, namely dUs/dlambda.  This
@@ -119,8 +121,8 @@ The scalar value will be in energy "units"_units.html.
 
 [Restrictions:]
 
-This compute is part of the MISC package.  It is only enabled if LAMMPS
-was built with that package.  See the "Making
+This compute is part of the MISC package.  It is only enabled if
+LAMMPS was built with that package.  See the "Making
 LAMMPS"_Section_start.html#start_3 section for more info.
 
 [Related commands:]
@@ -129,5 +131,7 @@ LAMMPS"_Section_start.html#start_3 section for more info.
 
 [Default:] none
 
+:line
+
 :link(Eike)
 [(Eike)] Eike and Maginn, Journal of Chemical Physics, 124, 164503 (2006).