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297 lines
14 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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<H3>fix langevin 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 langevin Tstart Tstop damp seed 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>langevin = style name of this fix command
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<LI>Tstart,Tstop = desired temperature at start/end of run (temperature units)
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<LI>Tstart can be a variable (see below)
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<LI>damp = damping parameter (time units)
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<LI>seed = random number seed to use for white noise (positive integer)
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>angmom</I> or <I>omega</I> or <I>scale</I> or <I>tally</I> or <I>zero</I>
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<PRE> <I>angmom</I> value = <I>no</I> or scale
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<I>no</I> = do not thermostat rotational degrees of freedom via the angular momentum
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factor = do thermostat rotational degrees of freedom via the angular momentum and apply numeric factor as discussed below
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<I>omega</I> value = <I>no</I> or <I>yes</I>
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<I>no</I> = do not thermostat rotational degrees of freedom via the angular velocity
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<I>yes</I> = do thermostat rotational degrees of freedom via the angular velocity
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<I>scale</I> values = type ratio
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type = atom type (1-N)
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ratio = factor by which to scale the damping coefficient
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<I>tally</I> value = <I>no</I> or <I>yes</I>
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<I>no</I> = do not tally the energy added/subtracted to atoms
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<I>yes</I> = do tally the energy added/subtracted to atoms
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<I>zero</I> value = <I>no</I> or <I>yes</I>
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<I>no</I> = do not set total random force to zero
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<I>yes</I> = set total random force to zero
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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 3 boundary langevin 1.0 1.0 1000.0 699483
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fix 1 all langevin 1.0 1.1 100.0 48279 scale 3 1.5
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fix 1 all langevin 1.0 1.1 100.0 48279 angmom 3.333
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Apply a Langevin thermostat as described in <A HREF = "#Schneider">(Schneider)</A>
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to a group of atoms which models an interaction with a background
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implicit solvent. Used with <A HREF = "fix_nve.html">fix nve</A>, this command
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performs Brownian dynamics (BD), since the total force on each atom
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will have the form:
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</P>
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<PRE>F = Fc + Ff + Fr
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Ff = - (m / damp) v
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Fr is proportional to sqrt(Kb T m / (dt damp))
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</PRE>
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<P>Fc is the conservative force computed via the usual inter-particle
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interactions (<A HREF = "pair_style.html">pair_style</A>,
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<A HREF = "bond_style.html">bond_style</A>, etc).
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</P>
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<P>The Ff and Fr terms are added by this fix on a per-particle basis.
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See the <A HREF = "pair_dpd.html">pair_style dpd/tstat</A> command for a
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thermostatting option that adds similar terms on a pairwise basis to
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pairs of interacting particles.
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</P>
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<P>Ff is a frictional drag or viscous damping term proportional to the
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particle's velocity. The proportionality constant for each atom is
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computed as m/damp, where m is the mass of the particle and damp is
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the damping factor specified by the user.
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</P>
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<P>Fr is a force due to solvent atoms at a temperature T randomly bumping
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into the particle. As derived from the fluctuation/dissipation
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theorem, its magnitude as shown above is proportional to sqrt(Kb T m /
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dt damp), where Kb is the Boltzmann constant, T is the desired
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temperature, m is the mass of the particle, dt is the timestep size,
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and damp is the damping factor. Random numbers are used to randomize
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the direction and magnitude of this force as described in
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<A HREF = "#Dunweg">(Dunweg)</A>, where a uniform random number is used (instead of
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a Gaussian random number) for speed.
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</P>
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<P>Note that unless you use the <I>omega</I> or <I>angmom</I> keywords, the
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thermostat effect of this fix is applied to only the translational
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degrees of freedom for the particles, which is an important
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consideration for finite-size particles, which have rotational degrees
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of freedom, are being thermostatted. The translational degrees of
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freedom can also have a bias velocity removed from them before
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thermostatting takes place; see the description below.
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</P>
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<P>IMPORTANT NOTE: Unlike the <A HREF = "fix_nh.html">fix nvt</A> command which
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performs Nose/Hoover thermostatting AND time integration, this fix
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does NOT perform time integration. It only modifies forces to effect
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thermostatting. Thus you must use a separate time integration fix,
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like <A HREF = "fix_nve.html">fix nve</A> to actually update the velocities and
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positions of atoms using the modified forces. Likewise, this fix
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should not normally be used on atoms that also have their temperature
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controlled by another fix - e.g. by <A HREF = "fix_nh.html">fix nvt</A> or <A HREF = "fix_temp_rescale.html">fix
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temp/rescale</A> commands.
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</P>
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<P>See <A HREF = "Section_howto.html#howto_16">this howto section</A> of the manual for
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a discussion of different ways to compute temperature and perform
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thermostatting.
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</P>
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<P>The desired temperature at each timestep is a ramped value during the
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run from <I>Tstart</I> to <I>Tstop</I>.
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</P>
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<P><I>Tstart</I> can be specified as an equal-style or atom-style
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<A HREF = "variable.html">variable</A>. In this case, the <I>Tstop</I> setting is
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ignored. If the value is a variable, it should be specified as
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v_name, where name is the variable name. In this case, the variable
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will be evaluated each timestep, and its value used to determine the
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target temperature.
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</P>
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<P>Equal-style variables can specify formulas with various mathematical
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functions, and include <A HREF = "thermo_style.html">thermo_style</A> command
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keywords for the simulation box parameters and timestep and elapsed
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time. Thus it is easy to specify a time-dependent temperature.
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</P>
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<P>Atom-style variables can specify the same formulas as equal-style
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variables but can also include per-atom values, such as atom
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coordinates. Thus it is easy to specify a spatially-dependent
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temperature with optional time-dependence as well.
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</P>
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<P>Like other fixes that perform thermostatting, this fix can be used
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with <A HREF = "compute.html">compute commands</A> that remove a "bias" from the
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atom velocities. E.g. removing the center-of-mass velocity from a
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group of atoms or removing the x-component of velocity from the
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calculation. This is not done by default, but only if the
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<A HREF = "fix_modify.html">fix_modify</A> command is used to assign a temperature
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compute to this fix that includes such a bias term. See the doc pages
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for individual <A HREF = "compute.html">compute commands</A> to determine which ones
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include a bias. In this case, the thermostat works in the following
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manner: bias is removed from each atom, thermostatting is performed on
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the remaining thermal degrees of freedom, and the bias is added back
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in.
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</P>
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<P>The <I>damp</I> parameter is specified in time units and determines how
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rapidly the temperature is relaxed. For example, a value of 100.0
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means to relax the temperature in a timespan of (roughly) 100 time
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units (tau or fmsec or psec - see the <A HREF = "units.html">units</A> command).
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The damp factor can be thought of as inversely related to the
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viscosity of the solvent. I.e. a small relaxation time implies a
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hi-viscosity solvent and vice versa. See the discussion about gamma
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and viscosity in the documentation for the <A HREF = "fix_viscous.html">fix
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viscous</A> command for more details.
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</P>
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<P>The random # <I>seed</I> must be a positive integer. A Marsaglia random
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number generator is used. Each processor uses the input seed to
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generate its own unique seed and its own stream of random numbers.
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Thus the dynamics of the system will not be identical on two runs on
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different numbers of processors.
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</P>
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<HR>
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<P>The keyword/value option pairs are used in the following ways.
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</P>
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<P>The keyword <I>angmom</I> and <I>omega</I> keywords enable thermostatting of
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rotational degrees of freedom in addition to the usual translational
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degrees of freedom. This can only be done for finite-size particles.
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</P>
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<P>A simulation using atom_style sphere defines an omega for finite-size
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spheres. A simulation using atom_style ellipsoid defines a finite
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size and shape for aspherical particles and an angular momentum.
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The Langevin formulas for thermostatting the rotational degrees of
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freedom are the same as those above, where force is replaced by
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torque, m is replaced by the moment of inertia I, and v is replaced by
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omega (which is derived from the angular momentum in the case of
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aspherical particles).
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</P>
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<P>The rotational temperature of the particles can be monitored by the
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<A HREF = "compute_temp_sphere.html">compute temp/sphere</A> and <A HREF = "compute_temp_asphere.html">compute
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temp/asphere</A> commands with their rotate
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options.
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</P>
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<P>For the <I>omega</I> keyword there is also a scale factor of 10.0/3.0 that
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is applied as a multiplier on the Ff (damping) term in the equation
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above and of sqrt(10.0/3.0) as a multiplier on the Fr term. This does
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not affect the thermostatting behaviour of the Langevin formalism but
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insures that the randomized rotational diffusivity of spherical
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particles is correct.
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</P>
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<P>For the <I>angmom</I> keyword a similar scale factor is needed which is
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10.0/3.0 for spherical particles, but is anisotropic for aspherical
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particles (e.g. ellipsoids). Currently LAMMPS only applies an
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isotropic scale factor, and you can choose its magnitude as the
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specified value of the <I>angmom</I> keyword. If your aspherical particles
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are (nearly) spherical than a value of 10.0/3.0 = 3.333 is a good
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choice. If they are highly aspherical, a value of 1.0 is as good a
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choice as any, since the effects on rotational diffusivity of the
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particles will be incorrect regardless. Note that for any reasonable
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scale factor, the thermostatting effect of the <I>angmom</I> keyword on the
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rotational temperature of the aspherical particles should still be
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valid.
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</P>
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<P>The keyword <I>scale</I> allows the damp factor to be scaled up or down by
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the specified factor for atoms of that type. This can be useful when
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different atom types have different sizes or masses. It can be used
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multiple times to adjust damp for several atom types. Note that
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specifying a ratio of 2 increases the relaxation time which is
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equivalent to the solvent's viscosity acting on particles with 1/2 the
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diameter. This is the opposite effect of scale factors used by the
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<A HREF = "fix_viscous.html">fix viscous</A> command, since the damp factor in fix
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<I>langevin</I> is inversely related to the gamma factor in fix <I>viscous</I>.
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Also note that the damping factor in fix <I>langevin</I> includes the
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particle mass in Ff, unlike fix <I>viscous</I>. Thus the mass and size of
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different atom types should be accounted for in the choice of ratio
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values.
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</P>
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<P>The keyword <I>tally</I> enables the calculation of the cumulative energy
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added/subtracted to the atoms as they are thermostatted. Effectively
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it is the energy exchanged between the infinite thermal reservoir and
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the particles. As described below, this energy can then be printed
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out or added to the potential energy of the system to monitor energy
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conservation.
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</P>
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<P>The keyword <I>zero</I> can be used to eliminate drift due to the
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thermostat. Because the random forces on different atoms are
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independent, they do not sum exactly to zero. As a result, this fix
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applies a small random force to the entire system, and the
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center-of-mass of the system undergoes a slow random walk. If the
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keyword <I>zero</I> is set to <I>yes</I>, the total random force is set exactly
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to zero by subtracting off an equal part of it from each atom in the
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group. As a result, the center-of-mass of a system with zero initial
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momentum will not drift over time.
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</P>
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<HR>
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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>. Because the state of the random number generator
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is not saved in restart files, this means you cannot do "exact"
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restarts with this fix, where the simulation continues on the same as
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if no restart had taken place. However, in a statistical sense, a
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restarted simulation should produce the same behavior.
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</P>
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<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>temp</I> option is supported by this
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fix. You can use it to assign a temperature <A HREF = "compute.html">compute</A>
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you have defined to this fix which will be used in its thermostatting
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procedure, as described above. For consistency, the group used by
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this fix and by the compute should be the same.
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</P>
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<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> option is supported by this
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fix to add the energy change induced by Langevin thermostatting to the
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system's potential energy as part of <A HREF = "thermo_style.html">thermodynamic
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output</A>. Note that use of this option requires
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setting the <I>tally</I> keyword to <I>yes</I>.
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</P>
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<P>This fix computes a global scalar which can be accessed by various
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<A HREF = "Section_howto.html#howto_15">output commands</A>. The scalar is the
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cummulative energy change due to this fix. The scalar value
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calculated by this fix is "extensive". Note that calculation of this
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quantity requires setting the <I>tally</I> keyword to <I>yes</I>.
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</P>
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<P>This fix can ramp its target temperature over multiple runs, using the
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<I>start</I> and <I>stop</I> keywords of the <A HREF = "run.html">run</A> command. See the
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<A HREF = "run.html">run</A> command for details of how to do this.
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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> none
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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 = "fix_nh.html">fix nvt</A>, <A HREF = "fix_temp_rescale.html">fix temp/rescale</A>, <A HREF = "fix_viscous.html">fix
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viscous</A>, <A HREF = "fix_nh.html">fix nvt</A>, <A HREF = "pair_dpd.html">pair_style
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dpd/tstat</A>
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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 angmom = no, omega = no, scale = 1.0 for all
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types, tally = no, zero = no.
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</P>
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<HR>
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<A NAME = "Dunweg"></A>
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<P><B>(Dunweg)</B> Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).
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</P>
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<A NAME = "Schneider"></A>
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<P><B>(Schneider)</B> Schneider and Stoll, Phys Rev B, 17, 1302 (1978).
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</P>
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</HTML>
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