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54 Commits

Author SHA1 Message Date
ad125bf36a Merge pull request #1881 from akohlmey/next_lammps_version
Update version string for next patch release
2020-02-17 14:53:17 -05:00
fe6f6b3002 Merge pull request #1869 from akohlmey/doc-continued-refactoring
More documentation refactoring for embedding math expressions
2020-02-17 13:06:07 -05:00
f9bee338dd Merge pull request #1875 from akohlmey/collected-small-fixes
Collected small bug fixes and updates
2020-02-17 11:40:27 -05:00
f69c6196a0 Merge branch 'master' into doc-continued-refactoring
# Conflicts:
#	doc/src/compute_fep.rst
2020-02-17 17:37:10 +01:00
c8561ecef0 Merge pull request #1879 from akohlmey/user-plumed-update
Update USER-PLUMED to include support for version 2.6.0. Fix bug in API check
2020-02-17 11:32:10 -05:00
d01b0ed543 Merge pull request #1882 from agiliopadua/docs
Convert documentation of compute_fep, pair_fep_soft, pair_nm to mathjax
2020-02-17 11:31:43 -05:00
b30670d405 correct some grammar and style issues in describing using/building LAMMPS on windows 2020-02-17 10:27:57 +01:00
4a2f05d333 convert pair styles srp to tersoff 2020-02-16 13:42:37 -05:00
3f5bb96aed pair ufm to pair zbl 2020-02-15 16:47:32 -05:00
a508138510 convert wall fixes to embedded math 2020-02-15 12:13:32 -05:00
b25f781071 convert docs for more fixes 2020-02-15 11:35:21 -05:00
0e2604fc80 Convert documentation of compute_fep and pair_fep_soft to mathjax 2020-02-15 16:19:39 +01:00
fd8cd6faa5 typeset hyperdynamics fix docs with embedded math 2020-02-15 06:50:04 -05:00
b0de48e47f convert some more fixes 2020-02-15 02:31:50 -05:00
f4b64e8d91 fix typo in comment 2020-02-14 18:29:11 -05:00
07c5adc57a we need more specific matches to correctly handle TIME and TIMESTEP items 2020-02-14 16:07:34 -05:00
381ac888c8 initialize cut_respa to NULL in constructor to avoid uninitialized access 2020-02-14 15:51:38 -05:00
9bff431553 make sure coulomb tables are initialized in all coul/long GPU pair styles 2020-02-14 15:50:49 -05:00
0b57549f4c must generate coulomb tables with pair style lj/class2/coul/long/gpu 2020-02-14 15:34:12 -05:00
c23f164639 Increase portability to more C++ compilers 2020-02-14 13:40:31 -05:00
2de515c671 improve layout 2020-02-14 12:31:55 +01:00
74a2fd973b convert docs for fixes eos/cv, eos/table/rx, gcmc, grem, langevin/spin, lb/fluid 2020-02-14 12:27:55 +01:00
c47245c629 update/correct lammps executable manpage 2020-02-14 10:33:08 +01:00
d7a7c103ca Update version string for next patch release 2020-02-14 09:55:56 +01:00
7b32b1e595 Update pair_body_rounded_polyhedron docs 2020-02-14 09:52:06 +01:00
b1493d651f Update pair_body_rounded_polygon docs 2020-02-14 09:44:03 +01:00
f70e39c366 update fix ave/correlate/long docs to include info about limitations in output options vs. ave/correlate 2020-02-14 09:30:06 +01:00
147d430a6d Update pair_body_nparticle docs 2020-02-14 09:27:55 +01:00
e339e1735d Update pair_beck docs 2020-02-14 09:19:32 +01:00
076c28538c Merge branch 'read_dump_item_time' of https://github.com/mkanski/lammps into collected-small-fixes 2020-02-13 13:13:24 -05:00
9e35b85335 Merge remote-tracking branch 'github/master' into collected-small-fixes 2020-02-13 13:13:12 -05:00
7c62bce7d9 Enable reading dump file with ITEM:TIME 2020-02-13 18:13:22 +01:00
4cacc4701d update plumed support to include version 2.6.0. Fix bug in API check 2020-02-13 16:03:58 +01:00
5d467bcc74 Merge pull request #1876 from Vsevak/tip4p_gpu_sharedtypes
TIP4P GPU kernel: shared memory optimization
2020-02-12 11:11:17 -05:00
10a76affd4 Merge pull request #1877 from ellio167/openkim-models-docs
Add openkim-models install instructions
2020-02-12 11:08:25 -05:00
cf67c16fcb Add openkim-models install instructions 2020-02-11 22:33:56 -06:00
d024b3d340 Add shared memory optimization 2020-02-12 01:35:44 +03:00
bfaae6860e fix controller 2020-02-11 16:28:45 +01:00
e4a730d57a fix bond/react, box/relax, ehex 2020-02-11 16:14:00 +01:00
6d5c001b61 delete no longer used equations 2020-02-11 14:57:31 +01:00
440f3b9492 correct for typo in txt style markup 2020-02-11 14:54:54 +01:00
3314b4853e convert compute xrd to use embedded math 2020-02-11 11:26:29 +01:00
002fff95c6 copy large target image files only once 2020-02-11 11:07:55 +01:00
ed9c8b4ea0 reset Modify::n_timeflag in post_run() so we won't skip computes defined between runs 2020-02-11 00:30:09 -05:00
23b7adc9b2 we must defer to Modify::addstep_compute_all() if Modify::addstep_compute() if n_timeflag has not been set 2020-02-11 00:06:41 -05:00
ec3e687b0c fix bug in set type/ratio when operating on subsets 2020-02-10 16:22:23 -05:00
c8034d19c4 fix up remaining computes for embedded math and a few other issues 2020-02-10 16:21:19 -05:00
e952bcb5ac Fix pdf build of pair_atm docs 2020-02-08 20:09:40 +01:00
86ebc8260e Update pair_atm docs 2020-02-08 19:24:27 +01:00
712dbe6acc Update pair_airebo docs 2020-02-08 19:07:54 +01:00
5bb28e9e84 Update pair_agni docs 2020-02-08 18:36:34 +01:00
01805cf6ce Update pair_adp 2020-02-08 18:09:19 +01:00
db805bc009 first chunk of compute commands to be converted to use embedded math 2020-02-04 17:05:23 -05:00
301a662a1d cosmetic corrections 2020-02-03 13:41:50 -05:00
313 changed files with 2338 additions and 2625 deletions

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@ -49,8 +49,8 @@ if(PKG_USER-PLUMED)
message(STATUS "PLUMED download requested - we will build our own")
include(ExternalProject)
ExternalProject_Add(plumed_build
URL https://github.com/plumed/plumed2/releases/download/v2.5.3/plumed-src-2.5.3.tgz
URL_MD5 de30d6e7c2dcc0973298e24a6da24286
URL https://github.com/plumed/plumed2/releases/download/v2.6.0/plumed-src-2.6.0.tgz
URL_MD5 204d2edae58d9b10ba3ad460cad64191
BUILD_IN_SOURCE 1
CONFIGURE_COMMAND <SOURCE_DIR>/configure --prefix=<INSTALL_DIR>
${CONFIGURE_REQUEST_PIC}

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@ -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]*

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@ -1,4 +1,4 @@
.TH LAMMPS "4 February 2020" "2020-02-04"
.TH LAMMPS "18 February 2020" "2020-02-18"
.SH NAME
.B LAMMPS
\- Molecular Dynamics Simulator.
@ -11,13 +11,18 @@ or
mpirun \-np 2
.B lmp
<input file> [OPTIONS] ...
\-in <input file> [OPTIONS] ...
or
.B lmp
\-r2data file.restart file.data
or
.B lmp
\-h
.SH DESCRIPTION
.B LAMMPS
is a classical molecular dynamics code, and an acronym for \fBL\fRarge-scale
@ -249,7 +254,7 @@ the chapter on errors in the
manual gives some additional information about error messages, if possible.
.SH COPYRIGHT
© 2003--2019 Sandia Corporation
© 2003--2020 Sandia Corporation
This package is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License version 2 as

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@ -880,6 +880,9 @@ USER-PLUMED package
Before building LAMMPS with this package, you must first build PLUMED.
PLUMED can be built as part of the LAMMPS build or installed separately
from LAMMPS using the generic `plumed installation instructions <plumedinstall_>`_.
The USER-PLUMED package has been tested to work with Plumed versions
2.4.x, 2.5.x, and 2.6.x and will error out, when trying to run calculations
with a different version of the Plumed kernel.
PLUMED can be linked into MD codes in three different modes: static,

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@ -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

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@ -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}

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@ -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}

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

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@ -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}

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

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@ -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}

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@ -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}

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@ -1,7 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\[ \left< \frac{1}{1 + \exp\left[\left(U_1 - U_0 - \Delta_0^1A \right) /kT \right]} \right>_0 = \left< \frac{1}{1 + \exp\left[\left(U_0 - U_1 + \Delta_0^1A \right) /kT \right]} \right>_1 \]
\end{document}

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\documentstyle[12pt]{article}
\begin{document}
\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left( \frac{\partial
A(\lambda)}{\partial\lambda} \right)_\lambda \mathrm{d}\lambda
\approx \sum_{i=0}^{n-1} w_i \frac{A(\lambda_{i} + \delta) -
A(\lambda_i)}{\delta} \]
\end{document}

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@ -1,9 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\[ \Delta_0^1 A = \sum_{i=0}^{n-1} \Delta_{\lambda_i}^{\lambda_{i+1}} A =
- kT \sum_{i=0}^{n-1} \ln \left< \exp \left( - \frac{U(\lambda_{i+1}) -
U(\lambda_i)}{kT} \right) \right>_{\lambda_i} \]
\end{document}

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@ -1,10 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\begin{eqnarray*}
\lambda = 0 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_0 \\
\lambda = 1 \quad\Rightarrow\quad U = U_{\mathrm{bg}} + U_1
\end{eqnarray*}
\end{document}

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@ -1,10 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\[ \Delta_0^1 A = \int_{\lambda=0}^{\lambda=1} \left< \frac{\partial
U(\lambda)}{\partial\lambda} \right>_\lambda \mathrm{d}\lambda
\approx \sum_{i=0}^{n-1} w_i \left< \frac{U(\lambda_{i} + \delta) -
U(\lambda_i)}{\delta} \right>_{\lambda_i} \]
\end{document}

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@ -1,7 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\[ U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \]
\end{document}

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@ -1,9 +0,0 @@
\documentstyle[12pt]{article}
\begin{document}
\[ \Delta_0^1 A = - kT \sum_{i=0}^{n-1} \ln \frac{\left< V \exp \left( -
\frac{U(\lambda_{i+1}) - U(\lambda_i)}{kT} \right)
\right>_{\lambda_i}}{\left< V \right>_{\lambda_i}} \]
\end{document}

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@ -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}

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@ -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}

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\documentstyle[12pt]{article}
\begin{document}
$$
I=\frac{F^{*}F}{N}
$$
\end{document}

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@ -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}

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\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}

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@ -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}

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\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}

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\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}

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@ -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}

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@ -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}

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@ -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}

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\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}

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\documentstyle[12pt]{article}
\begin{document}
$$
I=Lp(\theta)\frac{F^{*}F}{N}
$$
\end{document}

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@ -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}

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

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\documentstyle[12pt]{article}
\begin{document}
$$
\frac{sin(\theta)}{\lambda}=\frac{\left | \mathbf{k} \right |}{2}
$$
\end{document}

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\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}

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

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

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\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}

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

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\documentclass[24pt]{article}
\pagestyle{empty}
\Huge
\begin{document}
\begin{eqnarray*}
c_n &=&<EFBFBD> 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}

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\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}

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\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}

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

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\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}

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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
\mu &=&\mu^{id} + \mu^{ex}
\end{eqnarray*}
\end{document}

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\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}

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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
\Lambda &=& \sqrt{ \frac{h^2}{2 \pi m k T}}
\end{eqnarray*}
\end{document}

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\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}

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

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\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}

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\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}

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

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