convert remaining lj pair styles

doc/src/Eqs/pair_lj.tex

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

doc/src/Eqs/pair_lj96.tex

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

doc/src/Eqs/pair_lj_cubic.tex

@@ -1,12 +0,0 @@
-\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}

doc/src/Eqs/pair_lj_expand.tex

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

doc/src/Eqs/pair_lj_smooth.tex

@@ -1,15 +0,0 @@
-\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}
-
-

doc/src/Eqs/pair_lj_smooth_linear.tex

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

doc/src/Eqs/pair_lj_switch3.tex

@@ -1,11 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-  \thispagestyle{empty}
-
-\begin{eqnarray*}
-  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}

doc/src/pair_lj.rst

@@ -211,39 +211,51 @@ Description
 The *lj/cut* styles compute the standard 12/6 Lennard-Jones potential,
 given by
 
-.. image:: Eqs/pair_lj.jpg
-   :align: center
+.. math::
+
+   E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+       \left(\frac{\sigma}{r}\right)^6 \right]
+                       \qquad r < r_c
+
 
 Rc is the cutoff.
 
 Style *lj/cut/coul/cut* adds a Coulombic pairwise interaction given by
 
-.. image:: Eqs/pair_coulomb.jpg
-   :align: center
+.. math::
 
-where C is an energy-conversion constant, Qi and Qj are the charges on
-the 2 atoms, and epsilon is the dielectric constant which can be set
-by the :doc:`dielectric <dielectric>` command.  If one cutoff is
-specified in the pair\_style command, it is used for both the LJ and
-Coulombic terms.  If two cutoffs are specified, they are used as
-cutoffs for the LJ and Coulombic terms respectively.
+   E = \frac{C q_i q_j}{\epsilon  r} \qquad r < r_c
+
+
+where C is an energy-conversion constant, :math:`q_i` and :math:`q_j`
+are the charges on the 2 atoms, and :math:`\epsilon` is the dielectric
+constant which can be set by the :doc:`dielectric <dielectric>` command.
+If one cutoff is specified in the pair\_style command, it is used for
+both the LJ and Coulombic terms.  If two cutoffs are specified, they are
+used as cutoffs for the LJ and Coulombic terms respectively.
 
 Style *lj/cut/coul/debye* adds an additional exp() damping factor
 to the Coulombic term, given by
 
-.. image:: Eqs/pair_debye.jpg
-   :align: center
+.. math::
 
-where kappa is the inverse of the Debye length.  This potential is
-another way to mimic the screening effect of a polar solvent.
+   E = \frac{C q_i q_j}{\epsilon  r} \exp(- \kappa r) \qquad r < r_c
+
+
+where :math:`\kappa` is the inverse of the Debye length.  This potential
+is another way to mimic the screening effect of a polar solvent.
 
 Style *lj/cut/coul/dsf* computes the Coulombic term via the damped
 shifted force model described in :ref:`Fennell <Fennell2>`, given by:
 
-.. image:: Eqs/pair_coul_dsf.jpg
-   :align: center
+.. math::
 
-where *alpha* is the damping parameter and erfc() is the complementary
+  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 
+
+
+where :math:`\alpha` is the damping parameter and erfc() is the complementary
 error-function. This potential is essentially a short-range,
 spherically-truncated, charge-neutralized, shifted, pairwise *1/r*
 summation.  The potential is based on Wolf summation, proposed as an
@@ -253,7 +265,7 @@ effectively short-ranged. In order for the electrostatic sum to be
 absolutely convergent, charge neutralization within the cutoff radius
 is enforced by shifting the potential through placement of image
 charges on the cutoff sphere. Convergence can often be improved by
-setting *alpha* to a small non-zero value.
+setting :math:`\alpha` to a small non-zero value.
 
 Styles *lj/cut/coul/long* and *lj/cut/coul/msm* compute the same
 Coulombic interactions as style *lj/cut/coul/cut* except that an
@@ -267,21 +279,26 @@ computed in reciprocal space.
 Style *coul/wolf* adds a Coulombic pairwise interaction via the Wolf
 summation method, described in :ref:`Wolf <Wolf1>`, given by:
 
-.. image:: Eqs/pair_coul_wolf.jpg
-   :align: center
+.. math::
 
-where *alpha* is the damping parameter, and erfc() is the
-complementary error-function terms.  This potential
-is essentially a short-range, spherically-truncated,
-charge-neutralized, shifted, pairwise *1/r* summation.  With a
-manipulation of adding and subtracting a self term (for i = j) to the
-first and second term on the right-hand-side, respectively, and a
-small enough *alpha* damping parameter, the second term shrinks and
-the potential becomes a rapidly-converging real-space summation.  With
-a long enough cutoff and small enough alpha parameter, the energy and
-forces calculated by the Wolf summation method approach those of the
-Ewald sum.  So it is a means of getting effective long-range
-interactions with a short-range potential.
+  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
+
+
+where :math:`\alpha` is the damping parameter, and erfc() is the
+complementary error-function terms.  This potential is essentially a
+short-range, spherically-truncated, charge-neutralized, shifted,
+pairwise *1/r* summation.  With a manipulation of adding and subtracting
+a self term (for i = j) to the first and second term on the
+right-hand-side, respectively, and a small enough :math:`\alpha` damping
+parameter, the second term shrinks and the potential becomes a
+rapidly-converging real-space summation.  With a long enough cutoff and
+small enough alpha parameter, the energy and forces calculated by the
+Wolf summation method approach those of the Ewald sum.  So it is a means
+of getting effective long-range interactions with a short-range
+potential.
 
 Styles *lj/cut/tip4p/cut* and *lj/cut/tip4p/long* implement the TIP4P
 water model of :ref:`(Jorgensen) <Jorgensen2>`, which introduces a massless
@@ -319,14 +336,13 @@ the data file or restart files read by the :doc:`read_data <read_data>`
 or :doc:`read_restart <read_restart>` commands, or by mixing as
 described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 * cutoff1 (distance units)
 * cutoff2 (distance units)
 
-Note that sigma is defined in the LJ formula as the zero-crossing
-distance for the potential, not as the energy minimum at 2\^(1/6)
-sigma.
+Note that :math:`\sigma` is defined in the LJ formula as the zero-crossing
+distance for the potential, not as the energy minimum at :math:`2^{\frac{1}{6}} \sigma`.
 
 The latter 2 coefficients are optional.  If not specified, the global
 LJ and Coulombic cutoffs specified in the pair\_style command are used.
@@ -346,10 +362,12 @@ pair\_style command.
 ----------
 
 
-A version of these styles with a soft core, *lj/cut/soft*\ , suitable for use in
-free energy calculations, is part of the USER-FEP package and is documented with
-the :doc:`pair_style */soft <pair_fep_soft>` styles. The version with soft core is
-only available if LAMMPS was built with that package. See the :doc:`Build package <Build_package>` doc page for more info.
+A version of these styles with a soft core, *lj/cut/soft*\ , suitable
+for use in free energy calculations, is part of the USER-FEP package and
+is documented with the :doc:`pair_style */soft <pair_fep_soft>`
+styles. The version with soft core is only available if LAMMPS was built
+with that package. See the :doc:`Build package <Build_package>` doc page
+for more info.
 
 
 ----------

doc/src/pair_lj96.rst

@@ -35,10 +35,14 @@ Description
 The *lj96/cut* style compute a 9/6 Lennard-Jones potential, instead
 of the standard 12/6 potential, given by
 
-.. image:: Eqs/pair_lj96.jpg
-   :align: center
+.. math::
 
-Rc is the cutoff.
+   E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{9} - 
+   \left(\frac{\sigma}{r}\right)^6 \right]
+                       \qquad r < r_c
+
+
+:math:`r_c` is the cutoff.
 
 The following coefficients must be defined for each pair of atoms
 types via the :doc:`pair_coeff <pair_coeff>` command as in the examples
@@ -46,8 +50,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 * cutoff (distance units)
 
 The last coefficient is optional.  If not specified, the global LJ

doc/src/pair_lj_cubic.rst

@@ -39,15 +39,19 @@ point.  The cubic coefficient A3 is chosen so that both energy and
 force go to zero at the cutoff distance.  Outside the cutoff distance
 the energy and force are zero.
 
-.. image:: Eqs/pair_lj_cubic.jpg
-   :align: center
+.. math::
 
-The location of the inflection point rs is defined
-by the LJ diameter, rs/sigma = (26/7)\^1/6. The cutoff distance
-is defined by rc/rs = 67/48 or rc/sigma = 1.737....
+   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 
+
+
+The location of the inflection point :math:`r_s` is defined
+by the LJ diameter, :math:`r_s/\sigma = (26/7)^{1/6}`. The cutoff distance
+is defined by :math:`r_c/r_s = 67/48` or :math:`r_c/\sigma = 1.737...`
 The analytic expression for the
 the cubic coefficient
-A3\*rmin\^3/epsilon = 27.93... is given in the paper by
+:math:`A_3 r_{min}^3/\epsilon = 27.93...` is given in the paper by
 Holian and Ravelo :ref:`(Holian) <Holian>`.
 
 This potential is commonly used to study the shock mechanics of FCC
@@ -59,13 +63,13 @@ or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 
-Note that sigma is defined in the LJ formula as the zero-crossing
-distance for the potential, not as the energy minimum, which is
-located at rmin = 2\^(1/6)\*sigma. In the above example, sigma =
-0.8908987, so rmin = 1.
+Note that :math:`\sigma` is defined in the LJ formula as the
+zero-crossing distance for the potential, not as the energy minimum,
+which is located at :math:`r_{min} = 2^{\frac{1}{6}} \sigma`. In the
+above example, :math:`\sigma = 0.8908987`, so :math:`r_{min} = 1.0`.
 
 
 ----------

doc/src/pair_lj_expand.rst

@@ -51,36 +51,40 @@ delta which can be useful when particles are of different sizes, since
 it is different that using different sigma values in a standard LJ
 formula:
 
-.. image:: Eqs/pair_lj_expand.jpg
-   :align: center
+.. math::
 
-Rc is the cutoff which does not include the delta distance.  I.e. the
-actual force cutoff is the sum of cutoff + delta.
+  E = 4 \epsilon \left[ \left(\frac{\sigma}{r - \Delta}\right)^{12} - 
+    \left(\frac{\sigma}{r - \Delta}\right)^6 \right]
+    \qquad r < r_c + \Delta
+
+
+:math:`r_c` is the cutoff which does not include the :math:`\Delta`
+distance.  I.e. the actual force cutoff is the sum of :math:`r_c +
+\Delta`.
 
 For all of the *lj/expand* pair styles, 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 read by the :doc:`read_data <read_data>`
-or :doc:`read_restart <read_restart>` commands, or by mixing as
-described below:
+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 read by the :doc:`read_data <read_data>` or
+:doc:`read_restart <read_restart>` commands, or by mixing as described
+below:
 
-* epsilon (energy units)
-* sigma (distance units)
-* delta (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
+* :math:`\Delta` (distance units)
 * cutoff (distance units)
 
-The delta values can be positive or negative.  The last coefficient is
-optional.  If not specified, the global LJ cutoff is used.
+The :math:`\Delta` values can be positive or negative.  The last
+coefficient is optional.  If not specified, the global LJ cutoff is
+used.
 
 For *lj/expand/coul/long* only the LJ cutoff can be specified since a
 Coulombic cutoff cannot be specified for an individual I,J type pair.
 All type pairs use the same global Coulombic cutoff specified in the
 pair\_style command.
 
-
 ----------
 
-
 Styles with a *gpu*\ , *intel*\ , *kk*\ , *omp*\ , or *opt* suffix are
 functionally the same as the corresponding style without the suffix.
 They have been optimized to run faster, depending on your available

doc/src/pair_lj_long.rst

@@ -75,18 +75,25 @@ Examples
 Description
 """""""""""
 
-Style *lj/long/coul/long* computes the standard 12/6 Lennard-Jones and
-Coulombic potentials, given by
+Style *lj/long/coul/long* computes the standard 12/6 Lennard-Jones potential:
 
-.. image:: Eqs/pair_lj.jpg
-   :align: center
+.. math::
 
-.. image:: Eqs/pair_coulomb.jpg
-   :align: center
+   E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
+                       \left(\frac{\sigma}{r}\right)^6 \right]
+                       \qquad r < r_c \\
 
-where C is an energy-conversion constant, 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, and Rc is the cutoff.  If
+with :math:`\epsilon` and :math:`\sigma` being the usual Lennard-Jones
+potential parameters, plus the Coulomb potential, given by:
+
+.. math::
+
+   E = \frac{C q_i q_j}{\epsilon  r} \qquad r < r_c
+
+
+where C is an energy-conversion constant, :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, and :math:`r_c` is the cutoff.  If
 one cutoff is specified in the pair\_style command, it is used for both
 the LJ and Coulombic terms.  If two cutoffs are specified, they are
 used as cutoffs for the LJ and Coulombic terms respectively.
@@ -147,8 +154,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 * cutoff1 (distance units)
 * cutoff2 (distance units)
 

doc/src/pair_lj_smooth.rst

@@ -33,12 +33,18 @@ Description
 Style *lj/smooth* computes a LJ interaction with a force smoothing
 applied between the inner and outer cutoff.
 
-.. image:: Eqs/pair_lj_smooth.jpg
-   :align: center
+.. math::
+
+ 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
+
 
 The polynomial coefficients C1, C2, C3, C4 are computed by LAMMPS to
-cause the force to vary smoothly from the inner cutoff Rin to the
-outer cutoff Rc.
+cause the force to vary smoothly from the inner cutoff :math:`r_{in}` to the
+outer cutoff :math:`r_c`.
 
 At the inner cutoff the force and its 1st derivative
 will match the non-smoothed LJ formula.  At the outer cutoff the force
@@ -58,13 +64,13 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
-* inner (distance units)
-* outer (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
+* :math:`r_{in}` (distance units)
+* :math:`r_c` (distance units)
 
 The last 2 coefficients are optional inner and outer cutoffs.  If not
-specified, the global values for Rin and Rc are used.
+specified, the global values for :math:`r_{in}` and :math:`r_c` are used.
 
 
 ----------

doc/src/pair_lj_smooth_linear.rst

@@ -35,8 +35,12 @@ standard 12/6 Lennard-Jones function and subtracts a linear term based
 on the cutoff distance, so that both, the potential and the force, go
 continuously to zero at the cutoff Rc :ref:`(Toxvaerd) <Toxvaerd>`:
 
-.. image:: Eqs/pair_lj_smooth_linear.jpg
-   :align: center
+.. math::
+
+   \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 
+
 
 The following coefficients must be defined for each pair of atoms
 types via the :doc:`pair_coeff <pair_coeff>` command as in the examples
@@ -44,8 +48,8 @@ above, or in the data file or restart files read by the
 :doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
 commands, or by mixing as described below:
 
-* epsilon (energy units)
-* sigma (distance units)
+* :math:`\epsilon` (energy units)
+* :math:`\sigma` (distance units)
 * cutoff (distance units)
 
 The last coefficient is optional. If not specified, the global