Merge remote-tracking branch 'lammps-ro/master' into lammps-icms
# Resolved Conflicts: # doc/Manual.txt # doc/improper_distance.txt # doc/pair_mdf.txt # python/lammps.py # src/MANYBODY/pair_polymorphic.cpp # src/MANYBODY/pair_polymorphic.h
This commit is contained in:
Axel Kohlmeyer
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doc/Eqs/angle_dipole_couple.jpg
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@ -3,8 +3,8 @@
|
||||
\begin{document}
|
||||
|
||||
\begin{eqnarray*}
|
||||
F_{i1}^{SRP} & = & F^{SRP}_{ij}(L) \\
|
||||
F_{i2}^{SRP} & = & F^{SRP}_{ij}(1-L)
|
||||
-\vec{T_j} & = & \vec{r_{ij}} \times \vec{F_i}\\
|
||||
\vec{F_j} & = & -\vec{F_i} \\
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{document}
|
||||
@ -135,7 +135,7 @@
|
||||
<H1></H1><div class="section" id="lammps-documentation">
|
||||
<h1>LAMMPS-ICMS Documentation<a class="headerlink" href="#lammps-documentation" title="Permalink to this headline">¶</a></h1>
|
||||
<div class="section" id="dec-2015-version">
|
||||
<h2>7 Dec 2015 version<a class="headerlink" href="#dec-2015-version" title="Permalink to this headline">¶</a></h2>
|
||||
<h2>10 Dec 2015 version<a class="headerlink" href="#dec-2015-version" title="Permalink to this headline">¶</a></h2>
|
||||
</div>
|
||||
<div class="section" id="version-info">
|
||||
<h2>Version info:<a class="headerlink" href="#version-info" title="Permalink to this headline">¶</a></h2>
|
||||
|
||||
@ -1,7 +1,7 @@
|
||||
<!-- HTML_ONLY -->
|
||||
<HEAD>
|
||||
<TITLE>LAMMPS-ICMS Users Manual</TITLE>
|
||||
<META NAME="docnumber" CONTENT="7 Dec 2015 version">
|
||||
<META NAME="docnumber" CONTENT="10 Dec 2015 version">
|
||||
<META NAME="author" CONTENT="http://lammps.sandia.gov - Sandia National Laboratories">
|
||||
<META NAME="copyright" CONTENT="Copyright (2003) Sandia Corporation. This software and manual is distributed under the GNU General Public License.">
|
||||
</HEAD>
|
||||
@ -21,7 +21,7 @@
|
||||
<H1></H1>
|
||||
|
||||
LAMMPS-ICMS Documentation :c,h3
|
||||
7 Dec 2015 version :c,h4
|
||||
10 Dec 2015 version :c,h4
|
||||
|
||||
Version info: :h4
|
||||
|
||||
|
||||
@ -710,7 +710,7 @@ g = GPU, i = USER-INTEL, k = KOKKOS, o = USER-OMP, t = OPT.</p>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="fix_rigid.html"><em>rigid/small/npt</em></a></td>
|
||||
<td><a class="reference internal" href="fix_rigid.html"><em>rigid/small/nve</em></a></td>
|
||||
<td><a class="reference internal" href="fix_rigid.html"><em>rigid/small/nvt</em></a></td>
|
||||
<td><a class="reference internal" href="fix_setforce.html"><em>setforce (c)</em></a></td>
|
||||
<td><a class="reference internal" href="fix_setforce.html"><em>setforce (ck)</em></a></td>
|
||||
<td><a class="reference internal" href="fix_shake.html"><em>shake (c)</em></a></td>
|
||||
<td><a class="reference internal" href="fix_spring.html"><em>spring</em></a></td>
|
||||
<td><a class="reference internal" href="fix_spring_rg.html"><em>spring/rg</em></a></td>
|
||||
@ -1157,61 +1157,66 @@ KOKKOS, o = USER-OMP, t = OPT.</p>
|
||||
if <a class="reference internal" href="Section_start.html#start-3"><span>LAMMPS is built with the appropriate package</span></a>.</p>
|
||||
<table border="1" class="docutils">
|
||||
<colgroup>
|
||||
<col width="21%" />
|
||||
<col width="25%" />
|
||||
<col width="31%" />
|
||||
<col width="23%" />
|
||||
<col width="21%" />
|
||||
<col width="24%" />
|
||||
</colgroup>
|
||||
<tbody valign="top">
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_awpmd.html"><em>awpmd/cut</em></a></td>
|
||||
<td><a class="reference internal" href="pair_mdf.html"><em>buck/mdf</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>coul/cut/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_coul_diel.html"><em>coul/diel (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>coul/long/soft (o)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_eam.html"><em>eam/cd (o)</em></a></td>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>coul/long/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_eam.html"><em>eam/cd (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_edip.html"><em>edip (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_eff.html"><em>eff/cut</em></a></td>
|
||||
<td><a class="reference internal" href="pair_gauss.html"><em>gauss/cut</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_list.html"><em>list</em></a></td>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_gauss.html"><em>gauss/cut</em></a></td>
|
||||
<td><a class="reference internal" href="pair_mdf.html"><em>lennard/mdf</em></a></td>
|
||||
<td><a class="reference internal" href="pair_list.html"><em>list</em></a></td>
|
||||
<td><a class="reference internal" href="pair_charmm.html"><em>lj/charmm/coul/long/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/cut/soft (o)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/cut/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/coul/long/soft (o)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_dipole.html"><em>lj/cut/dipole/sf (go)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_dipole.html"><em>lj/cut/dipole/sf (go)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/tip4p/long/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk (gko)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk/coul/long (go)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk/coul/msm (o)</em></a></td>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_lj_soft.html"><em>lj/cut/tip4p/long/soft (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_mdf.html"><em>lj/mdf</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk (gko)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk/coul/long (go)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_sdk.html"><em>lj/sdk/coul/msm (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_sf.html"><em>lj/sf (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_meam_spline.html"><em>meam/spline</em></a></td>
|
||||
<td><a class="reference internal" href="pair_meam_sw_spline.html"><em>meam/sw/spline</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_meam_sw_spline.html"><em>meam/sw/spline</em></a></td>
|
||||
<td><a class="reference internal" href="pair_mgpt.html"><em>mgpt</em></a></td>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_mgpt.html"><em>mgpt</em></a></td>
|
||||
<td><a class="reference internal" href="pair_quip.html"><em>quip</em></a></td>
|
||||
<td><a class="reference internal" href="pair_reax_c.html"><em>reax/c</em></a></td>
|
||||
<td><a class="reference internal" href="pair_smd_hertz.html"><em>smd/hertz</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_smd_hertz.html"><em>smd/hertz</em></a></td>
|
||||
<td><a class="reference internal" href="pair_smd_tlsph.html"><em>smd/tlsph</em></a></td>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_smd_tlsph.html"><em>smd/tlsph</em></a></td>
|
||||
<td><a class="reference internal" href="pair_smd_triangulated_surface.html"><em>smd/triangulated/surface</em></a></td>
|
||||
<td><a class="reference internal" href="pair_smd_ulsph.html"><em>smd/ulsph</em></a></td>
|
||||
<td><a class="reference internal" href="pair_smtbq.html"><em>smtbq</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_smtbq.html"><em>smtbq</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_heatconduction.html"><em>sph/heatconduction</em></a></td>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_sph_heatconduction.html"><em>sph/heatconduction</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_idealgas.html"><em>sph/idealgas</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_lj.html"><em>sph/lj</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_rhosum.html"><em>sph/rhosum</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_sph_rhosum.html"><em>sph/rhosum</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_taitwater.html"><em>sph/taitwater</em></a></td>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_sph_taitwater.html"><em>sph/taitwater</em></a></td>
|
||||
<td><a class="reference internal" href="pair_sph_taitwater_morris.html"><em>sph/taitwater/morris</em></a></td>
|
||||
<td><a class="reference internal" href="pair_srp.html"><em>srp</em></a></td>
|
||||
<td><a class="reference internal" href="pair_tersoff.html"><em>tersoff/table (o)</em></a></td>
|
||||
</tr>
|
||||
<tr class="row-even"><td><a class="reference internal" href="pair_tersoff.html"><em>tersoff/table (o)</em></a></td>
|
||||
<td><a class="reference internal" href="pair_thole.html"><em>thole</em></a></td>
|
||||
<tr class="row-odd"><td><a class="reference internal" href="pair_thole.html"><em>thole</em></a></td>
|
||||
<td><a class="reference internal" href="pair_lj_soft.html"><em>tip4p/long/soft (o)</em></a></td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
@ -1406,12 +1411,14 @@ KOKKOS, o = USER-OMP, t = OPT.</p>
|
||||
used if <a class="reference internal" href="Section_start.html#start-3"><span>LAMMPS is built with the appropriate package</span></a>.</p>
|
||||
<table border="1" class="docutils">
|
||||
<colgroup>
|
||||
<col width="33%" />
|
||||
<col width="36%" />
|
||||
<col width="31%" />
|
||||
<col width="24%" />
|
||||
<col width="26%" />
|
||||
<col width="27%" />
|
||||
<col width="23%" />
|
||||
</colgroup>
|
||||
<tbody valign="top">
|
||||
<tr class="row-odd"><td><a class="reference internal" href="improper_cossq.html"><em>cossq (o)</em></a></td>
|
||||
<td><a class="reference internal" href="improper_distance.html"><em>distance</em></a></td>
|
||||
<td><a class="reference internal" href="improper_fourier.html"><em>fourier (o)</em></a></td>
|
||||
<td><a class="reference internal" href="improper_ring.html"><em>ring (o)</em></a></td>
|
||||
</tr>
|
||||
|
||||
@ -563,7 +563,7 @@ g = GPU, i = USER-INTEL, k = KOKKOS, o = USER-OMP, t = OPT.
|
||||
"rigid/small/npt"_fix_rigid.html,
|
||||
"rigid/small/nve"_fix_rigid.html,
|
||||
"rigid/small/nvt"_fix_rigid.html,
|
||||
"setforce (c)"_fix_setforce.html,
|
||||
"setforce (ck)"_fix_setforce.html,
|
||||
"shake (c)"_fix_shake.html,
|
||||
"spring"_fix_spring.html,
|
||||
"spring/rg"_fix_spring_rg.html,
|
||||
@ -898,6 +898,7 @@ if "LAMMPS is built with the appropriate
|
||||
package"_Section_start.html#start_3.
|
||||
|
||||
"awpmd/cut"_pair_awpmd.html,
|
||||
"buck/mdf"_pair_mdf.html,
|
||||
"coul/cut/soft (o)"_pair_lj_soft.html,
|
||||
"coul/diel (o)"_pair_coul_diel.html,
|
||||
"coul/long/soft (o)"_pair_lj_soft.html,
|
||||
@ -905,6 +906,7 @@ package"_Section_start.html#start_3.
|
||||
"edip (o)"_pair_edip.html,
|
||||
"eff/cut"_pair_eff.html,
|
||||
"gauss/cut"_pair_gauss.html,
|
||||
"lennard/mdf"_pair_mdf.html,
|
||||
"list"_pair_list.html,
|
||||
"lj/charmm/coul/long/soft (o)"_pair_charmm.html,
|
||||
"lj/cut/coul/cut/soft (o)"_pair_lj_soft.html,
|
||||
@ -912,6 +914,7 @@ package"_Section_start.html#start_3.
|
||||
"lj/cut/dipole/sf (go)"_pair_dipole.html,
|
||||
"lj/cut/soft (o)"_pair_lj_soft.html,
|
||||
"lj/cut/tip4p/long/soft (o)"_pair_lj_soft.html,
|
||||
"lj/mdf"_pair_mdf.html,
|
||||
"lj/sdk (gko)"_pair_sdk.html,
|
||||
"lj/sdk/coul/long (go)"_pair_sdk.html,
|
||||
"lj/sdk/coul/msm (o)"_pair_sdk.html,
|
||||
@ -1057,6 +1060,7 @@ used if "LAMMPS is built with the appropriate
|
||||
package"_Section_start.html#start_3.
|
||||
|
||||
"cossq (o)"_improper_cossq.html,
|
||||
"distance"_improper_distance.html,
|
||||
"fourier (o)"_improper_fourier.html,
|
||||
"ring (o)"_improper_ring.html :tb(c=4,ea=c)
|
||||
|
||||
|
||||
@ -411,9 +411,16 @@ downloaded and looked at a few of them, their documentation was
|
||||
incomplete and I had trouble with their installation. It’s not clear
|
||||
if some of the packages are still being actively developed and
|
||||
supported.</p>
|
||||
<p>The one I recommend, since I have successfully used it with LAMMPS, is
|
||||
Pypar. Pypar requires the ubiquitous <a class="reference external" href="http://numpy.scipy.org">Numpy package</a> be installed in your Python. After
|
||||
launching python, type</p>
|
||||
<p>The packages Pypar and mpi4py have both been successfully tested with
|
||||
LAMMPS. Pypar is simpler and easy to set up and use, but supports
|
||||
only a subset of MPI. Mpi4py is more MPI-feature complete, but also a
|
||||
bit more complex to use. As of version 2.0.0, mpi4py is the only
|
||||
python MPI wrapper that allows passing a custom MPI communicator to
|
||||
the LAMMPS constructor, which means one can easily run one or more
|
||||
LAMMPS instances on subsets of the total MPI ranks.</p>
|
||||
<hr class="docutils" />
|
||||
<p>Pypar requires the ubiquitous <a class="reference external" href="http://numpy.scipy.org">Numpy package</a>
|
||||
be installed in your Python. After launching Python, type</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">numpy</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -466,6 +473,51 @@ address, e.g. by moving other MPI installations so that Pypar finds
|
||||
the right one.</p>
|
||||
</div>
|
||||
<hr class="docutils" />
|
||||
<p>To install mpi4py (version mpi4py-2.0.0 as of Oct 2015), unpack it
|
||||
and from its main directory, type</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>python setup.py build
|
||||
sudo python setup.py install
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>Again, the “sudo” is only needed if required to copy mpi4py files into
|
||||
your Python distribution’s site-packages directory. To install with
|
||||
user privilege into the user local directory type</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>python setup.py install --user
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>If you have successully installed mpi4py, you should be able to run
|
||||
Python and type</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre><span class="kn">from</span> <span class="nn">mpi4py</span> <span class="kn">import</span> <span class="n">MPI</span>
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>without error. You should also be able to run python in parallel
|
||||
on a simple test script</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>% mpirun -np 4 python test.py
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>where test.py contains the lines</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>from mpi4py import MPI
|
||||
comm = MPI.COMM_WORLD
|
||||
print "Proc %d out of %d procs" % (comm.Get_rank(),comm.Get_size())
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>and see one line of output for each processor you run on.</p>
|
||||
<div class="admonition warning">
|
||||
<p class="first admonition-title">Warning</p>
|
||||
<p class="last">To use mpi4py and LAMMPS in parallel from Python, you
|
||||
must insure both are using the same version of MPI. If you only have
|
||||
one MPI installed on your system, this is not an issue, but it can be
|
||||
if you have multiple MPIs. Your LAMMPS build is explicit about which
|
||||
MPI it is using, since you specify the details in your lo-level
|
||||
src/MAKE/Makefile.foo file. Mpi4py uses the “mpicc” command to find
|
||||
information about the MPI it uses to build against. And it tries to
|
||||
load “libmpi.so” from the LD_LIBRARY_PATH. This may or may not find
|
||||
the MPI library that LAMMPS is using. If you have problems running
|
||||
both mpi4py and LAMMPS together, this is an issue you may need to
|
||||
address, e.g. by moving other MPI installations so that mpi4py finds
|
||||
the right one.</p>
|
||||
</div>
|
||||
<hr class="docutils" />
|
||||
</div>
|
||||
<div class="section" id="testing-the-python-lammps-interface">
|
||||
<span id="py-6"></span><h2>11.6. Testing the Python-LAMMPS interface<a class="headerlink" href="#testing-the-python-lammps-interface" title="Permalink to this headline">¶</a></h2>
|
||||
@ -517,8 +569,8 @@ typed something like:</p>
|
||||
<div class="section" id="test-lammps-and-python-in-parallel">
|
||||
<h3>11.6.2. <strong>Test LAMMPS and Python in parallel:</strong><a class="headerlink" href="#test-lammps-and-python-in-parallel" title="Permalink to this headline">¶</a></h3>
|
||||
<p>To run LAMMPS in parallel, assuming you have installed the
|
||||
<a class="reference external" href="http://datamining.anu.edu.au/~ole/pypar">Pypar</a> package as discussed
|
||||
above, create a test.py file containing these lines:</p>
|
||||
<a class="reference external" href="Pypar">Pypar</a> package as discussed above, create a test.py file
|
||||
containing these lines:</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>import pypar
|
||||
from lammps import lammps
|
||||
lmp = lammps()
|
||||
@ -527,7 +579,20 @@ print "Proc %d out of %d procs has" % (pypar.rank(),pypar.size()),lmp
|
||||
pypar.finalize()
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>You can then run it in parallel as:</p>
|
||||
<p>To run LAMMPS in parallel, assuming you have installed the
|
||||
<a class="reference external" href="mpi4py">mpi4py</a> package as discussed above, create a test.py file
|
||||
containing these lines:</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>from mpi4py import MPI
|
||||
from lammps import lammps
|
||||
lmp = lammps()
|
||||
lmp.file("in.lj")
|
||||
me = MPI.COMM_WORLD.Get_rank()
|
||||
nprocs = MPI.COMM_WORLD.Get_size()
|
||||
print "Proc %d out of %d procs has" % (me,nprocs),lmp
|
||||
MPI.Finalize()
|
||||
</pre></div>
|
||||
</div>
|
||||
<p>You can either script in parallel as:</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre>% mpirun -np 4 python test.py
|
||||
</pre></div>
|
||||
</div>
|
||||
@ -590,11 +655,12 @@ Python script, as follows:</p>
|
||||
the files src/library.cpp and src/library.h you will see that they
|
||||
correspond one-to-one with calls you can make to the LAMMPS library
|
||||
from a C++ or C or Fortran program.</p>
|
||||
<div class="highlight-python"><div class="highlight"><pre><span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">()</span> <span class="c"># create a LAMMPS object using the default liblammps.so library</span>
|
||||
<span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">(</span><span class="n">ptr</span><span class="o">=</span><span class="n">lmpptr</span><span class="p">)</span> <span class="c"># ditto, but use lmpptr as previously created LAMMPS object</span>
|
||||
<span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">(</span><span class="s">"g++"</span><span class="p">)</span> <span class="c"># create a LAMMPS object using the liblammps_g++.so library</span>
|
||||
<span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">(</span><span class="s">""</span><span class="p">,</span><span class="nb">list</span><span class="p">)</span> <span class="c"># ditto, with command-line args, e.g. list = ["-echo","screen"]</span>
|
||||
<span class="n">lmp</span> <span class="o">=</span> <span class="n">lammps</span><span class="p">(</span><span class="s">"g++"</span><span class="p">,</span><span class="nb">list</span><span class="p">)</span>
|
||||
<div class="highlight-python"><div class="highlight"><pre>lmp = lammps() # create a LAMMPS object using the default liblammps.so library
|
||||
4 optional args are allowed: name, cmdargs, ptr, comm
|
||||
lmp = lammps(ptr=lmpptr) # use lmpptr as previously created LAMMPS object
|
||||
lmp = lammps(comm=split) # create a LAMMPS object with a custom communicator, requires mpi4py 2.0.0 or later
|
||||
lmp = lammps(name="g++") # create a LAMMPS object using the liblammps_g++.so library
|
||||
lmp = lammps(name="g++",cmdargs=list) # add LAMMPS command-line args, e.g. list = ["-echo","screen"]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="highlight-python"><div class="highlight"><pre><span class="n">lmp</span><span class="o">.</span><span class="n">close</span><span class="p">()</span> <span class="c"># destroy a LAMMPS object</span>
|
||||
@ -706,8 +772,8 @@ argument.</p>
|
||||
returned, which you can use via normal Python subscripting. See the
|
||||
extract() method in the src/atom.cpp file for a list of valid names.
|
||||
Again, new names could easily be added. A pointer to a vector of
|
||||
doubles or integers, or a pointer to an array of doubles (double <a href="#id2"><span class="problematic" id="id3">**</span></a>)
|
||||
or integers (int <a href="#id4"><span class="problematic" id="id5">**</span></a>) is returned. You need to specify the appropriate
|
||||
doubles or integers, or a pointer to an array of doubles (double <a href="#id3"><span class="problematic" id="id4">**</span></a>)
|
||||
or integers (int <a href="#id5"><span class="problematic" id="id6">**</span></a>) is returned. You need to specify the appropriate
|
||||
data type via the type argument.</p>
|
||||
<p>For extract_compute() and extract_fix(), the global, per-atom, or
|
||||
local data calulated by the compute or fix can be accessed. What is
|
||||
@ -802,8 +868,8 @@ own scripts, send them to us and we can include them in the LAMMPS
|
||||
distribution.</p>
|
||||
<table border="1" class="docutils">
|
||||
<colgroup>
|
||||
<col width="27%" />
|
||||
<col width="73%" />
|
||||
<col width="56%" />
|
||||
<col width="44%" />
|
||||
</colgroup>
|
||||
<tbody valign="top">
|
||||
<tr class="row-odd"><td>trivial.py</td>
|
||||
@ -813,19 +879,25 @@ distribution.</p>
|
||||
<td>invoke various LAMMPS library interface routines</td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td>simple.py</td>
|
||||
<td>mimic operation of couple/simple/simple.cpp in Python</td>
|
||||
<td>run in parallel</td>
|
||||
</tr>
|
||||
<tr class="row-even"><td>gui.py</td>
|
||||
<td>GUI go/stop/temperature-slider to control LAMMPS</td>
|
||||
<tr class="row-even"><td>similar to examples/COUPLE/simple/simple.cpp</td>
|
||||
<td>split.py</td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td>plot.py</td>
|
||||
<td>real-time temeperature plot with GnuPlot via Pizza.py</td>
|
||||
<tr class="row-odd"><td>same as simple.py but running in parallel on a subset of procs</td>
|
||||
<td>gui.py</td>
|
||||
</tr>
|
||||
<tr class="row-even"><td>viz_tool.py</td>
|
||||
<td>real-time viz via some viz package</td>
|
||||
<tr class="row-even"><td>GUI go/stop/temperature-slider to control LAMMPS</td>
|
||||
<td>plot.py</td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td>vizplotgui_tool.py</td>
|
||||
<td>combination of viz_tool.py and plot.py and gui.py</td>
|
||||
<tr class="row-odd"><td>real-time temeperature plot with GnuPlot via Pizza.py</td>
|
||||
<td>viz_tool.py</td>
|
||||
</tr>
|
||||
<tr class="row-even"><td>real-time viz via some viz package</td>
|
||||
<td>vizplotgui_tool.py</td>
|
||||
</tr>
|
||||
<tr class="row-odd"><td>combination of viz_tool.py and plot.py and gui.py</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
@ -303,10 +303,18 @@ incomplete and I had trouble with their installation. It's not clear
|
||||
if some of the packages are still being actively developed and
|
||||
supported.
|
||||
|
||||
The one I recommend, since I have successfully used it with LAMMPS, is
|
||||
Pypar. Pypar requires the ubiquitous "Numpy
|
||||
package"_http://numpy.scipy.org be installed in your Python. After
|
||||
launching python, type
|
||||
The packages Pypar and mpi4py have both been successfully tested with
|
||||
LAMMPS. Pypar is simpler and easy to set up and use, but supports
|
||||
only a subset of MPI. Mpi4py is more MPI-feature complete, but also a
|
||||
bit more complex to use. As of version 2.0.0, mpi4py is the only
|
||||
python MPI wrapper that allows passing a custom MPI communicator to
|
||||
the LAMMPS constructor, which means one can easily run one or more
|
||||
LAMMPS instances on subsets of the total MPI ranks.
|
||||
|
||||
:line
|
||||
|
||||
Pypar requires the ubiquitous "Numpy package"_http://numpy.scipy.org
|
||||
be installed in your Python. After launching Python, type
|
||||
|
||||
import numpy :pre
|
||||
|
||||
@ -361,6 +369,51 @@ the right one.
|
||||
|
||||
:line
|
||||
|
||||
To install mpi4py (version mpi4py-2.0.0 as of Oct 2015), unpack it
|
||||
and from its main directory, type
|
||||
|
||||
python setup.py build
|
||||
sudo python setup.py install :pre
|
||||
|
||||
Again, the "sudo" is only needed if required to copy mpi4py files into
|
||||
your Python distribution's site-packages directory. To install with
|
||||
user privilege into the user local directory type
|
||||
|
||||
python setup.py install --user :pre
|
||||
|
||||
If you have successully installed mpi4py, you should be able to run
|
||||
Python and type
|
||||
|
||||
from mpi4py import MPI :pre
|
||||
|
||||
without error. You should also be able to run python in parallel
|
||||
on a simple test script
|
||||
|
||||
% mpirun -np 4 python test.py :pre
|
||||
|
||||
where test.py contains the lines
|
||||
|
||||
from mpi4py import MPI
|
||||
comm = MPI.COMM_WORLD
|
||||
print "Proc %d out of %d procs" % (comm.Get_rank(),comm.Get_size()) :pre
|
||||
|
||||
and see one line of output for each processor you run on.
|
||||
|
||||
IMPORTANT NOTE: To use mpi4py and LAMMPS in parallel from Python, you
|
||||
must insure both are using the same version of MPI. If you only have
|
||||
one MPI installed on your system, this is not an issue, but it can be
|
||||
if you have multiple MPIs. Your LAMMPS build is explicit about which
|
||||
MPI it is using, since you specify the details in your lo-level
|
||||
src/MAKE/Makefile.foo file. Mpi4py uses the "mpicc" command to find
|
||||
information about the MPI it uses to build against. And it tries to
|
||||
load "libmpi.so" from the LD_LIBRARY_PATH. This may or may not find
|
||||
the MPI library that LAMMPS is using. If you have problems running
|
||||
both mpi4py and LAMMPS together, this is an issue you may need to
|
||||
address, e.g. by moving other MPI installations so that mpi4py finds
|
||||
the right one.
|
||||
|
||||
:line
|
||||
|
||||
11.6 Testing the Python-LAMMPS interface :link(py_6),h4
|
||||
|
||||
To test if LAMMPS is callable from Python, launch Python interactively
|
||||
@ -413,8 +466,8 @@ lmp_g++ -in in.lj :pre
|
||||
[Test LAMMPS and Python in parallel:] :h5
|
||||
|
||||
To run LAMMPS in parallel, assuming you have installed the
|
||||
"Pypar"_http://datamining.anu.edu.au/~ole/pypar package as discussed
|
||||
above, create a test.py file containing these lines:
|
||||
"Pypar"_Pypar package as discussed above, create a test.py file
|
||||
containing these lines:
|
||||
|
||||
import pypar
|
||||
from lammps import lammps
|
||||
@ -423,7 +476,20 @@ lmp.file("in.lj")
|
||||
print "Proc %d out of %d procs has" % (pypar.rank(),pypar.size()),lmp
|
||||
pypar.finalize() :pre
|
||||
|
||||
You can then run it in parallel as:
|
||||
To run LAMMPS in parallel, assuming you have installed the
|
||||
"mpi4py"_mpi4py package as discussed above, create a test.py file
|
||||
containing these lines:
|
||||
|
||||
from mpi4py import MPI
|
||||
from lammps import lammps
|
||||
lmp = lammps()
|
||||
lmp.file("in.lj")
|
||||
me = MPI.COMM_WORLD.Get_rank()
|
||||
nprocs = MPI.COMM_WORLD.Get_size()
|
||||
print "Proc %d out of %d procs has" % (me,nprocs),lmp
|
||||
MPI.Finalize() :pre
|
||||
|
||||
You can either script in parallel as:
|
||||
|
||||
% mpirun -np 4 python test.py :pre
|
||||
|
||||
@ -491,10 +557,11 @@ correspond one-to-one with calls you can make to the LAMMPS library
|
||||
from a C++ or C or Fortran program.
|
||||
|
||||
lmp = lammps() # create a LAMMPS object using the default liblammps.so library
|
||||
lmp = lammps(ptr=lmpptr) # ditto, but use lmpptr as previously created LAMMPS object
|
||||
lmp = lammps("g++") # create a LAMMPS object using the liblammps_g++.so library
|
||||
lmp = lammps("",list) # ditto, with command-line args, e.g. list = \["-echo","screen"\]
|
||||
lmp = lammps("g++",list) :pre
|
||||
4 optional args are allowed: name, cmdargs, ptr, comm
|
||||
lmp = lammps(ptr=lmpptr) # use lmpptr as previously created LAMMPS object
|
||||
lmp = lammps(comm=split) # create a LAMMPS object with a custom communicator, requires mpi4py 2.0.0 or later
|
||||
lmp = lammps(name="g++") # create a LAMMPS object using the liblammps_g++.so library
|
||||
lmp = lammps(name="g++",cmdargs=list) # add LAMMPS command-line args, e.g. list = \["-echo","screen"\] :pre
|
||||
|
||||
lmp.close() # destroy a LAMMPS object :pre
|
||||
|
||||
@ -717,7 +784,8 @@ distribution.
|
||||
|
||||
trivial.py, read/run a LAMMPS input script thru Python,
|
||||
demo.py, invoke various LAMMPS library interface routines,
|
||||
simple.py, mimic operation of couple/simple/simple.cpp in Python,
|
||||
simple.py, run in parallel, similar to examples/COUPLE/simple/simple.cpp,
|
||||
split.py, same as simple.py but running in parallel on a subset of procs,
|
||||
gui.py, GUI go/stop/temperature-slider to control LAMMPS,
|
||||
plot.py, real-time temeperature plot with GnuPlot via Pizza.py,
|
||||
viz_tool.py, real-time viz via some viz package,
|
||||
|
||||
BIN
doc/_images/angle_dipole_couple.jpg
Normal file
BIN
doc/_images/angle_dipole_couple.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 2.9 KiB |
BIN
doc/_images/hexorder.jpg
Normal file
BIN
doc/_images/hexorder.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 16 KiB |
BIN
doc/_images/orientorder.jpg
Normal file
BIN
doc/_images/orientorder.jpg
Normal file
Binary file not shown.
|
After Width: | Height: | Size: 34 KiB |
@ -159,15 +159,17 @@ and the reference (bond) vector r_ij:</p>
|
||||
angle.</p>
|
||||
<p>The torque on the dipole can be obtained by differentiating the
|
||||
potential using the ‘chain rule’ as in appendix C.3 of
|
||||
<a class="reference internal" href="pair_gayberne.html#allen"><span>(Allen)</span></a>:</p>
|
||||
<a class="reference internal" href="#allen"><span>(Allen)</span></a>:</p>
|
||||
<img alt="_images/angle_dipole_torque.jpg" class="align-center" src="_images/angle_dipole_torque.jpg" />
|
||||
<p>Example: if gamma0 is set to 0 degrees, the torque generated by
|
||||
the potential will tend to align the dipole along the reference
|
||||
direction defined by the (bond) vector r_ij (in other words, mu_j is
|
||||
restrained to point towards atom ‘i’).</p>
|
||||
<p>Note that the angle dipole potential does not give rise to any force,
|
||||
because it does not depend on the distance between i and j (it only
|
||||
depends on the angle between mu_j and r_ij).</p>
|
||||
<p>The dipolar torque T_j must be counterbalanced in order to conserve
|
||||
the local angular momentum. This is achieved via an additional force
|
||||
couple generating a torque equivalent to the opposite of T_j:</p>
|
||||
<img alt="_images/angle_dipole_couple.jpg" class="align-center" src="_images/angle_dipole_couple.jpg" />
|
||||
<p>where F_i and F_j are applied on atoms i and j, respectively.</p>
|
||||
<p>The following coefficients must be defined for each angle type via the
|
||||
<a class="reference internal" href="angle_coeff.html"><em>angle_coeff</em></a> command as in the example above, or in
|
||||
the data file or restart files read by the <a class="reference internal" href="read_data.html"><em>read_data</em></a>
|
||||
|
||||
@ -50,9 +50,13 @@ the potential will tend to align the dipole along the reference
|
||||
direction defined by the (bond) vector r_ij (in other words, mu_j is
|
||||
restrained to point towards atom 'i').
|
||||
|
||||
Note that the angle dipole potential does not give rise to any force,
|
||||
because it does not depend on the distance between i and j (it only
|
||||
depends on the angle between mu_j and r_ij).
|
||||
The dipolar torque T_j must be counterbalanced in order to conserve
|
||||
the local angular momentum. This is achieved via an additional force
|
||||
couple generating a torque equivalent to the opposite of T_j:
|
||||
|
||||
:c,image(Eqs/angle_dipole_couple.jpg)
|
||||
|
||||
where F_i and F_j are applied on atoms i and j, respectively.
|
||||
|
||||
The following coefficients must be defined for each angle type via the
|
||||
"angle_coeff"_angle_coeff.html command as in the example above, or in
|
||||
|
||||
@ -145,8 +145,7 @@
|
||||
<div class="section" id="description">
|
||||
<h2>Description<a class="headerlink" href="#description" title="Permalink to this headline">¶</a></h2>
|
||||
<p>Define a computation that calculates the temperatures of core-Drude
|
||||
pairs. This compute is designed to be used with the thermalized Drude
|
||||
oscillator model. This compute is designed to be used with the
|
||||
pairs. This compute is designed to be used with the
|
||||
<a class="reference internal" href="tutorial_drude.html"><em>thermalized Drude oscillator model</em></a>. Polarizable
|
||||
models in LAMMPS are described in <a class="reference internal" href="Section_howto.html#howto-25"><span>this Section</span></a>.</p>
|
||||
<p>Drude oscillators consist of a core particle and a Drude particle
|
||||
@ -189,7 +188,7 @@ assumed to be constant for the duration of the run unless the
|
||||
</div>
|
||||
<div class="section" id="related-commands">
|
||||
<h2>Related commands<a class="headerlink" href="#related-commands" title="Permalink to this headline">¶</a></h2>
|
||||
<p><a class="reference internal" href="fix_drude.html"><em>fix drude</em></a>, <a class="reference internal" href="fix_langevin_drude.html"><em>fix langevin_drude</em></a>, <a class="reference internal" href="fix_drude_transform.html"><em>fix drude/transform</em></a>, <a class="reference internal" href="pair_thole.html"><em>pair_style thole</em></a>, <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a></p>
|
||||
<p><a class="reference internal" href="fix_drude.html"><em>fix drude</em></a>, <a class="reference internal" href="fix_langevin_drude.html"><em>fix langevin/drude</em></a>, <a class="reference internal" href="fix_drude_transform.html"><em>fix drude/transform</em></a>, <a class="reference internal" href="pair_thole.html"><em>pair_style thole</em></a>, <a class="reference internal" href="compute_temp.html"><em>compute temp</em></a></p>
|
||||
<p><strong>Default:</strong> none</p>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@ -22,8 +22,7 @@ compute TDRUDE all temp/drude :pre
|
||||
[Description:]
|
||||
|
||||
Define a computation that calculates the temperatures of core-Drude
|
||||
pairs. This compute is designed to be used with the thermalized Drude
|
||||
oscillator model. This compute is designed to be used with the
|
||||
pairs. This compute is designed to be used with the
|
||||
"thermalized Drude oscillator model"_tutorial_drude.html. Polarizable
|
||||
models in LAMMPS are described in "this
|
||||
Section"_Section_howto.html#howto_25.
|
||||
@ -75,7 +74,7 @@ assumed to be constant for the duration of the run unless the
|
||||
[Related commands:]
|
||||
|
||||
"fix drude"_fix_drude.html, "fix
|
||||
langevin_drude"_fix_langevin_drude.html, "fix
|
||||
langevin/drude"_fix_langevin_drude.html, "fix
|
||||
drude/transform"_fix_drude_transform.html, "pair_style
|
||||
thole"_pair_thole.html, "compute temp"_compute_temp.html
|
||||
|
||||
|
||||
@ -1,30 +0,0 @@
|
||||
This is TeX, Version 3.14159 (Web2C 7.4.5) (format=latex 2008.11.14) 27 AUG 2011 15:16
|
||||
**pair_sph_tait
|
||||
(/usr/share/texmf/tex/latex/tools/.tex
|
||||
LaTeX2e <2001/06/01>
|
||||
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, n
|
||||
ohyphenation, loaded.
|
||||
File ignored)
|
||||
*
|
||||
(Please type a command or say `\end')
|
||||
*x
|
||||
|
||||
! LaTeX Error: Missing \begin{document}.
|
||||
|
||||
See the LaTeX manual or LaTeX Companion for explanation.
|
||||
Type H <return> for immediate help.
|
||||
...
|
||||
|
||||
<*> x
|
||||
|
||||
? x
|
||||
|
||||
Here is how much of TeX's memory you used:
|
||||
6 strings out of 95847
|
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257 string characters out of 1195947
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44507 words of memory out of 1000001
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3034 multiletter control sequences out of 10000+50000
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3640 words of font info for 14 fonts, out of 500000 for 1000
|
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14 hyphenation exceptions out of 1000
|
||||
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K (\theta - \theta_0)^2 + K_{UB} (r - r_{UB})^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{eqnarray*}
|
||||
E & = & E_a + E_{bb} + E_{ba} \\
|
||||
E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
|
||||
E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
|
||||
E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{document}
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||||
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K [1 + \cos(\theta)]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K [1 - \cos(\theta - \theta_0)]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentstyle[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E=C\left[ 1-B(-1)^ncos\left( n\theta\right) \right]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentstyle[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E=-\frac{Umin}{2} \left[ 1+Cos(\theta-\theta_0) \right]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentstyle[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E=-U_{min}
|
||||
\frac{e^{-a U(\theta,\theta_0)}-1}{e^a-1}
|
||||
\quad\mbox{with}\quad
|
||||
U(\theta,\theta_0)
|
||||
=-0.5 \left(1+\cos(\theta-\theta_0) \right)
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K [\cos(\theta) - \cos(\theta_0)]^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
\cos\gamma = \frac{\vec{\mu_j}\bullet\vec{r_{ij}}}{\mu_j\,r_{ij}}
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K (\cos\gamma - \cos\gamma_0)^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
\vec{T_j} = \frac{2K(\cos\gamma - \cos\gamma_0)}{\mu_j\,r_{ij}}\,
|
||||
\vec{r_{ij}} \times \vec{\mu_j}
|
||||
$$
|
||||
\end{document}
|
||||
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K [C_0 + C_1 \cos ( \theta) + C_2 \cos( 2 \theta) ]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K [ 1.0 + c \cos ( n \theta) ]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K (\theta - \theta_0)^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K_2 (r - r_0)^2 + K_3 (r - r_0)^3 + K_4 (r - r_0)^4
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = -0.5 K R_0^2 \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] +
|
||||
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
|
||||
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = -0.5 K R_0^2
|
||||
\ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] +
|
||||
4 \epsilon \left[ \left(\frac{\sigma}{\left(r -
|
||||
\Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r -
|
||||
\Delta\right)}\right)^6 \right] + \epsilon
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K (r - r_0)^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = \frac{Umin}{(r_0-r_c)^2} \left[ (r-r_0)^2-(r_c-r_0)^2 \right]
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
% E = D \left[ 1 - \exp \left( -\alpha (r - r_0) \right) \right]^2
|
||||
E = D \left[ 1 - e^{-\alpha (r - r_0)} \right]^2
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = \frac{\epsilon (r - r_0)^2}{ [ \lambda^2 - (r - r_0)^2 ]}
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 +
|
||||
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
|
||||
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{eqnarray*}
|
||||
a &=& {\rm lx} \\
|
||||
b^2 &=& {\rm ly}^2 + {\rm xy}^2 \\
|
||||
c^2 &=& {\rm lz}^2 + {\rm xz}^2 + {\rm yz}^2 \\
|
||||
\cos{\alpha} &=& \frac{{\rm xy}*{\rm xz} + {\rm ly}*{\rm yz}}{b*c} \\
|
||||
\cos{\beta} &=& \frac{\rm xz}{c} \\
|
||||
\cos{\gamma} &=& \frac{\rm xy}{b} \\
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\documentclass[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\begin{eqnarray*}
|
||||
{\rm lx} &=& a \\
|
||||
{\rm xy} &=& b \cos{\gamma} \\
|
||||
{\rm xz} &=& c \cos{\beta}\\
|
||||
{\rm ly}^2 &=& b^2 - {\rm xy}^2 \\
|
||||
{\rm yz} &=& \frac{b*c \cos{\alpha} - {\rm xy}*{\rm xz}}{\rm ly} \\
|
||||
{\rm lz}^2 &=& c^2 - {\rm xz}^2 - {\rm yz}^2 \\
|
||||
\end{eqnarray*}
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\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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|
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|
||||
\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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|
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|
||||
\documentclass[12pt,article]{article}
|
||||
|
||||
\usepackage{indentfirst}
|
||||
\usepackage{amsmath}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
Rc + Rs > 2*{\rm cutoff}
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\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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|
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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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|
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|
||||
\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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|
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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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|
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|
||||
\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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|
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|
||||
\documentstyle[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
\[ U(\lambda) = U_{\mathrm{bg}} + U_1(\lambda) + U_0(\lambda) \]
|
||||
|
||||
\end{document}
|
||||
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|
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|
||||
\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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|
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|
||||
\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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|
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|
||||
\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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|
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|
||||
\documentstyle[12pt]{article}
|
||||
|
||||
\begin{document}
|
||||
|
||||
$$
|
||||
I=\frac{F^{*}F}{N}
|
||||
$$
|
||||
|
||||
\end{document}
|
||||
|
||||
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|
||||
\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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|
||||
\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}
|
||||
Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user