diff --git a/doc/src/Eqs/angle_charmm.jpg b/doc/src/Eqs/angle_charmm.jpg new file mode 100644 index 0000000000..c6e6c297d2 Binary files /dev/null and b/doc/src/Eqs/angle_charmm.jpg differ diff --git a/doc/src/Eqs/angle_charmm.tex b/doc/src/Eqs/angle_charmm.tex new file mode 100644 index 0000000000..00b37ba335 --- /dev/null +++ b/doc/src/Eqs/angle_charmm.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (\theta - \theta_0)^2 + K_{UB} (r - r_{UB})^2 +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_class2.jpg b/doc/src/Eqs/angle_class2.jpg new file mode 100644 index 0000000000..f0f2a5152e Binary files /dev/null and b/doc/src/Eqs/angle_class2.jpg differ diff --git a/doc/src/Eqs/angle_class2.tex b/doc/src/Eqs/angle_class2.tex new file mode 100644 index 0000000000..e5a542e87a --- /dev/null +++ b/doc/src/Eqs/angle_class2.tex @@ -0,0 +1,12 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/angle_cosine.jpg b/doc/src/Eqs/angle_cosine.jpg new file mode 100644 index 0000000000..23b9b64310 Binary files /dev/null and b/doc/src/Eqs/angle_cosine.jpg differ diff --git a/doc/src/Eqs/angle_cosine.tex b/doc/src/Eqs/angle_cosine.tex new file mode 100644 index 0000000000..e766676099 --- /dev/null +++ b/doc/src/Eqs/angle_cosine.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [1 + \cos(\theta)] +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_cosine_delta.jpg b/doc/src/Eqs/angle_cosine_delta.jpg new file mode 100644 index 0000000000..c6e90bb2c5 Binary files /dev/null and b/doc/src/Eqs/angle_cosine_delta.jpg differ diff --git a/doc/src/Eqs/angle_cosine_delta.tex b/doc/src/Eqs/angle_cosine_delta.tex new file mode 100644 index 0000000000..918e9e5046 --- /dev/null +++ b/doc/src/Eqs/angle_cosine_delta.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [1 - \cos(\theta - \theta_0)] +$$ + +\end{document} diff --git a/doc/src/Eqs/angle_cosine_periodic.jpg b/doc/src/Eqs/angle_cosine_periodic.jpg new file mode 100644 index 0000000000..a9d7d50cb3 Binary files /dev/null and b/doc/src/Eqs/angle_cosine_periodic.jpg differ diff --git a/doc/src/Eqs/angle_cosine_periodic.tex b/doc/src/Eqs/angle_cosine_periodic.tex new file mode 100644 index 0000000000..69aa1bba6a --- /dev/null +++ b/doc/src/Eqs/angle_cosine_periodic.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right] +$$ + +\end{document} diff --git a/doc/src/Eqs/angle_cosine_shift.jpg b/doc/src/Eqs/angle_cosine_shift.jpg new file mode 100644 index 0000000000..d9929939c8 Binary files /dev/null and b/doc/src/Eqs/angle_cosine_shift.jpg differ diff --git a/doc/src/Eqs/angle_cosine_shift.tex b/doc/src/Eqs/angle_cosine_shift.tex new file mode 100644 index 0000000000..e795d6beff --- /dev/null +++ b/doc/src/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/src/Eqs/angle_cosine_shift_exp.jpg b/doc/src/Eqs/angle_cosine_shift_exp.jpg new file mode 100644 index 0000000000..294986de4b Binary files /dev/null and b/doc/src/Eqs/angle_cosine_shift_exp.jpg differ diff --git a/doc/src/Eqs/angle_cosine_shift_exp.tex b/doc/src/Eqs/angle_cosine_shift_exp.tex new file mode 100644 index 0000000000..4afa01356c --- /dev/null +++ b/doc/src/Eqs/angle_cosine_shift_exp.tex @@ -0,0 +1,13 @@ +\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} diff --git a/doc/src/Eqs/angle_cosine_squared.jpg b/doc/src/Eqs/angle_cosine_squared.jpg new file mode 100644 index 0000000000..b992398b7d Binary files /dev/null and b/doc/src/Eqs/angle_cosine_squared.jpg differ diff --git a/doc/src/Eqs/angle_cosine_squared.tex b/doc/src/Eqs/angle_cosine_squared.tex new file mode 100644 index 0000000000..57ae47ae45 --- /dev/null +++ b/doc/src/Eqs/angle_cosine_squared.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [\cos(\theta) - \cos(\theta_0)]^2 +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_dipole_couple.jpg b/doc/src/Eqs/angle_dipole_couple.jpg new file mode 100644 index 0000000000..f16849b2f9 Binary files /dev/null and b/doc/src/Eqs/angle_dipole_couple.jpg differ diff --git a/doc/src/Eqs/angle_dipole_couple.tex b/doc/src/Eqs/angle_dipole_couple.tex new file mode 100644 index 0000000000..a857d83d7a --- /dev/null +++ b/doc/src/Eqs/angle_dipole_couple.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +-\vec{T_j} & = & \vec{r_{ij}} \times \vec{F_i}\\ +\vec{F_j} & = & -\vec{F_i} \\ +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/angle_dipole_gamma.jpg b/doc/src/Eqs/angle_dipole_gamma.jpg new file mode 100644 index 0000000000..4bf618e252 Binary files /dev/null and b/doc/src/Eqs/angle_dipole_gamma.jpg differ diff --git a/doc/src/Eqs/angle_dipole_gamma.tex b/doc/src/Eqs/angle_dipole_gamma.tex new file mode 100644 index 0000000000..965b74ad96 --- /dev/null +++ b/doc/src/Eqs/angle_dipole_gamma.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + \cos\gamma = \frac{\vec{\mu_j}\bullet\vec{r_{ij}}}{\mu_j\,r_{ij}} +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_dipole_potential.jpg b/doc/src/Eqs/angle_dipole_potential.jpg new file mode 100644 index 0000000000..b1285e8957 Binary files /dev/null and b/doc/src/Eqs/angle_dipole_potential.jpg differ diff --git a/doc/src/Eqs/angle_dipole_potential.tex b/doc/src/Eqs/angle_dipole_potential.tex new file mode 100644 index 0000000000..8949835eb7 --- /dev/null +++ b/doc/src/Eqs/angle_dipole_potential.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (\cos\gamma - \cos\gamma_0)^2 +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_dipole_torque.jpg b/doc/src/Eqs/angle_dipole_torque.jpg new file mode 100644 index 0000000000..996a9df3cb Binary files /dev/null and b/doc/src/Eqs/angle_dipole_torque.jpg differ diff --git a/doc/src/Eqs/angle_dipole_torque.tex b/doc/src/Eqs/angle_dipole_torque.tex new file mode 100644 index 0000000000..9527459fdc --- /dev/null +++ b/doc/src/Eqs/angle_dipole_torque.tex @@ -0,0 +1,9 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/angle_fourier.jpg b/doc/src/Eqs/angle_fourier.jpg new file mode 100644 index 0000000000..e748e67430 Binary files /dev/null and b/doc/src/Eqs/angle_fourier.jpg differ diff --git a/doc/src/Eqs/angle_fourier.tex b/doc/src/Eqs/angle_fourier.tex new file mode 100644 index 0000000000..f7f76462e3 --- /dev/null +++ b/doc/src/Eqs/angle_fourier.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [C_0 + C_1 \cos ( \theta) + C_2 \cos( 2 \theta) ] +$$ + +\end{document} diff --git a/doc/src/Eqs/angle_fourier_simple.jpg b/doc/src/Eqs/angle_fourier_simple.jpg new file mode 100644 index 0000000000..6c9297b970 Binary files /dev/null and b/doc/src/Eqs/angle_fourier_simple.jpg differ diff --git a/doc/src/Eqs/angle_fourier_simple.tex b/doc/src/Eqs/angle_fourier_simple.tex new file mode 100644 index 0000000000..3228315a13 --- /dev/null +++ b/doc/src/Eqs/angle_fourier_simple.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [ 1.0 + c \cos ( n \theta) ] +$$ + +\end{document} diff --git a/doc/src/Eqs/angle_harmonic.jpg b/doc/src/Eqs/angle_harmonic.jpg new file mode 100644 index 0000000000..352be0b544 Binary files /dev/null and b/doc/src/Eqs/angle_harmonic.jpg differ diff --git a/doc/src/Eqs/angle_harmonic.tex b/doc/src/Eqs/angle_harmonic.tex new file mode 100644 index 0000000000..c566376b5b --- /dev/null +++ b/doc/src/Eqs/angle_harmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (\theta - \theta_0)^2 +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/angle_quartic.jpg b/doc/src/Eqs/angle_quartic.jpg new file mode 100644 index 0000000000..744ce7a35f Binary files /dev/null and b/doc/src/Eqs/angle_quartic.jpg differ diff --git a/doc/src/Eqs/angle_quartic.tex b/doc/src/Eqs/angle_quartic.tex new file mode 100644 index 0000000000..ff9ff9a7dc --- /dev/null +++ b/doc/src/Eqs/angle_quartic.tex @@ -0,0 +1,9 @@ +\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} diff --git a/doc/src/Eqs/bond_class2.jpg b/doc/src/Eqs/bond_class2.jpg new file mode 100644 index 0000000000..493048100e Binary files /dev/null and b/doc/src/Eqs/bond_class2.jpg differ diff --git a/doc/src/Eqs/bond_class2.tex b/doc/src/Eqs/bond_class2.tex new file mode 100644 index 0000000000..0735b61025 --- /dev/null +++ b/doc/src/Eqs/bond_class2.tex @@ -0,0 +1,9 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/bond_fene.jpg b/doc/src/Eqs/bond_fene.jpg new file mode 100644 index 0000000000..e8b909c08f Binary files /dev/null and b/doc/src/Eqs/bond_fene.jpg differ diff --git a/doc/src/Eqs/bond_fene.tex b/doc/src/Eqs/bond_fene.tex new file mode 100644 index 0000000000..ec4dd8efa2 --- /dev/null +++ b/doc/src/Eqs/bond_fene.tex @@ -0,0 +1,11 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/bond_fene_expand.jpg b/doc/src/Eqs/bond_fene_expand.jpg new file mode 100644 index 0000000000..1d04acec32 Binary files /dev/null and b/doc/src/Eqs/bond_fene_expand.jpg differ diff --git a/doc/src/Eqs/bond_fene_expand.tex b/doc/src/Eqs/bond_fene_expand.tex new file mode 100644 index 0000000000..5fd96e7ad5 --- /dev/null +++ b/doc/src/Eqs/bond_fene_expand.tex @@ -0,0 +1,13 @@ +\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} diff --git a/doc/src/Eqs/bond_harmonic.jpg b/doc/src/Eqs/bond_harmonic.jpg new file mode 100644 index 0000000000..fe9ef5619b Binary files /dev/null and b/doc/src/Eqs/bond_harmonic.jpg differ diff --git a/doc/src/Eqs/bond_harmonic.tex b/doc/src/Eqs/bond_harmonic.tex new file mode 100644 index 0000000000..2461086898 --- /dev/null +++ b/doc/src/Eqs/bond_harmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (r - r_0)^2 +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/bond_harmonic_shift.jpg b/doc/src/Eqs/bond_harmonic_shift.jpg new file mode 100644 index 0000000000..3e66d853a5 Binary files /dev/null and b/doc/src/Eqs/bond_harmonic_shift.jpg differ diff --git a/doc/src/Eqs/bond_harmonic_shift.tex b/doc/src/Eqs/bond_harmonic_shift.tex new file mode 100644 index 0000000000..3daa16724f --- /dev/null +++ b/doc/src/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 diff --git a/doc/src/Eqs/bond_harmonic_shift_cut.jpg b/doc/src/Eqs/bond_harmonic_shift_cut.jpg new file mode 100644 index 0000000000..06640e4fe0 Binary files /dev/null and b/doc/src/Eqs/bond_harmonic_shift_cut.jpg differ diff --git a/doc/src/Eqs/bond_harmonic_shift_cut.tex b/doc/src/Eqs/bond_harmonic_shift_cut.tex new file mode 100644 index 0000000000..3daa16724f --- /dev/null +++ b/doc/src/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/src/Eqs/bond_morse.jpg b/doc/src/Eqs/bond_morse.jpg new file mode 100644 index 0000000000..6795c9e527 Binary files /dev/null and b/doc/src/Eqs/bond_morse.jpg differ diff --git a/doc/src/Eqs/bond_morse.tex b/doc/src/Eqs/bond_morse.tex new file mode 100644 index 0000000000..a0d7a89961 --- /dev/null +++ b/doc/src/Eqs/bond_morse.tex @@ -0,0 +1,10 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/bond_nonlinear.jpg b/doc/src/Eqs/bond_nonlinear.jpg new file mode 100644 index 0000000000..0f18d8e73f Binary files /dev/null and b/doc/src/Eqs/bond_nonlinear.jpg differ diff --git a/doc/src/Eqs/bond_nonlinear.tex b/doc/src/Eqs/bond_nonlinear.tex new file mode 100644 index 0000000000..b8cdc96169 --- /dev/null +++ b/doc/src/Eqs/bond_nonlinear.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \frac{\epsilon (r - r_0)^2}{ [ \lambda^2 - (r - r_0)^2 ]} +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/bond_quartic.jpg b/doc/src/Eqs/bond_quartic.jpg new file mode 100644 index 0000000000..9d092883b2 Binary files /dev/null and b/doc/src/Eqs/bond_quartic.jpg differ diff --git a/doc/src/Eqs/bond_quartic.tex b/doc/src/Eqs/bond_quartic.tex new file mode 100644 index 0000000000..0d0cceb353 --- /dev/null +++ b/doc/src/Eqs/bond_quartic.tex @@ -0,0 +1,11 @@ +\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} \ No newline at end of file diff --git a/doc/src/Eqs/box.jpg b/doc/src/Eqs/box.jpg new file mode 100644 index 0000000000..4cb43df953 Binary files /dev/null and b/doc/src/Eqs/box.jpg differ diff --git a/doc/src/Eqs/box.tex b/doc/src/Eqs/box.tex new file mode 100644 index 0000000000..8442ea85b6 --- /dev/null +++ b/doc/src/Eqs/box.tex @@ -0,0 +1,14 @@ +\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} diff --git a/doc/src/Eqs/box_inverse.jpg b/doc/src/Eqs/box_inverse.jpg new file mode 100644 index 0000000000..5d0895b87e Binary files /dev/null and b/doc/src/Eqs/box_inverse.jpg differ diff --git a/doc/src/Eqs/box_inverse.tex b/doc/src/Eqs/box_inverse.tex new file mode 100644 index 0000000000..68994f2868 --- /dev/null +++ b/doc/src/Eqs/box_inverse.tex @@ -0,0 +1,14 @@ +\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} diff --git a/doc/src/Eqs/centro_symmetry.jpg b/doc/src/Eqs/centro_symmetry.jpg new file mode 100644 index 0000000000..1e89d11a11 Binary files /dev/null and b/doc/src/Eqs/centro_symmetry.jpg differ diff --git a/doc/src/Eqs/centro_symmetry.tex b/doc/src/Eqs/centro_symmetry.tex new file mode 100644 index 0000000000..8d9a9a33e6 --- /dev/null +++ b/doc/src/Eqs/centro_symmetry.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + CS = \sum_{i = 1}^{N/2} | \vec{R}_i + \vec{R}_{i+N/2} |^2 +$$ + +\end{document} diff --git a/doc/src/Eqs/cna_cutoff1.jpg b/doc/src/Eqs/cna_cutoff1.jpg new file mode 100644 index 0000000000..fae5c6b636 Binary files /dev/null and b/doc/src/Eqs/cna_cutoff1.jpg differ diff --git a/doc/src/Eqs/cna_cutoff1.tex b/doc/src/Eqs/cna_cutoff1.tex new file mode 100644 index 0000000000..f74166e608 --- /dev/null +++ b/doc/src/Eqs/cna_cutoff1.tex @@ -0,0 +1,14 @@ +\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} diff --git a/doc/src/Eqs/cna_cutoff2.jpg b/doc/src/Eqs/cna_cutoff2.jpg new file mode 100644 index 0000000000..744b61e9b4 Binary files /dev/null and b/doc/src/Eqs/cna_cutoff2.jpg differ diff --git a/doc/src/Eqs/cna_cutoff2.tex b/doc/src/Eqs/cna_cutoff2.tex new file mode 100644 index 0000000000..fcec31fd24 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_dpd.jpg b/doc/src/Eqs/compute_dpd.jpg new file mode 100644 index 0000000000..42ed03db15 Binary files /dev/null and b/doc/src/Eqs/compute_dpd.jpg differ diff --git a/doc/src/Eqs/compute_dpd.tex b/doc/src/Eqs/compute_dpd.tex new file mode 100644 index 0000000000..3d4338db08 --- /dev/null +++ b/doc/src/Eqs/compute_dpd.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} +\pagestyle{empty} +\begin{document} + +\begin{eqnarray*} + U^{cond} = \displaystyle\sum_{i=1}^{N} u_{i}^{cond} \\ + U^{mech} = \displaystyle\sum_{i=1}^{N} u_{i}^{mech} \\ + U = \displaystyle\sum_{i=1}^{N} (u_{i}^{cond} + u_{i}^{mech}) \\ + \theta_{avg} = (\frac{1}{N}\displaystyle\sum_{i=1}^{N} \frac{1}{\theta_{i}})^{-1} \\ +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/compute_fep_bar.jpg b/doc/src/Eqs/compute_fep_bar.jpg new file mode 100644 index 0000000000..772ec9c045 Binary files /dev/null and b/doc/src/Eqs/compute_fep_bar.jpg differ diff --git a/doc/src/Eqs/compute_fep_bar.tex b/doc/src/Eqs/compute_fep_bar.tex new file mode 100644 index 0000000000..a40aa1c297 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_fdti.jpg b/doc/src/Eqs/compute_fep_fdti.jpg new file mode 100644 index 0000000000..ae8de241cc Binary files /dev/null and b/doc/src/Eqs/compute_fep_fdti.jpg differ diff --git a/doc/src/Eqs/compute_fep_fdti.tex b/doc/src/Eqs/compute_fep_fdti.tex new file mode 100644 index 0000000000..fdea6faa3d --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_fep.jpg b/doc/src/Eqs/compute_fep_fep.jpg new file mode 100644 index 0000000000..d84a76b0dd Binary files /dev/null and b/doc/src/Eqs/compute_fep_fep.jpg differ diff --git a/doc/src/Eqs/compute_fep_fep.tex b/doc/src/Eqs/compute_fep_fep.tex new file mode 100644 index 0000000000..718aad3c40 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_lambda.jpg b/doc/src/Eqs/compute_fep_lambda.jpg new file mode 100644 index 0000000000..5ef9e8b9f2 Binary files /dev/null and b/doc/src/Eqs/compute_fep_lambda.jpg differ diff --git a/doc/src/Eqs/compute_fep_lambda.tex b/doc/src/Eqs/compute_fep_lambda.tex new file mode 100644 index 0000000000..08c8faaa3c --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_ti.jpg b/doc/src/Eqs/compute_fep_ti.jpg new file mode 100644 index 0000000000..6b0c8fdc19 Binary files /dev/null and b/doc/src/Eqs/compute_fep_ti.jpg differ diff --git a/doc/src/Eqs/compute_fep_ti.tex b/doc/src/Eqs/compute_fep_ti.tex new file mode 100644 index 0000000000..6222dbd503 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_u.jpg b/doc/src/Eqs/compute_fep_u.jpg new file mode 100644 index 0000000000..62df5dd0c0 Binary files /dev/null and b/doc/src/Eqs/compute_fep_u.jpg differ diff --git a/doc/src/Eqs/compute_fep_u.tex b/doc/src/Eqs/compute_fep_u.tex new file mode 100644 index 0000000000..e847a9ac44 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_fep_vol.jpg b/doc/src/Eqs/compute_fep_vol.jpg new file mode 100644 index 0000000000..a66facad39 Binary files /dev/null and b/doc/src/Eqs/compute_fep_vol.jpg differ diff --git a/doc/src/Eqs/compute_fep_vol.tex b/doc/src/Eqs/compute_fep_vol.tex new file mode 100644 index 0000000000..0301e39788 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_gyration.jpg b/doc/src/Eqs/compute_gyration.jpg new file mode 100644 index 0000000000..2285444434 Binary files /dev/null and b/doc/src/Eqs/compute_gyration.jpg differ diff --git a/doc/src/Eqs/compute_gyration.tex b/doc/src/Eqs/compute_gyration.tex new file mode 100644 index 0000000000..97204f1ded --- /dev/null +++ b/doc/src/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} \ No newline at end of file diff --git a/doc/src/Eqs/compute_msd_nongauss.jpg b/doc/src/Eqs/compute_msd_nongauss.jpg new file mode 100644 index 0000000000..d57f6a4af8 Binary files /dev/null and b/doc/src/Eqs/compute_msd_nongauss.jpg differ diff --git a/doc/src/Eqs/compute_msd_nongauss.tex b/doc/src/Eqs/compute_msd_nongauss.tex new file mode 100644 index 0000000000..168d8f72ed --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_saed1.jpg b/doc/src/Eqs/compute_saed1.jpg new file mode 100644 index 0000000000..6bad3a6104 Binary files /dev/null and b/doc/src/Eqs/compute_saed1.jpg differ diff --git a/doc/src/Eqs/compute_saed1.tex b/doc/src/Eqs/compute_saed1.tex new file mode 100644 index 0000000000..0db2f55ecd --- /dev/null +++ b/doc/src/Eqs/compute_saed1.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + I=\frac{F^{*}F}{N} +$$ + +\end{document} + diff --git a/doc/src/Eqs/compute_saed2.jpg b/doc/src/Eqs/compute_saed2.jpg new file mode 100644 index 0000000000..2b3b0bc090 Binary files /dev/null and b/doc/src/Eqs/compute_saed2.jpg differ diff --git a/doc/src/Eqs/compute_saed2.tex b/doc/src/Eqs/compute_saed2.tex new file mode 100644 index 0000000000..d005602339 --- /dev/null +++ b/doc/src/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} + diff --git a/doc/src/Eqs/compute_saed3.jpg b/doc/src/Eqs/compute_saed3.jpg new file mode 100644 index 0000000000..1bbc920908 Binary files /dev/null and b/doc/src/Eqs/compute_saed3.jpg differ diff --git a/doc/src/Eqs/compute_saed3.tex b/doc/src/Eqs/compute_saed3.tex new file mode 100644 index 0000000000..5988a620c7 --- /dev/null +++ b/doc/src/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} + diff --git a/doc/src/Eqs/compute_sna_atom1.jpg b/doc/src/Eqs/compute_sna_atom1.jpg new file mode 100644 index 0000000000..fe4b641aa6 Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom1.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom1.tex b/doc/src/Eqs/compute_sna_atom1.tex new file mode 100644 index 0000000000..93e2709bf9 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_sna_atom2.jpg b/doc/src/Eqs/compute_sna_atom2.jpg new file mode 100644 index 0000000000..7a4b2c2111 Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom2.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom2.tex b/doc/src/Eqs/compute_sna_atom2.tex new file mode 100644 index 0000000000..98d8f2efa6 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_sna_atom3.jpg b/doc/src/Eqs/compute_sna_atom3.jpg new file mode 100644 index 0000000000..41d6774e9c Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom3.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom3.tex b/doc/src/Eqs/compute_sna_atom3.tex new file mode 100644 index 0000000000..5e3212f7bd --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_sna_atom4.jpg b/doc/src/Eqs/compute_sna_atom4.jpg new file mode 100644 index 0000000000..5d53943bf4 Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom4.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom4.tex b/doc/src/Eqs/compute_sna_atom4.tex new file mode 100644 index 0000000000..3477d163e3 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_sna_atom5.jpg b/doc/src/Eqs/compute_sna_atom5.jpg new file mode 100644 index 0000000000..732731fe13 Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom5.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom5.tex b/doc/src/Eqs/compute_sna_atom5.tex new file mode 100644 index 0000000000..72f5a0fe7c --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_sna_atom6.jpg b/doc/src/Eqs/compute_sna_atom6.jpg new file mode 100644 index 0000000000..963dd81416 Binary files /dev/null and b/doc/src/Eqs/compute_sna_atom6.jpg differ diff --git a/doc/src/Eqs/compute_sna_atom6.tex b/doc/src/Eqs/compute_sna_atom6.tex new file mode 100644 index 0000000000..7da589548b --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/compute_xrd1.jpg b/doc/src/Eqs/compute_xrd1.jpg new file mode 100644 index 0000000000..8432fad4aa Binary files /dev/null and b/doc/src/Eqs/compute_xrd1.jpg differ diff --git a/doc/src/Eqs/compute_xrd1.tex b/doc/src/Eqs/compute_xrd1.tex new file mode 100644 index 0000000000..6e749c768d --- /dev/null +++ b/doc/src/Eqs/compute_xrd1.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + I=Lp(\theta)\frac{F^{*}F}{N} +$$ + +\end{document} + diff --git a/doc/src/Eqs/compute_xrd2.jpg b/doc/src/Eqs/compute_xrd2.jpg new file mode 100644 index 0000000000..1bcf0494ea Binary files /dev/null and b/doc/src/Eqs/compute_xrd2.jpg differ diff --git a/doc/src/Eqs/compute_xrd2.tex b/doc/src/Eqs/compute_xrd2.tex new file mode 100644 index 0000000000..d005602339 --- /dev/null +++ b/doc/src/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} + diff --git a/doc/src/Eqs/compute_xrd3.jpg b/doc/src/Eqs/compute_xrd3.jpg new file mode 100644 index 0000000000..19f7aa99b5 Binary files /dev/null and b/doc/src/Eqs/compute_xrd3.jpg differ diff --git a/doc/src/Eqs/compute_xrd3.tex b/doc/src/Eqs/compute_xrd3.tex new file mode 100644 index 0000000000..da0254134c --- /dev/null +++ b/doc/src/Eqs/compute_xrd3.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + Lp(\theta)=\frac{1+cos^{2}(2\theta)}{cos(\theta)sin^{2}(\theta)} +$$ +\end{document} + diff --git a/doc/src/Eqs/compute_xrd4.jpg b/doc/src/Eqs/compute_xrd4.jpg new file mode 100644 index 0000000000..385bb1efd7 Binary files /dev/null and b/doc/src/Eqs/compute_xrd4.jpg differ diff --git a/doc/src/Eqs/compute_xrd4.tex b/doc/src/Eqs/compute_xrd4.tex new file mode 100644 index 0000000000..d4deb7ca55 --- /dev/null +++ b/doc/src/Eqs/compute_xrd4.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + \frac{sin(\theta)}{\lambda}=\frac{\left | \mathbf{k} \right |}{2} +$$ +\end{document} + diff --git a/doc/src/Eqs/compute_xrd5.jpg b/doc/src/Eqs/compute_xrd5.jpg new file mode 100644 index 0000000000..c6f0a2609a Binary files /dev/null and b/doc/src/Eqs/compute_xrd5.jpg differ diff --git a/doc/src/Eqs/compute_xrd5.tex b/doc/src/Eqs/compute_xrd5.tex new file mode 100644 index 0000000000..2d97a3288b --- /dev/null +++ b/doc/src/Eqs/compute_xrd5.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + f_j\left ( \frac{sin(\theta)}{\lambda} \right )=\sum_{i}^{4} +a_i exp\left ( -b_i \frac{sin^{2}(\theta)}{\lambda^{2}} \right )+c +$$ +\end{document} + diff --git a/doc/src/Eqs/dihedral_charmm.jpg b/doc/src/Eqs/dihedral_charmm.jpg new file mode 100644 index 0000000000..810afa3cd2 Binary files /dev/null and b/doc/src/Eqs/dihedral_charmm.jpg differ diff --git a/doc/src/Eqs/dihedral_charmm.tex b/doc/src/Eqs/dihedral_charmm.tex new file mode 100644 index 0000000000..c3d860b265 --- /dev/null +++ b/doc/src/Eqs/dihedral_charmm.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [ 1 + \cos (n \phi - d) ] +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_class2.jpg b/doc/src/Eqs/dihedral_class2.jpg new file mode 100644 index 0000000000..6a6780e769 Binary files /dev/null and b/doc/src/Eqs/dihedral_class2.jpg differ diff --git a/doc/src/Eqs/dihedral_class2.tex b/doc/src/Eqs/dihedral_class2.tex new file mode 100644 index 0000000000..02acc16fb9 --- /dev/null +++ b/doc/src/Eqs/dihedral_class2.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\ + E_d & = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\ + E_{mbt} & = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\ + E_{ebt} & = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\ + & & (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\ + E_{at} & = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\ + & & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\ + E_{aat} & = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\ + E_{bb13} & = & N (r_{ij} - r_1) (r_{kl} - r_3) +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_cosine_shift_exp.jpg b/doc/src/Eqs/dihedral_cosine_shift_exp.jpg new file mode 100644 index 0000000000..ea0a7550f8 Binary files /dev/null and b/doc/src/Eqs/dihedral_cosine_shift_exp.jpg differ diff --git a/doc/src/Eqs/dihedral_cosine_shift_exp.tex b/doc/src/Eqs/dihedral_cosine_shift_exp.tex new file mode 100644 index 0000000000..4afa01356c --- /dev/null +++ b/doc/src/Eqs/dihedral_cosine_shift_exp.tex @@ -0,0 +1,13 @@ +\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} diff --git a/doc/src/Eqs/dihedral_fourier.jpg b/doc/src/Eqs/dihedral_fourier.jpg new file mode 100644 index 0000000000..663ac17ee6 Binary files /dev/null and b/doc/src/Eqs/dihedral_fourier.jpg differ diff --git a/doc/src/Eqs/dihedral_fourier.tex b/doc/src/Eqs/dihedral_fourier.tex new file mode 100644 index 0000000000..960d3a8ea8 --- /dev/null +++ b/doc/src/Eqs/dihedral_fourier.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \sum_{i=1,m} K_i [ 1.0 + \cos ( n_i \phi - d_i ) ] +$$ + +\end{document} diff --git a/doc/src/Eqs/dihedral_harmonic.jpg b/doc/src/Eqs/dihedral_harmonic.jpg new file mode 100644 index 0000000000..cb5c16a8ca Binary files /dev/null and b/doc/src/Eqs/dihedral_harmonic.jpg differ diff --git a/doc/src/Eqs/dihedral_harmonic.tex b/doc/src/Eqs/dihedral_harmonic.tex new file mode 100644 index 0000000000..9d02036fcc --- /dev/null +++ b/doc/src/Eqs/dihedral_harmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K [ 1 + d \cos (n \phi) ] +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_helix.jpg b/doc/src/Eqs/dihedral_helix.jpg new file mode 100644 index 0000000000..01a0ec982c Binary files /dev/null and b/doc/src/Eqs/dihedral_helix.jpg differ diff --git a/doc/src/Eqs/dihedral_helix.tex b/doc/src/Eqs/dihedral_helix.tex new file mode 100644 index 0000000000..ae25776f2c --- /dev/null +++ b/doc/src/Eqs/dihedral_helix.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = A [1 - \cos(\theta)] + B [1 + \cos(3 \theta)] + + C [1 + \cos(\theta + \frac{\pi}{4})] +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_multi_harmonic.jpg b/doc/src/Eqs/dihedral_multi_harmonic.jpg new file mode 100644 index 0000000000..d066cd212b Binary files /dev/null and b/doc/src/Eqs/dihedral_multi_harmonic.jpg differ diff --git a/doc/src/Eqs/dihedral_multi_harmonic.tex b/doc/src/Eqs/dihedral_multi_harmonic.tex new file mode 100644 index 0000000000..819aa7c57c --- /dev/null +++ b/doc/src/Eqs/dihedral_multi_harmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \sum_{n=1,5} A_n \cos^{n-1}(\phi) +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_nharmonic.jpg b/doc/src/Eqs/dihedral_nharmonic.jpg new file mode 100644 index 0000000000..4f4928bdd5 Binary files /dev/null and b/doc/src/Eqs/dihedral_nharmonic.jpg differ diff --git a/doc/src/Eqs/dihedral_nharmonic.tex b/doc/src/Eqs/dihedral_nharmonic.tex new file mode 100644 index 0000000000..57a1d25284 --- /dev/null +++ b/doc/src/Eqs/dihedral_nharmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \sum_{n=1,n} A_n \cos^{n-1}(\phi) +$$ + +\end{document} diff --git a/doc/src/Eqs/dihedral_opls.jpg b/doc/src/Eqs/dihedral_opls.jpg new file mode 100644 index 0000000000..0546aebfde Binary files /dev/null and b/doc/src/Eqs/dihedral_opls.jpg differ diff --git a/doc/src/Eqs/dihedral_opls.tex b/doc/src/Eqs/dihedral_opls.tex new file mode 100644 index 0000000000..5e4aada53a --- /dev/null +++ b/doc/src/Eqs/dihedral_opls.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \frac{1}{2} K_1 [1 + \cos(\phi)] + \frac{1}{2} K_2 [1 - \cos(2 \phi)] + + \frac{1}{2} K_3 [1 + \cos(3 \phi)] + \frac{1}{2} K_4 [1 - \cos(4 \phi)] +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/dihedral_quadratic.jpg b/doc/src/Eqs/dihedral_quadratic.jpg new file mode 100644 index 0000000000..8fb17622f8 Binary files /dev/null and b/doc/src/Eqs/dihedral_quadratic.jpg differ diff --git a/doc/src/Eqs/dihedral_quadratic.tex b/doc/src/Eqs/dihedral_quadratic.tex new file mode 100644 index 0000000000..049e4b2ec4 --- /dev/null +++ b/doc/src/Eqs/dihedral_quadratic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (\phi - \phi_0)^2 +$$ + +\end{document} diff --git a/doc/src/Eqs/dihedral_sign.jpg b/doc/src/Eqs/dihedral_sign.jpg new file mode 100644 index 0000000000..8d8352e8fc Binary files /dev/null and b/doc/src/Eqs/dihedral_sign.jpg differ diff --git a/doc/src/Eqs/dreiding_hbond.jpg b/doc/src/Eqs/dreiding_hbond.jpg new file mode 100644 index 0000000000..76cc42a45b Binary files /dev/null and b/doc/src/Eqs/dreiding_hbond.jpg differ diff --git a/doc/src/Eqs/eff_ECP1.jpg b/doc/src/Eqs/eff_ECP1.jpg new file mode 100644 index 0000000000..3b8a3f8ff3 Binary files /dev/null and b/doc/src/Eqs/eff_ECP1.jpg differ diff --git a/doc/src/Eqs/eff_ECP1.tex b/doc/src/Eqs/eff_ECP1.tex new file mode 100644 index 0000000000..ebd581163c --- /dev/null +++ b/doc/src/Eqs/eff_ECP1.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +E_{Pauli(ECP_s)}=p_1\exp\left(-\frac{p_2r^2}{p_3+s^2} \right) +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/eff_ECP2.jpg b/doc/src/Eqs/eff_ECP2.jpg new file mode 100644 index 0000000000..195ed55e43 Binary files /dev/null and b/doc/src/Eqs/eff_ECP2.jpg differ diff --git a/doc/src/Eqs/eff_ECP2.tex b/doc/src/Eqs/eff_ECP2.tex new file mode 100644 index 0000000000..0c3c366562 --- /dev/null +++ b/doc/src/Eqs/eff_ECP2.tex @@ -0,0 +1,8 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +E_{Pauli(ECP_p)}=p_1\left( \frac{2}{p_2/s+s/p_2} \right)\left( r-p_3s\right)^2\exp \left[ -\frac{p_4\left( r-p_3s \right)^2}{p_5+s^2} \right] +$$ + \end{document} \ No newline at end of file diff --git a/doc/src/Eqs/eff_KE.jpg b/doc/src/Eqs/eff_KE.jpg new file mode 100644 index 0000000000..40eed0df65 Binary files /dev/null and b/doc/src/Eqs/eff_KE.jpg differ diff --git a/doc/src/Eqs/eff_KE.tex b/doc/src/Eqs/eff_KE.tex new file mode 100644 index 0000000000..9f9af2fa25 --- /dev/null +++ b/doc/src/Eqs/eff_KE.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E_{KE} = \frac{\hbar^2 }{{m_{e} }}\sum\limits_i {\frac{3}{{2s_i^2 }}} +$$ + +\end{document} diff --git a/doc/src/Eqs/eff_NN.jpg b/doc/src/Eqs/eff_NN.jpg new file mode 100644 index 0000000000..c3c52e19b4 Binary files /dev/null and b/doc/src/Eqs/eff_NN.jpg differ diff --git a/doc/src/Eqs/eff_NN.tex b/doc/src/Eqs/eff_NN.tex new file mode 100644 index 0000000000..4f9bb6d132 --- /dev/null +++ b/doc/src/Eqs/eff_NN.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E_{NN} = \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{{Z_i Z_j }}{{R_{ij} }}} +$$ + +\end{document} diff --git a/doc/src/Eqs/eff_Ne.jpg b/doc/src/Eqs/eff_Ne.jpg new file mode 100644 index 0000000000..e23ceacc88 Binary files /dev/null and b/doc/src/Eqs/eff_Ne.jpg differ diff --git a/doc/src/Eqs/eff_Ne.tex b/doc/src/Eqs/eff_Ne.tex new file mode 100644 index 0000000000..e6813b125c --- /dev/null +++ b/doc/src/Eqs/eff_Ne.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E_{Ne} = - \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i,j} {\frac{{Z_i }}{{R_{ij} }}Erf\left( {\frac{{\sqrt 2 R_{ij} }}{{s_j }}} \right)} +$$ + +\end{document} diff --git a/doc/src/Eqs/eff_Pauli.jpg b/doc/src/Eqs/eff_Pauli.jpg new file mode 100644 index 0000000000..61bb8652e3 Binary files /dev/null and b/doc/src/Eqs/eff_Pauli.jpg differ diff --git a/doc/src/Eqs/eff_Pauli.tex b/doc/src/Eqs/eff_Pauli.tex new file mode 100644 index 0000000000..b6b8070cc7 --- /dev/null +++ b/doc/src/Eqs/eff_Pauli.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E_{Pauli} = \sum\limits_{\sigma _i = \sigma _j } {E\left( { \uparrow \uparrow } \right)_{ij}} + \sum\limits_{\sigma _i \ne \sigma _j } {E\left( { \uparrow \downarrow } \right)_{ij}} +$$ + +\end{document} diff --git a/doc/src/Eqs/eff_ee.jpg b/doc/src/Eqs/eff_ee.jpg new file mode 100644 index 0000000000..aef84d0fd4 Binary files /dev/null and b/doc/src/Eqs/eff_ee.jpg differ diff --git a/doc/src/Eqs/eff_ee.tex b/doc/src/Eqs/eff_ee.tex new file mode 100644 index 0000000000..5d17e5557b --- /dev/null +++ b/doc/src/Eqs/eff_ee.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E_{ee} = \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{1}{{r_{ij} }}Erf\left( {\frac{{\sqrt 2 r_{ij} }}{{\sqrt {s_i^2 + s_j^2 } }}} \right)} +$$ + +\end{document} diff --git a/doc/src/Eqs/eff_energy_expression.jpg b/doc/src/Eqs/eff_energy_expression.jpg new file mode 100644 index 0000000000..e06fe8ff2f Binary files /dev/null and b/doc/src/Eqs/eff_energy_expression.jpg differ diff --git a/doc/src/Eqs/eff_energy_expression.tex b/doc/src/Eqs/eff_energy_expression.tex new file mode 100644 index 0000000000..f56380f646 --- /dev/null +++ b/doc/src/Eqs/eff_energy_expression.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +U\left(R,r,s\right) = E_{NN} \left( R \right) + E_{Ne} \left( {R,r,s} \right) + E_{ee} \left( {r,s} \right) + E_{KE} \left( {r,s} \right) + E_{PR} \left( { \uparrow \downarrow ,S} \right) +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_box_relax1.jpg b/doc/src/Eqs/fix_box_relax1.jpg new file mode 100644 index 0000000000..d425526046 Binary files /dev/null and b/doc/src/Eqs/fix_box_relax1.jpg differ diff --git a/doc/src/Eqs/fix_box_relax1.tex b/doc/src/Eqs/fix_box_relax1.tex new file mode 100644 index 0000000000..a332360666 --- /dev/null +++ b/doc/src/Eqs/fix_box_relax1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E = U + P_t \left(V-V_0 \right) + E_{strain} +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_box_relax2.jpg b/doc/src/Eqs/fix_box_relax2.jpg new file mode 100644 index 0000000000..8fac42e0fa Binary files /dev/null and b/doc/src/Eqs/fix_box_relax2.jpg differ diff --git a/doc/src/Eqs/fix_box_relax2.tex b/doc/src/Eqs/fix_box_relax2.tex new file mode 100644 index 0000000000..bc9cddef4e --- /dev/null +++ b/doc/src/Eqs/fix_box_relax2.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\mathbf P = P_t \mathbf I + {\mathbf S_t} \left( \mathbf h_0^{-1} \right)^t \mathbf h_{0d} +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_eos-cv.jpg b/doc/src/Eqs/fix_eos-cv.jpg new file mode 100644 index 0000000000..37eeac8e2d Binary files /dev/null and b/doc/src/Eqs/fix_eos-cv.jpg differ diff --git a/doc/src/Eqs/fix_eos-cv.tex b/doc/src/Eqs/fix_eos-cv.tex new file mode 100644 index 0000000000..e084bac9bc --- /dev/null +++ b/doc/src/Eqs/fix_eos-cv.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} +\pagestyle{empty} +\begin{document} + +$$ + u_{i} = u^{mech}_{i} + u^{cond}_{i} = C_{V} \theta_{i} +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_gld1.jpg b/doc/src/Eqs/fix_gld1.jpg new file mode 100644 index 0000000000..d54ce57a6c Binary files /dev/null and b/doc/src/Eqs/fix_gld1.jpg differ diff --git a/doc/src/Eqs/fix_gld1.tex b/doc/src/Eqs/fix_gld1.tex new file mode 100644 index 0000000000..baa0f32a5b --- /dev/null +++ b/doc/src/Eqs/fix_gld1.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\usepackage{amsmath} + +\begin{document} + +\begin{align*} + &{\bf F}_{j}(t) = {\bf F}^C_j(t)-\int \limits_{0}^{t} \Gamma_j(t-s) {\bf v}_j(s)~\text{d}s + {\bf F}^R_j(t) \\ + &\Gamma_j(t-s) = \sum \limits_{k=1}^{N_k} \frac{c_k}{\tau_k} e^{-(t-s)/\tau_k} \\ + &\langle{\bf F}^R_j(t),{\bf F}^R_j(s)\rangle = \text{k$_\text{B}$T} ~\Gamma_j(t-s) +\end{align*} + +\end{document} diff --git a/doc/src/Eqs/fix_lb_fluid_boltzmann.jpg b/doc/src/Eqs/fix_lb_fluid_boltzmann.jpg new file mode 100644 index 0000000000..9d82b40ecb Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_boltzmann.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_boltzmann.tex b/doc/src/Eqs/fix_lb_fluid_boltzmann.tex new file mode 100755 index 0000000000..4a6ca6fe01 --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_boltzmann.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\left(\partial_t + e_{i\alpha}\partial_{\alpha}\right)f_i = -\frac{1}{\tau}\left(f_i - f_i^{eq}\right) + W_i +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_fluidforce.jpg b/doc/src/Eqs/fix_lb_fluid_fluidforce.jpg new file mode 100644 index 0000000000..d3149616ca Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_fluidforce.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_fluidforce.tex b/doc/src/Eqs/fix_lb_fluid_fluidforce.tex new file mode 100755 index 0000000000..8433c9264a --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_fluidforce.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +{\bf F}_{j \alpha} = \gamma \left({\bf v}_n - {\bf u}_f \right) \zeta_{j\alpha} +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_gammadefault.jpg b/doc/src/Eqs/fix_lb_fluid_gammadefault.jpg new file mode 100644 index 0000000000..cd10239c9b Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_gammadefault.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_gammadefault.tex b/doc/src/Eqs/fix_lb_fluid_gammadefault.tex new file mode 100755 index 0000000000..1af82c4972 --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_gammadefault.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\gamma = \frac{2m_um_v}{m_u+m_v}\left(\frac{1}{\Delta t_{collision}}\right) +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_navierstokes.jpg b/doc/src/Eqs/fix_lb_fluid_navierstokes.jpg new file mode 100644 index 0000000000..0a1c104141 Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_navierstokes.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_navierstokes.tex b/doc/src/Eqs/fix_lb_fluid_navierstokes.tex new file mode 100755 index 0000000000..41ca4674e9 --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_navierstokes.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\partial_t \rho + \partial_{\beta}\left(\rho u_{\beta}\right)= 0 +$$ +$$ +\partial_t\left(\rho u_{\alpha}\right) + \partial_{\beta}\left(\rho u_{\alpha} u_{\beta}\right) = \partial_{\beta}\sigma_{\alpha \beta} + F_{\alpha} + \partial_{\beta}\left(\eta_{\alpha \beta \gamma \nu}\partial_{\gamma} u_{\nu}\right) +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_properties.jpg b/doc/src/Eqs/fix_lb_fluid_properties.jpg new file mode 100644 index 0000000000..3d70cd7667 Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_properties.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_properties.tex b/doc/src/Eqs/fix_lb_fluid_properties.tex new file mode 100755 index 0000000000..fe1290be12 --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_properties.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\rho = \displaystyle\sum\limits_{i} f_i +$$ +$$ +\rho u_{\alpha} = \displaystyle\sum\limits_{i} f_i e_{i\alpha} +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_stress.jpg b/doc/src/Eqs/fix_lb_fluid_stress.jpg new file mode 100644 index 0000000000..8f730e9d70 Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_stress.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_stress.tex b/doc/src/Eqs/fix_lb_fluid_stress.tex new file mode 100755 index 0000000000..b4e0982536 --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_stress.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\sigma_{\alpha \beta} = -P_{\alpha \beta} = -\rho a_0 \delta_{\alpha \beta} +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_lb_fluid_viscosity.jpg b/doc/src/Eqs/fix_lb_fluid_viscosity.jpg new file mode 100644 index 0000000000..1816317ee6 Binary files /dev/null and b/doc/src/Eqs/fix_lb_fluid_viscosity.jpg differ diff --git a/doc/src/Eqs/fix_lb_fluid_viscosity.tex b/doc/src/Eqs/fix_lb_fluid_viscosity.tex new file mode 100755 index 0000000000..d5925f213f --- /dev/null +++ b/doc/src/Eqs/fix_lb_fluid_viscosity.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\eta_{\alpha \beta \gamma \nu} = \eta\left[\delta_{\alpha \gamma}\delta_{\beta \nu} + \delta_{\alpha \nu}\delta_{\beta \gamma} - \frac{2}{3}\delta_{\alpha \beta}\delta_{\gamma \nu}\right] + \Lambda \delta_{\alpha \beta}\delta_{\gamma \nu} +$$ + + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_nh1.jpg b/doc/src/Eqs/fix_nh1.jpg new file mode 100644 index 0000000000..af07ea3a4b Binary files /dev/null and b/doc/src/Eqs/fix_nh1.jpg differ diff --git a/doc/src/Eqs/fix_nh1.tex b/doc/src/Eqs/fix_nh1.tex new file mode 100644 index 0000000000..3e780f2772 --- /dev/null +++ b/doc/src/Eqs/fix_nh1.tex @@ -0,0 +1,36 @@ +\documentclass[24pt]{article} + +\pagestyle{empty} +\Huge + +\begin{document} + +\mathchardef\mhyphen="2D + +% The imaginary unit +\providecommand*{\iu}% + {\ensuremath{{\rm i}}} + + +\begin{eqnarray*} +\exp \left(\iu{} L \Delta t \right) &=&Ê +\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) \\ +&&\times \left[ +\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) +\exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{2n} \right) +\exp \left(\iu{} L_1 \frac{\Delta t}{n} \right) +\exp \left(\iu{} L_{\epsilon , 1} \frac{\Delta t}{2n} \right) +\exp \left(\iu{} L_{2}^{(1)} \frac{\Delta t}{2n} \right) +\right]^n \\ +&&\times +\exp \left(\iu{} L_{2}^{(2)} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\epsilon , 2} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen part} \frac{\Delta t}{2} \right) +\exp \left(\iu{} L_{\rm T\mhyphen baro} \frac{\Delta t}{2} \right) \\ +&&+ \mathcal{O} \left(\Delta t^3 \right) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/fix_nphug.jpg b/doc/src/Eqs/fix_nphug.jpg new file mode 100644 index 0000000000..a3a67e7b7b Binary files /dev/null and b/doc/src/Eqs/fix_nphug.jpg differ diff --git a/doc/src/Eqs/fix_nphug.tex b/doc/src/Eqs/fix_nphug.tex new file mode 100644 index 0000000000..4e162b69b7 --- /dev/null +++ b/doc/src/Eqs/fix_nphug.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +T_t - T = \frac{\left(\frac{1}{2}\left(P + P_0\right)\left(V_0 - V\right) + E_0 - E\right)}{N_{dof} k_B } = Delta +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_orient_fcc.jpg b/doc/src/Eqs/fix_orient_fcc.jpg new file mode 100644 index 0000000000..b22e6c9c20 Binary files /dev/null and b/doc/src/Eqs/fix_orient_fcc.jpg differ diff --git a/doc/src/Eqs/fix_orient_fcc.tex b/doc/src/Eqs/fix_orient_fcc.tex new file mode 100644 index 0000000000..5596848eb5 --- /dev/null +++ b/doc/src/Eqs/fix_orient_fcc.tex @@ -0,0 +1,30 @@ +\newcommand{\br}{\mathbf{r}} + +\documentclass[12pt]{article} + +\begin{document} + +\begin{equation} + \xi_{i} = \sum_{j=1}^{12} \left| \br_{j} - \br_{j}^{\rm I} \right| +\end{equation} + +\begin{equation} + \xi_{\rm IJ} = \sum_{j=1}^{12} \left| \br_{j}^{\rm J} - \br_{j}^{\rm I} \right| +\end{equation} + +\begin{eqnarray} + \xi_{\rm low} &=& {\rm cutlo} \, \xi_{\rm IJ} \\ + \xi_{\rm high} &=& {\rm cuthi} \, \xi_{\rm IJ} +\end{eqnarray} + +\begin{eqnarray} + \omega_{i} &=& \frac{\pi}{2} + \frac{\xi_{i} - \xi_{\rm low}}{\xi_{\rm high} - \xi_{\rm low}} \\ + \mbox{\hspace*{72pt}} \nonumber \\ + u_{i} &=& 0 \mbox{\hspace{84pt} for } \xi_{i} < \xi_{\rm low} \nonumber \\ + &=& {\rm dE}\,\frac{1 - \cos(2 \omega_{i})}{2} + \mbox{\hspace{10pt} for } \xi_{\rm low} < \xi_{i} < \xi_{\rm high} \\ + &=& {\rm dE} \mbox{\hspace{80pt} for } \xi_{\rm high} < \xi_{i} + \nonumber +\end{eqnarray} +\end{document} diff --git a/doc/src/Eqs/fix_pimd.jpg b/doc/src/Eqs/fix_pimd.jpg new file mode 100644 index 0000000000..b6e8f5831b Binary files /dev/null and b/doc/src/Eqs/fix_pimd.jpg differ diff --git a/doc/src/Eqs/fix_pimd.tex b/doc/src/Eqs/fix_pimd.tex new file mode 100644 index 0000000000..983fead8e4 --- /dev/null +++ b/doc/src/Eqs/fix_pimd.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + Z = \int d{\bf q} d{\bf p} \cdot \textrm{exp} [ -\beta H_{eff} ] +$$ + +$$ + H_{eff} = \bigg(\sum_{i=1}^P \frac{p_i^2}{2m_i}\bigg) + V_{eff} +$$ + +$$ + V_{eff} = \sum_{i=1}^P \bigg[ \frac{mP}{2\beta^2 \hbar^2} (q_i - q_{i+1})^2 + \frac{1}{P} V(q_i)\bigg] +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_rattle_constraints.jpg b/doc/src/Eqs/fix_rattle_constraints.jpg new file mode 100644 index 0000000000..2ba86095cd Binary files /dev/null and b/doc/src/Eqs/fix_rattle_constraints.jpg differ diff --git a/doc/src/Eqs/fix_rattle_constraints.tex b/doc/src/Eqs/fix_rattle_constraints.tex new file mode 100644 index 0000000000..daff0ce775 --- /dev/null +++ b/doc/src/Eqs/fix_rattle_constraints.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} +\usepackage{amsmath} + +\begin{document} +\begin{align*} +\mathbf r^{n+1}_{ij} \cdot \mathbf r^{n+1}_{ij} &= d^2_{ij} \quad \text{and} \\ +\mathbf v^{n+1}_{ij} \cdot \mathbf r^{n+1}_{ij} &= 0, \label{eq:velcon} +\end{align*} +\end{document} diff --git a/doc/src/Eqs/fix_rattle_rij.jpg b/doc/src/Eqs/fix_rattle_rij.jpg new file mode 100644 index 0000000000..b08e2fe02e Binary files /dev/null and b/doc/src/Eqs/fix_rattle_rij.jpg differ diff --git a/doc/src/Eqs/fix_rattle_rij.tex b/doc/src/Eqs/fix_rattle_rij.tex new file mode 100644 index 0000000000..fae0457c60 --- /dev/null +++ b/doc/src/Eqs/fix_rattle_rij.tex @@ -0,0 +1,8 @@ +\documentclass[12pt]{article} +\usepackage{amsmath} +\begin{document} +$$ + \mathbf r^{n+1}_{ij} = \mathbf r^n_j - \mathbf r^n_i +$$ +\end{document} + diff --git a/doc/src/Eqs/fix_spring_rg.jpg b/doc/src/Eqs/fix_spring_rg.jpg new file mode 100644 index 0000000000..313844f555 Binary files /dev/null and b/doc/src/Eqs/fix_spring_rg.jpg differ diff --git a/doc/src/Eqs/fix_spring_rg.tex b/doc/src/Eqs/fix_spring_rg.tex new file mode 100644 index 0000000000..b772aaf652 --- /dev/null +++ b/doc/src/Eqs/fix_spring_rg.tex @@ -0,0 +1,19 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +{R_G}^2 = \frac{1}{M}\sum_{i}^{N}{m_{i}\left( x_{i} - +\frac{1}{M}\sum_{j}^{N}{m_{j}x_{j}} \right)^{2}} +$$ + +$$ + E = K\left( R_G - R_{G0} \right)^{2} +$$ + +$$ +F_{i} = 2K\frac{m_{i}}{M}\left( 1-\frac{R_{G0}}{R_G} +\right)\left( x_{i} - \frac{1}{M}\sum_{j}^{N}{m_{j}x_{j}} \right) +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/fix_ti_rs_force.jpg b/doc/src/Eqs/fix_ti_rs_force.jpg new file mode 100644 index 0000000000..a09bcb66c5 Binary files /dev/null and b/doc/src/Eqs/fix_ti_rs_force.jpg differ diff --git a/doc/src/Eqs/fix_ti_rs_force.tex b/doc/src/Eqs/fix_ti_rs_force.tex new file mode 100644 index 0000000000..849c0ccc97 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/fix_ti_rs_function_1.jpg b/doc/src/Eqs/fix_ti_rs_function_1.jpg new file mode 100644 index 0000000000..478dc5781d Binary files /dev/null and b/doc/src/Eqs/fix_ti_rs_function_1.jpg differ diff --git a/doc/src/Eqs/fix_ti_rs_function_1.tex b/doc/src/Eqs/fix_ti_rs_function_1.tex new file mode 100644 index 0000000000..033d8d7559 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/fix_ti_rs_function_2.jpg b/doc/src/Eqs/fix_ti_rs_function_2.jpg new file mode 100644 index 0000000000..4fbfe45c63 Binary files /dev/null and b/doc/src/Eqs/fix_ti_rs_function_2.jpg differ diff --git a/doc/src/Eqs/fix_ti_rs_function_2.tex b/doc/src/Eqs/fix_ti_rs_function_2.tex new file mode 100644 index 0000000000..a1dd377dcc --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/fix_ti_rs_function_3.jpg b/doc/src/Eqs/fix_ti_rs_function_3.jpg new file mode 100644 index 0000000000..94ab0f468c Binary files /dev/null and b/doc/src/Eqs/fix_ti_rs_function_3.jpg differ diff --git a/doc/src/Eqs/fix_ti_rs_function_3.tex b/doc/src/Eqs/fix_ti_rs_function_3.tex new file mode 100644 index 0000000000..2d2790fa97 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/fix_ti_spring_force.jpg b/doc/src/Eqs/fix_ti_spring_force.jpg new file mode 100644 index 0000000000..347102b3e7 Binary files /dev/null and b/doc/src/Eqs/fix_ti_spring_force.jpg differ diff --git a/doc/src/Eqs/fix_ti_spring_force.tex b/doc/src/Eqs/fix_ti_spring_force.tex new file mode 100644 index 0000000000..0acd0e54ae --- /dev/null +++ b/doc/src/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/src/Eqs/fix_ti_spring_function_1.jpg b/doc/src/Eqs/fix_ti_spring_function_1.jpg new file mode 100644 index 0000000000..8d3c9a78e3 Binary files /dev/null and b/doc/src/Eqs/fix_ti_spring_function_1.jpg differ diff --git a/doc/src/Eqs/fix_ti_spring_function_1.tex b/doc/src/Eqs/fix_ti_spring_function_1.tex new file mode 100644 index 0000000000..0673410b00 --- /dev/null +++ b/doc/src/Eqs/fix_ti_spring_function_1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + \lambda(\tau) = \tau +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_ti_spring_function_2.jpg b/doc/src/Eqs/fix_ti_spring_function_2.jpg new file mode 100644 index 0000000000..96a17e63e6 Binary files /dev/null and b/doc/src/Eqs/fix_ti_spring_function_2.jpg differ diff --git a/doc/src/Eqs/fix_ti_spring_function_2.tex b/doc/src/Eqs/fix_ti_spring_function_2.tex new file mode 100644 index 0000000000..f2cb51e47d --- /dev/null +++ b/doc/src/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/src/Eqs/fix_ttm.jpg b/doc/src/Eqs/fix_ttm.jpg new file mode 100644 index 0000000000..8d9fac3fed Binary files /dev/null and b/doc/src/Eqs/fix_ttm.jpg differ diff --git a/doc/src/Eqs/fix_ttm.tex b/doc/src/Eqs/fix_ttm.tex new file mode 100644 index 0000000000..d5a3238f82 --- /dev/null +++ b/doc/src/Eqs/fix_ttm.tex @@ -0,0 +1,15 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + C_e \rho_e \frac{\partial T_e}{\partial t} = + \bigtriangledown (\kappa_e \bigtriangledown T_e) - + g_p (T_e - T_a) + g_s T_a' +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_ttm_blast.jpg b/doc/src/Eqs/fix_ttm_blast.jpg new file mode 100644 index 0000000000..d4ffe05f12 Binary files /dev/null and b/doc/src/Eqs/fix_ttm_blast.jpg differ diff --git a/doc/src/Eqs/fix_ttm_blast.tex b/doc/src/Eqs/fix_ttm_blast.tex new file mode 100644 index 0000000000..6871ed5cc6 --- /dev/null +++ b/doc/src/Eqs/fix_ttm_blast.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + {\vec F}_i = - \partial U / \partial {\vec r}_i + {\vec F}_{langevin} - \nabla P_e/n_{ion} +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_ttm_blast1.jpg b/doc/src/Eqs/fix_ttm_blast1.jpg new file mode 100644 index 0000000000..1106c627cb Binary files /dev/null and b/doc/src/Eqs/fix_ttm_blast1.jpg differ diff --git a/doc/src/Eqs/fix_ttm_blast1.tex b/doc/src/Eqs/fix_ttm_blast1.tex new file mode 100644 index 0000000000..642afe4300 --- /dev/null +++ b/doc/src/Eqs/fix_ttm_blast1.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + \nabla_x P_e = \left[\frac{C_e{}T_e(x)\lambda}{(x+\lambda)^2} + \frac{x}{x+\lambda}\frac{(C_e{}T_e)_{x+\Delta x}-(C_e{}T_e)_{x}}{\Delta x} \right] +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_ttm_ce.jpg b/doc/src/Eqs/fix_ttm_ce.jpg new file mode 100644 index 0000000000..4f439e31e6 Binary files /dev/null and b/doc/src/Eqs/fix_ttm_ce.jpg differ diff --git a/doc/src/Eqs/fix_ttm_ce.tex b/doc/src/Eqs/fix_ttm_ce.tex new file mode 100644 index 0000000000..f787590b8f --- /dev/null +++ b/doc/src/Eqs/fix_ttm_ce.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + C_e = C_0 + (a_0 + a_1 X + a_2 X^2 + a_3 X^3 + a_4 X^4) \exp (-(AX)^2) +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_ttm_mod.jpg b/doc/src/Eqs/fix_ttm_mod.jpg new file mode 100644 index 0000000000..7cc67200f9 Binary files /dev/null and b/doc/src/Eqs/fix_ttm_mod.jpg differ diff --git a/doc/src/Eqs/fix_ttm_mod.tex b/doc/src/Eqs/fix_ttm_mod.tex new file mode 100644 index 0000000000..d0a313e676 --- /dev/null +++ b/doc/src/Eqs/fix_ttm_mod.tex @@ -0,0 +1,15 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + C_e \rho_e \frac{\partial T_e}{\partial t} = + \bigtriangledown (\kappa_e \bigtriangledown T_e) - + g_p (T_e - T_a) + g_s T_a' + \theta (x-x_{surface})I_0 \exp(-x/l_{skin}) +$$ + +\end{document} + + + + diff --git a/doc/src/Eqs/fix_wall_colloid.jpg b/doc/src/Eqs/fix_wall_colloid.jpg new file mode 100644 index 0000000000..8168d3a792 Binary files /dev/null and b/doc/src/Eqs/fix_wall_colloid.jpg differ diff --git a/doc/src/Eqs/fix_wall_colloid.tex b/doc/src/Eqs/fix_wall_colloid.tex new file mode 100644 index 0000000000..3ed716c263 --- /dev/null +++ b/doc/src/Eqs/fix_wall_colloid.tex @@ -0,0 +1,14 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray} +E &=& \epsilon \left[ \frac{\sigma^{6}}{7560} + \left(\frac{6R-D}{D^{7}} + \frac{D+8R}{(D+2R)^{7}} \right) - + \frac{}{} \right. \nonumber \\ + &&\qquad \left. \frac{1}{6} \left(\frac{2R(D+R) + D(D+2R) + \left[ \ln D - \ln (D+2R) \right]}{D(D+2R)} \right) \right] +\qquad r < r_c \nonumber +\end{eqnarray} + +\end{document} diff --git a/doc/src/Eqs/fix_wall_harmonic.jpg b/doc/src/Eqs/fix_wall_harmonic.jpg new file mode 100644 index 0000000000..3c605690c3 Binary files /dev/null and b/doc/src/Eqs/fix_wall_harmonic.jpg differ diff --git a/doc/src/Eqs/fix_wall_harmonic.tex b/doc/src/Eqs/fix_wall_harmonic.tex new file mode 100644 index 0000000000..86dcb80a0e --- /dev/null +++ b/doc/src/Eqs/fix_wall_harmonic.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = \epsilon \hspace{0.1cm} (r - r_c)^2 \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/fix_wall_lj1043.jpg b/doc/src/Eqs/fix_wall_lj1043.jpg new file mode 100644 index 0000000000..303743bf3e Binary files /dev/null and b/doc/src/Eqs/fix_wall_lj1043.jpg differ diff --git a/doc/src/Eqs/fix_wall_lj1043.tex b/doc/src/Eqs/fix_wall_lj1043.tex new file mode 100644 index 0000000000..06fc4dd33e --- /dev/null +++ b/doc/src/Eqs/fix_wall_lj1043.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = 2 \pi \epsilon \left[ \frac{2}{5} \left(\frac{\sigma}{r}\right)^{10} - + \left(\frac{\sigma}{r}\right)^4 - + \frac{\sqrt(2)\sigma^3}{3\left(r+\left(0.61/\sqrt(2)\right)\sigma\right)^3}\right] + \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/fix_wall_lj93.jpg b/doc/src/Eqs/fix_wall_lj93.jpg new file mode 100644 index 0000000000..18e502cfbf Binary files /dev/null and b/doc/src/Eqs/fix_wall_lj93.jpg differ diff --git a/doc/src/Eqs/fix_wall_lj93.tex b/doc/src/Eqs/fix_wall_lj93.tex new file mode 100644 index 0000000000..7372e55c15 --- /dev/null +++ b/doc/src/Eqs/fix_wall_lj93.tex @@ -0,0 +1,11 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = \epsilon \left[ \frac{2}{15} \left(\frac{\sigma}{r}\right)^{9} - + \left(\frac{\sigma}{r}\right)^3 \right] + \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/fld.jpg b/doc/src/Eqs/fld.jpg new file mode 100644 index 0000000000..3d80d436ff Binary files /dev/null and b/doc/src/Eqs/fld.jpg differ diff --git a/doc/src/Eqs/fld.tex b/doc/src/Eqs/fld.tex new file mode 100644 index 0000000000..7c75cfbe60 --- /dev/null +++ b/doc/src/Eqs/fld.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +F^{H} = -R_{FU}(U-U^{\infty}) + R_{FE}E^{\infty} +$$ + +\end{document} diff --git a/doc/src/Eqs/fld2.jpg b/doc/src/Eqs/fld2.jpg new file mode 100644 index 0000000000..42de943c90 Binary files /dev/null and b/doc/src/Eqs/fld2.jpg differ diff --git a/doc/src/Eqs/fld2.tex b/doc/src/Eqs/fld2.tex new file mode 100644 index 0000000000..43adae11db --- /dev/null +++ b/doc/src/Eqs/fld2.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +-R_{FU}(U-U^{\infty}) = -R_{FE}E^{\infty} - F^{rest} +$$ + +\end{document} diff --git a/doc/src/Eqs/heat_flux_J.jpg b/doc/src/Eqs/heat_flux_J.jpg new file mode 100644 index 0000000000..cf3e220caa Binary files /dev/null and b/doc/src/Eqs/heat_flux_J.jpg differ diff --git a/doc/src/Eqs/heat_flux_J.tex b/doc/src/Eqs/heat_flux_J.tex new file mode 100644 index 0000000000..53c0ff494a --- /dev/null +++ b/doc/src/Eqs/heat_flux_J.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\mathbf{J} & = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i - \sum_{i} \mathbf{S}_{i} \mathbf{v}_i \right] \\ +& = & \frac{1}{V} \left[ \sum_i e_i \mathbf{v}_i + \sum_{i r_{\rm out} \\ + E & = & C(r) \qquad \qquad \qquad r < r_{\rm in} \\ + & = & S(r) * C(r) \qquad \qquad r_{\rm in} < r < r_{\rm out} \\ + & = & 0 \qquad \qquad \qquad \qquad r > r_{\rm out} \\ + LJ(r) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] \\ + C(r) & = & \frac{C q_i q_j}{ \epsilon r} \\ + S(r) & = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2 + \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} + { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 } +\end{eqnarray*} + +\end{document} + + diff --git a/doc/src/Eqs/pair_class2.jpg b/doc/src/Eqs/pair_class2.jpg new file mode 100644 index 0000000000..abec072e79 Binary files /dev/null and b/doc/src/Eqs/pair_class2.jpg differ diff --git a/doc/src/Eqs/pair_class2.tex b/doc/src/Eqs/pair_class2.tex new file mode 100644 index 0000000000..e2acc00bb6 --- /dev/null +++ b/doc/src/Eqs/pair_class2.tex @@ -0,0 +1,11 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = \epsilon \left[ 2 \left(\frac{\sigma}{r}\right)^9 - + 3 \left(\frac{\sigma}{r}\right)^6 \right] + \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_cmm.jpg b/doc/src/Eqs/pair_cmm.jpg new file mode 100644 index 0000000000..1ec60f7305 Binary files /dev/null and b/doc/src/Eqs/pair_cmm.jpg differ diff --git a/doc/src/Eqs/pair_cmm.tex b/doc/src/Eqs/pair_cmm.tex new file mode 100644 index 0000000000..9bab1e9002 --- /dev/null +++ b/doc/src/Eqs/pair_cmm.tex @@ -0,0 +1,16 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E = & \frac{27}{4} \epsilon \left[ \left(\frac{\sigma}{r}\right)^{9} - + \left(\frac{\sigma}{r}\right)^6 \right] & + \qquad r < r_c \\ + E = & \frac{3\sqrt{3}}{2} \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^4 \right] & + \qquad r < r_c \\ + E = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] & + \qquad r < r_c +\end{eqnarray*} +\end{document} diff --git a/doc/src/Eqs/pair_colloid_cc.jpg b/doc/src/Eqs/pair_colloid_cc.jpg new file mode 100644 index 0000000000..a64094ddad Binary files /dev/null and b/doc/src/Eqs/pair_colloid_cc.jpg differ diff --git a/doc/src/Eqs/pair_colloid_cc.tex b/doc/src/Eqs/pair_colloid_cc.tex new file mode 100644 index 0000000000..e1485d325a --- /dev/null +++ b/doc/src/Eqs/pair_colloid_cc.tex @@ -0,0 +1,31 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray} +U_A &=& - \frac{A_{cc}}{6} \left[ + \frac{2 a_1 a_2}{r^2-\left(a_1+a_2\right)^2} + + \frac{2 a_1 a_2}{r^2 - \left(a_1 - a_2\right)^2} + + \mathrm{ln} + \left( + \frac{r^2-\left(a_1+a_2\right)^2}{r^2-\left(a_1-a_2\right)^2} + \right) + \right] \nonumber \\ +\nonumber \\ +U_R &=& \frac{A_{cc}}{37800} \frac{\sigma^6}{r} +\left[ \frac{}{} \right. \nonumber \\ + &&\qquad \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} + {\left(r-a_1-a_2\right)^7} \nonumber \\ + &&\qquad +\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)} + {\left(r+a_1+a_2\right)^7} \nonumber \\ + &&\qquad -\frac{r^2+7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)} + {\left(r+a_1-a_2\right)^7} \nonumber \\ + &&\qquad \left. -\frac{r^2-7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)} + {\left(r-a_1+a_2\right)^7} + \right] \nonumber \\ +\nonumber \\ +U &=& U_A + U_R, \qquad r < r_c \nonumber +\end{eqnarray} + +\end{document} + diff --git a/doc/src/Eqs/pair_colloid_cs.jpg b/doc/src/Eqs/pair_colloid_cs.jpg new file mode 100644 index 0000000000..8f5948fa54 Binary files /dev/null and b/doc/src/Eqs/pair_colloid_cs.jpg differ diff --git a/doc/src/Eqs/pair_colloid_cs.tex b/doc/src/Eqs/pair_colloid_cs.tex new file mode 100644 index 0000000000..760215ee08 --- /dev/null +++ b/doc/src/Eqs/pair_colloid_cs.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray} + U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A_{cs}}{9 \left( a^2 - r^2 \right)^3} + \left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6} + {15 \left(a-r\right)^6 \left( a+r \right)^6} \right], ~~ r < r_c \nonumber +\end{eqnarray} + +\end{document} + diff --git a/doc/src/Eqs/pair_colloid_ss.jpg b/doc/src/Eqs/pair_colloid_ss.jpg new file mode 100644 index 0000000000..4ce19ba1e8 Binary files /dev/null and b/doc/src/Eqs/pair_colloid_ss.jpg differ diff --git a/doc/src/Eqs/pair_colloid_ss.tex b/doc/src/Eqs/pair_colloid_ss.tex new file mode 100644 index 0000000000..1cc511ed06 --- /dev/null +++ b/doc/src/Eqs/pair_colloid_ss.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray} + U &=& \frac{A_{ss}}{36} \left[ \left( \frac{\sigma}{r} + \right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], ~~ + r < r_c \nonumber +\end{eqnarray} + +\end{document} + diff --git a/doc/src/Eqs/pair_comb1.jpg b/doc/src/Eqs/pair_comb1.jpg new file mode 100644 index 0000000000..e0711ca972 Binary files /dev/null and b/doc/src/Eqs/pair_comb1.jpg differ diff --git a/doc/src/Eqs/pair_comb1.tex b/doc/src/Eqs/pair_comb1.tex new file mode 100644 index 0000000000..82c6be056e --- /dev/null +++ b/doc/src/Eqs/pair_comb1.tex @@ -0,0 +1,7 @@ +\documentclass[12pt]{article} +\begin{document} \large +\begin{eqnarray*} +E_T & = & \sum_i [ E_i^{self} (q_i) + \sum_{j>i} [E_{ij}^{short} (r_{ij}, q_i, q_j) + E_{ij}^{Coul} (r_{ij}, q_i, q_j)] + \\ +&& E^{polar} (q_i, r_{ij}) + E^{vdW} (r_{ij}) + E^{barr} (q_i) + E^{corr} (r_{ij}, \theta_{jik})] \\ +\end{eqnarray*} +\end{document} diff --git a/doc/src/Eqs/pair_comb2.jpg b/doc/src/Eqs/pair_comb2.jpg new file mode 100644 index 0000000000..8b0e5ba51a Binary files /dev/null and b/doc/src/Eqs/pair_comb2.jpg differ diff --git a/doc/src/Eqs/pair_comb2.tex b/doc/src/Eqs/pair_comb2.tex new file mode 100644 index 0000000000..3ba72f0726 --- /dev/null +++ b/doc/src/Eqs/pair_comb2.tex @@ -0,0 +1,23 @@ +\documentclass[10pt]{article} + +\begin{document} + +\begin{table}[h] +\begin{tabular}{|c|c|c|c|c|c|c|c|c|} +\hline + & $O$ & $Cu$ & $N$ & $C$ & $H$ & $Ti$ & $Zn$ & $Zr$ \\ \hline +$O$ & F & F & F & F & F & F & F & F\\ \hline +$Cu$ & F & F & P & F & F & P & F & P \\ \hline +$N$ & F & P & F & M & F & P & P & P \\ \hline +$C$ & F & F & M & F & F & M & M & M \\ \hline +$H$ & F & F & F & F & F & M & M & F \\ \hline +$Ti$ & F & P & P & M & M & F & P & P \\ \hline +$Zn$ & F & F & P & M & M & P & F & P \\ \hline +$Zr$ & F & P & P & M & F & P & P & F \\ \hline +\multicolumn{9}{l}{F: Fully optimized} \\ +\multicolumn{9}{l}{M: Only optimized for dimer molecule} \\ +\multicolumn{9}{l}{P: in Progress but have it from mixing rule} \\ +\end{tabular} +\end{table} + +\end{document} diff --git a/doc/src/Eqs/pair_coul_diel.jpg b/doc/src/Eqs/pair_coul_diel.jpg new file mode 100644 index 0000000000..70cb84f7a5 Binary files /dev/null and b/doc/src/Eqs/pair_coul_diel.jpg differ diff --git a/doc/src/Eqs/pair_coul_diel.tex b/doc/src/Eqs/pair_coul_diel.tex new file mode 100644 index 0000000000..f0b893d887 --- /dev/null +++ b/doc/src/Eqs/pair_coul_diel.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} +\pagestyle{empty} +\begin{document} + +\begin{eqnarray*} + E & = & \frac{Cq_iq_j}{\epsilon r} \left( \frac{\epsilon}{\epsilon_D(r)}-1\right) \qquad r < r_c \\ + \epsilon_D(r) & = & \frac{5.2+\epsilon}{2} + \frac{\epsilon-5.2}{2}\tanh\left(\frac{r-r_{me}}{\sigma_e}\right) +\end{eqnarray*} +\end{document} diff --git a/doc/src/Eqs/pair_coul_dsf.jpg b/doc/src/Eqs/pair_coul_dsf.jpg new file mode 100644 index 0000000000..a891b3ad15 Binary files /dev/null and b/doc/src/Eqs/pair_coul_dsf.jpg differ diff --git a/doc/src/Eqs/pair_coul_dsf.tex b/doc/src/Eqs/pair_coul_dsf.tex new file mode 100644 index 0000000000..ec69680fc8 --- /dev/null +++ b/doc/src/Eqs/pair_coul_dsf.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} +$$ + E = + q_iq_j \left[ \frac{\mbox{erfc} (\alpha r)}{r} - \frac{\mbox{erfc} (\alpha r_c)}{r_c} + + \left( \frac{\mbox{erfc} (\alpha r_c)}{r_c^2} + \frac{2\alpha}{\sqrt{\pi}}\frac{\exp (-\alpha^2 r^2_c)}{r_c} \right)(r-r_c) \right] \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_coul_soft.jpg b/doc/src/Eqs/pair_coul_soft.jpg new file mode 100644 index 0000000000..dad9c745ba Binary files /dev/null and b/doc/src/Eqs/pair_coul_soft.jpg differ diff --git a/doc/src/Eqs/pair_coul_soft.tex b/doc/src/Eqs/pair_coul_soft.tex new file mode 100644 index 0000000000..2ff42a25b6 --- /dev/null +++ b/doc/src/Eqs/pair_coul_soft.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ +E = \lambda^n \frac{ C q_i q_j}{\epsilon +\left[ \alpha_{\mathrm{C}} (1-\lambda)^2 + r^2 \right]^{1/2}} \qquad r < r_c +\] + +\end{document} diff --git a/doc/src/Eqs/pair_coul_wolf.jpg b/doc/src/Eqs/pair_coul_wolf.jpg new file mode 100644 index 0000000000..fd64cb6c03 Binary files /dev/null and b/doc/src/Eqs/pair_coul_wolf.jpg differ diff --git a/doc/src/Eqs/pair_coul_wolf.tex b/doc/src/Eqs/pair_coul_wolf.tex new file mode 100644 index 0000000000..4a6592638f --- /dev/null +++ b/doc/src/Eqs/pair_coul_wolf.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} +$$ + E_i = \frac{1}{2} \sum_{j \neq i} + \frac{q_i q_j {\rm erfc}(\alpha r_{ij})}{r_{ij}} + + \frac{1}{2} \sum_{j \neq i} + \frac{q_i q_j {\rm erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_coulomb.jpg b/doc/src/Eqs/pair_coulomb.jpg new file mode 100644 index 0000000000..39aaebac31 Binary files /dev/null and b/doc/src/Eqs/pair_coulomb.jpg differ diff --git a/doc/src/Eqs/pair_coulomb.tex b/doc/src/Eqs/pair_coulomb.tex new file mode 100644 index 0000000000..9dacdc1af3 --- /dev/null +++ b/doc/src/Eqs/pair_coulomb.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \frac{C q_i q_j}{\epsilon r} \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_cs.jpg b/doc/src/Eqs/pair_cs.jpg new file mode 100644 index 0000000000..b870a3bdf4 Binary files /dev/null and b/doc/src/Eqs/pair_cs.jpg differ diff --git a/doc/src/Eqs/pair_cs.tex b/doc/src/Eqs/pair_cs.tex new file mode 100644 index 0000000000..b7eacb8d5b --- /dev/null +++ b/doc/src/Eqs/pair_cs.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = \frac{C q_i q_j}{\epsilon (r + r_{min})} \qquad r \rightarrow 0 +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_debye.jpg b/doc/src/Eqs/pair_debye.jpg new file mode 100644 index 0000000000..42bcb5cc63 Binary files /dev/null and b/doc/src/Eqs/pair_debye.jpg differ diff --git a/doc/src/Eqs/pair_debye.tex b/doc/src/Eqs/pair_debye.tex new file mode 100644 index 0000000000..392a6516ce --- /dev/null +++ b/doc/src/Eqs/pair_debye.tex @@ -0,0 +1,8 @@ +\documentclass[12pt]{article} + +\begin{document} +$$ + E = \frac{C q_i q_j}{\epsilon r} \exp(- \kappa r) \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_dipole.jpg b/doc/src/Eqs/pair_dipole.jpg new file mode 100644 index 0000000000..e106c17c91 Binary files /dev/null and b/doc/src/Eqs/pair_dipole.jpg differ diff --git a/doc/src/Eqs/pair_dipole.tex b/doc/src/Eqs/pair_dipole.tex new file mode 100644 index 0000000000..bc0ae82f80 --- /dev/null +++ b/doc/src/Eqs/pair_dipole.tex @@ -0,0 +1,38 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] \\ +E_{qq} & = & \frac{q_i q_j}{r} \\ +E_{qp} & = & \frac{q}{r^3} (p \bullet \vec{r}) \\ +E_{pp} & = & \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}) +\end{eqnarray*} + +\begin{eqnarray*} +F_{qq} & = & \frac{q_i q_j}{r^3} \vec{r} \\ +F_{qp} & = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5} + (\vec{p} \bullet \vec{r}) \vec{r} \\ +F_{pp} & = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} - + \frac{15}{r^7} (\vec{p_i} \bullet \vec{r}) + (\vec{p_j} \bullet \vec{r}) \vec{r} + + \frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + + (\vec{p_i} \bullet \vec{r}) \vec{p_j} \right] +\end{eqnarray*} + +\begin{eqnarray*} +T_{pq} = T_{ij} & = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\ +T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\ +T_{pp} = T_{ij} & = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) + + \frac{3}{r^5} (\vec{p_j} \bullet \vec{r}) + (\vec{p_i} \times \vec{r}) \\ +T_{pp} = T_{ji} & = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) + + \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) + (\vec{p_j} \times \vec{r}) \\ +\end{eqnarray*} + +\end{document} + + diff --git a/doc/src/Eqs/pair_dipole_sf.jpg b/doc/src/Eqs/pair_dipole_sf.jpg new file mode 100644 index 0000000000..c591534550 Binary files /dev/null and b/doc/src/Eqs/pair_dipole_sf.jpg differ diff --git a/doc/src/Eqs/pair_dipole_sf.tex b/doc/src/Eqs/pair_dipole_sf.tex new file mode 100644 index 0000000000..c653a37740 --- /dev/null +++ b/doc/src/Eqs/pair_dipole_sf.tex @@ -0,0 +1,51 @@ +\documentclass[12pt]{article} + +\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_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_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} + diff --git a/doc/src/Eqs/pair_dipole_sf2.jpg b/doc/src/Eqs/pair_dipole_sf2.jpg new file mode 100644 index 0000000000..b9e57becf6 Binary files /dev/null and b/doc/src/Eqs/pair_dipole_sf2.jpg differ diff --git a/doc/src/Eqs/pair_dipole_sf2.tex b/doc/src/Eqs/pair_dipole_sf2.tex new file mode 100644 index 0000000000..74758ba230 --- /dev/null +++ b/doc/src/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} diff --git a/doc/src/Eqs/pair_dpd.jpg b/doc/src/Eqs/pair_dpd.jpg new file mode 100644 index 0000000000..e9bb8a69af Binary files /dev/null and b/doc/src/Eqs/pair_dpd.jpg differ diff --git a/doc/src/Eqs/pair_dpd.tex b/doc/src/Eqs/pair_dpd.tex new file mode 100644 index 0000000000..ba47f0d6b6 --- /dev/null +++ b/doc/src/Eqs/pair_dpd.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + \vec{f} & = & (F^C + F^D + F^R) \hat{r_{ij}} \qquad \qquad r < r_c \\ + F^C & = & A w(r) \\ + F^D & = & - \gamma w^2(r) (\hat{r_{ij}} \bullet \vec{v_{ij}}) \\ + F^R & = & \sigma w(r) \alpha (\Delta t)^{-1/2} \\ + w(r) & = & 1 - r/r_c +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_dpd_conservative.jpg b/doc/src/Eqs/pair_dpd_conservative.jpg new file mode 100644 index 0000000000..aa0006caa2 Binary files /dev/null and b/doc/src/Eqs/pair_dpd_conservative.jpg differ diff --git a/doc/src/Eqs/pair_dpd_conservative.tex b/doc/src/Eqs/pair_dpd_conservative.tex new file mode 100644 index 0000000000..db89b987aa --- /dev/null +++ b/doc/src/Eqs/pair_dpd_conservative.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} +\pagestyle{empty} +\begin{document} + +$$ +F^C = A \omega_{ij} \qquad \qquad r_{ij} < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_dpd_omega.jpg b/doc/src/Eqs/pair_dpd_omega.jpg new file mode 100644 index 0000000000..fd25f00f19 Binary files /dev/null and b/doc/src/Eqs/pair_dpd_omega.jpg differ diff --git a/doc/src/Eqs/pair_dpd_omega.tex b/doc/src/Eqs/pair_dpd_omega.tex new file mode 100644 index 0000000000..fbd533abfa --- /dev/null +++ b/doc/src/Eqs/pair_dpd_omega.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} +\pagestyle{empty} +\begin{document} + +$$ + \omega_{ij} = 1 - \frac{r_{ij}}{r_{c}} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_eam.jpg b/doc/src/Eqs/pair_eam.jpg new file mode 100644 index 0000000000..95c86b4ced Binary files /dev/null and b/doc/src/Eqs/pair_eam.jpg differ diff --git a/doc/src/Eqs/pair_eam.tex b/doc/src/Eqs/pair_eam.tex new file mode 100644 index 0000000000..2ea20b2198 --- /dev/null +++ b/doc/src/Eqs/pair_eam.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E_i = F_\alpha \left(\sum_{j \neq i}\ \rho_\beta (r_{ij})\right) + + \frac{1}{2} \sum_{j \neq i} \phi_{\alpha\beta} (r_{ij}) +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_eam_fs.jpg b/doc/src/Eqs/pair_eam_fs.jpg new file mode 100644 index 0000000000..fa72f8fc73 Binary files /dev/null and b/doc/src/Eqs/pair_eam_fs.jpg differ diff --git a/doc/src/Eqs/pair_eam_fs.tex b/doc/src/Eqs/pair_eam_fs.tex new file mode 100644 index 0000000000..32ca605e2e --- /dev/null +++ b/doc/src/Eqs/pair_eam_fs.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E_i = F_\alpha \left(\sum_{j \neq i}\ + \rho_{\alpha\beta} (r_{ij})\right) + + \frac{1}{2} \sum_{j \neq i} \phi_{\alpha\beta} (r_{ij}) +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_edip.jpg b/doc/src/Eqs/pair_edip.jpg new file mode 100644 index 0000000000..3933280480 Binary files /dev/null and b/doc/src/Eqs/pair_edip.jpg differ diff --git a/doc/src/Eqs/pair_edip.tex b/doc/src/Eqs/pair_edip.tex new file mode 100644 index 0000000000..27f5dd9eec --- /dev/null +++ b/doc/src/Eqs/pair_edip.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{article} + +\usepackage{amssymb,amsmath} + +\begin{document} + +\begin{eqnarray*} +E & = & \sum_{j \ne i} \phi_{2}(R_{ij}, Z_{i}) + \sum_{j \ne i} \sum_{k \ne i,k > j} \phi_{3}(R_{ij}, R_{ik}, Z_{i}) \\ +\phi_{2}(r, Z) & = & A\left[\left(\frac{B}{r}\right)^{\rho} - e^{-\beta Z^2}\right]exp{\left(\frac{\sigma}{r-a}\right)} \\ +\phi_{3}(R_{ij}, R_{ik}, Z_i) & = & exp{\left(\frac{\gamma}{R_{ij}-a}\right)}exp{\left(\frac{\gamma}{R_{ik}-a}\right)}h(cos\theta_{ijk},Z_i) \\ +Z_i & = & \sum_{m \ne i} f(R_{im}) \qquad + f(r) = \begin{cases} + 1 & \quad ra + \end{cases} \\ +h(l,Z) & = & \lambda [(1-e^{-Q(Z)(l+\tau(Z))^2}) + \eta Q(Z)(l+\tau(Z))^2 ] \\ +Q(Z) & = & Q_0 e^{-\mu Z} \qquad \tau(Z) = u_1 + u_2 (u_3 e^{-u_4 Z} - e^{-2u_4 Z}) +\end{eqnarray*} + +\end{document} + diff --git a/doc/src/Eqs/pair_eim1.jpg b/doc/src/Eqs/pair_eim1.jpg new file mode 100644 index 0000000000..c243120b2a Binary files /dev/null and b/doc/src/Eqs/pair_eim1.jpg differ diff --git a/doc/src/Eqs/pair_eim1.tex b/doc/src/Eqs/pair_eim1.tex new file mode 100644 index 0000000000..bfa5b6ebc4 --- /dev/null +++ b/doc/src/Eqs/pair_eim1.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ +E = \frac{1}{2} \sum_{i=1}^{N} \sum_{j=i_1}^{i_N} \phi_{ij} \left(r_{ij}\right) + \sum_{i=1}^{N}E_i\left(q_i,\sigma_i\right) +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_eim2.jpg b/doc/src/Eqs/pair_eim2.jpg new file mode 100644 index 0000000000..4896f658f1 Binary files /dev/null and b/doc/src/Eqs/pair_eim2.jpg differ diff --git a/doc/src/Eqs/pair_eim2.tex b/doc/src/Eqs/pair_eim2.tex new file mode 100644 index 0000000000..d8c4181342 --- /dev/null +++ b/doc/src/Eqs/pair_eim2.tex @@ -0,0 +1,11 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +q_i & = & \sum_{j=i_1}^{i_N} \eta_{ji}\left(r_{ij}\right) \\ +\sigma_i & = & \sum_{j=i_1}^{i_N} q_j \cdot \psi_{ij} \left(r_{ij}\right) \\ +E_i\left(q_i,\sigma_i\right) & = & \frac{1}{2} \cdot q_i \cdot \sigma_i +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_eim3.jpg b/doc/src/Eqs/pair_eim3.jpg new file mode 100644 index 0000000000..57366bc15d Binary files /dev/null and b/doc/src/Eqs/pair_eim3.jpg differ diff --git a/doc/src/Eqs/pair_eim3.tex b/doc/src/Eqs/pair_eim3.tex new file mode 100644 index 0000000000..84343c6acf --- /dev/null +++ b/doc/src/Eqs/pair_eim3.tex @@ -0,0 +1,25 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\phi_{ij}\left(r\right) = \left\{ \begin{array}{lr} +\left[\frac{E_{b,ij}\beta_{ij}}{\beta_{ij}-\alpha_{ij}}\exp\left(-\alpha_{ij} \frac{r-r_{e,ij}}{r_{e,ij}}\right)-\frac{E_{b,ij}\alpha_{ij}}{\beta_{ij}-\alpha_{ij}}\exp\left(-\beta_{ij} \frac{r-r_{e,ij}}{r_{e,ij}}\right)\right]f_c\left(r,r_{e,ij},r_{c,\phi,ij}\right),& p_{ij}=1 \\ +\left[\frac{E_{b,ij}\beta_{ij}}{\beta_{ij}-\alpha_{ij}} \left(\frac{r_{e,ij}}{r}\right)^{\alpha_{ij}} -\frac{E_{b,ij}\alpha_{ij}}{\beta_{ij}-\alpha_{ij}} \left(\frac{r_{e,ij}}{r}\right)^{\beta_{ij}}\right]f_c\left(r,r_{e,ij},r_{c,\phi,ij}\right),& p_{ij}=2 +\end{array} +\right. +\end{eqnarray*} + +$$ +\eta_{ji} = A_{\eta,ij}\left(\chi_j-\chi_i\right)f_c\left(r,r_{s,\eta,ij},r_{c,\eta,ij}\right) +$$ + +$$ +\psi_{ij}\left(r\right) = A_{\psi,ij}\exp\left(-\zeta_{ij}r\right)f_c\left(r,r_{s,\psi,ij},r_{c,\psi,ij}\right) +$$ + +$$ +f_{c}\left(r,r_p,r_c\right) = 0.510204 erfc\left[\frac{1.64498\left(2r-r_p-r_c\right)}{r_c-r_p}\right] - 0.010204 +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_gauss.jpg b/doc/src/Eqs/pair_gauss.jpg new file mode 100644 index 0000000000..97c2f0ecb2 Binary files /dev/null and b/doc/src/Eqs/pair_gauss.jpg differ diff --git a/doc/src/Eqs/pair_gauss.tex b/doc/src/Eqs/pair_gauss.tex new file mode 100644 index 0000000000..ed38e13943 --- /dev/null +++ b/doc/src/Eqs/pair_gauss.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} +\pagestyle{empty} +\begin{document} + +$$ + E = - A \exp(-B r^2) \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_gauss_cut.jpg b/doc/src/Eqs/pair_gauss_cut.jpg new file mode 100644 index 0000000000..e47bb8cc06 Binary files /dev/null and b/doc/src/Eqs/pair_gauss_cut.jpg differ diff --git a/doc/src/Eqs/pair_gauss_cut.tex b/doc/src/Eqs/pair_gauss_cut.tex new file mode 100644 index 0000000000..5d0bb430f3 --- /dev/null +++ b/doc/src/Eqs/pair_gauss_cut.tex @@ -0,0 +1,8 @@ +\documentclass[12pt]{article} +\pagestyle{empty} +\begin{document} + +\begin{eqnarray*} + E = & \frac{H}{\sigma_h\sqrt{2\pi}} \exp\left[-\frac{(r-r_{mh})^2}{2\sigma_h^2}\right] +\end{eqnarray*} +\end{document} diff --git a/doc/src/Eqs/pair_gayberne.jpg b/doc/src/Eqs/pair_gayberne.jpg new file mode 100644 index 0000000000..e9b1f3ca93 Binary files /dev/null and b/doc/src/Eqs/pair_gayberne.jpg differ diff --git a/doc/src/Eqs/pair_gayberne.tex b/doc/src/Eqs/pair_gayberne.tex new file mode 100644 index 0000000000..d3c199e826 --- /dev/null +++ b/doc/src/Eqs/pair_gayberne.tex @@ -0,0 +1,14 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ U ( \mathbf{A}_1, \mathbf{A}_2, \mathbf{r}_{12} ) = U_r ( +\mathbf{A}_1, \mathbf{A}_2, \mathbf{r}_{12}, \gamma ) \cdot \eta_{12} ( +\mathbf{A}_1, \mathbf{A}_2, \upsilon ) \cdot \chi_{12} ( \mathbf{A}_1, +\mathbf{A}_2, \mathbf{r}_{12}, \mu ) $$ + +$$ U_r = 4 \epsilon ( \varrho^{12} - \varrho^6) $$ + +$$ \varrho = \frac{\sigma}{ h_{12} + \gamma \sigma} $$ + +\end{document} diff --git a/doc/src/Eqs/pair_gayberne2.jpg b/doc/src/Eqs/pair_gayberne2.jpg new file mode 100644 index 0000000000..a4e6c6f70f Binary files /dev/null and b/doc/src/Eqs/pair_gayberne2.jpg differ diff --git a/doc/src/Eqs/pair_gayberne2.tex b/doc/src/Eqs/pair_gayberne2.tex new file mode 100644 index 0000000000..6efb755774 --- /dev/null +++ b/doc/src/Eqs/pair_gayberne2.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ \epsilon_a = \sigma \cdot { \frac{a}{ b \cdot c } }; \epsilon_b = +\sigma \cdot { \frac{b}{ a \cdot c } }; \epsilon_c = \sigma \cdot { +\frac{c}{ a \cdot b } } $$ + +\end{document} diff --git a/doc/src/Eqs/pair_gran_hertz.jpg b/doc/src/Eqs/pair_gran_hertz.jpg new file mode 100644 index 0000000000..733875fee6 Binary files /dev/null and b/doc/src/Eqs/pair_gran_hertz.jpg differ diff --git a/doc/src/Eqs/pair_gran_hertz.tex b/doc/src/Eqs/pair_gran_hertz.tex new file mode 100644 index 0000000000..d6e09493b2 --- /dev/null +++ b/doc/src/Eqs/pair_gran_hertz.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + F_{hz} = \sqrt{\delta} \sqrt{\frac{R_i R_j}{R_i + R_j}} F_{hk} = + \sqrt{\delta} \sqrt{\frac{R_i R_j}{R_i + R_j}} + \Big[ (k_n \delta \mathbf{n}_{ij} - + m_{\mbox{\scriptsize{eff}}} \: \gamma_n \mathbf{ v}_n) - + (k_t \mathbf{ \Delta s}_t + + m_{\mbox{\scriptsize{eff}}} \: \gamma_t \mathbf{v}_t) \Big] +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_gran_hooke.jpg b/doc/src/Eqs/pair_gran_hooke.jpg new file mode 100644 index 0000000000..36f34db6c6 Binary files /dev/null and b/doc/src/Eqs/pair_gran_hooke.jpg differ diff --git a/doc/src/Eqs/pair_gran_hooke.tex b/doc/src/Eqs/pair_gran_hooke.tex new file mode 100644 index 0000000000..e1901e66a3 --- /dev/null +++ b/doc/src/Eqs/pair_gran_hooke.tex @@ -0,0 +1,12 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + F_{hk} = (k_n \delta \mathbf{n}_{ij} - + m_{\mbox{\scriptsize{eff}}} \gamma_n\mathbf{ v}_n) - + (k_t \mathbf{ \Delta s}_t + + m_{\mbox{\scriptsize{eff}}} \gamma_t \mathbf{v}_t) +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_gromacs.jpg b/doc/src/Eqs/pair_gromacs.jpg new file mode 100644 index 0000000000..885c059e65 Binary files /dev/null and b/doc/src/Eqs/pair_gromacs.jpg differ diff --git a/doc/src/Eqs/pair_gromacs.tex b/doc/src/Eqs/pair_gromacs.tex new file mode 100644 index 0000000000..88dbe15909 --- /dev/null +++ b/doc/src/Eqs/pair_gromacs.tex @@ -0,0 +1,17 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] + S_{LJ}(r) + \qquad r < r_c \\ +E_C & = & \frac{C q_i q_j}{\epsilon r} + S_C(r) \qquad r < r_c \\ +S(r) & = & C \qquad r < r_1 \\ +S(r) & = & \frac{A}{3} (r - r_1)^3 + \frac{B}{4} (r - r_1)^4 + C \qquad r_1 < r < r_c \\ +A & = & (-3 E'(r_c) + (r_c - r_1) E''(r_c))/(r_c - r_1)^2 \\ +B & = & (2 E'(r_c) - (r_c - r_1) E''(r_c))/(r_c - r_1)^3 \\ +C & = & -E(r_c) + \frac{1}{2} (r_c - r_1) E'(r_c) - \frac{1}{12} (r_c - r_1)^2 E''(r_c)) \\ +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_hbond_dreiding.jpg b/doc/src/Eqs/pair_hbond_dreiding.jpg new file mode 100644 index 0000000000..b93044ed31 Binary files /dev/null and b/doc/src/Eqs/pair_hbond_dreiding.jpg differ diff --git a/doc/src/Eqs/pair_hbond_dreiding.tex b/doc/src/Eqs/pair_hbond_dreiding.tex new file mode 100644 index 0000000000..9663ee5608 --- /dev/null +++ b/doc/src/Eqs/pair_hbond_dreiding.tex @@ -0,0 +1,18 @@ +\documentstyle[12pt]{article} + +\begin{document} +\begin{eqnarray*} + E & = & \left[LJ(r) | Morse(r) \right] \qquad \qquad \qquad r < r_{\rm in} \\ + & = & S(r) * \left[LJ(r) | Morse(r) \right] \qquad \qquad r_{\rm in} < r < r_{\rm out} \\ + & = & 0 \qquad \qquad \qquad \qquad \qquad \qquad \qquad r > r_{\rm out} \\ + LJ(r) & = & AR^{-12}-BR^{-10}cos^n\theta= + \epsilon\left\lbrace 5\left[ \frac{\sigma}{r}\right]^{12}- + 6\left[ \frac{\sigma}{r}\right]^{10} \right\rbrace cos^n\theta\\ + Morse(r) & = & D_0\left\lbrace \chi^2 - 2\chi\right\rbrace cos^n\theta= + D_{0}\left\lbrace e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} + \right\rbrace cos^n\theta \\ + S(r) & = & \frac{ \left[r_{\rm out}^2 - r^2\right]^2 + \left[r_{\rm out}^2 + 2r^2 - 3{r_{\rm in}^2}\right]} + { \left[r_{\rm out}^2 - {r_{\rm in}}^2\right]^3 } +\end{eqnarray*} +\end{document} diff --git a/doc/src/Eqs/pair_lj.jpg b/doc/src/Eqs/pair_lj.jpg new file mode 100644 index 0000000000..49cf7f5eb9 Binary files /dev/null and b/doc/src/Eqs/pair_lj.jpg differ diff --git a/doc/src/Eqs/pair_lj.tex b/doc/src/Eqs/pair_lj.tex new file mode 100644 index 0000000000..011fb8b769 --- /dev/null +++ b/doc/src/Eqs/pair_lj.tex @@ -0,0 +1,11 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] + \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_lj96.jpg b/doc/src/Eqs/pair_lj96.jpg new file mode 100644 index 0000000000..6462de180e Binary files /dev/null and b/doc/src/Eqs/pair_lj96.jpg differ diff --git a/doc/src/Eqs/pair_lj96.tex b/doc/src/Eqs/pair_lj96.tex new file mode 100644 index 0000000000..e970624892 --- /dev/null +++ b/doc/src/Eqs/pair_lj96.tex @@ -0,0 +1,11 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{9} - + \left(\frac{\sigma}{r}\right)^6 \right] + \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_lj_cubic.jpg b/doc/src/Eqs/pair_lj_cubic.jpg new file mode 100644 index 0000000000..69ec4f6e84 Binary files /dev/null and b/doc/src/Eqs/pair_lj_cubic.jpg differ diff --git a/doc/src/Eqs/pair_lj_cubic.tex b/doc/src/Eqs/pair_lj_cubic.tex new file mode 100644 index 0000000000..e2e1b67dd7 --- /dev/null +++ b/doc/src/Eqs/pair_lj_cubic.tex @@ -0,0 +1,12 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E &=& u_{LJ}(r) \qquad r \leq r_s \\ + &=& u_{LJ}(r_s) + (r-r_s) u'_{LJ}(r_s) - \frac{1}{6} A_3 (r-r_s)^3 \qquad r_s < r \leq r_c \\ + &=& 0 \qquad r > r_c +\end{eqnarray*} + + +\end{document} diff --git a/doc/src/Eqs/pair_lj_expand.jpg b/doc/src/Eqs/pair_lj_expand.jpg new file mode 100644 index 0000000000..e274818892 Binary files /dev/null and b/doc/src/Eqs/pair_lj_expand.jpg differ diff --git a/doc/src/Eqs/pair_lj_expand.tex b/doc/src/Eqs/pair_lj_expand.tex new file mode 100644 index 0000000000..0aaa2f44d8 --- /dev/null +++ b/doc/src/Eqs/pair_lj_expand.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = 4 \epsilon \left[ \left(\frac{\sigma}{r - \Delta}\right)^{12} - + \left(\frac{\sigma}{r - \Delta}\right)^6 \right] + \qquad r < r_c + \Delta +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_lj_sf.jpg b/doc/src/Eqs/pair_lj_sf.jpg new file mode 100644 index 0000000000..a702240003 Binary files /dev/null and b/doc/src/Eqs/pair_lj_sf.jpg differ diff --git a/doc/src/Eqs/pair_lj_sf.tex b/doc/src/Eqs/pair_lj_sf.tex new file mode 100644 index 0000000000..e78e2ca75f --- /dev/null +++ b/doc/src/Eqs/pair_lj_sf.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + F & = & F_{\mathrm{LJ}}(r) - F_{\mathrm{LJ}}(r_{\mathrm{c}}) \qquad r < r_{\mathrm{c}} \\ + E & = & E_{\mathrm{LJ}}(r) - E_{\mathrm{LJ}}(r_{\mathrm{c}}) + (r - r_{\mathrm{c}}) F_{\mathrm{LJ}}(r_{\mathrm{c}}) \qquad r < r_{\mathrm{c}} \\ + \mathrm{with} \qquad E_{\mathrm{LJ}}(r) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] \qquad \mathrm{and} \qquad F_{\mathrm{LJ}}(r) = - E^\prime_{\mathrm{LJ}}(r) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_lj_smooth.jpg b/doc/src/Eqs/pair_lj_smooth.jpg new file mode 100644 index 0000000000..d380fd345c Binary files /dev/null and b/doc/src/Eqs/pair_lj_smooth.jpg differ diff --git a/doc/src/Eqs/pair_lj_smooth.tex b/doc/src/Eqs/pair_lj_smooth.tex new file mode 100644 index 0000000000..5aa5495c27 --- /dev/null +++ b/doc/src/Eqs/pair_lj_smooth.tex @@ -0,0 +1,15 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] + \qquad r < r_{in} \\ + F & = & C_1 + C_2 (r - r_{in}) + C_3 (r - r_{in})^2 + C_4 (r - r_{in})^3 + \qquad r_{in} < r < r_c +\end{eqnarray*} + +\end{document} + + diff --git a/doc/src/Eqs/pair_lj_smooth_linear.jpg b/doc/src/Eqs/pair_lj_smooth_linear.jpg new file mode 100644 index 0000000000..b0626abae1 Binary files /dev/null and b/doc/src/Eqs/pair_lj_smooth_linear.jpg differ diff --git a/doc/src/Eqs/pair_lj_smooth_linear.tex b/doc/src/Eqs/pair_lj_smooth_linear.tex new file mode 100644 index 0000000000..b8980f8d25 --- /dev/null +++ b/doc/src/Eqs/pair_lj_smooth_linear.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\phi\left(r\right) & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - + \left(\frac{\sigma}{r}\right)^6 \right] \\ +E\left(r\right) & = & \phi\left(r\right) - \phi\left(R_c\right) - \left(r - R_c\right) \left.\frac{d\phi}{d r} \right|_{r=R_c} \qquad r < R_c +\end{eqnarray*} + +\end{document} + + diff --git a/doc/src/Eqs/pair_lj_soft.jpg b/doc/src/Eqs/pair_lj_soft.jpg new file mode 100644 index 0000000000..856d6d5bbc Binary files /dev/null and b/doc/src/Eqs/pair_lj_soft.jpg differ diff --git a/doc/src/Eqs/pair_lj_soft.tex b/doc/src/Eqs/pair_lj_soft.tex new file mode 100644 index 0000000000..e32f11f0aa --- /dev/null +++ b/doc/src/Eqs/pair_lj_soft.tex @@ -0,0 +1,15 @@ +\documentstyle[12pt]{article} + +\begin{document} + +\[ +E = \lambda^n 4 \epsilon +\left\{ + \frac{1}{ \left[ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 \right]^2 } - + \frac{1}{ \alpha_{\mathrm{LJ}} (1-\lambda)^2 + + \left( \displaystyle\frac{r}{\sigma} \right)^6 } +\right\} \qquad r < r_c + \] + +\end{document} diff --git a/doc/src/Eqs/pair_lubricate.jpg b/doc/src/Eqs/pair_lubricate.jpg new file mode 100644 index 0000000000..560591765a Binary files /dev/null and b/doc/src/Eqs/pair_lubricate.jpg differ diff --git a/doc/src/Eqs/pair_lubricate.tex b/doc/src/Eqs/pair_lubricate.tex new file mode 100644 index 0000000000..c7e3dd96ed --- /dev/null +++ b/doc/src/Eqs/pair_lubricate.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + W & = & - a_{sq} | (v_1 - v_2) \bullet \mathbf{nn} |^2 - + a_{sh} | (\omega_1 + \omega_2) \bullet + (\mathbf{I} - \mathbf{nn}) - 2 \Omega_N |^2 - \\ + & & a_{pu} | (\omega_1 - \omega_2) \bullet (\mathbf{I} - \mathbf{nn}) |^2 - + a_{tw} | (\omega_1 - \omega_2) \bullet \mathbf{nn} |^2 \qquad r < r_c +\end{eqnarray*} + +$$ +\Omega_N = \mathbf{n} \times (v_1 - v_2) / r +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-1.jpg b/doc/src/Eqs/pair_mdf-1.jpg new file mode 100644 index 0000000000..fb0d9d644f Binary files /dev/null and b/doc/src/Eqs/pair_mdf-1.jpg differ diff --git a/doc/src/Eqs/pair_mdf-1.tex b/doc/src/Eqs/pair_mdf-1.tex new file mode 100644 index 0000000000..f3e6f36bcf --- /dev/null +++ b/doc/src/Eqs/pair_mdf-1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E_{smooth}(r) = E(r)*f(r) +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-2.jpg b/doc/src/Eqs/pair_mdf-2.jpg new file mode 100644 index 0000000000..ae6358e5cc Binary files /dev/null and b/doc/src/Eqs/pair_mdf-2.jpg differ diff --git a/doc/src/Eqs/pair_mdf-2.tex b/doc/src/Eqs/pair_mdf-2.tex new file mode 100644 index 0000000000..9bb3be16c0 --- /dev/null +++ b/doc/src/Eqs/pair_mdf-2.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\begin{array}{lcl} +f(r) = 1.0 &\mathrm{for}& r < r_m \\ +f(r) = (1 - x)^3*(1+3x+6x^2) &\mathrm{for}& r_m < r < r_{cut} \\ +f(r) = 0.0 &\mathrm{for}& r >= r_{cut} \\ +\end{array} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-3.jpg b/doc/src/Eqs/pair_mdf-3.jpg new file mode 100644 index 0000000000..45a1a68e05 Binary files /dev/null and b/doc/src/Eqs/pair_mdf-3.jpg differ diff --git a/doc/src/Eqs/pair_mdf-3.tex b/doc/src/Eqs/pair_mdf-3.tex new file mode 100644 index 0000000000..6ba1444466 --- /dev/null +++ b/doc/src/Eqs/pair_mdf-3.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + x = \frac{(r-r_m)}{(r_{cut}-r_m)} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-4.jpg b/doc/src/Eqs/pair_mdf-4.jpg new file mode 100644 index 0000000000..05d08c01a0 Binary files /dev/null and b/doc/src/Eqs/pair_mdf-4.jpg differ diff --git a/doc/src/Eqs/pair_mdf-4.tex b/doc/src/Eqs/pair_mdf-4.tex new file mode 100644 index 0000000000..948be2e40f --- /dev/null +++ b/doc/src/Eqs/pair_mdf-4.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E(r) = 4\epsilon\Big[\Big(\frac{\sigma}{r}\Big)^{12} - \Big(\frac{\sigma}{r}\Big)^6\Big] +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-5.jpg b/doc/src/Eqs/pair_mdf-5.jpg new file mode 100644 index 0000000000..9e047a50a8 Binary files /dev/null and b/doc/src/Eqs/pair_mdf-5.jpg differ diff --git a/doc/src/Eqs/pair_mdf-5.tex b/doc/src/Eqs/pair_mdf-5.tex new file mode 100644 index 0000000000..9b6a28c9d9 --- /dev/null +++ b/doc/src/Eqs/pair_mdf-5.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E(r) = A e^{(-r/\rho)} -\frac{C}{r^6} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mdf-6.jpg b/doc/src/Eqs/pair_mdf-6.jpg new file mode 100644 index 0000000000..54a08b25d6 Binary files /dev/null and b/doc/src/Eqs/pair_mdf-6.jpg differ diff --git a/doc/src/Eqs/pair_mdf-6.tex b/doc/src/Eqs/pair_mdf-6.tex new file mode 100644 index 0000000000..9f25e09bc7 --- /dev/null +++ b/doc/src/Eqs/pair_mdf-6.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E(r) = \frac{A}{r^{12}} - \frac{A}{r^{6}} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_meam.jpg b/doc/src/Eqs/pair_meam.jpg new file mode 100644 index 0000000000..f6de50a998 Binary files /dev/null and b/doc/src/Eqs/pair_meam.jpg differ diff --git a/doc/src/Eqs/pair_meam.tex b/doc/src/Eqs/pair_meam.tex new file mode 100644 index 0000000000..cb9bb1702e --- /dev/null +++ b/doc/src/Eqs/pair_meam.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \sum_i \left\{ F_i(\bar{\rho}_i) + + \frac{1}{2} \sum_{i \neq j} \phi_{ij} (r_{ij}) \right\} +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_meam_spline.jpg b/doc/src/Eqs/pair_meam_spline.jpg new file mode 100644 index 0000000000..29f1c72543 Binary files /dev/null and b/doc/src/Eqs/pair_meam_spline.jpg differ diff --git a/doc/src/Eqs/pair_meam_spline.tex b/doc/src/Eqs/pair_meam_spline.tex new file mode 100644 index 0000000000..55d42f801c --- /dev/null +++ b/doc/src/Eqs/pair_meam_spline.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E=\sum_{ij}\phi(r_{ij})+\sum_{i}U(\rho_{i}), +$$ + +$$ + \rho_{i}=\sum_{j}\rho(r_{ij})+\sum_{jk}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})] +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_meam_sw_spline.jpg b/doc/src/Eqs/pair_meam_sw_spline.jpg new file mode 100644 index 0000000000..80078999d7 Binary files /dev/null and b/doc/src/Eqs/pair_meam_sw_spline.jpg differ diff --git a/doc/src/Eqs/pair_meam_sw_spline.tex b/doc/src/Eqs/pair_meam_sw_spline.tex new file mode 100644 index 0000000000..28abc433b5 --- /dev/null +++ b/doc/src/Eqs/pair_meam_sw_spline.tex @@ -0,0 +1,23 @@ +\documentclass[showpacs,amsmath,amssymb,prb]{revtex4} + + +\usepackage{graphicx} +\usepackage{dcolumn} +\usepackage{bm} + +\newcommand{\etal}{{\em et al.}} +\newcommand{\OO}{{\mathcal{O}}} +\newtheorem{theorem}{Theorem} + +\begin{document} + +\begin{eqnarray} +E & = & E_{MEAM} + E_{SW} \nonumber \\ +E_{MEAM} & = & \sum _{IJ} \phi (r_{IJ}) + \sum _{I} U(\rho _I) \nonumber \\ +E_{SW} & = & \sum _{I} \sum _{JK} F(r_{IJ}) \, F(r_{IK}) \, G(\cos(\theta _{JIK})) \nonumber \\ +\rho _I & = & \sum _J \rho(r_{IJ}) + \sum _{JK} f(r_{IJ}) \, f(r_{IK}) \, g(\cos(\theta _{JIK})) \nonumber +\end{eqnarray} + +\end{document} + + diff --git a/doc/src/Eqs/pair_mgpt.jpg b/doc/src/Eqs/pair_mgpt.jpg new file mode 100644 index 0000000000..2bede7f90f Binary files /dev/null and b/doc/src/Eqs/pair_mgpt.jpg differ diff --git a/doc/src/Eqs/pair_mgpt.tex b/doc/src/Eqs/pair_mgpt.tex new file mode 100644 index 0000000000..9c314df916 --- /dev/null +++ b/doc/src/Eqs/pair_mgpt.tex @@ -0,0 +1,12 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E_{\rm tot}({\bf R}_1 \ldots {\bf R}_N) = NE_{\rm vol}(\Omega ) + + \frac{1}{2} \sum _{i,j} \mbox{}^\prime \ v_2(ij;\Omega ) + + \frac{1}{6} \sum _{i,j,k} \mbox{}^\prime \ v_3(ijk;\Omega ) + + \frac{1}{24} \sum _{i,j,k,l} \mbox{}^\prime \ v_4(ijkl;\Omega ) +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mie.jpg b/doc/src/Eqs/pair_mie.jpg new file mode 100644 index 0000000000..05a8221a93 Binary files /dev/null and b/doc/src/Eqs/pair_mie.jpg differ diff --git a/doc/src/Eqs/pair_mie.tex b/doc/src/Eqs/pair_mie.tex new file mode 100644 index 0000000000..2702ce9bcf --- /dev/null +++ b/doc/src/Eqs/pair_mie.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = C \epsilon \left[ \left(\frac{\sigma}{r}\right)^{\gamma_{rep}} - \left(\frac{\sigma}{r}\right)^{\gamma_{att}} \right] + \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_mie2.jpg b/doc/src/Eqs/pair_mie2.jpg new file mode 100644 index 0000000000..216ca1554a Binary files /dev/null and b/doc/src/Eqs/pair_mie2.jpg differ diff --git a/doc/src/Eqs/pair_mie2.tex b/doc/src/Eqs/pair_mie2.tex new file mode 100644 index 0000000000..2ee9e9b34e --- /dev/null +++ b/doc/src/Eqs/pair_mie2.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + C = \left(\frac{\gamma_{rep}}{\gamma_{rep}-\gamma_{att}}\right) \left(\frac{\gamma_{rep}}{\gamma_{att}}\right)^{\left(\frac{\gamma_{att}}{\gamma_{rep}-\gamma_{att}}\right)} +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_morse.jpg b/doc/src/Eqs/pair_morse.jpg new file mode 100644 index 0000000000..5ebcdb2e1d Binary files /dev/null and b/doc/src/Eqs/pair_morse.jpg differ diff --git a/doc/src/Eqs/pair_morse.tex b/doc/src/Eqs/pair_morse.tex new file mode 100644 index 0000000000..21204daa20 --- /dev/null +++ b/doc/src/Eqs/pair_morse.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right] + \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_morse_smooth_linear.jpg b/doc/src/Eqs/pair_morse_smooth_linear.jpg new file mode 100644 index 0000000000..b951023609 Binary files /dev/null and b/doc/src/Eqs/pair_morse_smooth_linear.jpg differ diff --git a/doc/src/Eqs/pair_morse_smooth_linear.tex b/doc/src/Eqs/pair_morse_smooth_linear.tex new file mode 100644 index 0000000000..f021d018f5 --- /dev/null +++ b/doc/src/Eqs/pair_morse_smooth_linear.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} +\pagestyle{empty} + +\begin{document} + +\begin{eqnarray*} +\phi\left(r\right) & = & D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right] \qquad r < r_c \\ +E\left(r\right) & = & \phi\left(r\right) - \phi\left(R_c\right) - \left(r - R_c\right) \left.\frac{d\phi}{d r} \right|_{r=R_c} \qquad r < R_c +\end{eqnarray*} + +\end{document} + + diff --git a/doc/src/Eqs/pair_nb3b_harmonic.jpg b/doc/src/Eqs/pair_nb3b_harmonic.jpg new file mode 100644 index 0000000000..c8d23da042 Binary files /dev/null and b/doc/src/Eqs/pair_nb3b_harmonic.jpg differ diff --git a/doc/src/Eqs/pair_nb3b_harmonic.tex b/doc/src/Eqs/pair_nb3b_harmonic.tex new file mode 100644 index 0000000000..7f7aa8078e --- /dev/null +++ b/doc/src/Eqs/pair_nb3b_harmonic.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = K (\theta - \theta_0)^2 +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_nm.jpg b/doc/src/Eqs/pair_nm.jpg new file mode 100644 index 0000000000..1e7fe0981c Binary files /dev/null and b/doc/src/Eqs/pair_nm.jpg differ diff --git a/doc/src/Eqs/pair_nm.tex b/doc/src/Eqs/pair_nm.tex new file mode 100644 index 0000000000..4adf9331cc --- /dev/null +++ b/doc/src/Eqs/pair_nm.tex @@ -0,0 +1,10 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ + E = \frac{E_0}{(n-m)} \left[ m \left(\frac{r_0}{r}\right)^n - + n \left(\frac{r_0}{r}\right)^m \right] \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_resquared.jpg b/doc/src/Eqs/pair_resquared.jpg new file mode 100644 index 0000000000..c290c68dfd Binary files /dev/null and b/doc/src/Eqs/pair_resquared.jpg differ diff --git a/doc/src/Eqs/pair_resquared.tex b/doc/src/Eqs/pair_resquared.tex new file mode 100755 index 0000000000..e5c758aec0 --- /dev/null +++ b/doc/src/Eqs/pair_resquared.tex @@ -0,0 +1,7 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3)^2 $$ + +\end{document} diff --git a/doc/src/Eqs/pair_resquared2.jpg b/doc/src/Eqs/pair_resquared2.jpg new file mode 100644 index 0000000000..d2ed21a62a Binary files /dev/null and b/doc/src/Eqs/pair_resquared2.jpg differ diff --git a/doc/src/Eqs/pair_resquared2.tex b/doc/src/Eqs/pair_resquared2.tex new file mode 100755 index 0000000000..ff2c3ca749 --- /dev/null +++ b/doc/src/Eqs/pair_resquared2.tex @@ -0,0 +1,7 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3) $$ + +\end{document} diff --git a/doc/src/Eqs/pair_resquared3.jpg b/doc/src/Eqs/pair_resquared3.jpg new file mode 100644 index 0000000000..3916062a1c Binary files /dev/null and b/doc/src/Eqs/pair_resquared3.jpg differ diff --git a/doc/src/Eqs/pair_resquared3.tex b/doc/src/Eqs/pair_resquared3.tex new file mode 100755 index 0000000000..136bcf73dc --- /dev/null +++ b/doc/src/Eqs/pair_resquared3.tex @@ -0,0 +1,7 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ A_{12} = \epsilon_{\mathrm{LJ}} $$ + +\end{document} diff --git a/doc/src/Eqs/pair_resquared4.jpg b/doc/src/Eqs/pair_resquared4.jpg new file mode 100644 index 0000000000..79ad067fa7 Binary files /dev/null and b/doc/src/Eqs/pair_resquared4.jpg differ diff --git a/doc/src/Eqs/pair_resquared4.tex b/doc/src/Eqs/pair_resquared4.tex new file mode 100755 index 0000000000..6efb755774 --- /dev/null +++ b/doc/src/Eqs/pair_resquared4.tex @@ -0,0 +1,9 @@ +\documentstyle[12pt]{article} + +\begin{document} + +$$ \epsilon_a = \sigma \cdot { \frac{a}{ b \cdot c } }; \epsilon_b = +\sigma \cdot { \frac{b}{ a \cdot c } }; \epsilon_c = \sigma \cdot { +\frac{c}{ a \cdot b } } $$ + +\end{document} diff --git a/doc/src/Eqs/pair_smtbq1.jpg b/doc/src/Eqs/pair_smtbq1.jpg new file mode 100644 index 0000000000..6bfb07b778 Binary files /dev/null and b/doc/src/Eqs/pair_smtbq1.jpg differ diff --git a/doc/src/Eqs/pair_smtbq1.tex b/doc/src/Eqs/pair_smtbq1.tex new file mode 100755 index 0000000000..21ae0e9a49 --- /dev/null +++ b/doc/src/Eqs/pair_smtbq1.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{tot} & = & E_{ES} + E_{OO} + E_{MO} \\ +E_{ES} & = & \sum_i{\Big[ \chi_{i}^{0}Q_i + \frac{1}{2}J_{i}^{0}Q_{i}^{2} + + \frac{1}{2} \sum_{j\neq i}{ J_{ij}(r_{ij})f_{cut}^{R_{coul}}(r_{ij})Q_i Q_j } \Big] } \\ +E_{OO} & = & \sum_{i,j}^{i,j = O}{\Bigg[Cexp( -\frac{r_{ij}}{\rho} ) - Df_{cut}^{r_1^{OO}r_2^{OO}}(r_{ij}) exp(Br_{ij})\Bigg]} \\ +E_{MO} & = & \sum_i{E_{cov}^{i} + \sum_{j\neq i}{ Af_{cut}^{r_{c1}r_{c2}}(r_{ij})exp\Big[-p(\frac{r_{ij}}{r_0} -1) \Big] } } \\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_smtbq2.jpg b/doc/src/Eqs/pair_smtbq2.jpg new file mode 100644 index 0000000000..0e20248788 Binary files /dev/null and b/doc/src/Eqs/pair_smtbq2.jpg differ diff --git a/doc/src/Eqs/pair_smtbq2.tex b/doc/src/Eqs/pair_smtbq2.tex new file mode 100755 index 0000000000..8524c2586c --- /dev/null +++ b/doc/src/Eqs/pair_smtbq2.tex @@ -0,0 +1,12 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +E_{cov}^{i(i=M,O)} & = & - \Bigg\{\eta_i(\mu \xi^{0})^2 f_{cut}^{r_{c1}r_{c2}}(r_{ij}) +\Bigg( \sum_{j(j=O,M)}{ exp[ -2q(\frac{r_{ij}}{r_0} - 1)] } \Bigg) +\delta Q_i \Big( 2\frac{n_0}{\eta_i} - \delta Q_i \Big) \Bigg\}^{1/2} \\ +\delta Q_i & = & | Q_i^{F} | - | Q_i | +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_smtbq3.jpg b/doc/src/Eqs/pair_smtbq3.jpg new file mode 100644 index 0000000000..1d60459165 Binary files /dev/null and b/doc/src/Eqs/pair_smtbq3.jpg differ diff --git a/doc/src/Eqs/pair_smtbq3.tex b/doc/src/Eqs/pair_smtbq3.tex new file mode 100755 index 0000000000..5bc6e465d1 --- /dev/null +++ b/doc/src/Eqs/pair_smtbq3.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\xi^0 & = & \frac{\xi_O}{m} = \frac{\xi_C}{n} \\ +\frac{\beta_O}{\sqrt{m}} & = & \frac{\beta_C}{\sqrt{n}} = \xi^0 \frac{\sqrt{m}+\sqrt{n}}{2}\\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_snap.jpg b/doc/src/Eqs/pair_snap.jpg new file mode 100644 index 0000000000..af48357b5e Binary files /dev/null and b/doc/src/Eqs/pair_snap.jpg differ diff --git a/doc/src/Eqs/pair_snap.tex b/doc/src/Eqs/pair_snap.tex new file mode 100644 index 0000000000..d0a17de1fb --- /dev/null +++ b/doc/src/Eqs/pair_snap.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E^i_{SNAP}(B_1^i,...,B_K^i) = \beta^{\alpha_i}_0 + \sum_{k=1}^K \beta_k^{\alpha_i} B_k^i +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_soft.jpg b/doc/src/Eqs/pair_soft.jpg new file mode 100644 index 0000000000..e8a654e1ed Binary files /dev/null and b/doc/src/Eqs/pair_soft.jpg differ diff --git a/doc/src/Eqs/pair_soft.tex b/doc/src/Eqs/pair_soft.tex new file mode 100644 index 0000000000..c2db15c2ee --- /dev/null +++ b/doc/src/Eqs/pair_soft.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = A \left[ 1 + \cos\left(\frac{\pi r}{r_c}\right) \right] + \qquad r < r_c +$$ + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_sph_ideal.jpg b/doc/src/Eqs/pair_sph_ideal.jpg new file mode 100644 index 0000000000..370b75fe94 Binary files /dev/null and b/doc/src/Eqs/pair_sph_ideal.jpg differ diff --git a/doc/src/Eqs/pair_sph_ideal.tex b/doc/src/Eqs/pair_sph_ideal.tex new file mode 100644 index 0000000000..91c64f00bc --- /dev/null +++ b/doc/src/Eqs/pair_sph_ideal.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + p = (\gamma - 1) \rho e +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_sph_tait.jpg b/doc/src/Eqs/pair_sph_tait.jpg new file mode 100644 index 0000000000..8bbfe80512 Binary files /dev/null and b/doc/src/Eqs/pair_sph_tait.jpg differ diff --git a/doc/src/Eqs/pair_sph_tait.tex b/doc/src/Eqs/pair_sph_tait.tex new file mode 100644 index 0000000000..4e1fa9cfed --- /dev/null +++ b/doc/src/Eqs/pair_sph_tait.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + p = B [(\frac{\rho}{\rho_0})^{\gamma} - 1] +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_srp1.jpg b/doc/src/Eqs/pair_srp1.jpg new file mode 100644 index 0000000000..bbbdc43e05 Binary files /dev/null and b/doc/src/Eqs/pair_srp1.jpg differ diff --git a/doc/src/Eqs/pair_srp1.tex b/doc/src/Eqs/pair_srp1.tex new file mode 100644 index 0000000000..45aa005d86 --- /dev/null +++ b/doc/src/Eqs/pair_srp1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + F^{SRP}_{ij} & = & C(1-r/r_c)\hat{r}_{ij} \qquad r < r_c \\ +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_srp2.jpg b/doc/src/Eqs/pair_srp2.jpg new file mode 100644 index 0000000000..c5d20dc212 Binary files /dev/null and b/doc/src/Eqs/pair_srp2.jpg differ diff --git a/doc/src/Eqs/pair_srp2.tex b/doc/src/Eqs/pair_srp2.tex new file mode 100644 index 0000000000..19cb19ae72 --- /dev/null +++ b/doc/src/Eqs/pair_srp2.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + F_{i1}^{SRP} & = & F^{SRP}_{ij}(L) \\ + F_{i2}^{SRP} & = & F^{SRP}_{ij}(1-L) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_sw.jpg b/doc/src/Eqs/pair_sw.jpg new file mode 100644 index 0000000000..f60f07fd27 Binary files /dev/null and b/doc/src/Eqs/pair_sw.jpg differ diff --git a/doc/src/Eqs/pair_sw.tex b/doc/src/Eqs/pair_sw.tex new file mode 100644 index 0000000000..ebcc39d77b --- /dev/null +++ b/doc/src/Eqs/pair_sw.tex @@ -0,0 +1,18 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & \sum_i \sum_{j > i} \phi_2 (r_{ij}) + + \sum_i \sum_{j \neq i} \sum_{k > j} + \phi_3 (r_{ij}, r_{ik}, \theta_{ijk}) \\ + \phi_2(r_{ij}) & = & A_{ij} \epsilon_{ij} \left[ B_{ij} (\frac{\sigma_{ij}}{r_{ij}})^{p_{ij}} - + (\frac{\sigma_{ij}}{r_{ij}})^{q_{ij}} \right] + \exp \left( \frac{\sigma_{ij}}{r_{ij} - a_{ij} \sigma_{ij}} \right) \\ + \phi_3(r_{ij},r_{ik},\theta_{ijk}) & = & \lambda_{ijk} \epsilon_{ijk} \left[ \cos \theta_{ijk} - + \cos \theta_{0ijk} \right]^2 + \exp \left( \frac{\gamma_{ij} \sigma_{ij}}{r_{ij} - a_{ij} \sigma_{ij}} \right) + \exp \left( \frac{\gamma_{ik} \sigma_{ik}}{r_{ik} - a_{ik} \sigma_{ik}} \right) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_tersoff.jpg b/doc/src/Eqs/pair_tersoff.jpg new file mode 100644 index 0000000000..bd3e147192 Binary files /dev/null and b/doc/src/Eqs/pair_tersoff.jpg differ diff --git a/doc/src/Eqs/pair_tersoff_1.jpg b/doc/src/Eqs/pair_tersoff_1.jpg new file mode 100644 index 0000000000..79600b499c Binary files /dev/null and b/doc/src/Eqs/pair_tersoff_1.jpg differ diff --git a/doc/src/Eqs/pair_tersoff_1.tex b/doc/src/Eqs/pair_tersoff_1.tex new file mode 100644 index 0000000000..7d34712491 --- /dev/null +++ b/doc/src/Eqs/pair_tersoff_1.tex @@ -0,0 +1,24 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ + V_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\ + f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l} + 1 & r < R - D \\ + \frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) & + R-D < r < R + D \\ + 0 & r > R + D + \end{array} \right. \\ + f_R(r) & = & A \exp (-\lambda_1 r) \\ + f_A(r) & = & -B \exp (-\lambda_2 r) \\ + b_{ij} & = & \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\ + \zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk}) + \exp \left[ {\lambda_3}^m (r_{ij} - r_{ik})^m \right] \\ + g(\theta) & = & \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} - + \frac{c^2}{\left[ d^2 + + (\cos \theta - \cos \theta_0)^2\right]} \right) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_tersoff_2.jpg b/doc/src/Eqs/pair_tersoff_2.jpg new file mode 100644 index 0000000000..6cb8778a09 Binary files /dev/null and b/doc/src/Eqs/pair_tersoff_2.jpg differ diff --git a/doc/src/Eqs/pair_tersoff_2.tex b/doc/src/Eqs/pair_tersoff_2.tex new file mode 100644 index 0000000000..7b5beb8ef3 --- /dev/null +++ b/doc/src/Eqs/pair_tersoff_2.tex @@ -0,0 +1,14 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\lambda_1^{i,j} &=& \frac{1}{2}(\lambda_1^i + \lambda_1^j)\\ +\lambda_2^{i,j} &=& \frac{1}{2}(\lambda_2^i + \lambda_2^j)\\ +A_{i,j} &=& (A_{i}A_{j})^{1/2}\\ +B_{i,j} &=& \chi_{ij}(B_{i}B_{j})^{1/2}\\ +R_{i,j} &=& (R_{i}R_{j})^{1/2}\\ +S_{i,j} &=& (S_{i}S_{j})^{1/2}\\ +\end{eqnarray*} + +\end{document} \ No newline at end of file diff --git a/doc/src/Eqs/pair_tersoff_mod.jpg b/doc/src/Eqs/pair_tersoff_mod.jpg new file mode 100644 index 0000000000..2618943d85 Binary files /dev/null and b/doc/src/Eqs/pair_tersoff_mod.jpg differ diff --git a/doc/src/Eqs/pair_tersoff_mod.tex b/doc/src/Eqs/pair_tersoff_mod.tex new file mode 100644 index 0000000000..eafc4fdeeb --- /dev/null +++ b/doc/src/Eqs/pair_tersoff_mod.tex @@ -0,0 +1,24 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ + V_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\ + f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l} + 1 & r < R - D \\ + \frac{1}{2} - \frac{9}{16} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) - \frac{1}{16} \sin \left( \frac{3\pi}{2} \frac{r-R}{D} \right) & + R-D < r < R + D \\ + 0 & r > R + D + \end{array} \right. \\ + f_R(r) & = & A \exp (-\lambda_1 r) \\ + f_A(r) & = & -B \exp (-\lambda_2 r) \\ + b_{ij} & = & \left( 1 + {\zeta_{ij}}^\eta \right)^{-\frac{1}{2n}} \\ + \zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk}) + \exp \left[ \alpha (r_{ij} - r_{ik})^\beta \right] \\ + g(\theta) & = & c_1 + g_o(\theta) g_a(\theta) \\ + g_o(\theta) & = & \frac{c_2 (h - \cos \theta)^2}{c_3 + (h - \cos \theta)^2} \\ + g_a(\theta) & = & 1 + c_4 \exp \left[ -c_5 (h - \cos \theta)^2 \right] \\ +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_tersoff_zbl.jpg b/doc/src/Eqs/pair_tersoff_zbl.jpg new file mode 100644 index 0000000000..20d60d2256 Binary files /dev/null and b/doc/src/Eqs/pair_tersoff_zbl.jpg differ diff --git a/doc/src/Eqs/pair_tersoff_zbl.tex b/doc/src/Eqs/pair_tersoff_zbl.tex new file mode 100644 index 0000000000..902819aa1b --- /dev/null +++ b/doc/src/Eqs/pair_tersoff_zbl.tex @@ -0,0 +1,33 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\ + V_{ij} & = & (1 - f_F(r_{ij})) V^{ZBL}_{ij} + f_F(r_{ij}) V^{Tersoff}_{ij} \\ +f_F(r_{ij}) & = & \frac{1}{1 + e^{-A_F(r_{ij} - r_C)}}\\ + \\ + \\ + V^{ZBL}_{ij} & = & \frac{1}{4\pi\epsilon_0} \frac{Z_1 Z_2 \,e^2}{r_{ij}} \phi(r_{ij}/a) \\ + a & = & \frac{0.8854\,a_0}{Z_{1}^{0.23} + Z_{2}^{0.23}}\\ + \phi(x) & = & 0.1818e^{-3.2x} + 0.5099e^{-0.9423x} + 0.2802e^{-0.4029x} + 0.02817e^{-0.2016x}\\ + \\ + \\ + V^{Tersoff}_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\ + f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l} + 1 & r < R - D \\ + \frac{1}{2} - \frac{1}{2} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) & + R-D < r < R + D \\ + 0 & r > R + D + \end{array} \right. \\ + f_R(r) & = & A \exp (-\lambda_1 r) \\ + f_A(r) & = & -B \exp (-\lambda_2 r) \\ + b_{ij} & = & \left( 1 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\ + \zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk}) + \exp \left[ {\lambda_3}^m (r_{ij} - r_{ik})^m \right] \\ + g(\theta) & = & \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} - + \frac{c^2}{\left[ d^2 + + (\cos \theta - \cos \theta_0)^2\right]} \right) +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_vashishta.jpg b/doc/src/Eqs/pair_vashishta.jpg new file mode 100644 index 0000000000..ca5f118a87 Binary files /dev/null and b/doc/src/Eqs/pair_vashishta.jpg differ diff --git a/doc/src/Eqs/pair_vashishta.tex b/doc/src/Eqs/pair_vashishta.tex new file mode 100644 index 0000000000..b65056a254 --- /dev/null +++ b/doc/src/Eqs/pair_vashishta.tex @@ -0,0 +1,22 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + U & = & \sum_i^N \sum_{j > i}^N U_{ij}^{(2)} (r_{ij}) + + \sum_i^N \sum_{j \neq i}^N \sum_{k > j, k \neq i}^N + U_{ijk}^{(3)} (r_{ij}, r_{ik}, \theta_{ijk}) + \\ + U_{ij}^{(2)} (r) & = & \frac{H_{ij}}{r^{\eta_{ij}}} + + \frac{Z_i Z_j}{r}\exp(-r/\lambda_{1,ij}) + - \frac{D_{ij}}{r^4}\exp(-r/\lambda_{4,ij}) + - \frac{W_{ij}}{r^6}, r < r_{c,{ij}} + \\ + U_{ijk}^{(3)}(r_{ij},r_{ik},\theta_{ijk}) & = & B_{ijk} + \frac{\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} + {1+C_{ijk}\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} \times \\ +& & \exp \left( \frac{\gamma_{ij}}{r_{ij} - r_{0,ij}} \right) + \exp \left( \frac{\gamma_{ik}}{r_{ik} - r_{0,ik}} \right), r_{ij} < r_{0,ij}, r_{ik} < r_{0,ik} +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/pair_yukawa.jpg b/doc/src/Eqs/pair_yukawa.jpg new file mode 100644 index 0000000000..103edc6043 Binary files /dev/null and b/doc/src/Eqs/pair_yukawa.jpg differ diff --git a/doc/src/Eqs/pair_yukawa.tex b/doc/src/Eqs/pair_yukawa.tex new file mode 100644 index 0000000000..382cf249a8 --- /dev/null +++ b/doc/src/Eqs/pair_yukawa.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = A \frac{e^{- \kappa r}}{r} \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_yukawa_colloid.jpg b/doc/src/Eqs/pair_yukawa_colloid.jpg new file mode 100644 index 0000000000..1d83624757 Binary files /dev/null and b/doc/src/Eqs/pair_yukawa_colloid.jpg differ diff --git a/doc/src/Eqs/pair_yukawa_colloid.tex b/doc/src/Eqs/pair_yukawa_colloid.tex new file mode 100644 index 0000000000..dbdbbcd140 --- /dev/null +++ b/doc/src/Eqs/pair_yukawa_colloid.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ + E = \frac{A}{\kappa} e^{- \kappa (r - (r_i + r_j))} \qquad r < r_c +$$ + +\end{document} diff --git a/doc/src/Eqs/pair_zbl.jpg b/doc/src/Eqs/pair_zbl.jpg new file mode 100644 index 0000000000..88656af5eb Binary files /dev/null and b/doc/src/Eqs/pair_zbl.jpg differ diff --git a/doc/src/Eqs/pair_zbl.tex b/doc/src/Eqs/pair_zbl.tex new file mode 100644 index 0000000000..3d68dbed23 --- /dev/null +++ b/doc/src/Eqs/pair_zbl.tex @@ -0,0 +1,11 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} + E^{ZBL}_{ij} & = & \frac{1}{4\pi\epsilon_0} \frac{Z_i Z_j \,e^2}{r_{ij}} \phi(r_{ij}/a)+ S(r_{ij})\\ + a & = & \frac{0.46850}{Z_{i}^{0.23} + Z_{j}^{0.23}}\\ + \phi(x) & = & 0.18175e^{-3.19980x} + 0.50986e^{-0.94229x} + 0.28022e^{-0.40290x} + 0.02817e^{-0.20162x}\\ + \end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/polymorphic1.jpg b/doc/src/Eqs/polymorphic1.jpg new file mode 100644 index 0000000000..4757cb7ad8 Binary files /dev/null and b/doc/src/Eqs/polymorphic1.jpg differ diff --git a/doc/src/Eqs/polymorphic1.tex b/doc/src/Eqs/polymorphic1.tex new file mode 100644 index 0000000000..b4b925ccf8 --- /dev/null +++ b/doc/src/Eqs/polymorphic1.tex @@ -0,0 +1,9 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +E=\frac{1}{2}\sum_{i=1}^{i=N}\sum_{j=1}^{j=N}\left[\left(1-\delta_{ij}\right)\cdot U_{IJ}\left(r_{ij}\right)-\left(1-\eta_{ij}\right)\cdot F_{IJ}\left(r_{ij}\right)\cdot V_{IJ}\left(r_{ij}\right)\right] +$$ + +\end{document} diff --git a/doc/src/Eqs/polymorphic2.jpg b/doc/src/Eqs/polymorphic2.jpg new file mode 100644 index 0000000000..05133f4849 Binary files /dev/null and b/doc/src/Eqs/polymorphic2.jpg differ diff --git a/doc/src/Eqs/polymorphic2.tex b/doc/src/Eqs/polymorphic2.tex new file mode 100644 index 0000000000..80b1c93821 --- /dev/null +++ b/doc/src/Eqs/polymorphic2.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +X_{ij}=\sum_{k=i_1,k\neq i,j}^{i_N}W_{IK}\left(r_{ik}\right)\cdot G_{JIK}\left(\theta_{jik}\right)\cdot P_{IK}\left(\Delta r_{jik}\right) +\label{X_eq2} +$$ + +\end{document} diff --git a/doc/src/Eqs/polymorphic3.jpg b/doc/src/Eqs/polymorphic3.jpg new file mode 100644 index 0000000000..ba748e63c5 Binary files /dev/null and b/doc/src/Eqs/polymorphic3.jpg differ diff --git a/doc/src/Eqs/polymorphic3.tex b/doc/src/Eqs/polymorphic3.tex new file mode 100644 index 0000000000..71db8d81b0 --- /dev/null +++ b/doc/src/Eqs/polymorphic3.tex @@ -0,0 +1,10 @@ +\documentclass[12pt]{article} + +\begin{document} + +$$ +\Delta r_{jik}=r_{ij}-\xi_{IJ}\cdot r_{ik} +\label{Dr_eq3} +$$ + +\end{document} diff --git a/doc/src/Eqs/polymorphic4.jpg b/doc/src/Eqs/polymorphic4.jpg new file mode 100644 index 0000000000..7a094d6a21 Binary files /dev/null and b/doc/src/Eqs/polymorphic4.jpg differ diff --git a/doc/src/Eqs/polymorphic4.tex b/doc/src/Eqs/polymorphic4.tex new file mode 100644 index 0000000000..b792df82a0 --- /dev/null +++ b/doc/src/Eqs/polymorphic4.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=0 \\ +U_{IJ}\left(r\right)=A_{IJ}\cdot\epsilon_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^q\cdot \left[B_{IJ}\cdot \left(\frac{\sigma_{IJ}}{r}\right)^{p-q}-1\right]\cdot exp\left(\frac{\sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +V_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +F_{IJ}\left(X\right)=-X \\ +P_{IJ}\left(\Delta r\right)=1 \\ +W_{IJ}\left(r\right)=\sqrt{\lambda_{IJ}\cdot \epsilon_{IJ}}\cdot exp\left(\frac{\gamma_{IJ}\cdot \sigma_{IJ}}{r-a_{IJ}\cdot \sigma_{IJ}}\right) \\ +G_{JIK}\left(\theta\right)=\left(cos\theta+\frac{1}{3}\right)^2 +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/polymorphic5.jpg b/doc/src/Eqs/polymorphic5.jpg new file mode 100644 index 0000000000..500238b2a9 Binary files /dev/null and b/doc/src/Eqs/polymorphic5.jpg differ diff --git a/doc/src/Eqs/polymorphic5.tex b/doc/src/Eqs/polymorphic5.tex new file mode 100644 index 0000000000..a5451b98d6 --- /dev/null +++ b/doc/src/Eqs/polymorphic5.tex @@ -0,0 +1,17 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +\left\{\begin{array}{l} +\eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\ +U_{IJ}\left(r\right)=\frac{D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{2S_{IJ}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +V_{IJ}\left(r\right)=\frac{S_{IJ}\cdot D_{e,IJ}}{S_{IJ}-1}\cdot exp\left[-\beta_{IJ}\sqrt{\frac{2}{S_{IJ}}\left(r-r_{e,IJ}\right)}\right]\cdot f_{c,IJ}\left(r\right) \\ +F_{IJ}\left(X\right)=\left(1+X\right)^{-\frac{1}{2}} \\ +P_{IJ}\left(\Delta r\right)=exp\left(2\mu_{IK}\cdot \Delta r\right) \\ +W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\ +G_{JIK}\left(\theta\right)=\gamma_{IK}\left[1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}\right] +\end{array}\right. +\end{eqnarray*} + +\end{document} diff --git a/doc/src/Eqs/polymorphic6.jpg b/doc/src/Eqs/polymorphic6.jpg new file mode 100644 index 0000000000..65ea78bf21 Binary files /dev/null and b/doc/src/Eqs/polymorphic6.jpg differ diff --git a/doc/src/Eqs/polymorphic6.tex b/doc/src/Eqs/polymorphic6.tex new file mode 100644 index 0000000000..c8f9f2f25b --- /dev/null +++ b/doc/src/Eqs/polymorphic6.tex @@ -0,0 +1,13 @@ +\documentclass[12pt]{article} + +\begin{document} + +\begin{eqnarray*} +f_{c,IJ}=\left\{\begin{array}{lr} +1, & r\leq r_{s,IJ} \\ +\frac{1}{2}+\frac{1}{2} cos \left[\frac{\pi \left(r-r_{s,IJ}\right)}{r_{c,IJ}-r_{s,IJ}}\right], & r_{s,IJ}