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fix_langevin.html
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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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<H3>fix langevin command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID langevin Tstart Tstop damp seed keyword values ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>langevin = style name of this fix command
<LI>Tstart,Tstop = desired temperature at start/end of run (temperature units)
<LI>damp = damping parameter (time units)
<LI>seed = random number seed to use for white noise (positive integer)
<LI>zero or more keyword/value pairs may be appended
<PRE>keyword = <I>scale</I> or <I>tally</I>
<I>scale</I> values = type ratio
type = atom type (1-N)
ratio = factor by which to scale the damping coefficient
<I>tally</I> values = <I>no</I> or <I>yes</I>
<I>no</I> = do not tally the energy added/subtracted to atoms
<I>yes</I> = do tally the energy added/subtracted to atoms
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 3 boundary langevin 1.0 1.0 1000.0 699483
fix 1 all langevin 1.0 1.1 100.0 48279 scale 3 1.5
</PRE>
<P><B>Description:</B>
</P>
<P>Apply a Langevin thermostat as described in <A HREF = "#Schneider">(Schneider)</A>
to a group of atoms which models an interaction with a background
implicit solvent. Used with <A HREF = "fix_nve.html">fix nve</A>, this command
performs Brownian dynamics (BD), since the total force on each atom
will have the form:
</P>
<PRE>F = Fc + Ff + Fr
Ff = - (m / damp) v
Fr is proportional to sqrt(Kb T m / (dt damp))
</PRE>
<P>Fc is the conservative force computed via the usual inter-particle
interactions (<A HREF = "pair_style.html">pair_style</A>,
<A HREF = "bond_style.html">bond_style</A>, etc).
</P>
<P>The Ff and Fr terms are added by this fix.
</P>
<P>Ff is a frictional drag or viscous damping term proportional to the
particle's velocity. The proportionality constant for each atom is
computed as m/damp, where m is the mass of the particle and damp is
the damping factor specified by the user.
</P>
<P>Fr is a force due to solvent atoms at a temperature T randomly bumping
into the particle. As derived from the fluctuation/dissipation
theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
dt damp), where Kb is the Boltzmann constant, T is the desired
temperature, m is the mass of the particle, dt is the timestep size,
and damp is the damping factor. Random numbers are used to randomize
the direction and magnitude of this force as described in
<A HREF = "#Dunweg">(Dunweg)</A>, where a uniform random number is used (instead of
a Gaussian random number) for speed.
</P>
<P>Note that the thermostat effect of this fix is applied to only the
translational degrees of freedom for the particles, which is an
important consideration if extended spherical or aspherical particles
which have rotational degrees of freedom are being thermostatted with
this fix. The translational degrees of freedom can also have a bias
velocity removed from them before thermostatting takes place; see the
description below.
</P>
<P>IMPORTANT NOTE: Unlike the <A HREF = "fix_nh.html">fix nvt</A> command which
performs Nose/Hoover thermostatting AND time integration, this fix
does NOT perform time integration. It only modifies forces to effect
thermostatting. Thus you must use a separate time integration fix,
like <A HREF = "fix_nve.html">fix nve</A> to actually update the velocities and
positions of atoms using the modified forces. Likewise, this fix
should not normally be used on atoms that also have their temperature
controlled by another fix - e.g. by <A HREF = "fix_nh.html">fix nvt</A> or <A HREF = "fix_temp_rescale.html">fix
temp/rescale</A> commands.
</P>
<P>See <A HREF = "Section_howto.html#4_16">this howto section</A> of the manual for a
discussion of different ways to compute temperature and perform
thermostatting.
</P>
<P>The desired temperature at each timestep is a ramped value during the
run from <I>Tstart</I> to <I>Tstop</I>.
</P>
<P>Like other fixes that perform thermostatting, this fix can be used
with <A HREF = "compute.html">compute commands</A> that remove a "bias" from the
atom velocities. E.g. removing the center-of-mass velocity from a
group of atoms or removing the x-component of velocity from the
calculation. This is not done by default, but only if the
<A HREF = "fix_modify.html">fix_modify</A> command is used to assign a temperature
compute to this fix that includes such a bias term. See the doc pages
for individual <A HREF = "compute.html">compute commands</A> to determine which ones
include a bias. In this case, the thermostat works in the following
manner: bias is removed from each atom, thermostatting is performed on
the remaining thermal degrees of freedom, and the bias is added back
in.
</P>
<P>The <I>damp</I> parameter is specified in time units and determines how
rapidly the temperature is relaxed. For example, a value of 100.0
means to relax the temperature in a timespan of (roughly) 100 time
units (tau or fmsec or psec - see the <A HREF = "units.html">units</A> command).
The damp factor can be thought of as inversely related to the
viscosity of the solvent. I.e. a small relaxation time implies a
hi-viscosity solvent and vice versa. See the discussion about gamma
and viscosity in the documentation for the <A HREF = "fix_viscous.html">fix
viscous</A> command for more details.
</P>
<P>The random # <I>seed</I> must be a positive integer. A Marsaglia random
number generator is used. Each processor uses the input seed to
generate its own unique seed and its own stream of random numbers.
Thus the dynamics of the system will not be identical on two runs on
different numbers of processors.
</P>
<P>The keyword <I>scale</I> allows the damp factor to be scaled up or down by
the specified factor for atoms of that type. This can be useful when
different atom types have different sizes or masses. It can be used
multiple times to adjust damp for several atom types. Note that
specifying a ratio of 2 increases the relaxation time which is
equivalent to the solvent's viscosity acting on particles with 1/2 the
diameter. This is the opposite effect of scale factors used by the
<A HREF = "fix_viscous.html">fix viscous</A> command, since the damp factor in fix
<I>langevin</I> is inversely related to the gamma factor in fix <I>viscous</I>.
Also note that the damping factor in fix <I>langevin</I> includes the
particle mass in Ff, unlike fix <I>viscous</I>. Thus the mass and size of
different atom types should be accounted for in the choice of ratio
values.
</P>
<P>The keyword <I>tally</I> enables the calculation of the cummulative energy
added/subtracted to the atoms as they are thermostatted. Effectively
it is the energy exchanged between the infinite thermal reservoir and
the particles. As described below, this energy can then be printed
out or added to the potential energy of the system to monitor energy
conservation.
</P>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>. Because the state of the random number generator
is not saved in restart files, this means you cannot do "exact"
restarts with this fix, where the simulation continues on the same as
if no restart had taken place. However, in a statistical sense, a
restarted simulation should produce the same behavior.
</P>
<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>temp</I> option is supported by this
fix. You can use it to assign a temperature <A HREF = "compute.html">compute</A>
you have defined to this fix which will be used in its thermostatting
procedure, as described above. For consistency, the group used by
this fix and by the compute should be the same.
</P>
<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> option is supported by this
fix to add the energy change induced by Langevin thermostatting to the
system's potential energy as part of <A HREF = "thermo_style.html">thermodynamic
output</A>. Note that use of this option requires
setting the <I>tally</I> keyword to <I>yes</I>.
</P>
<P>This fix computes a global scalar which can be accessed by various
<A HREF = "Section_howto.html#4_15">output commands</A>. The scalar is the
cummulative energy change due to this fix. The scalar value
calculated by this fix is "extensive". Note that calculation of this
quantity requires setting the <I>tally</I> keyword to <I>yes</I>.
</P>
<P>This fix can ramp its target temperature over multiple runs, using the
<I>start</I> and <I>stop</I> keywords of the <A HREF = "run.html">run</A> command. See the
<A HREF = "run.html">run</A> command for details of how to do this.
</P>
<P>This fix is not invoked during <A HREF = "minimize.html">energy minimization</A>.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_nh.html">fix nvt</A>, <A HREF = "fix_temp_rescale.html">fix temp/rescale</A>, <A HREF = "fix_viscous.html">fix
viscous</A>, <A HREF = "fix_nh.html">fix nvt</A>
</P>
<P><B>Default:</B>
</P>
<P>The option defaults are scale = 1.0 for all types and tally = no.
</P>
<HR>
<A NAME = "Dunweg"></A>
<P><B>(Dunweg)</B> Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).
</P>
<A NAME = "Schneider"></A>
<P><B>(Schneider)</B> Schneider and Stoll, Phys Rev B, 17, 1302 (1978).
</P>
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