convert math in spin and sph pair styles

doc/src/Eqs/pair_sph_ideal.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  p = (\gamma - 1) \rho e
-$$
-
-\end{document}

doc/src/Eqs/pair_sph_tait.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  p = B [(\frac{\rho}{\rho_0})^{\gamma} - 1]
-$$
-
-\end{document}

doc/src/Eqs/pair_spin_dmi_forces.tex

@@ -1,14 +0,0 @@
-\documentclass[preview]{standalone}
-\usepackage{varwidth}
-\usepackage[utf8x]{inputenc}
-\usepackage{amsmath,amssymb,amsthm,bm}
-\begin{document}
-\begin{varwidth}{50in}
-  \begin{equation}
-    \vec{\omega}_i = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times \left(\vec{e}_{ij}\times \vec{D} \right) 
-    ~~{\rm and}~~
-    \vec{F}_i = -\sum_{j}^{Neighb} \frac{1}{r_{ij}} \vec{D} \times \left( \vec{s}_{i}\times \vec{s}_{j} \right) 
-    , \nonumber
-  \end{equation}
-\end{varwidth}
-\end{document}

doc/src/Eqs/pair_spin_dmi_interaction.tex

@@ -1,16 +0,0 @@
-\documentclass[preview]{standalone}
-\usepackage{varwidth}
-\usepackage[utf8x]{inputenc}
-\usepackage{amsmath,amssymb,amsthm,bm}
-\begin{document}
-\begin{varwidth}{50in}
-  \begin{equation}
-    \bm{H}_{dm} = \sum_{{ i,j}=1,i\neq j}^{N} 
-    \left( \vec{e}_{ij} \times \vec{D} \right)
-    \cdot\left(\vec{s}_{i}\times \vec{s}_{j}\right), 
-    \nonumber
-  \end{equation}
-\end{varwidth}
-\end{document}
-    \vec{D}\left(r_{ij}\right) 
-    {\rm ~and~}  \vec{D}\left(r_{ij}\right) = \vec{e}_{ij} \times \vec{D}  

doc/src/pair_sdpd_taitwater_isothermal.rst

@@ -47,11 +47,13 @@ imagine for a mesoscopic particle.
 The pressure forces between particles will be computed according to
 Tait's equation of state:
 
-.. image:: Eqs/pair_sph_tait.jpg
-   :align: center
+.. math::
 
-where gamma = 7 and B = c\_0\^2 rho\_0 / gamma, with rho\_0 being the
-reference density and c\_0 the reference speed of sound.
+  p = B [(\frac{\rho}{\rho_0})^{\gamma} - 1]
+
+where :math:`\gamma = 7` and :math:`B = c_0^2 \rho_0 / \gamma`, with
+:math:`\rho_0` being the reference density and :math:`c_0` the reference
+speed of sound.
 
 The laminar viscosity and the random forces will be computed according
 to formulas described in :ref:`(Espanol and Revenga) <Espanol_Revenga>`.
@@ -75,11 +77,10 @@ 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.
 
-* rho0 reference density (mass/volume units)
-* c0 reference soundspeed (distance/time units)
+* :math:`\rho_0` reference density (mass/volume units)
+* :math:`c_0` reference soundspeed (distance/time units)
 * h kernel function cutoff (distance units)
 
-
 ----------
 
 
@@ -107,7 +108,8 @@ if LAMMPS was built with that package.  See the :doc:`Build package <Build_packa
 Related commands
 """"""""""""""""
 
-:doc:`pair coeff <pair_coeff>`, :doc:`pair sph/rhosum <pair_sph_rhosum>`
+:doc:`pair coeff <pair_coeff>`, :doc:`pair sph/rhosum <pair_sph_rhosum>`,
+:doc:`pair sph/taitwater <pair_sph_taitwater>`
 
 Default
 """""""

doc/src/pair_sph_idealgas.rst

@@ -26,13 +26,15 @@ Description
 The sph/idealgas style computes pressure forces between particles
 according to the ideal gas equation of state:
 
-.. image:: Eqs/pair_sph_ideal.jpg
-   :align: center
+.. math::
 
-where gamma = 1.4 is the heat capacity ratio, rho is the local
-density, and e is the internal energy per unit mass.  This pair style
-also computes Monaghan's artificial viscosity to prevent particles
-from interpenetrating :ref:`(Monaghan) <ideal-Monoghan>`.
+  p = (\gamma - 1) \rho e
+
+
+where :math:`\gamma = 1.4` is the heat capacity ratio, :math:`\rho` is
+the local density, and e is the internal energy per unit mass.  This
+pair style also computes Monaghan's artificial viscosity to prevent
+particles from interpenetrating :ref:`(Monaghan) <ideal-Monoghan>`.
 
 See `this PDF guide <USER/sph/SPH_LAMMPS_userguide.pdf>`_ to using SPH in
 LAMMPS.
@@ -41,7 +43,7 @@ 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.
 
-* nu artificial viscosity (no units)
+* :math:`\nu` artificial viscosity (no units)
 * h kernel function cutoff (distance units)
 
 

doc/src/pair_sph_lj.rst

@@ -37,7 +37,7 @@ 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.
 
-* nu artificial viscosity (no units)
+* :math:`\nu` artificial viscosity (no units)
 * h kernel function cutoff (distance units)
 
 

doc/src/pair_sph_taitwater.rst

@@ -26,11 +26,14 @@ Description
 The sph/taitwater style computes pressure forces between SPH particles
 according to Tait's equation of state:
 
-.. image:: Eqs/pair_sph_tait.jpg
-   :align: center
+.. math::
 
-where gamma = 7 and B = c\_0\^2 rho\_0 / gamma, with rho\_0 being the
-reference density and c\_0 the reference speed of sound.
+  p = B \biggl[\left(\frac{\rho}{\rho_0}\right)^{\gamma} - 1\biggr]
+
+
+where :math:`\gamma = 7` and :math:`B = c_0^2 \rho_0 / \gamma`, with
+:math:`\rho_0` being the reference density and :math:`c_0` the reference
+speed of sound.
 
 This pair style also computes Monaghan's artificial viscosity to
 prevent particles from interpenetrating :ref:`(Monaghan) <Monaghan>`.
@@ -42,9 +45,9 @@ 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.
 
-* rho0 reference density (mass/volume units)
-* c0 reference soundspeed (distance/time units)
-* nu artificial viscosity (no units)
+* :math:`\rho_0` reference density (mass/volume units)
+* :math:`c_0` reference soundspeed (distance/time units)
+* :math:`\nu` artificial viscosity (no units)
 * h kernel function cutoff (distance units)
 
 

doc/src/pair_sph_taitwater_morris.rst

@@ -26,11 +26,14 @@ Description
 The sph/taitwater/morris style computes pressure forces between SPH
 particles according to Tait's equation of state:
 
-.. image:: Eqs/pair_sph_tait.jpg
-   :align: center
+.. math::
 
-where gamma = 7 and B = c\_0\^2 rho\_0 / gamma, with rho\_0 being the
-reference density and c\_0 the reference speed of sound.
+  p = B \biggl[\left(\frac{\rho}{\rho_0}\right)^{\gamma} - 1\biggr]
+
+
+where :math:`\gamma = 7` and :math:`B = c_0^2 \rho_0 / \gamma`, with
+:math:`\rho_0` being the reference density and :math:`c_0` the reference
+speed of sound.
 
 This pair style also computes laminar viscosity :ref:`(Morris) <Morris>`.
 
@@ -41,9 +44,9 @@ 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.
 
-* rho0 reference density (mass/volume units)
-* c0 reference soundspeed (distance/time units)
-* nu dynamic viscosity (mass\*distance/time units)
+* :math:`\rho_0` reference density (mass/volume units)
+* :math:`c_0` reference soundspeed (distance/time units)
+* :math:`\nu` dynamic viscosity (mass\*distance/time units)
 * h kernel function cutoff (distance units)
 
 

doc/src/pair_spin_dipole.rst

@@ -43,12 +43,38 @@ The magnetic dipole-dipole interactions are computed by the
 following formulas for the magnetic energy, magnetic precession
 vector omega and mechanical force between particles I and J.
 
-.. image:: Eqs/pair_spin_dipole.jpg
-   :align: center
+.. math::
 
-where si and sj are the spin on two magnetic particles,
-r is their separation distance, and the vector e = (Ri - Rj)/\|Ri - Rj\|
-is the direction vector between the two particles.
+   \mathcal{H}_{\rm long} & = 
+   -\frac{\mu_{0} \left( \mu_B\right)^2}{4\pi} 
+   \sum_{i,j,i\neq j}^{N}
+    \frac{g_i g_j}{r_{ij}^3}
+    \biggl(3 
+    \left(\vec{e}_{ij}\cdot \vec{s}_{i}\right) 
+    \left(\vec{e}_{ij}\cdot \vec{s}_{j}\right) 
+    -\vec{s}_i\cdot\vec{s}_j \biggr) \\
+    \mathbf{\omega}_i & = 
+    \frac{\mu_0 (\mu_B)^2}{4\pi\hbar}\sum_{j}
+    \frac{g_i g_j}{r_{ij}^3}
+    \, \biggl(
+    3\,(\vec{e}_{ij}\cdot\vec{s}_{j})\vec{e}_{ij}
+    -\vec{s}_{j} \biggr) \\
+    \mathbf{F}_i & =
+    \frac{3\, \mu_0 (\mu_B)^2}{4\pi} \sum_j
+    \frac{g_i g_j}{r_{ij}^4}
+    \biggl[\bigl( (\vec{s}_i\cdot\vec{s}_j) 
+    -5(\vec{e}_{ij}\cdot\vec{s}_i)
+    (\vec{e}_{ij}\cdot\vec{s}_j)\bigr) \vec{e}_{ij}+
+    \bigl(
+    (\vec{e}_{ij}\cdot\vec{s}_i)\vec{s}_j+
+    (\vec{e}_{ij}\cdot\vec{s}_j)\vec{s}_i
+    \bigr)
+    \biggr]
+
+where :math:`\vec{s}_i` and :math:`\vec{s}_j` are the spin on two magnetic
+particles, r is their separation distance, and the vector :math:`\vec{e}_{ij}
+= \frac{r_i - r_j}{\left| r_i - r_j \right|}` is the direction vector
+between the two particles.
 
 Style *spin/dipole/long* computes long-range magnetic dipole-dipole
 interaction.

doc/src/pair_spin_dmi.rst

@@ -32,15 +32,19 @@ between pairs of magnetic spins.
 According to the expression reported in :ref:`(Rohart) <Rohart>`, one has
 the following DM energy:
 
-.. image:: Eqs/pair_spin_dmi_interaction.jpg
-   :align: center
+.. math::
 
-where si and sj are two neighboring magnetic spins of two particles,
-eij = (ri - rj)/\|ri-rj\| is the unit vector between sites i and j,
-and D is the DM vector defining the intensity (in eV) and the direction
-of the interaction.
+    \mathbf{H}_{dm} = \sum_{{ i,j}=1,i\neq j}^{N} 
+    \left( \vec{e}_{ij} \times \vec{D} \right)
+    \cdot\left(\vec{s}_{i}\times \vec{s}_{j}\right), 
 
-In :ref:`(Rohart) <Rohart>`, D is defined as the direction normal to the film oriented
+where :math:`\vec{s}_i` and :math:`\vec{s}_j` are two neighboring magnetic spins of
+two particles, :math:`\vec{e}_ij = \frac{r_i - r_j}{\left| r_i - r_j \right|}`
+is the unit vector between sites *i* and *j*, and :math:`\vec{D}` is the
+DM vector defining the intensity (in eV) and the direction of the
+interaction.
+
+In :ref:`(Rohart) <Rohart>`, :math:`\vec{D}` is defined as the direction normal to the film oriented
 from the high spin-orbit layer to the magnetic ultra-thin film.
 
 The application of a spin-lattice Poisson bracket to this energy (as described
@@ -48,8 +52,11 @@ in :ref:`(Tranchida) <Tranchida5>`) allows to derive a magnetic torque omega, an
 mechanical force F (for spin-lattice calculations only) for each magnetic
 particle i:
 
-.. image:: Eqs/pair_spin_dmi_forces.jpg
-   :align: center
+.. math::
+
+    \vec{\omega}_i = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times \left(\vec{e}_{ij}\times \vec{D} \right) 
+    ~~{\rm and}~~
+    \vec{F}_i = -\sum_{j}^{Neighb} \frac{1}{r_{ij}} \vec{D} \times \left( \vec{s}_{i}\times \vec{s}_{j} \right) 
 
 More details about the derivation of these torques/forces are reported in
 :ref:`(Tranchida) <Tranchida5>`.
@@ -93,11 +100,8 @@ Related commands
 
 ----------
 
-
 .. _Rohart:
 
-
-
 .. _Tranchida5:
 
 **(Rohart)** Rohart and Thiaville,

doc/src/pair_spin_magelec.rst

@@ -30,24 +30,29 @@ Style *spin/me* computes a magneto-electric interaction between
 pairs of magnetic spins. According to the derivation reported in
 :ref:`(Katsura) <Katsura1>`, this interaction is defined as:
 
-.. image:: Eqs/pair_spin_me_interaction.jpg
-   :align: center
+.. math::
 
-where si and sj are neighboring magnetic spins of two particles,
-eij = (ri - rj)/\|ri-rj\| is the normalized separation vector between the
-two particles, and E is an electric polarization vector.
-The norm and direction of E are giving the intensity and the
-direction of a screened dielectric atomic polarization (in eV).
+   \vec{\omega}_i & = -\frac{1}{\hbar} \sum_{j}^{Neighb} \vec{s}_{j}\times\vec{D}(r_{ij}) \\
+   \vec{F}_i & = -\sum_{j}^{Neighb} \frac{\partial D(r_{ij})}{\partial r_{ij}} \left(\vec{s}_{i}\times \vec{s}_{j} \right) \cdot \vec{r}_{ij}
+
+where :math:`\vec{s}_i` and :math:`\vec{s}_j` are neighboring magnetic
+spins of two particles.
 
 From this magneto-electric interaction, each spin i will be submitted
 to a magnetic torque omega, and its associated atom can be submitted to a
 force F for spin-lattice calculations (see :doc:`fix nve/spin <fix_nve_spin>`),
 such as:
 
-.. image:: Eqs/pair_spin_me_forces.jpg
-   :align: center
+.. math::
+
+    \vec{F}^{i} & = -\sum_{j}^{Neighbor} \left( \vec{s}_{i}\times \vec{s}_{j} \right) \times \vec{E} \\
+    \vec{\omega}^{i} = -\frac{1}{\hbar} \sum_{j}^{Neighbor} \vec{s}_j \times \left(\vec{E}\times r_{ij} \right)
+
+with h the Planck constant (in metal units) and :math:`\vec{E}` an
+electric polarization vector.  The norm and direction of E are giving
+the intensity and the direction of a screened dielectric atomic
+polarization (in eV).
 
-with h the Planck constant (in metal units).
 
 More details about the derivation of these torques/forces are reported in
 :ref:`(Tranchida) <Tranchida4>`.