Merge pull request #1869 from akohlmey/doc-continued-refactoring

More documentation refactoring for embedding math expressions

doc/Makefile

@@ -75,8 +75,11 @@ html: $(ANCHORCHECK)
 	@rm -rf html/_sources
 	@rm -rf html/PDF
 	@rm -rf html/USER
+	@rm -rf html/JPG
 	@cp -r src/PDF html/PDF
 	@cp -r src/USER html/USER
+	@mkdir -p html/JPG
+	@cp `grep -A2 '\.\. image::' src/*.rst | grep ':target:' | sed -e 's,.*:target: JPG/,src/JPG/,' | sort | uniq` html/JPG/
 	@rm -rf html/PDF/.[sg]*
 	@rm -rf html/USER/.[sg]*
 	@rm -rf html/USER/*/.[sg]*

doc/src/Build_windows.rst

@@ -17,9 +17,9 @@ General remarks
 
 LAMMPS is developed and tested primarily on Linux machines.  The vast
 majority of HPC clusters and supercomputers today runs on Linux as well.
-Thus portability to other platforms is desired, but not always achieved.
+While portability to other platforms is desired, it is not always achieved.
 The LAMMPS developers strongly rely on LAMMPS users giving feedback and
-providing assistance in resolving portability issues. This particularly
+providing assistance in resolving portability issues. This is particularly
 true for compiling LAMMPS on Windows, since this platform has significant
 differences with some low-level functionality.
 
@@ -31,18 +31,20 @@ Running Linux on Windows
 So before trying to build LAMMPS on Windows, please consider if using
 the pre-compiled Windows binary packages are sufficient for your needs
 (as an aside, those packages themselves are build on a Linux machine
-using cross-compilers).  If it is necessary for your to compile LAMMPS
+using cross-compilers).  If it is necessary for you to compile LAMMPS
 on a Windows machine (e.g. because it is your main desktop), please also
-consider using a virtual machine software and run a Linux virtual machine,
-or - if have a recently updated Windows 10 installation - consider using
-the Windows subsystem for Linux, which allows to run a bash shell from
-Ubuntu and from there on, you can pretty much use that shell like you
-are running on an Ubuntu Linux machine (e.g. installing software via
-apt-get). For more details on that, please see :doc:`this tutorial <Howto_bash>`
+consider using a virtual machine software and compile and run LAMMPS in
+a Linux virtual machine, or - if you have a recently updated Windows 10
+installation - consider using the Windows subsystem for Linux.  This
+optional Windows feature allows you to run the bash shell from Ubuntu
+from within Windows and from there on, you can pretty much use that
+shell like you are running on an Ubuntu Linux machine (e.g. installing
+software via apt-get and more). For more details on that, please
+see :doc:`this tutorial <Howto_bash>`
 
 .. _gnu:
 
-Using GNU GCC ported to Windows
+Using a GNU GCC ported to Windows
 -----------------------------------------
 
 One option for compiling LAMMPS on Windows natively, that has been known
@@ -83,13 +85,13 @@ traditional build system, but CMake has also been successfully tested
 using the mingw32-cmake and mingw64-cmake wrappers that are bundled
 with the cross-compiler environment on Fedora machines. A CMake preset
 selecting all packages compatible with this cross-compilation build
-is provided. You likely need to disable the GPU package unless you
+is provided. You will likely need to disable the GPU package unless you
 download and install the contents of the pre-compiled `OpenCL ICD loader library <https://download.lammps.org/thirdparty/opencl-win-devel.tar.gz>`_
 into your MinGW64 cross-compiler environment. The cross-compilation
 currently will only produce non-MPI serial binaries.
 
-Please keep in mind, though, that this only applies to compiling LAMMPS.
-Whether the resulting binaries do work correctly is no tested by the
+Please keep in mind, though, that this only applies to **compiling** LAMMPS.
+Whether the resulting binaries do work correctly is not tested by the
 LAMMPS developers.  We instead rely on the feedback of the users
 of these pre-compiled LAMMPS packages for Windows.  We will try to resolve
 issues to the best of our abilities if we become aware of them. However

doc/src/Eqs/centro_symmetry.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   CS = \sum_{i = 1}^{N/2} | \vec{R}_i + \vec{R}_{i+N/2} |^2
-$$
-
-\end{document}

doc/src/Eqs/cna_cutoff1.tex

@@ -1,14 +0,0 @@
-\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}

doc/src/Eqs/cna_cutoff2.tex

@@ -1,12 +0,0 @@
-\documentclass[12pt,article]{article}
-
-\usepackage{indentfirst}
-\usepackage{amsmath}
-
-\begin{document}
-
-$$
-  Rc + Rs > 2*{\rm cutoff}
-$$
-
-\end{document}

doc/src/Eqs/cnp_cutoff.tex

@@ -1,14 +0,0 @@
-\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}

doc/src/Eqs/cnp_cutoff2.tex

@@ -1,12 +0,0 @@
-\documentclass[12pt,article]{article}
-
-\usepackage{indentfirst}
-\usepackage{amsmath}
-
-\begin{document}
-
-$$
-  Rc + Rs > 2*{\rm cutoff}
-$$
-
-\end{document}

doc/src/Eqs/cnp_eq.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-   Q_{i} = \frac{1}{n_i}\sum_{j = 1}^{n_i} | \sum_{k = 1}^{n_{ij}}  \vec{R}_{ik} + \vec{R}_{jk} |^2
-$$
-
-\end{document}

doc/src/Eqs/compute_dpd.tex

@@ -1,13 +0,0 @@
-\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^{chem} = \displaystyle\sum_{i=1}^{N} u_{i}^{chem} \\
-   U = \displaystyle\sum_{i=1}^{N} (u_{i}^{cond} + u_{i}^{mech} + u_{i}^{chem}) \\
-   \theta_{avg} = (\frac{1}{N}\displaystyle\sum_{i=1}^{N} \frac{1}{\theta_{i}})^{-1} \\
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/compute_gyration.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
- {R_g}^2 = \frac{1}{M} \sum_i m_i (r_i - r_{cm})^2
-$$
-
-\end{document}

doc/src/Eqs/compute_msd_nongauss.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$
- NGP(t) = 3<(r(t)-r(0))^4>/(5<(r(t)-r(0))^2>^2) - 1
-$$
-
-\end{document}

doc/src/Eqs/compute_saed1.tex

@@ -1,10 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$ 
-  I=\frac{F^{*}F}{N}
-$$
-
-\end{document}
-

doc/src/Eqs/compute_saed2.tex

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

doc/src/Eqs/compute_saed3.tex

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

doc/src/Eqs/compute_shape_parameters.tex

@@ -1,13 +0,0 @@
-\documentclass[12pt]{article}
-
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
- c = l_z - 0.5(l_y+l_x) \\
- b = l_y - l_x \\
- k = \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2} 
-\end{eqnarray*}
-
-\end{document}
-

doc/src/Eqs/compute_sna_atom1.tex

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

doc/src/Eqs/compute_sna_atom2.tex

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

doc/src/Eqs/compute_sna_atom3.tex

@@ -1,16 +0,0 @@
-\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}

doc/src/Eqs/compute_sna_atom4.tex

@@ -1,14 +0,0 @@
-\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}

doc/src/Eqs/compute_sna_atom5.tex

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

doc/src/Eqs/compute_sna_atom6.tex

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

doc/src/Eqs/compute_xrd1.tex

@@ -1,10 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$ 
-  I=Lp(\theta)\frac{F^{*}F}{N}
-$$
-
-\end{document}
-

doc/src/Eqs/compute_xrd2.tex

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

doc/src/Eqs/compute_xrd3.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$ 
-  Lp(\theta)=\frac{1+cos^{2}(2\theta)}{cos(\theta)sin^{2}(\theta)}
-$$
-\end{document}
-

doc/src/Eqs/compute_xrd4.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-
-\begin{document}
-
-$$ 
-  \frac{sin(\theta)}{\lambda}=\frac{\left | \mathbf{k} \right |}{2}
-$$
-\end{document}
-

doc/src/Eqs/compute_xrd5.tex

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

doc/src/Eqs/fix_bond_react.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-   k = AT^{n}e^{\frac{-E_{a}}{k_{B}T}}
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/fix_box_relax1.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-E = U + P_t \left(V-V_0 \right) + E_{strain}
-$$
-
-\end{document}

doc/src/Eqs/fix_box_relax2.tex

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

doc/src/Eqs/fix_controller1.tex

@@ -1,12 +0,0 @@
-\documentclass[24pt]{article}
-
-\pagestyle{empty}
-\Huge
-
-\begin{document}
-
-\begin{eqnarray*}
-\frac{dc}{dt}  &=&Ê -\alpha (K_p e + K_i \int_0^t e \, dt + K_d \frac{de}{dt} ) \\
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/fix_controller2.tex

@@ -1,12 +0,0 @@
-\documentclass[24pt]{article}
-
-\pagestyle{empty}
-\Huge
-
-\begin{document}
-
-\begin{eqnarray*}
-c_n  &=&Ê c_{n-1} -\alpha (K_p \tau e_n + K_i \tau^2 \sum_{i=1}^n e_i + K_d (e_n - e_{n-1}) )
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/fix_ehex_eom.tex

@@ -1,8 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-\begin{document}
-   \begin{align*}
-     \dot{\mathbf r}_i &= \mathbf v_i,  \\
-     \dot{\mathbf v}_i &= \frac{\mathbf f_i}{m_i} + \frac{\mathbf g_i}{m_i}.
-   \end{align*}
-\end{document}

doc/src/Eqs/fix_ehex_f.tex

@@ -1,12 +0,0 @@
-\documentclass[12pt]{article}
-\usepackage{amsmath}
-\begin{document}
- \begin{equation*}
-      \mathbf g_i = 
-      \begin{cases} \frac{m_i}{2}   \frac{ F_{\Gamma_{k(\mathbf r_i)}}}{ K_{\Gamma_{k(\mathbf r_i)}}} 
-               \left(\mathbf v_i -  \mathbf v_{\Gamma_{k(\mathbf r_i)}} \right) &  \mbox{$k(\mathbf r_i)> 0$ (inside a reservoir),} \\
-                  0                                     &  \mbox{otherwise, } 
-      \end{cases}
-  \end{equation*}
-\end{document}
-

doc/src/Eqs/fix_eos-cv.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-$$
-   u_{i} = u^{mech}_{i} + u^{cond}_{i} = C_{V} \theta_{i}
-$$
-
-\end{document}

doc/src/Eqs/fix_eos_table_rx.tex

@@ -1,9 +0,0 @@
-\documentstyle[12pt]{article}
-\pagestyle{empty}
-\begin{document}
-
-\begin{eqnarray*}
-   U_{i} = \displaystyle\sum_{j=1}^{m} c_{i,j}(u_{j} + \Delta H_{f,j}) + \frac{3k_{b}T}{2} + Nk_{b}T \\ 
-\end{eqnarray*}                           
-
-\end{document}

doc/src/Eqs/fix_gcmc1.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-\mu &=&\mu^{id} + \mu^{ex}
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/fix_gcmc2.tex

@@ -1,10 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-\mu^{id} &=& k T \ln{\rho \Lambda^3} \\
-&=& k T \ln{\frac{\phi P \Lambda^3}{k T}} 
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/fix_gcmc3.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-\begin{eqnarray*}
-\Lambda &=& \sqrt{ \frac{h^2}{2 \pi m k T}}
-\end{eqnarray*}
-
-\end{document}

doc/src/Eqs/fix_gld1.tex

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

doc/src/Eqs/fix_grem.tex

@@ -1,9 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  T_{eff} = \lambda + \eta (H - H_0)
-$$
-
-\end{document}

doc/src/Eqs/fix_integration_spin_stdecomposition.tex

@@ -1,40 +0,0 @@
-\documentclass[preview]{standalone}
-\usepackage{varwidth}
-\usepackage[utf8x]{inputenc}
-\usepackage{amsmath,amssymb,amsthm,bm,tikz}
-\usetikzlibrary{automata,arrows,shapes,snakes}
-\begin{document}
-\begin{varwidth}{50in}
-\begin{tikzpicture}
-
-%Global
-\node (v1) at (0,6.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] { $\bm{v} \leftarrow \bm{v}+L_v.\Delta t/2$ };
-\node (s1) at (0,4.5) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] { $\bm{s} \leftarrow \bm{s}+L_s.\Delta t/2$ };
-\node (r)  at (0,3.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] { $\bm{r} \leftarrow \bm{r}+L_r.\Delta t$ };
-\node (s2) at (0,1.5) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] { $\bm{s} \leftarrow \bm{s}+L_s.\Delta t/2$ };
-\node (v2) at (0,0.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] { $\bm{v} \leftarrow \bm{v}+L_v.\Delta t/2$ };
-
-\draw[line width=2pt, ->] (v1) -- (s1);
-\draw[line width=2pt, ->] (s1) -- (r);
-\draw[line width=2pt, ->] (r) -- (s2);
-\draw[line width=2pt, ->] (s2) -- (v2);
-
-%Spin
-\node (s01) at (6,6.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] {$\bm{s}_0 \leftarrow \bm{s}_0+L_{s_0}.\Delta t/4$ };
-\node (sN1) at (6,4.5) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] {$\bm{s}_{\rm N-1}\leftarrow\bm{s}_{\rm N-1}+L_{s_{\rm N-1}}.\Delta t/4$};
-\node (sN)  at (6,3.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] {$\bm{s}_{\rm N} \leftarrow \bm{s}_{\rm N}+L_{s_{\rm N}}.\Delta t/2$ };
-\node (sN2) at (6,1.5) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] {$\bm{s}_{\rm N-1}\leftarrow\bm{s}_{\rm N-1}+L_{s_{\rm N-1}}.\Delta t/4$};
-\node (s02) at (6,0.0) [draw,thick,minimum width=0.2cm,minimum height=0.2cm] {$\bm{s}_0 \leftarrow \bm{s}_0+L_{s_0}.\Delta t/4$ };
-
-\draw[line width=2pt,dashed, ->] (s01) -- (sN1);
-\draw[line width=2pt, ->] (sN1) -- (sN);
-\draw[line width=2pt, ->] (sN) -- (sN2);
-\draw[line width=2pt,dashed, ->] (sN2) -- (s02);
-
-%from Global to Spin
-\draw[line width=2pt, dashed, ->] (s1) -- (s01.west);
-\draw[line width=2pt, dashed, ->] (s1) -- (s02.west);
-
-\end{tikzpicture}
-\end{varwidth}
-\end{document}

doc/src/Eqs/fix_lb_fluid_boltzmann.tex

@@ -1,14 +0,0 @@
-\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}
-
-
-
-

doc/src/Eqs/fix_lb_fluid_fluidforce.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$ 
-{\bf F}_{j \alpha} = \gamma \left({\bf v}_n - {\bf u}_f \right) \zeta_{j\alpha}
-$$
-
-
-\end{document}
-
-
-
-

doc/src/Eqs/fix_lb_fluid_gammadefault.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$ 
-\gamma = \frac{2m_um_v}{m_u+m_v}\left(\frac{1}{\Delta t_{collision}}\right)
-$$
-
-
-\end{document}
-
-
-
-

doc/src/Eqs/fix_lb_fluid_navierstokes.tex

@@ -1,16 +0,0 @@
-\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}
-
-
-
-

doc/src/Eqs/fix_lb_fluid_properties.tex

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

doc/src/Eqs/fix_lb_fluid_stress.tex

@@ -1,14 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$ 
-\sigma_{\alpha \beta} = -P_{\alpha \beta} = -\rho a_0 \delta_{\alpha \beta}
-$$
-
-
-\end{document}
-
-
-
-

doc/src/Eqs/fix_lb_fluid_viscosity.tex

@@ -1,14 +0,0 @@
-\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}
-
-
-
-

doc/src/Eqs/fix_mvv_dpd.tex

@@ -1,21 +0,0 @@
-\documentclass[12pt]{article}
-
-\begin{document}
-
-$$
-  v(t+\frac{\Delta t}{2}) = v(t) + \frac{\Delta t}{2}\cdot a(t),
-$$
-
-$$
-  r(t+\Delta t) = r(t) + \Delta t\cdot v(t+\frac{\Delta t}{2}),
-$$
-
-$$
-  a(t+\Delta t) = \frac{1}{m}\cdot F\left[ r(t+\Delta t), v(t) +\lambda \cdot \Delta t\cdot a(t)\right],
-$$
-
-$$
-  v(t+\Delta t) = v(t+\frac{\Delta t}{2}) + \frac{\Delta t}{2}\cdot a(t+\Delta t)
-$$
-
-\end{document}

doc/src/Eqs/fix_nh1.tex

@@ -1,36 +0,0 @@
-\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}

doc/src/Eqs/fix_nphug.tex

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