convert pair styles dpd to exp6

doc/src/Eqs/e3b.tex

@@ -1,15 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-\begin{document}
-
-\begin{align*}
-E =& E_2 \sum_{i,j}e^{-k_2 r_{ij}} + E_A \sum_{\substack{i,j,k,\ell \\\in \textrm{type A}}} f(r_{ij})f(r_{k\ell}) + E_B \sum_{\substack{i,j,k,\ell \\\in \textrm{type B}}} f(r_{ij})f(r_{k\ell}) + E_C \sum_{\substack{i,j,k,\ell \\\in \textrm{type C}}} f(r_{ij})f(r_{k\ell}) \\
-f(r) =& e^{-k_3 r}s(r) \\
-s(r) =& \begin{cases}
-  1 & r<R_s \\
-  \displaystyle\frac{(R_f-r)^2(R_f-3R_s+2r)}{(R_f-R_s)^3} & R_s\leq r\leq R_f \\
-  0 & r>R_f\\
-\end{cases}
-\end{align*}
-
-\end{document}

doc/src/Eqs/eff_ECP1.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
-E_{Pauli(ECP_s)}=p_1\exp\left(-\frac{p_2r^2}{p_3+s^2} \right)
-$$
-
-\end{document}  

doc/src/Eqs/eff_ECP2.tex

@@ -1,8 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
-E_{Pauli(ECP_p)}=p_1\left( \frac{2}{p_2/s+s/p_2} \right)\left( r-p_3s\right)^2\exp \left[ -\frac{p_4\left( r-p_3s \right)^2}{p_5+s^2} \right] 
-$$
-

doc/src/Eqs/eff_KE.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$ 
-E_{KE}  = \frac{\hbar^2 }{{m_{e} }}\sum\limits_i {\frac{3}{{2s_i^2 }}}
-$$
-
-\end{document}

doc/src/Eqs/eff_NN.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/eff_Ne.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/eff_Pauli.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/eff_ee.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/eff_energy_expression.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/pair_dpd.tex

@@ -1,13 +0,0 @@
-\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}

doc/src/Eqs/pair_dpd_energy.tex

@@ -1,12 +0,0 @@
-\documentclass[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-  du_{i}^{cond} & = & \kappa_{ij}(\frac{1}{\theta_{i}}-\frac{1}{\theta_{j}})\omega_{ij}^{2} + \alpha_{ij}\omega_{ij}\zeta_{ij}^{q}(\Delta{t})^{-1/2} \\
-  du_{i}^{mech} & = & -\frac{1}{2}\gamma_{ij}\omega_{ij}^{2}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})^{2} - 
-  \frac{\sigma^{2}_{ij}}{4}(\frac{1}{m_{i}}+\frac{1}{m_{j}})\omega_{ij}^{2} - 
-  \frac{1}{2}\sigma_{ij}\omega_{ij}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})\zeta_{ij}(\Delta{t})^{-1/2} \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/pair_dpd_energy_terms.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-  \alpha_{ij}^{2} & = & 2k_{B}\kappa_{ij} \\
-  \sigma^{2}_{ij} & = & 2\gamma_{ij}k_{B}\Theta_{ij} \\
-  \Theta_{ij}^{-1} & = & \frac{1}{2}(\frac{1}{\theta_{i}}+\frac{1}{\theta_{j}}) \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/pair_dpd_omega.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-$$
- \omega_{ij} = 1 - \frac{r_{ij}}{r_{c}}
-$$
-
-\end{document}

doc/src/Eqs/pair_drip.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-\usepackage{bm}
-
-\begin{document}
-
-\begin{eqnarray*}
-E &=& \frac{1}{2} \sum_{i} \sum_{j\notin\text{layer}\,i} \phi_{ij} \\\phi_{ij} &=& f_\text{c}(x_r) \left[ e^{-\lambda(r_{ij} - z_0 )} \left[C+f(\rho_{ij})+  g(\rho_{ij}, \{\alpha_{ij}^{(m)}\}) \right]- A\left (\frac{z_0}{r_{ij}} \right)^6 \right] \\
-\end{eqnarray*}  
-
-
-
-                        
-\end{document}

doc/src/Eqs/pair_eam.tex

@@ -1,10 +0,0 @@
-\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}

doc/src/Eqs/pair_eam_fs.tex

@@ -1,11 +0,0 @@
-\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}

doc/src/Eqs/pair_edip.tex

@@ -1,22 +0,0 @@
-\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 r<c \\
-         \exp\left(\frac{\alpha}{1-x^{-3}}\right) & \quad c<r<a \\
-         0 & \quad r>a
-         \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}
-

doc/src/Eqs/pair_eim1.tex

@@ -1,9 +0,0 @@
-\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}

doc/src/Eqs/pair_eim2.tex

@@ -1,11 +0,0 @@
-\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}

doc/src/Eqs/pair_eim3.tex

@@ -1,25 +0,0 @@
-\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}

doc/src/Eqs/pair_exp6_rx.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-$$
-U_{ij}(r) = \frac{\epsilon}{\alpha-6}\{6exp[\alpha(1-\frac{r_{ij}}{R_{m}})]-\alpha(\frac{R_{m}}{r_{ij}})^6\}
-$$
-
-\end{document}

doc/src/Eqs/pair_exp6_rx_oneFluid.tex

@@ -1,11 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-   R_{m}^{3} &=& \displaystyle\sum_{a}\displaystyle\sum_{b} x_{a}x_{b}R_{m,ab}^{3} \\
-   \epsilon  &=& \frac{1}{R_{m}^{3}}\displaystyle\sum_{a}\displaystyle\sum_{b} x_{a}x_{b}\epsilon_{ab}R_{m,ab}^{3} \\
-   \alpha    &=& \frac{1}{\epsilon R_{m}^{3}}\displaystyle\sum_{a}\displaystyle\sum_{b} x_{a}x_{b}\alpha_{ab}\epsilon_{ab}R_{m,ab}^{3} \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/pair_exp6_rx_oneFluid2.tex

@@ -1,11 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-   \epsilon_{ab} &=& \sqrt{\epsilon_{a}\epsilon_{b}} \\
-   R_{m,ab} &=& \frac{R_{m,a}+R_{m,b}}{2} \\ 
-   \alpha_{ab} &=& \sqrt{\alpha_{a}\alpha_{b}} \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/pair_dpd.rst

@@ -67,17 +67,25 @@ pair interaction and the thermostat for each pair of particles.
 For style *dpd*\ , the force on atom I due to atom J is given as a sum
 of 3 terms
 
-.. image:: Eqs/pair_dpd.jpg
-   :align: center
+.. math::
 
-where Fc is a conservative force, Fd is a dissipative force, and Fr is
-a random force.  Rij is a unit vector in the direction Ri - Rj, Vij is
-the vector difference in velocities of the two atoms = Vi - Vj, alpha
-is a Gaussian random number with zero mean and unit variance, dt is
-the timestep size, and w(r) is a weighting factor that varies between
-0 and 1.  Rc is the cutoff.  Sigma is set equal to sqrt(2 Kb T gamma),
-where Kb is the Boltzmann constant and T is the temperature parameter
-in the pair\_style command.
+   \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
+
+
+where :math:`F^C` is a conservative force, :math:`F^D` is a dissipative
+force, and :math:`F^R` is a random force.  :math:`r_{ij}` is a unit
+vector in the direction :math:`r_i - r_j`, :math:`V_{ij} is the vector
+difference in velocities of the two atoms :math:`= \vec{v}_i -
+\vec{v}_j, :math:`\alpha` is a Gaussian random number with zero mean and
+unit variance, dt is the timestep size, and w(r) is a weighting factor
+that varies between 0 and 1.  :math:`r_c` is the cutoff.  :math:`\sigma`
+is set equal to :math:`\sqrt{2 k_B T \gamma}`, where :math:`k_B` is the
+Boltzmann constant and T is the temperature parameter in the pair\_style
+command.
 
 For style *dpd/tstat*\ , the force on atom I due to atom J is the same
 as the above equation, except that the conservative Fc term is
@@ -97,7 +105,7 @@ the examples above, or in the data file or restart files read by the
 commands:
 
 * A (force units)
-* gamma (force/velocity units)
+* :math:`\gamma` (force/velocity units)
 * cutoff (distance units)
 
 The last coefficient is optional.  If not specified, the global DPD
@@ -125,7 +133,6 @@ the work of :ref:`(Afshar) <Afshar>` and :ref:`(Phillips) <Phillips>`.
    includes all the components of force listed above, including the
    random force.
 
-
 ----------
 
 

doc/src/pair_dpd_fdt.rst

@@ -54,25 +54,34 @@ under isoenergetic and isoenthalpic conditions (see :ref:`(Lisal) <Lisal3>`).
 For DPD simulations in general, the force on atom I due to atom J is
 given as a sum of 3 terms
 
-.. image:: Eqs/pair_dpd.jpg
-   :align: center
+.. math::
 
-where Fc is a conservative force, Fd is a dissipative force, and Fr is
-a random force.  Rij is a unit vector in the direction Ri - Rj, Vij is
-the vector difference in velocities of the two atoms = Vi - Vj, alpha
-is a Gaussian random number with zero mean and unit variance, dt is
-the timestep size, and w(r) is a weighting factor that varies between
-0 and 1.  Rc is the cutoff.  The weighting factor, omega\_ij, varies
-between 0 and 1, and is chosen to have the following functional form:
+   \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
 
-.. image:: Eqs/pair_dpd_omega.jpg
-   :align: center
+
+where :math:`F^C` is a conservative force, :math:`F^D` is a dissipative
+force, and :math:`F^R` is a random force.  :math:`r_{ij}` is a unit
+vector in the direction :math:`r_i - r_j`, :math:`V_{ij} is the vector
+difference in velocities of the two atoms :math:`= \vec{v}_i -
+\vec{v}_j, :math:`\alpha` is a Gaussian random number with zero mean and
+unit variance, dt is the timestep size, and w(r) is a weighting factor
+that varies between 0 and 1.  Rc is the cutoff.  The weighting factor,
+:math:`\omega_{ij}`, varies between 0 and 1, and is chosen to have the
+following functional form:
+
+.. math::
+
+   \omega_{ij} = 1 - \frac{r_{ij}}{r_{c}}
 
 Note that alternative definitions of the weighting function exist, but
 would have to be implemented as a separate pair style command.
 
-For style *dpd/fdt*\ , the fluctuation-dissipation theorem defines gamma
-to be set equal to sigma\*sigma/(2 T), where T is the set point
+For style *dpd/fdt*\ , the fluctuation-dissipation theorem defines :math:`\gamma`
+to be set equal to :math:`\sigma^2/(2 T)`, where T is the set point
 temperature specified as a pair style parameter in the above examples.
 The following coefficients must be defined for each pair of atoms types
 via the :doc:`pair_coeff <pair_coeff>` command as in the examples above,
@@ -80,33 +89,42 @@ or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>` commands:
 
 * A (force units)
-* sigma (force\*time\^(1/2) units)
+* :math:`\sigma` (force\*time\^(1/2) units)
 * cutoff (distance units)
 
 The last coefficient is optional.  If not specified, the global DPD
 cutoff is used.
 
-Style *dpd/fdt/energy* is used to perform DPD simulations
-under isoenergetic and isoenthalpic conditions.  The fluctuation-dissipation
-theorem defines gamma to be set equal to sigma\*sigma/(2 dpdTheta), where
-dpdTheta is the average internal temperature for the pair. The particle
-internal temperature is related to the particle internal energy through
-a mesoparticle equation of state (see :doc:`fix eos <fix>`). The
-differential internal conductive and mechanical energies are computed
-within style *dpd/fdt/energy* as:
+Style *dpd/fdt/energy* is used to perform DPD simulations under
+isoenergetic and isoenthalpic conditions.  The fluctuation-dissipation
+theorem defines :math:`\gamma` to be set equal to :math:`sigma^2/(2
+\theta)`, where :math:theta` is the average internal temperature for the
+pair. The particle internal temperature is related to the particle
+internal energy through a mesoparticle equation of state (see :doc:`fix
+eos <fix>`). The differential internal conductive and mechanical
+energies are computed within style *dpd/fdt/energy* as:
+
+.. math::
+
+   du_{i}^{cond}  = & \kappa_{ij}(\frac{1}{\theta_{i}}-\frac{1}{\theta_{j}})\omega_{ij}^{2} + \alpha_{ij}\omega_{ij}\zeta_{ij}^{q}(\Delta{t})^{-1/2} \\
+  du_{i}^{mech}  = & -\frac{1}{2}\gamma_{ij}\omega_{ij}^{2}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})^{2} - 
+  \frac{\sigma^{2}_{ij}}{4}(\frac{1}{m_{i}}+\frac{1}{m_{j}})\omega_{ij}^{2} - 
+  \frac{1}{2}\sigma_{ij}\omega_{ij}(\frac{\vec{r_{ij}}}{r_{ij}}\bullet\vec{v_{ij}})\zeta_{ij}(\Delta{t})^{-1/2} 
 
-.. image:: Eqs/pair_dpd_energy.jpg
-   :align: center
 
 where
 
-.. image:: Eqs/pair_dpd_energy_terms.jpg
-   :align: center
+.. math::
 
-Zeta\_ij\^q is a second Gaussian random number with zero mean and unit
+  \alpha_{ij}^{2}  = & 2k_{B}\kappa_{ij} \\
+  \sigma^{2}_{ij}  = & 2\gamma_{ij}k_{B}\Theta_{ij} \\
+  \Theta_{ij}^{-1}  = & \frac{1}{2}(\frac{1}{\theta_{i}}+\frac{1}{\theta_{j}})
+
+
+:math:`\zeta_ij^q` is a second Gaussian random number with zero mean and unit
 variance that is used to compute the internal conductive energy. The
-fluctuation-dissipation theorem defines alpha\*alpha to be set
-equal to 2\*kB\*kappa, where kappa is the mesoparticle thermal
+fluctuation-dissipation theorem defines :math:`alpha^2` to be set
+equal to :math:2k_B\kappa`, where :math:`\kappa` is the mesoparticle thermal
 conductivity parameter.   The following coefficients must be defined for
 each pair of atoms types via the :doc:`pair_coeff <pair_coeff>`
 command as in the examples above, or in the data file or restart files
@@ -114,8 +132,8 @@ read by the :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
 * A (force units)
-* sigma (force\*time\^(1/2) units)
-* kappa (energy\*temperature/time units)
+* :math:`\sigma` (force\*time\^(1/2) units)
+* :math:`\kappa` (energy\*temperature/time units)
 * cutoff (distance units)
 
 The last coefficient is optional.  If not specified, the global DPD

doc/src/pair_drip.rst

@@ -40,8 +40,11 @@ in :ref:`(Wen) <Wen2018>`, which is based on the :ref:`(Kolmogorov) <Kolmogorov2
 potential and provides an improved prediction for forces.
 The total potential energy of a system is
 
-.. image:: Eqs/pair_drip.jpg
-   :align: center
+.. math::
+
+   E = & \frac{1}{2} \sum_{i} \sum_{j\notin\text{layer}\,i} \phi_{ij} \\
+   \phi_{ij} = &f_\text{c}(x_r) \left[ e^{-\lambda(r_{ij} - z_0 )} \left[C+f(\rho_{ij})+  g(\rho_{ij}, \{\alpha_{ij}^{(m)}\}) \right]- A\left (\frac{z_0}{r_{ij}} \right)^6 \right]
+
 
 where the *r\^-6* term models the attractive London dispersion,
 the exponential term is designed to capture the registry effect due to

doc/src/pair_e3b.rst

@@ -57,8 +57,19 @@ Description
 
 The *e3b* style computes an \"explicit three-body\" (E3B) potential for water :ref:`(Kumar 2008) <Kumar>`.
 
-.. image:: Eqs/e3b.jpg
-   :align: center
+.. math::
+
+   E =& E_2 \sum_{i,j}e^{-k_2 r_{ij}} + E_A \sum_{\substack{i,j,k,\ell \\
+   \in \textrm{type A}}} f(r_{ij})f(r_{k\ell}) + E_B \sum_{\substack{i,j,k,\ell \\
+   \in \textrm{type B}}} f(r_{ij})f(r_{k\ell}) + E_C \sum_{\substack{i,j,k,\ell \\
+   \in \textrm{type C}}} f(r_{ij})f(r_{k\ell}) \\
+   f(r) =& e^{-k_3 r}s(r) \\
+   s(r) =& \begin{cases}
+   1 & r<R_s \\
+   \displaystyle\frac{(R_f-r)^2(R_f-3R_s+2r)}{(R_f-R_s)^3} & R_s\leq r\leq R_f \\
+   0 & r>R_f\\
+   \end{cases}
+
 
 This potential was developed as a water model that includes the three-body cooperativity of hydrogen bonding explicitly.
 To use it in this way, it must be applied in conjunction with a conventional two-body water model, through *pair\_style hybrid/overlay*.
@@ -103,7 +114,7 @@ If the neigh setting is too large, the pair style will use more memory than nece
 This pair style tallies a breakdown of the total E3B potential energy into sub-categories, which can be accessed via the :doc:`compute pair <compute_pair>` command as a vector of values of length 4.
 The 4 values correspond to the terms in the first equation above: the E2 term, the Ea term, the Eb term, and the Ec term.
 
-See the examples/USER/e3b directory for a complete example script.
+See the examples/USER/misc/e3b directory for a complete example script.
 
 
 ----------

doc/src/pair_eam.rst

@@ -102,8 +102,11 @@ Style *eam* computes pairwise interactions for metals and metal alloys
 using embedded-atom method (EAM) potentials :ref:`(Daw) <Daw>`.  The total
 energy Ei of an atom I is given by
 
-.. image:: Eqs/pair_eam.jpg
-   :align: center
+.. math::
+
+   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})
+
 
 where F is the embedding energy which is a function of the atomic
 electron density rho, phi is a pair potential interaction, and alpha
@@ -371,8 +374,12 @@ alloys using a generalized form of EAM potentials due to Finnis and
 Sinclair :ref:`(Finnis) <Finnis1>`.  The total energy Ei of an atom I is
 given by
 
-.. image:: Eqs/pair_eam_fs.jpg
-   :align: center
+.. math::
+
+   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})
+
 
 This has the same form as the EAM formula above, except that rho is
 now a functional specific to the atomic types of both atoms I and J,

doc/src/pair_edip.rst

@@ -37,15 +37,27 @@ potentials, while *edip/multi* supports multi-element EDIP runs.
 
 In EDIP, the energy E of a system of atoms is
 
-.. image:: Eqs/pair_edip.jpg
-   :align: center
+.. math::
 
-where phi2 is a two-body term and phi3 is a three-body term.  The
-summations in the formula are over all neighbors J and K of atom I
-within a cutoff distance = a.
-Both terms depend on the local environment of atom I through its
-effective coordination number defined by Z, which is unity for a
-cutoff distance < c and gently goes to 0 at distance = a.
+   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 r<c \\
+         \exp\left(\frac{\alpha}{1-x^{-3}}\right) & \quad c<r<a \\
+         0 & \quad r>a
+         \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})
+
+
+where :math:`\phi_2` is a two-body term and :math:`\phi_3` is a
+three-body term.  The summations in the formula are over all neighbors J
+and K of atom I within a cutoff distance = a.  Both terms depend on the
+local environment of atom I through its effective coordination number
+defined by Z, which is unity for a cutoff distance < c and gently goes
+to 0 at distance = a.
 
 Only a single pair\_coeff command is used with the *edip* style which
 specifies a EDIP potential file with parameters for all

doc/src/pair_eff.rst

@@ -98,25 +98,19 @@ and the quantum-derived Pauli (E\_PR) and Kinetic energy interactions
 potentials between electrons (E\_KE) for a total energy expression
 given as,
 
-.. image:: Eqs/eff_energy_expression.jpg
-   :align: center
+.. math::
+
+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)
 
 The individual terms are defined as follows:
 
-.. image:: Eqs/eff_KE.jpg
-   :align: center
+.. math::
 
-.. image:: Eqs/eff_NN.jpg
-   :align: center
-
-.. image:: Eqs/eff_Ne.jpg
-   :align: center
-
-.. image:: Eqs/eff_ee.jpg
-   :align: center
-
-.. image:: Eqs/eff_Pauli.jpg
-   :align: center
+   E_{KE}  = & \frac{\hbar^2 }{{m_{e} }}\sum\limits_i {\frac{3}{{2s_i^2 }}} \\
+   E_{NN}  = & \frac{1}{{4\pi \varepsilon _0 }}\sum\limits_{i < j} {\frac{{Z_i Z_j }}{{R_{ij} }}} \\
+   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)} \\
+   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)} \\
+   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}} \\
 
 where, s\_i correspond to the electron sizes, the sigmas i's to the
 fixed spins of the electrons, Z\_i to the charges on the nuclei, R\_ij
@@ -229,11 +223,9 @@ representations, after the "ecp" keyword.
    Si.  The ECP captures the orbital overlap between the core and valence
    electrons (i.e. Pauli repulsion) with one of the functional forms:
 
-.. image:: Eqs/eff_ECP1.jpg
-   :align: center
-
-.. image:: Eqs/eff_ECP2.jpg
-   :align: center
+.. math::
+   E_{Pauli(ECP_s)} = & p_1\exp\left(-\frac{p_2r^2}{p_3+s^2} \right) \\
+   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] 
 
 Where the 1st form correspond to core interactions with s-type valence
 electrons and the 2nd to core interactions with p-type valence

doc/src/pair_eim.rst

@@ -34,30 +34,42 @@ Style *eim* computes pairwise interactions for ionic compounds
 using embedded-ion method (EIM) potentials :ref:`(Zhou) <Zhou2>`.  The
 energy of the system E is given by
 
-.. image:: Eqs/pair_eim1.jpg
-   :align: center
+.. math::
+
+   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)
 
 The first term is a double pairwise sum over the J neighbors of all I
-atoms, where phi\_ij is a pair potential.  The second term sums over
+atoms, where :math:`\phi_{ij}` is a pair potential.  The second term sums over
 the embedding energy E\_i of atom I, which is a function of its charge
-q\_i and the electrical potential sigma\_i at its location.  E\_i, q\_i,
-and sigma\_i are calculated as
+q\_i and the electrical potential :math:`\sigma_i` at its location.  E\_i, q\_i,
+and :math:`sigma_i` are calculated as
 
-.. image:: Eqs/pair_eim2.jpg
-   :align: center
+.. math::
 
-where eta\_ji is a pairwise function describing electron flow from atom
-I to atom J, and psi\_ij is another pairwise function.  The multi-body
+   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
+
+where :math:`\eta_{ji} is a pairwise function describing electron flow from atom
+I to atom J, and :math:`\psi_{ij}` is another pairwise function.  The multi-body
 nature of the EIM potential is a result of the embedding energy term.
 A complete list of all the pair functions used in EIM is summarized
 below
 
-.. image:: Eqs/pair_eim3.jpg
-   :align: center
+.. math::
 
-Here E\_b, r\_e, r\_(c,phi), alpha, beta, A\_(psi), zeta, r\_(s,psi),
-r\_(c,psi), A\_(eta), r\_(s,eta), r\_(c,eta), chi, and pair function type
-p are parameters, with subscripts ij indicating the two species of
+   \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.\\
+   \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 \mathrm{erfc}\left[\frac{1.64498\left(2r-r_p-r_c\right)}{r_c-r_p}\right] - 0.010204
+
+Here :math:`E_b, r_e, r_(c,\phi), \alpha, \beta, A_(\psi), \zeta, r_(s,\psi),
+r_(c,\psi), A_(\eta), r_(s,\eta), r_(c,\eta), \chi,` and pair function type
+*p* are parameters, with subscripts *ij* indicating the two species of
 atoms in the atomic pair.
 
 .. note::

doc/src/pair_exp6_rx.rst

@@ -43,17 +43,20 @@ one CG particle can interact with a species in a neighboring CG
 particle through a site-site interaction potential model.  The
 *exp6/rx* style computes an exponential-6 potential given by
 
-.. image:: Eqs/pair_exp6_rx.jpg
-   :align: center
+.. math::
 
-where the *epsilon* parameter determines the depth of the potential
-minimum located at *Rm*\ , and *alpha* determines the softness of the repulsion.
+   U_{ij}(r) = \frac{\epsilon}{\alpha-6}\{6\exp[\alpha(1-\frac{r_{ij}}{R_{m}})]-\alpha(\frac{R_{m}}{r_{ij}})^6\}
+
+
+where the :math:`\epsilon` parameter determines the depth of the
+potential minimum located at :math:`R_m`, and :math:`\alpha` determines
+the softness of the repulsion.
 
 The coefficients must be defined for each species in a given particle
 type via the :doc:`pair_coeff <pair_coeff>` command as in the examples
 above, where the first argument is the filename that includes the
 exponential-6 parameters for each species.  The file includes the
-species tag followed by the *alpha*\ , *epsilon* and *Rm*
+species tag followed by the :math:`\alpha, \epsilon` and :math:`R_m`
 parameters. The format of the file is described below.
 
 The second and third arguments specify the site-site interaction
@@ -74,22 +77,22 @@ to scale the EXP-6 parameters as reactions occur.  Currently, there
 are three scaling options:  *exponent*\ , *polynomial* and *none*\ .
 
 Exponent scaling requires two additional arguments for scaling
-the *Rm* and *epsilon* parameters, respectively.  The scaling factor
+the :math:`R_m` and :math:`\epsilon` parameters, respectively.  The scaling factor
 is computed by phi\^exponent, where phi is the number of molecules
 represented by the coarse-grain particle and exponent is specified
-as a pair coefficient argument for *Rm* and *epsilon*\ , respectively.
-The *Rm* and *epsilon* parameters are multiplied by the scaling
+as a pair coefficient argument for :math:`R_m` and :math:`\epsilon`, respectively.
+The :math:`R_m` and :math:`\epsilon` parameters are multiplied by the scaling
 factor to give the scaled interaction parameters for the CG particle.
 
 Polynomial scaling requires a filename to be specified as a pair
 coeff argument.  The file contains the coefficients to a fifth order
-polynomial for the *alpha*\ , *epsilon* and *Rm* parameters that depend
+polynomial for the :math:`\alpha`, :math:`\epsilon` and :math:`R_m` parameters that depend
 upon phi (the number of molecules represented by the CG particle).
 The format of a polynomial file is provided below.
 
 The *none* option to the scaling does not have any additional pair coeff
 arguments.  This is equivalent to specifying the *exponent* option with
-*Rm* and *epsilon* exponents of 0.0 and 0.0, respectively.
+:math:`R_m` and :math:`\epsilon` exponents of 0.0 and 0.0, respectively.
 
 The final argument specifies the interaction cutoff (optional).
 
@@ -133,23 +136,30 @@ between sections.
 
 Following a blank line, the next N lines list the species and their
 corresponding parameters.  The first argument is the species tag, the
-second argument is the exp6 tag, the 3rd argument is the *alpha*
-parameter (energy units), the 4th argument is the *epsilon* parameter
-(energy-distance\^6 units), and the 5th argument is the *Rm* parameter
+second argument is the exp6 tag, the 3rd argument is the :math:`\alpha`
+parameter (energy units), the 4th argument is the :math:`\epsilon` parameter
+(energy-distance\^6 units), and the 5th argument is the :math:`R_m` parameter
 (distance units).  If a species tag of "1fluid" is listed as a pair
 coefficient, a one-fluid approximation is specified where a
 concentration-dependent combination of the parameters is computed
 through the following equations:
 
-.. image:: Eqs/pair_exp6_rx_oneFluid.jpg
-   :align: center
+.. math::
+
+   R_{m}^{3} = & \sum_{a}\sum_{b} x_{a}x_{b}R_{m,ab}^{3} \\
+   \epsilon  = & \frac{1}{R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\epsilon_{ab}R_{m,ab}^{3} \\
+   \alpha    = & \frac{1}{\epsilon R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\alpha_{ab}\epsilon_{ab}R_{m,ab}^{3}
 
 where
 
-.. image:: Eqs/pair_exp6_rx_oneFluid2.jpg
-   :align: center
+.. math::
 
-and xa and xb are the mole fractions of a and b, respectively, which
+   \epsilon_{ab} = & \sqrt{\epsilon_{a}\epsilon_{b}} \\
+   R_{m,ab}      = & \frac{R_{m,a}+R_{m,b}}{2} \\ 
+   \alpha_{ab}   = & \sqrt{\alpha_{a}\alpha_{b}}
+
+
+and :math:`x_a` and :math:`x_b` are the mole fractions of a and b, respectively, which
 comprise the gas mixture.