forked from lijiext/lammps
211 lines
8.7 KiB
HTML
211 lines
8.7 KiB
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>fix phonon command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>fix ID group-ID phonon N Noutput Nwait map_file prefix keyword values ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>phonon = style name of this fix command
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<LI>N = measure the Green's function every this many timesteps
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<LI>Noutput = output the dynamical matrix every this many measurements
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<LI>Nwait = wait this many timesteps before measuring
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<LI>map_file = file containing the mapping info between atom ID and the lattice indices
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<LI>prefix = prefix for output files
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<LI>one or none keyword/value pairs may be appended
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<LI>keyword = <I>sysdim</I> or <I>nasr</I>
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<PRE> <I>sysdim</I> value = d
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d = dimension of the system, usually is the same as the MD dimension.
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<I>nasr</I> value = n
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n = number of iterations to enforce the acoustic sum rule.
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>fix 1 all phonon 20 5000 200000 map.in LJ1D sysdim 1
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fix 1 all phonon 20 5000 200000 map.in EAM3D
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>To measure the dynamical matrix from molecular dynamics simulations
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based on fluctuation-dissipation theory for a group of atoms.
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</P>
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<P>Consider a crystal with <I>N</I> unit cells in three dimensions labelled <I>l
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= (l<sub>1</sub>,l<sub>2</sub>,l<sub>3</sub>)</I> where <I>l<sub>i</sub></I>
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are integers. Each unit cell is defined by three linearly independent
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vectors <B>a</B><sub>1</sub>, <B>a</B><sub>2</sub>, <B>a</B><sub>3</sub> forming a
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parallelipiped, containing <I>K</I> basis atoms labelled <I>k</I>.
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</P>
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<P>Based on fluctuation-dissipation theory, the force costant
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coefficients of the system in the reciprocal space could be given by
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(<A HREF = "#campana">Campañá</A> , <A HREF = "#kong">Kong</A>)
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<center><b>Φ</b><sub>kα,k'β</sub>(<b>q</b>) =
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k<sub>B</sub>T
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<b>G</b><sup>-1</sup><sub>kα,k'β</sub>(<b>q</b>),</center>
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</P>
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<P>where <B>G</B> is the Green's functions coefficients given by
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</P>
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<center><b>G</b><sub>kα,k'β</sub>(<b>q</b>) =
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<<b>u</b><sub>kα</sub>(<b>q</b>)•<b>u</b><sub>k'β</sub><sup>*</sup>(<b>q</b>)>,</center>
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<P>where <...> denotes the enssemble average and
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<center><B>u</B><sub>kα</sub>(<b>q</b>) = ∑<sub>l</sub>
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<b>u</b><sub>lkα</sub> exp(i<B>qr</B><sub>l</sub>)</center>
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</P>
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<P>is the α component of the atomic displacement for the <I>k</I>th atom
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in the unit cell in the reciprocal space at <B>q</B>. In practice, the
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Green's functions coefficients can also be measured according to the
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following formula,
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</P>
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<center><b>G</b><sub>kα,k'β</sub>(<b>q</b>) =
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<<b>R</b><sub>kα</sub>(<b>q</b>)•<b>R</b><sup>*</sup><sub>k'β</sub>(<b>q</b>)>
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- <<b>R</b>><sub>kα</sub>(<b>q</b>)•<<b>R</b>><sup>*</sup><sub>k'β</sub>(<b>q</b>),
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</center>
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<P>where <B>R</B> is the instantaneous positions of atoms, and <<B>R</B>> is the
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averaged atomic positions. It gives essentially the same
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results as the displacement method and is easier to implement into an MD code.
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</P>
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<P>Once the force constant matrix is known, the dynamical matrix <B>D</B>
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could then be obtained by
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</P>
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<center><b>D</b><sub>kα, k'β</sub>(<b>q</b>) = (m<sub>k</sub>m<sub>k'</sub>)<sup>-1/2</sup> <b>Φ</b><sub>kα,k'β</sub>(<b>q</b>)</center>
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<P>whose eigenvalues are exactly the phonon frequencies at <B>q</B>.
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</P>
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<P>This fix observes the positions of atoms in the corresponding group
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and the two-point correlations. To achieve this the positions of the
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atoms are examined every Nevery steps and are Fourier-transformed
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(with <A HREF = "kspace_style.html">FFT3d wrapper</A> from kspace package of LAMMPS)
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into reciprocal space, in which the averaging process and correlation
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computation is then done. After every Noutput measurements, the matrix
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<B>G</B>(<B>q</B>) is calculated and inverted to get the elastic stiffness
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coefficients. The dynamical matrices are then constructed and written
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to file "prefix".bin."timestep" in binary format and to file
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"prefix".log for each wavevector <B>q</B>.
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</P>
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<P>A detailed description of this method can be found in (<A HREF = "#kong2011">Kong2011</A>).
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</P>
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<P>The <I>sysdim</I> keyword is optional, if specified and its value is
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smaller than the dimensionality of the molecular dynamics simulation,
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its value will be taken as the dimensionality of the system under
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study. For example, in LAMMPS, one can simulate a 2D or 3D system,
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while if one wants to study the phonon dispersion of a 1D atomic
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chain, one can set the <I>sysdim</I> keyword to be <I>1</I> and the code will
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assume a 1D system is studied.
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</P>
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<P>The <I>nasr</I> keyword is optional. An iterative procedure is employed to
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enforce the acoustic sum rule on Φ at Γ, and the number
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provided by keyword <I>nasr</I> gives the total number of iterations. For
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system whose unit cell has only one atom, <I>nasr</I> = 1 is sufficient;
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while for other systems, <I>nasr</I> = 10 should be enough.
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</P>
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<P>The <I>map_file</I> contains the mapping information between the lattice
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indices and the atom IDs, which simply tells the code which atom sits
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at which lattice point; the lattice indices start from 0. An auxiliary
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code, <A HREF = "http://code.google.com/p/latgen">latgen</A>, can be employed to
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generate the compatible map file for various crystals.
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</P>
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<P>The unit of the measured dynamical matrix is
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<A HREF = "units.html">energy/distance^2/mass</A>. The coordinates for <I>q</I> points
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in the log file is in unit of the basis vectors of the corresponding
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reciprocal lattice.
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</P>
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<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
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</P>
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<P>No information about this fix is written to <A HREF = "restart.html">binary restart
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files</A>.
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</P>
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<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>temp</I> option
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is supported by this fix. You can use it to change the
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temperature compute from thermo_temp to the one that reflects the true
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temperature of atoms in the group.
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</P>
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<P>No global scalar or vector or per-atom
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quantities are stored by this fix for access by various <A HREF = "Section_howto.html#4_15">output
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commands</A>.
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Instead, this fix outputs the initialization information (in which the
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mapping information can be found) and the calculated
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dynamical matrices into file "prefix".log, where "prefix" will be
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replaced by the prefix given; besides, the
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dynamical matrices will also be written to file
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"prefix".bin."timestep" in binary format, which could be
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used by a postprocessing code <I>phana</I> to get the phonon density of states
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and/or phonon dispersion curves.
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At the end of run, these information will also be written.
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</P>
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<P>No parameter of this fix can be used with the <I>start/stop</I> keywords
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of the <A HREF = "run.html">run</A> command.
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</P>
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<P>This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
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</P>
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<P><B>Restrictions:</B>
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</P>
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<P>This fix assumes a crystalline system with periodical lattice. The temperature
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of the system should not exceed the melting temperature to keep in solid state.
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "compute_msd.html">compute msd</A>
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</P>
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<P><A HREF = "http://code.google.com/p/fix-gfmd">fix gfc</A>
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</P>
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<P><B>Note:</B> Compiling of this fix along with LAMMPS requires that the
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<A HREF = "kspace_style.html">FFT3d wrappers of kspace</A> of LAMMPS is included
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while compiling.
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</P>
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<P><B>Default:</B>
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</P>
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<P>The option defaults are <I>sysdim</I> = domain->dimension, <I>nasr</I> = 20.
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</P>
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<HR>
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<A NAME = "campana"></A>
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<P><B>(Campañá)</B> C. Campañá and
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M. H. Müser, <I>Practical Green's function approach to the
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simulation of elastic semi-infinite solids</I>, <A HREF = "http://dx.doi.org/10.1103/PhysRevB.74.075420">Phys. Rev. B <B>74</B>,
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075420 (2006)</A>
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</P>
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<A NAME = "kong"></A>
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<P><B>(Kong)</B> L.T. Kong, G. Bartels, C. Campañá,
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C. Denniston, and Martin H. Müser, <I>Implementation of Green's
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function molecular dynamics: An extension to LAMMPS</I>, <A HREF = "http://dx.doi.org/10.1016/j.cpc.2008.12.035">Computer
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Physics Communications <B>180</B>(6):1004-1010
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(2009).</A>
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</P>
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<P>L.T. Kong, C. Denniston, and Martin H. Müser,
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<I>An improved version of the Green's function molecular dynamics
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method</I>, <A HREF = "http://dx.doi.org/10.1016/j.cpc.2010.10.006">Computer Physics Communications <B>182</B>(2):540-541
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(2011).</A>
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</P>
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<A NAME = "kong2011"></A>
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<P><B>(Kong2011)</B> L.T. Kong, <I>Phonon dispersion measured directly from
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molecular dynamics simulations</I>, <A HREF = "http://dx.doi.org/10.1016/j.cpc.2011.04.019">Computer Physics Communications
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<B>182</B>(10):2201-2207,
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(2011).</A>
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</P>
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</HTML>
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