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doc/doc2/Eqs/.log

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+**pair_sph_tait
+(/usr/share/texmf/tex/latex/tools/.tex
+LaTeX2e <2001/06/01>
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+! LaTeX Error: Missing \begin{document}.
+
+See the LaTeX manual or LaTeX Companion for explanation.
+Type  H <return>  for immediate help.
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+No pages of output.

doc/doc2/Eqs/angle_charmm.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+  E = K (\theta - \theta_0)^2 + K_{UB} (r - r_{UB})^2 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_class2.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray*}
+  E & = & E_a + E_{bb} + E_{ba} \\
+  E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
+  E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
+  E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/angle_cosine.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = K [1 + \cos(\theta)] 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_cosine_delta.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = K [1 - \cos(\theta - \theta_0)]
+$$
+
+\end{document}

doc/doc2/Eqs/angle_cosine_periodic.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right]  
+$$
+
+\end{document}

doc/doc2/Eqs/angle_cosine_shift.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]
+$$
+
+\end{document}

doc/doc2/Eqs/angle_cosine_shift_exp.tex

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+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+E=-U_{min} 
+\frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1}
+\quad\mbox{with}\quad
+U(\theta,\theta_0)
+=-0.5 \left(1+\cos(\theta-\theta_0) \right)
+$$
+
+\end{document}

doc/doc2/Eqs/angle_cosine_squared.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = K [\cos(\theta) - \cos(\theta_0)]^2 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_dipole_gamma.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   \cos\gamma = \frac{\vec{\mu_j}\bullet\vec{r_{ij}}}{\mu_j\,r_{ij}}
+$$
+
+\end{document}

doc/doc2/Eqs/angle_dipole_potential.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = K (\cos\gamma - \cos\gamma_0)^2 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_dipole_torque.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+\vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\,
+           \vec{r_{ij}} \times \vec{\mu_j}
+$$
+\end{document}

doc/doc2/Eqs/angle_fourier.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = K [C_0 + C_1 \cos ( \theta) + C_2 \cos( 2 \theta) ] 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_fourier_simple.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = K [ 1.0 + c \cos ( n \theta) ] 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_harmonic.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = K (\theta - \theta_0)^2 
+$$
+
+\end{document}

doc/doc2/Eqs/angle_quartic.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4
+$$
+
+\end{document}

doc/doc2/Eqs/bond_class2.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = K_2 (r - r_0)^2 + K_3 (r - r_0)^3 + K_4 (r - r_0)^4 
+$$
+
+\end{document}

doc/doc2/Eqs/bond_fene.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+  E = -0.5 K R_0^2  \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] +
+  4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+    \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
+$$
+
+\end{document}

doc/doc2/Eqs/bond_fene_expand.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+  E = -0.5 K R_0^2
+  \ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] + 
+  4 \epsilon \left[ \left(\frac{\sigma}{\left(r - 
+      \Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r - 
+      \Delta\right)}\right)^6 \right] + \epsilon
+$$
+
+\end{document}

doc/doc2/Eqs/bond_harmonic.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   E = K (r - r_0)^2 
+$$
+
+\end{document}

doc/doc2/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}

doc/doc2/Eqs/bond_harmonic_shift_cut.tex

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+\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}

doc/doc2/Eqs/bond_morse.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+%   E = D \left[ 1 - \exp \left( -\alpha (r - r_0) \right) \right]^2 
+   E = D \left[ 1 - e^{-\alpha (r - r_0)} \right]^2 
+$$
+
+\end{document}

doc/doc2/Eqs/bond_nonlinear.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+  E = \frac{\epsilon (r - r_0)^2}{ [ \lambda^2 - (r - r_0)^2 ]}
+$$
+
+\end{document}

doc/doc2/Eqs/bond_quartic.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$ 
+  E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 +
+  4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+    \left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
+$$
+
+\end{document}

doc/doc2/Eqs/box.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray*}
+a &=& {\rm lx} \\
+b^2 &=&  {\rm ly}^2 +  {\rm xy}^2 \\
+c^2 &=&  {\rm lz}^2 +  {\rm xz}^2 +  {\rm yz}^2 \\
+\cos{\alpha} &=& \frac{{\rm xy}*{\rm xz} + {\rm ly}*{\rm yz}}{b*c} \\
+\cos{\beta} &=& \frac{\rm xz}{c} \\
+\cos{\gamma} &=& \frac{\rm xy}{b} \\
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/box_inverse.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray*}
+{\rm lx} &=& a \\
+{\rm xy} &=& b \cos{\gamma}  \\
+{\rm xz} &=& c \cos{\beta}\\
+{\rm ly}^2 &=&   b^2 - {\rm xy}^2 \\
+{\rm yz} &=& \frac{b*c \cos{\alpha} - {\rm xy}*{\rm xz}}{\rm ly} \\
+{\rm lz}^2 &=&  c^2 - {\rm xz}^2 - {\rm yz}^2 \\
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/centro_symmetry.tex

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+\documentclass[12pt]{article}
+
+\begin{document}
+
+$$
+   CS = \sum_{i = 1}^{N/2} | \vec{R}_i + \vec{R}_{i+N/2} |^2
+$$
+
+\end{document}

doc/doc2/Eqs/cna_cutoff1.tex

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+\documentclass[12pt,article]{article}
+
+\usepackage{indentfirst}
+\usepackage{amsmath}
+
+\begin{document}
+
+\begin{eqnarray*}
+  r_{c}^{fcc} & = & \frac{1}{2} \left(\frac{\sqrt{2}}{2} + 1\right) \mathrm{a} \simeq 0.8536 \:\mathrm{a} \\
+  r_{c}^{bcc} & = & \frac{1}{2}(\sqrt{2} + 1) \mathrm{a} \simeq 1.207 \:\mathrm{a} \\
+  r_{c}^{hcp} & = & \frac{1}{2}\left(1+\sqrt{\frac{4+2x^{2}}{3}}\right) \mathrm{a}
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/cna_cutoff2.tex

@@ -0,0 +1,12 @@
+\documentclass[12pt,article]{article}
+
+\usepackage{indentfirst}
+\usepackage{amsmath}
+
+\begin{document}
+
+$$
+  Rc + Rs > 2*{\rm cutoff}
+$$
+
+\end{document}

doc/doc2/Eqs/compute_fep_bar.tex

@@ -0,0 +1,7 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /kT \right]} \right>_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + \Delta_0^1A \right) /kT \right]} \right>_1 \]
+
+\end{document}

doc/doc2/Eqs/compute_fep_fdti.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left( \frac{\partial
+    A(\lambda)}{\partial\lambda} \right)_\lambda \mathrm{d}\lambda
+\approx \sum_{i=0}^{n-1} w_i \frac{A(\lambda_{i} + \delta) -
+  A(\lambda_i)}{\delta} \]
+
+\end{document}

doc/doc2/Eqs/compute_fep_fep.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A =
+- kT \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) -
+      U(\lambda_i)}{kT} \right) \right>_{\lambda_i} \]
+
+\end{document}

doc/doc2/Eqs/compute_fep_lambda.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\begin{eqnarray*}
+  \lambda = 0 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_0 \\
+  \lambda = 1 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_1 
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/compute_fep_ti.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left< \frac{\partial
+    U(\lambda)}{\partial\lambda} \right>_\lambda \mathrm{d}\lambda
+\approx \sum_{i=0}^{n-1} w_i \left< \frac{U(\lambda_{i} + \delta) -
+    U(\lambda_i)}{\delta} \right>_{\lambda_i} \]
+
+\end{document}

doc/doc2/Eqs/compute_fep_u.tex

@@ -0,0 +1,7 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[  U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \]
+
+\end{document}

doc/doc2/Eqs/compute_fep_vol.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+\[ \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( -
+    \frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right)
+\right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} \]
+
+\end{document}

doc/doc2/Eqs/compute_gyration.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+ {R_g}^2 = \frac{1}{M} \sum_i m_i (r_i - r_{cm})^2
+$$
+
+\end{document}

doc/doc2/Eqs/compute_msd_nongauss.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$
+ NGP(t) = 3<(r(t)-r(0))^4>/(5<(r(t)-r(0))^2>^2) - 1
+$$
+
+\end{document}

doc/doc2/Eqs/compute_saed1.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$ 
+  I=\frac{F^{*}F}{N}
+$$
+
+\end{document}
+

doc/doc2/Eqs/compute_saed2.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$ 
+  F(\mathbf{k})=\sum_{j=1}^{N}f_j(\theta)exp(2\pi i \mathbf{k}\cdot \mathbf{r}_j)
+$$
+\end{document}
+

doc/doc2/Eqs/compute_saed3.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$ 
+  f_j\left ( \frac{sin(\theta)}{\lambda} \right )=\sum_{i}^{5}
+a_i exp\left ( -b_i \frac{sin^{2}(\theta)}{\lambda^{2}} \right )
+$$
+\end{document}
+

doc/doc2/Eqs/compute_sna_atom1.tex

@@ -0,0 +1,11 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+\theta_0 = {\tt rfac0} \frac{r-r_{min0}}{R_{ii'}-r_{min0}} \pi
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/compute_sna_atom2.tex

@@ -0,0 +1,11 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+u^j_{m,m'} = U^j_{m,m'}(0,0,0) + \sum_{r_{ii'} < R_{ii'}}{f_c(r_{ii'}) w_{i'} U^j_{m,m'}(\theta_0,\theta,\phi)} 
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/compute_sna_atom3.tex

@@ -0,0 +1,16 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\newcommand{\hcoeff}[9]{H\!\!{\tiny\begin{array}{l}#1 #2 #3 \\ #4 #5 #6 \\ #7 #8 #9 \end{array}}}
+
+\begin{equation}
+B_{j_1,j_2,j}  = \\
+\sum_{m_1,m'_1=-j_1}^{j_1}\sum_{m_2,m'_2=-j_2}^{j_2}\sum_{m,m'=-j}^{j} (u^j_{m,m'})^*
+\hcoeff{j}{m}{m'}{j_1}{\!m_1}{\!m'_1}{j_2}{m_2}{m'_2}
+u^{j_1}_{m_1,m'_1} u^{j_2}_{m_2,m'_2}
+\end{equation}
+
+\end{document}

doc/doc2/Eqs/compute_sna_atom4.tex

@@ -0,0 +1,14 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+\begin{eqnarray*}
+\label{eqn:f_c}
+f_c(r)  & = & \frac{1}{2}(\cos(\pi \frac{r-r_{min0}}{R_{ii'}-r_{min0}}) + 1), r \leq R_{ii'} \\
+& = & 0,  r > R_{ii'}
+\end{eqnarray*}
+
+
+\end{document}

doc/doc2/Eqs/compute_sna_atom5.tex

@@ -0,0 +1,12 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+
+\begin{equation}
+- \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}  }}{\partial {\bf r}_i}
+\end{equation}
+
+\end{document}

doc/doc2/Eqs/compute_sna_atom6.tex

@@ -0,0 +1,12 @@
+\documentclass[24pt]{article}
+
+\pagestyle{empty}
+
+\begin{document}
+
+
+\begin{eqnarray*}
+- {\bf r}_i \otimes \sum_{i' \in I} \frac{\partial {B^{i'}_{j_1,j_2,j}}}{\partial {\bf r}_i}
+\end{eqnarray*}
+
+\end{document}

doc/doc2/Eqs/compute_xrd1.tex

@@ -0,0 +1,10 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$ 
+  I=Lp(\theta)\frac{F^{*}F}{N}
+$$
+
+\end{document}
+

doc/doc2/Eqs/compute_xrd2.tex

@@ -0,0 +1,9 @@
+\documentstyle[12pt]{article}
+
+\begin{document}
+
+$$ 
+  F(\mathbf{k})=\sum_{j=1}^{N}f_j(\theta)exp(2\pi i \mathbf{k}\cdot \mathbf{r}_j)
+$$
+\end{document}
+