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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>
</CENTER>
<HR>
<H3>compute heat/flux command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID heat/flux pe-ID
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>heat/flux = style name of this compute command
<LI>pe-ID = ID of a compute that calculates per-atom potential energy
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute myFlux all heat/flux myPE
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the heat flux vector based on
interactions between atoms in the specified group. This can be used
by itself to measure the heat flux between a hot and cold reservoir of
particles or to calculate a thermal conductivity using the Green-Kubo
formalism.
</P>
<P>See the <A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
command for details on how to compute thermal conductivity in an
alternate way, via the Muller-Plathe method.
</P>
<P>The compute takes a <I>pe-ID</I> argument which is the ID of a <A HREF = "compute_pe_atom.html">compute
pe/atom</A> that calculates per-atom potential
energy. Normally, it should be defined for the same group used by
compute heat/flux, though LAMMPS does not check for this.
</P>
<P>The Green-Kubo formulas relate the ensemble average of the
auto-correlation of the heat flux J to the thermal conductivity kappa.
</P>
<CENTER><IMG SRC = "Eqs/heat_flux_k.jpg">
</CENTER>
<CENTER><IMG SRC = "Eqs/heat_flux_J.jpg">
</CENTER>
<P>Ei is the per-atom energy (potential and kinetic). The potential
portion is calculated by the compute <I>pe-ID</I> specified as an argument
to the compute heat/flux command.
</P>
<P>IMPORTANT NOTE: The per-atom potential energy calculated by the
<I>pe-ID</I> compute should only include pairwise energy, to be consistent
with the second virial-like term in the formula for J. Thus if any
bonds, angles, etc exist in the system, the compute should limit its
calculation to only the pair contribution. E.g. it could be defined
as follows. Note that if <I>pair</I> is not listed as the last argument,
it will be included by default, but so will other contributions such
as bond, angle, etc.
</P>
<PRE>compute myPE all pe/atom pair
</PRE>
<P>The second term of the heat flux equation for J is calculated by
compute heat/flux for pairwise interactions for any I,J pair where one
of the 2 atoms in is the compute group.
</P>
<HR>
<P>These quantities can be output every so many timesteps (e.g. via the
thermo_style custom command). Then as post-processing steps, an
autocorrelation can be performed, its integral estimated, and the
Green-Kubo formula evaluated.
</P>
<P>Here is an example of this procedure. First a LAMMPS input script for
solid Ar is appended below. A Python script
<A HREF = "Scripts/correlate.py">correlate.py</A> is also given, which calculates
the autocorrelation of the flux output in the logfile flux.log,
produced by the LAMMPS run. It is invoked as
</P>
<PRE>correlate.py flux.log -c 3 -s 200
</PRE>
<P>The resulting data lists the autocorrelation in column 1 and the
integral of the autocorrelation in column 2. The integral of the
correlation needs to be multiplied by V/(kB T^2) times the sample
interval and the appropriate unit conversion factors. For real
<A HREF = "units.html">units</A> in LAMMPS, this is 2917703220.0 in this case. The
final thermal conductivity value obtained is 0.25 W/mK.
</P>
<P>The 6 components of the vector calculated by this compute are as
follows. The first 3 components are the x, y, z components of the
full heat flux. The next 3 components are the x, y, z components of
just the convective portion of the flux, which is the energy per atom
times the velocity of the atom.
</P>
<P><B>Output info:</B>
</P>
<P>This compute calculates a global vector of length 6 (heat flux
vector), which can be accessed by indices 1-6. These values can be
used by any command that uses global vector values from a compute as
input. See <A HREF = "Section_howto.html#4_15">this section</A> for an overview of
LAMMPS output options.
</P>
<P>The vector values calculated by this compute are "extensive". They
should be divided by the appropriate volume to get a flux. The vector
values will be in energy*velocity <A HREF = "units.html">units</A>.
</P>
<P><B>Restrictions:</B>
</P>
<P>Only pairwise interactions, as defined by the pair_style command, are
included in this calculation.
</P>
<P>This compute requires you to use the <A HREF = "communicate.html">communicate vel
yes</A> option so that velocites are stored by ghost
atoms.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_thermal_conductivity.html">fix thermal/conductivity</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<H4>Sample LAMMPS input script
</H4>
<PRE>atom_style dpd
units real
dimension 3
boundary p p p
lattice fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
region box block 0 4 0 4 0 4
create_box 1 box
create_atoms 1 box
mass 1 39.948
pair_style lj/cut 13.0
pair_coeff * * 0.2381 3.405
group every region box
velocity all create 70 102486 mom yes rot yes dist gaussian
timestep 4.0
thermo 10
</PRE>
<PRE># ------------- Equilibration and thermalisation ----------------
</PRE>
<PRE>fix NPT all npt 70 70 10 xyz 0.0 0.0 100.0 drag 0.2
run 8000
unfix NPT
</PRE>
<PRE># --------------- Equilibration in nve -----------------
</PRE>
<PRE>fix NVE all nve
run 8000
</PRE>
<PRE># -------------- Flux calculation in nve ---------------
</PRE>
<PRE>reset_timestep 0
compute myPE all pe/atom pair
compute flux all heat/flux myPE
log flux.log
variable J equal c_flux[1]/vol
thermo_style custom step temp v_J
run 100000
</PRE>
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