convert pair styles local/density to meam/c

doc/src/Eqs/fld.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
-F^{H} = -R_{FU}(U-U^{\infty}) + R_{FE}E^{\infty}
-$$
-
-\end{document}

doc/src/Eqs/fld2.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
--R_{FU}(U-U^{\infty}) = -R_{FE}E^{\infty} - F^{rest}
-$$
-
-\end{document}

doc/src/Eqs/pair_local_density_energy.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
- U_{LD} = \sum_i F(\rho_i)
-$$
-
-
-\end{document}
-~                  

doc/src/Eqs/pair_local_density_energy_implement.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-U_{LD} = \sum_k U_{LD}^{(k)} = \sum_i \left[ \sum_k a_\alpha^{(k)} F^{(k)} \left(\rho_i^{(k)}\right) \right] 
-$$
-
-\end{document}

doc/src/Eqs/pair_local_density_energy_multi.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-U_{LD} = \sum_i a_\alpha F(\rho_i)
-$$
-
-\end{document}

doc/src/Eqs/pair_local_density_indicator_func.tex

@@ -1,16 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage[utf8]{inputenc}
-\usepackage{amsmath}
-\usepackage{amsfonts}
-
-\begin{document}
-\[
-  \varphi(r) = 
-    \begin{cases}
-       1 & r \le R_1 \\
-       c_0 + c_2r^2 + c_4r^4 + c_6r^6  & r \in (R_1, R_2) \\
-       0 & r \ge R_2
-  \end{cases}
-\]
-
-\end{document}

doc/src/Eqs/pair_local_density_ld.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-
-$$
-\rho_i = \sum_{j \neq i} \varphi(r_{ij})
-$$
-
-\end{document}

doc/src/Eqs/pair_local_density_ld_implement.tex

@@ -1,10 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-
-$$
-\rho_i^{(k)} = \sum_j b_\beta^{(k)} \varphi^{(k)} (r_{ij})
-$$
-
-\end{document}

doc/src/Eqs/pair_local_density_ld_multi.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-
-$$
-\rho_i = \sum_{j \neq i} b_\beta \varphi(r_{ij})
-$$
-
-\end{document}

doc/src/Eqs/pair_lubricate.tex

@@ -1,17 +0,0 @@
-\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}

doc/src/Eqs/pair_mdf-1.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E_{smooth}(r) = E(r)*f(r)
-$$
-
-\end{document}

doc/src/Eqs/pair_mdf-2.tex

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

doc/src/Eqs/pair_mdf-3.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   x = \frac{(r-r_m)}{(r_{cut}-r_m)}
-$$
-
-\end{document}

doc/src/Eqs/pair_mdf-4.tex

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

doc/src/Eqs/pair_mdf-5.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   E(r) = A e^{(-r/\rho)} -\frac{C}{r^6}
-$$
-
-\end{document}

doc/src/Eqs/pair_mdf-6.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-$$
-   E(r) = \frac{A}{r^{12}} - \frac{B}{r^{6}}
-$$
-
-\end{document}

doc/src/Eqs/pair_meam.tex

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

doc/src/Eqs/pair_meam_spline.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-
-\begin{document}
-
-$$
-   E=\sum_{i<j}\phi(r_{ij})+\sum_{i}U(n_{i}),
-$$
-
-$$
-   n_{i}=\sum_{j}\rho(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})]
-$$
-
-\end{document}

doc/src/Eqs/pair_meam_spline_multicomponent.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-
-\begin{document}
-
-$$
-   E=\sum_{i<j}\phi_{ij}(r_{ij})+\sum_{i}U_i(n_{i}),
-$$
-
-$$
-   n_{i}=\sum_{j\ne i}\rho_j(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f_{j}(r_{ij})f_{k}(r_{ik})g_{jk}[\cos(\theta_{jik})]
-$$
-
-\end{document}

doc/src/Eqs/pair_meam_sw_spline.tex

@@ -1,23 +0,0 @@
-\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}
-
-

doc/src/pair_lj_switch3_coulgauss_long.rst

@@ -40,26 +40,35 @@ Description
 The *lj/switch3/coulgauss* style evaluates the LJ
 vdW potential
 
-.. image:: Eqs/pair_lj_switch3.jpg
-   :align: center
+.. math::
+
+   E = 4\epsilon \left[ \left(\frac{\sigma}{r}\right)^{12}-\left(\frac{\sigma}{r}\right)^{6} \right]
 
 , which goes smoothly to zero at the cutoff r\_c as defined
 by the switching function
 
-.. image:: Eqs/pair_switch3.jpg
-   :align: center
+.. math::
+
+ S_3(r) = \left\lbrace \begin{array}{ll}
+                     1 & \quad\mathrm{if}\quad r < r_\mathrm{c} - w \\
+                     3x^2 - 2x^3 & \quad\mathrm{if}\quad r < r_\mathrm{c} \quad\mathrm{with\quad} x=\frac{r_\mathrm{c} - r}{w} \\
+                     0 & \quad\mathrm{if}\quad r >= r_\mathrm{c}
+                 \end{array} \right.
+
 
 where w is the width defined in the arguments. This potential
 is combined with Coulomb interaction between Gaussian charge densities:
 
-.. image:: Eqs/pair_coulgauss.jpg
-   :align: center
+.. math::
 
-where qi and qj are the
-charges on the 2 atoms, epsilon is the dielectric constant which
-can be set by the :doc:`dielectric <dielectric>` command, gamma\_i and gamma\_j
-are the widths of the Gaussian charge distribution and erf() is the error-function.
-This style has to be used in conjunction with the :doc:`kspace_style <kspace_style>` command
+   E = \frac{q_i q_j \mathrm{erf}\left( r/\sqrt{\gamma_1^2+\gamma_2^2} \right) }{\epsilon r_{ij}}
+
+where :math:`q_i` and :math:`q_j` are the charges on the 2 atoms,
+:math:`\epsilon` is the dielectric constant which can be set by the
+:doc:`dielectric <dielectric>` command, :math:`\gamma_i` and
+:math:`\gamma_j` are the widths of the Gaussian charge distribution and
+erf() is the error-function.  This style has to be used in conjunction
+with the :doc:`kspace_style <kspace_style>` command
 
 If one cutoff is specified it is used for both the vdW and Coulomb
 terms.  If two cutoffs are specified, the first is used as the cutoff
@@ -71,10 +80,9 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands:
 
-* epsilon (energy)
-* sigma (distance)
-* gamma (distance)
-
+* :math:`\epsilon` (energy)
+* :math:`\sigma` (distance)
+* :math:`\gamma` (distance)
 
 ----------
 

doc/src/pair_local_density.rst

@@ -62,22 +62,34 @@ upon initialization.
 A system of a single atom type (e.g., LJ argon) with a single local density (LD)
 potential would have an energy given by:
 
-.. image:: Eqs/pair_local_density_energy.jpg
-   :align: center
+.. math::
 
-where rho\_i is the LD at atom i and F(rho) is similar in spirit to the 
-embedding function used in EAM potentials. The LD at atom i is given by the sum
+   U_{LD} = \sum_i F(\rho_i)
 
-.. image:: Eqs/pair_local_density_ld.jpg
-   :align: center
 
-where phi is an indicator function that is one at r=0 and zero beyond a cutoff 
-distance R2. The choice of the functional form of phi is somewhat arbitrary, 
-but the following piecewise cubic function has proven sufficiently general: 
-:ref:`(Sanyal1) <Sanyal1>`, :ref:`(Sanyal2) <Sanyal2>` :ref:`(Rosenberger) <Rosenberger>`
+where :math:`\rho_i` is the LD at atom *i* and :math:`F(\rho)` is
+similar in spirit to the embedding function used in EAM potentials. The
+LD at atom *i* is given by the sum
 
-.. image:: Eqs/pair_local_density_indicator_func.jpg
-   :align: center
+.. math::
+
+   \rho_i = \sum_{j \neq i} \varphi(r_{ij})
+
+
+where :math:`\varphi` is an indicator function that is one at r=0 and
+zero beyond a cutoff distance R2. The choice of the functional form of
+:math:`\varphi` is somewhat arbitrary, but the following piecewise cubic
+function has proven sufficiently general: :ref:`(Sanyal1) <Sanyal1>`,
+:ref:`(Sanyal2) <Sanyal2>` :ref:`(Rosenberger) <Rosenberger>`
+
+.. math::
+
+   \varphi(r) = 
+   \begin{cases}
+   1 & r \le R_1 \\
+   c_0 + c_2r^2 + c_4r^4 + c_6r^6  & r \in (R_1, R_2) \\
+   0 & r \ge R_2
+   \end{cases}
 
 The constants *c* are chosen so that the indicator function smoothly 
 interpolates between 1 and 0 between the distances R1 and R2, which are 
@@ -100,34 +112,38 @@ pair style. Please see :ref:`(Sanyal1) <Sanyal1>` for details of the derivation.
 
 The potential is easily generalized to systems involving multiple atom types:
 
-.. image:: Eqs/pair_local_density_energy_multi.jpg
-   :align: center
+.. math::
+
+   U_{LD} = \sum_i a_\alpha F(\rho_i)
+
 
 with the LD expressed as
 
-.. image:: Eqs/pair_local_density_ld_multi.jpg
-   :align: center
+.. math::
 
-where alpha gives the type of atom i, beta the type of atom j, and the 
-coefficients a and b filter for atom types as specified by the user. a is 
-called the central atom filter as it determines to which atoms the 
-potential applies; a\_alpha = 1 if the LD potential applies to atom type alpha 
-else zero. On the other hand, b is called the neighbor atom filter because it 
-specifies which atom types to use in the calculation of the LD; b\_beta = 1 if 
-atom type beta contributes to the LD and zero otherwise.
+   \rho_i = \sum_{j \neq i} b_\beta \varphi(r_{ij})
+
+
+where :math:`\alpha` gives the type of atom *i*\ , :math:`\beta` the
+type of atom *j*\ , and the coefficients *a* and *b* filter for atom
+types as specified by the user. *a* is called the central atom filter as
+it determines to which atoms the potential applies; :math:`a_{\alpha} =
+1` if the LD potential applies to atom type alpha else zero. On the
+other hand, *b* is called the neighbor atom filter because it specifies
+which atom types to use in the calculation of the LD; :math:`b_{\beta} =
+1` if atom type :math:`\beta` contributes to the LD and zero otherwise.
 
 .. note::
 
-   Note that the potentials need not be symmetric with respect to atom types, 
-   which is the reason for two distinct sets of coefficients a and b. An atom type 
-   may contribute to the LD but not the potential, or to the potential but not the 
-   LD. Such decisions are made by the user and should (ideally) be motivated on 
-   physical grounds for the problem at hand.
-
+   Note that the potentials need not be symmetric with respect to atom
+   types, which is the reason for two distinct sets of coefficients *a*
+   and *b*\ . An atom type may contribute to the LD but not the
+   potential, or to the potential but not the LD. Such decisions are
+   made by the user and should (ideally) be motivated on physical
+   grounds for the problem at hand.
 
 ----------
 
-
 **General form for implementation in LAMMPS:**
 
 Of course, a system with many atom types may have many different possible LD 
@@ -135,14 +151,18 @@ potentials, each with their own atom type filters, cutoffs, and embedding
 functions. The most general form of this potential as implemented in the 
 pair\_style local/density is:
 
-.. image:: Eqs/pair_local_density_energy_implement.jpg
-   :align: center
+.. math::
 
-where, k is an index that spans the (arbitrary) number of applied LD potentials 
-N\_LD. Each LD is calculated as before with:
+   U_{LD} = \sum_k U_{LD}^{(k)} = \sum_i \left[ \sum_k a_\alpha^{(k)} F^{(k)} \left(\rho_i^{(k)}\right) \right] 
+
+
+where, *k* is an index that spans the (arbitrary) number of applied LD
+potentials N\_LD. Each LD is calculated as before with:
+
+.. math::
+
+   \rho_i^{(k)} = \sum_j b_\beta^{(k)} \varphi^{(k)} (r_{ij})
 
-.. image:: Eqs/pair_local_density_ld_implement.jpg
-   :align: center
 
 The superscript on the indicator function phi simply indicates that it is 
 associated with specific values of the cutoff distances R1(k) and R2(k). In 
@@ -154,10 +174,8 @@ one must specify:
 * the neighbor type filter b(k), where k = 1,2,...N\_LD
 * the LD potential function F(k)(rho), typically as a table that is later spline-interpolated
 
-
 ----------
 
-
 **Tabulated input file format:**
 
 
@@ -189,10 +207,8 @@ Lines 5 to 9+N\_rho constitute the first block. Thus the input file is separated
 each specifying its own upper and lower cutoffs, central and neighbor atoms, 
 and potential.  In general, blank lines anywhere are ignored.
 
-
 ----------
 
-
 **Mixing, shift, table, tail correction, restart, info**\ :
 This pair style does not support automatic mixing. For atom type pairs alpha,
 beta and alpha != beta, even if LD potentials of type (alpha, alpha) and 

doc/src/pair_lubricate.rst

@@ -51,8 +51,16 @@ interactions between mono-disperse finite-size spherical particles in
 a pairwise fashion.  The interactions have 2 components.  The first is
 Ball-Melrose lubrication terms via the formulas in :ref:`(Ball and Melrose) <Ball1>`
 
-.. image:: Eqs/pair_lubricate.jpg
-   :align: center
+.. math::
+
+   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 \\
+   & \\
+   \Omega_N & = \mathbf{n} \times (v_1 - v_2) / r
+
 
 which represents the dissipation W between two nearby particles due to
 their relative velocities in the presence of a background solvent with
@@ -82,12 +90,14 @@ The other component is due to the Fast Lubrication Dynamics (FLD)
 approximation, described in :ref:`(Kumar) <Kumar1>`, which can be
 represented by the following equation
 
-.. image:: Eqs/fld.jpg
-   :align: center
+.. math::
+
+   F^{H} = -R_{FU}(U-U^{\infty}) + R_{FE}E^{\infty}
+
 
 where U represents the velocities and angular velocities of the
-particles, U\^\ *infty* represents the velocity and the angular velocity
-of the undisturbed fluid, and E\^\ *infty* represents the rate of strain
+particles, :math:`U^{\infty}` represents the velocity and the angular velocity
+of the undisturbed fluid, and :math:`E^{\infty}` represents the rate of strain
 tensor of the undisturbed fluid with viscosity *mu*\ . Again, note that
 this is dynamic viscosity which has units of mass/distance/time, not
 kinematic viscosity. Volume fraction corrections to R\_FU are included

doc/src/pair_lubricateU.rst

@@ -43,8 +43,16 @@ other types of interactions.
 The interactions have 2 components.  The first is
 Ball-Melrose lubrication terms via the formulas in :ref:`(Ball and Melrose) <Ball2>`
 
-.. image:: Eqs/pair_lubricate.jpg
-   :align: center
+.. math::
+
+   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 \\
+   & \\
+   \Omega_N & = \mathbf{n} \times (v_1 - v_2) / r
+
 
 which represents the dissipation W between two nearby particles due to
 their relative velocities in the presence of a background solvent with
@@ -75,13 +83,15 @@ The other component is due to the Fast Lubrication Dynamics (FLD)
 approximation, described in :ref:`(Kumar) <Kumar2>`.  The equation being
 solved to balance the forces and torques is
 
-.. image:: Eqs/fld2.jpg
-   :align: center
+.. math::
+
+   -R_{FU}(U-U^{\infty}) = -R_{FE}E^{\infty} - F^{rest}
+
 
 where U represents the velocities and angular velocities of the
-particles, U\^\ *infty* represents the velocities and the angular
-velocities of the undisturbed fluid, and E\^\ *infty* represents the rate
-of strain tensor of the undisturbed fluid flow with viscosity
+particles, :math:`U^{\infty}` represents the velocities and the angular
+velocities of the undisturbed fluid, and :math:`E^{\infty}` represents
+the rate of strain tensor of the undisturbed fluid flow with viscosity
 *mu*\ . Again, note that this is dynamic viscosity which has units of
 mass/distance/time, not kinematic viscosity.  Volume fraction
 corrections to R\_FU are included if *flagVF* is set to 1 (default).

doc/src/pair_mdf.rst

@@ -60,22 +60,29 @@ Lennard-Jones and Buckingham potential with the addition of a taper
 function that ramps the energy and force smoothly to zero between an
 inner and outer cutoff.
 
-.. image:: Eqs/pair_mdf-1.jpg
-   :align: center
+.. math::
+
+   E_{smooth}(r) = E(r)*f(r)
+
 
 The tapering, *f(r)*\ , is done by using the Mei, Davenport, Fernando
 function :ref:`(Mei) <Mei>`.
 
-.. image:: Eqs/pair_mdf-2.jpg
-   :align: center
+.. math::
+
+   f(r) & = 1.0  \qquad \qquad \mathrm{for} \qquad r < r_m \\
+   f(r) & = (1 - x)^3*(1+3x+6x^2) \quad \mathrm{for} \qquad r_m < r < r_{cut} \\
+   f(r) & = 0.0  \qquad \qquad \mathrm{for} \qquad  r >= r_{cut} \\
 
 where
 
-.. image:: Eqs/pair_mdf-3.jpg
-   :align: center
+.. math::
 
-Here *r\_m* is the inner cutoff radius and *r\_cut* is the outer cutoff
-radius.
+   x = \frac{(r-r_m)}{(r_{cut}-r_m)}
+
+
+Here :math:`r_m` is the inner cutoff radius and :math:`r_{cut}` is the
+outer cutoff radius.
 
 
 ----------
@@ -84,48 +91,50 @@ radius.
 For the *lj/mdf* pair\_style, the potential energy, *E(r)*\ , is the
 standard 12-6 Lennard-Jones written in the epsilon/sigma form:
 
-.. image:: Eqs/pair_mdf-4.jpg
-   :align: center
+.. math::
+
+   E(r) = 4\epsilon\biggl[\bigl(\frac{\sigma}{r}\bigr)^{12} - \bigl(\frac{\sigma}{r}\bigr)^6\biggr]
+
 
 Either the first two or all of the following coefficients must be
-defined for each pair of atoms types via the pair\_coeff command as
-in the examples above, or in the data file read by the
-:doc:`read_data <read_data>`. The two cutoffs default to the global
-values and epsilon and sigma can also be determined by mixing as
+defined for each pair of atoms types via the pair\_coeff command as in
+the examples above, or in the data file read by the :doc:`read_data
+<read_data>`. The two cutoffs default to the global values and
+:math:`\epsilon` and :math:`\sigma` can also be determined by mixing as
 described below:
 
-* epsilon (energy units)
-* sigma (distance units)
-* r\_m (distance units)
-* r\_\ *cut* (distance units)
-
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
+* :math:`r_m` (distance units)
+* :math:`r_{cut}` (distance units)
 
 ----------
 
-
 For the *buck/mdf* pair\_style, the potential energy, *E(r)*\ , is the
 standard Buckingham potential with three required coefficients.
 The two cutoffs can be omitted and default to the corresponding
 global values:
 
-.. image:: Eqs/pair_mdf-5.jpg
-   :align: center
+.. math::
 
-* A (energy units)
-* \rho (distance units)
-* C (energy-distance\^6 units)
-* r\_m (distance units)
-* r\_\ *cut* (distance units)
+   E(r) = A e^{(-r/\rho)} -\frac{C}{r^6}
 
 
+* *A* (energy units)
+* :math:`\rho` (distance units)
+* *C* (energy-distance\^6 units)
+* :math:`r_m` (distance units)
+* :math:`r_{cut}` (distance units)
+
 ----------
 
-
 For the *lennard/mdf* pair\_style, the potential energy, *E(r)*\ , is the
 standard 12-6 Lennard-Jones written in the A/B form:
 
-.. image:: Eqs/pair_mdf-6.jpg
-   :align: center
+.. math::
+
+   E(r) = \frac{A}{r^{12}} - \frac{B}{r^{6}}
+
 
 The following coefficients must be defined for each pair of atoms
 types via the pair\_coeff command as in the examples above, or in the
@@ -133,23 +142,21 @@ data file read by the read\_data commands, or by mixing as described below.
 The two cutoffs default to their global values and must be either both
 given or both left out:
 
-* A (energy-distance\^12 units)
-* B (energy-distance\^6 units)
-* r\_m (distance units)
-* r\_\ *cut* (distance units)
-
+* *A* (energy-distance\^12 units)
+* *B* (energy-distance\^6 units)
+* :math:`r_m` (distance units)
+* :math:`r_{cut}` (distance units)
 
 ----------
 
-
 **Mixing, shift, table, tail correction, restart, rRESPA info**\ :
 
-For atom type pairs I,J and I != J, the epsilon and sigma coefficients
-and cutoff distances for the lj/mdf pair style can be mixed.
-The default mix value is *geometric*\ .  See the "pair\_modify" command
-for details. The other two pair styles buck/mdf and lennard/mdf do not
-support mixing, so all I,J pairs of coefficients must be specified
-explicitly.
+For atom type pairs I,J and I != J, the :math:`\epsilon` and
+:math:`sigma` coefficients and cutoff distances for the lj/mdf pair
+style can be mixed.  The default mix value is *geometric*\ .  See the
+"pair\_modify" command for details. The other two pair styles buck/mdf
+and lennard/mdf do not support mixing, so all I,J pairs of coefficients
+must be specified explicitly.
 
 None of the lj/mdf, buck/mdf, or lennard/mdf pair styles supports
 the :doc:`pair_modify <pair_modify>` shift option or long-range
@@ -161,14 +168,11 @@ to be specified in an input script that reads a restart file.
 These styles can only be used via the *pair* keyword of the :doc:`run_style respa <run_style>` command.  They do not support the *inner*\ ,
 *middle*\ , *outer* keywords.
 
-
 ----------
 
-
 Restrictions
 """"""""""""
 
-
 These pair styles can only be used if LAMMPS was built with the
 USER-MISC package.  See the :doc:`Build package <Build_package>` doc
 page for more info.

doc/src/pair_meam_spline.rst

@@ -32,27 +32,31 @@ using a variant of modified embedded-atom method (MEAM) potentials
 :ref:`(Lenosky) <Lenosky1>`.  For a single species ("old-style") MEAM,
 the total energy E is given by
 
-.. image:: Eqs/pair_meam_spline.jpg
-   :align: center
+.. math::
 
-where rho\_i is the density at atom I, theta\_jik is the angle between
-atoms J, I, and K centered on atom I. The five functions Phi, U, rho,
-f, and g are represented by cubic splines.
+   E & =\sum_{i<j}\phi(r_{ij})+\sum_{i}U(n_{i}) \\
+   n_{i} & =\sum_{j}\rho(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f(r_{ij})f(r_{ik})g[\cos(\theta_{jik})]
+
+where :math:`\rho_i` is the density at atom I, :math:`\theta_{jik}` is
+the angle between atoms J, I, and K centered on atom I. The five
+functions :math:`\phi, U, \rho, f,` and *g* are represented by cubic splines.
 
 The *meam/spline* style also supports a new style multicomponent
 modified embedded-atom method (MEAM) potential :ref:`(Zhang) <Zhang4>`, where
 the total energy E is given by
 
-.. image:: Eqs/pair_meam_spline_multicomponent.jpg
-   :align: center
+.. math::
 
-where the five functions Phi, U, rho, f, and g depend on the chemistry
-of the atoms in the interaction.  In particular, if there are N different
-chemistries, there are N different U, rho, and f functions, while there
-are N(N+1)/2 different Phi and g functions.  The new style multicomponent
-MEAM potential files are indicated by the second line in the file starts
-with "meam/spline" followed by the number of elements and the name of each
-element.
+   E &= \sum_{i<j}\phi_{ij}(r_{ij})+\sum_{i}U_i(n_{i}) \\
+   n_{i} & = \sum_{j\ne i}\rho_j(r_{ij})+\sum_{\substack{j<k,\\j,k\neq i}}f_{j}(r_{ij})f_{k}(r_{ik})g_{jk}[\cos(\theta_{jik})]
+
+where the five functions :math:`\phi, U, \rho, f,` and *g* depend on the
+chemistry of the atoms in the interaction.  In particular, if there are
+N different chemistries, there are N different *U*\ , :math:`\rho`, and
+*f* functions, while there are N(N+1)/2 different :math:`\phi` and *g*
+functions.  The new style multicomponent MEAM potential files are
+indicated by the second line in the file starts with "meam/spline"
+followed by the number of elements and the name of each element.
 
 The cutoffs and the coefficients for these spline functions are listed
 in a parameter file which is specified by the

doc/src/pair_meam_sw_spline.rst

@@ -32,12 +32,17 @@ was first proposed by Nicklas, Fellinger, and Park
 :ref:`(Nicklas) <Nicklas>`.  We refer to it as MEAM+SW.  The total energy E
 is given by
 
-.. image:: Eqs/pair_meam_sw_spline.jpg
-   :align: center
+.. math::
 
-where rho\_I is the density at atom I, theta\_JIK is the angle between
-atoms J, I, and K centered on atom I. The seven functions
-Phi, F, G, U, rho, f, and g are represented by cubic splines.
+   E & = E_{MEAM} + E_{SW} \\
+   E_{MEAM} & =  \sum _{IJ} \phi (r_{IJ}) + \sum _{I} U(\rho _I) \\
+   E_{SW} & =  \sum _{I} \sum _{JK} F(r_{IJ}) \, F(r_{IK}) \, G(\cos(\theta _{JIK})) \\
+   \rho _I & = \sum _J \rho(r_{IJ}) + \sum _{JK} f(r_{IJ}) \, f(r_{IK}) \, g(\cos(\theta _{JIK}))
+
+where :math:`\rho_I` is the density at atom I, :math:`\theta_{JIK}` is
+the angle between atoms J, I, and K centered on atom I. The seven
+functions :math:`\phi, F, G, U, \rho, f,` and *g* are represented by
+cubic splines.
 
 The cutoffs and the coefficients for these spline functions are listed
 in a parameter file which is specified by the

doc/src/pair_meamc.rst

@@ -46,15 +46,18 @@ the 12 December 2018 release.
 In the MEAM formulation, the total energy E of a system of atoms is
 given by:
 
-.. image:: Eqs/pair_meam.jpg
-   :align: center
+.. math::
 
-where F is the embedding energy which is a function of the atomic
-electron density rho, and phi is a pair potential interaction.  The
-pair interaction is summed over all neighbors J of atom I within the
-cutoff distance.  As with EAM, the multi-body nature of the MEAM
-potential is a result of the embedding energy term.  Details of the
-computation of the embedding and pair energies, as implemented in
+  E = \sum_i \left\{ F_i(\bar{\rho}_i)
+      + \frac{1}{2} \sum_{i \neq j} \phi_{ij} (r_{ij}) \right\}
+
+
+where *F* is the embedding energy which is a function of the atomic
+electron density :math:`\rho`, and :math:`\phi` is a pair potential
+interaction.  The pair interaction is summed over all neighbors J of
+atom I within the cutoff distance.  As with EAM, the multi-body nature
+of the MEAM potential is a result of the embedding energy term.  Details
+of the computation of the embedding and pair energies, as implemented in
 LAMMPS, are given in :ref:`(Gullet) <Gullet>` and references therein.
 
 The various parameters in the MEAM formulas are listed in two files

doc/src/pair_mm3_switch3_coulgauss_long.rst

@@ -64,7 +64,7 @@ is combined with Coulomb interaction between Gaussian charge densities:
 
 .. math::
 
-  E & = \frac{q_i q_j \mathrm{erf}\left( r/\sqrt{\gamma_1^2+\gamma_2^2} \right) }{\epsilon r_{ij}}
+  E = \frac{q_i q_j \mathrm{erf}\left( r/\sqrt{\gamma_1^2+\gamma_2^2} \right) }{\epsilon r_{ij}}
 
 
 where :math:`q_i` and :math:`q_j` are the charges on the 2 atoms,