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< span id = "index-0" > < / span > < h1 > fix langevin command< a class = "headerlink" href = "#fix-langevin-command" title = "Permalink to this headline" > ¶< / a > < / h1 >
< / div >
< div class = "section" id = "fix-langevin-kk-command" >
< h1 > fix langevin/kk command< a class = "headerlink" href = "#fix-langevin-kk-command" title = "Permalink to this headline" > ¶< / a > < / h1 >
< div class = "section" id = "syntax" >
< h2 > Syntax< a class = "headerlink" href = "#syntax" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < pre > fix ID group-ID langevin Tstart Tstop damp seed keyword values ...
< / pre > < / div >
< / div >
< ul class = "simple" >
< li > ID, group-ID are documented in < a class = "reference internal" href = "fix.html" > < em > fix< / em > < / a > command< / li >
< li > langevin = style name of this fix command< / li >
< li > Tstart,Tstop = desired temperature at start/end of run (temperature units)< / li >
< li > Tstart can be a variable (see below)< / li >
< li > damp = damping parameter (time units)< / li >
< li > seed = random number seed to use for white noise (positive integer)< / li >
< li > zero or more keyword/value pairs may be appended< / li >
< li > keyword = < em > angmom< / em > or < em > omega< / em > or < em > scale< / em > or < em > tally< / em > or < em > zero< / em > < / li >
< / ul >
< pre class = "literal-block" >
< em > angmom< / em > value = < em > no< / em > or scale
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< em > no< / em > = do not thermostat rotational degrees of freedom via the angular momentum
factor = do thermostat rotational degrees of freedom via the angular momentum and apply numeric factor as discussed below
< em > gjf< / em > value = < em > no< / em > or < em > yes< / em >
< em > no< / em > = use standard formulation
< em > yes< / em > = use Gronbech-Jensen/Farago formulation
< em > omega< / em > value = < em > no< / em > or < em > yes< / em >
< em > no< / em > = do not thermostat rotational degrees of freedom via the angular velocity
< em > yes< / em > = do thermostat rotational degrees of freedom via the angular velocity
< em > scale< / em > values = type ratio
type = atom type (1-N)
ratio = factor by which to scale the damping coefficient
< em > tally< / em > value = < em > no< / em > or < em > yes< / em >
< em > no< / em > = do not tally the energy added/subtracted to atoms
< em > yes< / em > = do tally the energy added/subtracted to atoms
< em > zero< / em > value = < em > no< / em > or < em > yes< / em >
< em > no< / em > = do not set total random force to zero
< em > yes< / em > = set total random force to zero
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< / pre >
< / div >
< div class = "section" id = "examples" >
< h2 > Examples< a class = "headerlink" href = "#examples" title = "Permalink to this headline" > ¶< / a > < / h2 >
< div class = "highlight-python" > < div class = "highlight" > < 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
< / pre > < / div >
< / div >
< / div >
< div class = "section" id = "description" >
< h2 > Description< a class = "headerlink" href = "#description" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > Apply a Langevin thermostat as described in < a class = "reference internal" href = "fix_langevin_eff.html#schneider" > < span > (Schneider)< / span > < / 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 class = "reference internal" href = "fix_nve.html" > < em > fix nve< / em > < / 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:< / p >
< div class = "highlight-python" > < div class = "highlight" > < 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))
< / pre > < / div >
< / div >
< p > Fc is the conservative force computed via the usual inter-particle
interactions (< a class = "reference internal" href = "pair_style.html" > < em > pair_style< / em > < / a > ,
< a class = "reference internal" href = "bond_style.html" > < em > bond_style< / em > < / a > , etc).< / p >
< p > The Ff and Fr terms are added by this fix on a per-particle basis.
See the < a class = "reference internal" href = "pair_dpd.html" > < em > pair_style dpd/tstat< / em > < / 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.< / p >
< p > Ff is a frictional drag or viscous damping term proportional to the
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.< / p >
< 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 /
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
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< a class = "reference internal" href = "fix_langevin_eff.html#dunweg" > < span > (Dunweg)< / span > < / a > , where a uniform random number is used (instead of
a Gaussian random number) for speed.< / p >
< p > Note that unless you use the < em > omega< / em > or < em > angmom< / em > keywords, the
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thermostat effect of this fix is applied to only the translational
degrees of freedom for the particles, which is an important
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consideration for finite-size particles, which have rotational degrees
of freedom, are being thermostatted. The translational degrees of
freedom can also have a bias velocity removed from them before
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thermostatting takes place; see the description below.< / p >
< div class = "admonition warning" >
< p class = "first admonition-title" > Warning< / p >
< p class = "last" > Unlike the < a class = "reference internal" href = "fix_nh.html" > < em > fix nvt< / em > < / a > command which
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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,
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like < a class = "reference internal" href = "fix_nve.html" > < em > fix nve< / em > < / 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 class = "reference internal" href = "fix_nh.html" > < em > fix nvt< / em > < / a > or < a class = "reference internal" href = "fix_temp_rescale.html" > < em > fix temp/rescale< / em > < / a > commands.< / p >
< / div >
< p > See < a class = "reference internal" href = "Section_howto.html#howto-16" > < span > this howto section< / span > < / a > of the manual for
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a discussion of different ways to compute temperature and perform
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thermostatting.< / p >
< p > The desired temperature at each timestep is a ramped value during the
run from < em > Tstart< / em > to < em > Tstop< / em > .< / p >
< p > < em > Tstart< / em > can be specified as an equal-style or atom-style
< a class = "reference internal" href = "variable.html" > < em > variable< / em > < / a > . In this case, the < em > Tstop< / em > setting is
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ignored. If the value is a variable, it should be specified as
v_name, where name is the variable name. In this case, the variable
will be evaluated each timestep, and its value used to determine the
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target temperature.< / p >
< p > Equal-style variables can specify formulas with various mathematical
functions, and include < a class = "reference internal" href = "thermo_style.html" > < em > thermo_style< / em > < / 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.< / p >
< 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
coordinates. Thus it is easy to specify a spatially-dependent
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temperature with optional time-dependence as well.< / p >
< p > Like other fixes that perform thermostatting, this fix can be used
with < a class = "reference internal" href = "compute.html" > < em > compute commands< / em > < / a > that remove a “ bias” from the
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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
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< a class = "reference internal" href = "fix_modify.html" > < em > fix_modify< / em > < / 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 class = "reference internal" href = "compute.html" > < em > compute commands< / em > < / a > to determine which ones
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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
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in.< / p >
< p > The < em > damp< / em > 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
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 class = "reference internal" href = "units.html" > < em > units< / em > < / a > command).
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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
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and viscosity in the documentation for the < a class = "reference internal" href = "fix_viscous.html" > < em > fix viscous< / em > < / a > command for more details.< / p >
< p > The random # < em > seed< / em > must be a positive integer. A Marsaglia random
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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
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different numbers of processors.< / p >
< hr class = "docutils" / >
< p > The keyword/value option pairs are used in the following ways.< / p >
< p > The keyword < em > angmom< / em > and < em > omega< / em > 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.< / p >
< 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.
The Langevin formulas for thermostatting the rotational degrees of
freedom are the same as those above, where force is replaced by
torque, m is replaced by the moment of inertia I, and v is replaced by
omega (which is derived from the angular momentum in the case of
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aspherical particles).< / p >
< p > The rotational temperature of the particles can be monitored by the
< a class = "reference internal" href = "compute_temp_sphere.html" > < em > compute temp/sphere< / em > < / a > and < a class = "reference internal" href = "compute_temp_asphere.html" > < em > compute temp/asphere< / em > < / a > commands with their rotate
options.< / p >
< p > For the < em > omega< / em > 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
above and of sqrt(10.0/3.0) as a multiplier on the Fr term. This does
not affect the thermostatting behaviour of the Langevin formalism but
insures that the randomized rotational diffusivity of spherical
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particles is correct.< / p >
< p > For the < em > angmom< / em > 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
particles (e.g. ellipsoids). Currently LAMMPS only applies an
isotropic scale factor, and you can choose its magnitude as the
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specified value of the < em > angmom< / em > 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
choice. If they are highly aspherical, a value of 1.0 is as good a
choice as any, since the effects on rotational diffusivity of the
particles will be incorrect regardless. Note that for any reasonable
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scale factor, the thermostatting effect of the < em > angmom< / em > keyword on the
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rotational temperature of the aspherical particles should still be
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valid.< / p >
< p > The keyword < em > scale< / em > 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
different atom types have different sizes or masses. It can be used
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 class = "reference internal" href = "fix_viscous.html" > < em > fix viscous< / em > < / a > command, since the damp factor in fix
< em > langevin< / em > is inversely related to the gamma factor in fix < em > viscous< / em > .
Also note that the damping factor in fix < em > langevin< / em > includes the
particle mass in Ff, unlike fix < em > viscous< / em > . 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.< / p >
< p > The keyword < em > tally< / em > enables the calculation of the cumulative energy
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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
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conservation.< / p >
< div class = "admonition warning" >
< p class = "first admonition-title" > Warning< / p >
< p class = "last" > this accumulated energy does NOT include kinetic
energy removed by the < em > zero< / em > flag. LAMMPS will print a warning when
both options are active.< / p >
< / div >
< p > The keyword < em > zero< / em > can be used to eliminate drift due to the
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thermostat. Because the random forces on different atoms are
independent, they do not sum exactly to zero. As a result, this fix
applies a small random force to the entire system, and the
center-of-mass of the system undergoes a slow random walk. If the
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keyword < em > zero< / em > is set to < em > yes< / em > , 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
group. As a result, the center-of-mass of a system with zero initial
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momentum will not drift over time.< / p >
< p > The keyword < em > gjf< / em > can be used to run the < a class = "reference internal" href = "#gronbech-jensen" > < span > Gronbech-Jensen/Farago< / span > < / a > time-discretization of the Langevin model. As
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described in the papers cited below, the purpose of this method is to
enable longer timesteps to be used (up to the numerical stability
limit of the integrator), while still producing the correct Boltzmann
distribution of atom positions. It is implemented within LAMMPS, by
changing how the the random force is applied so that it is composed of
the average of two random forces representing half-contributions from
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the previous and current time intervals.< / p >
< p > In common with all methods based on Verlet integration, the
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discretized velocities generated by this method in conjunction with
velocity-Verlet time integration are not exactly conjugate to the
positions. As a result the temperature (computed from the discretized
velocities) will be systematically lower than the target temperature,
by a small amount which grows with the timestep. Nonetheless, the
distribution of atom positions will still be consistent with the
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target temperature.< / p >
< p > As an example of using the < em > gjf< / em > keyword, for molecules containing C-H
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bonds, configurational properties generated with dt = 2.5 fs and tdamp
= 100 fs are indistinguishable from dt = 0.5 fs. Because the velocity
distribution systematically decreases with increasing timestep, the
method should not be used to generate properties that depend on the
velocity distribution, such as the velocity autocorrelation function
(VACF). In this example, the velocity distribution at dt = 2.5fs
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generates an average temperature of 220 K, instead of 300 K.< / p >
< hr class = "docutils" / >
< p > Styles with a < em > cuda< / em > , < em > gpu< / em > , < em > intel< / em > , < em > kk< / em > , < em > omp< / em > , or < em > opt< / em > suffix are
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functionally the same as the corresponding style without the suffix.
They have been optimized to run faster, depending on your available
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hardware, as discussed in < a class = "reference internal" href = "Section_accelerate.html" > < em > Section_accelerate< / em > < / a >
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of the manual. The accelerated styles take the same arguments and
should produce the same results, except for round-off and precision
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issues.< / p >
< p > These accelerated styles are part of the USER-CUDA, GPU, USER-INTEL,
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KOKKOS, USER-OMP and OPT packages, respectively. They are only
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enabled if LAMMPS was built with those packages. See the < a class = "reference internal" href = "Section_start.html#start-3" > < span > Making LAMMPS< / span > < / a > section for more info.< / p >
< p > You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the < a class = "reference internal" href = "Section_start.html#start-7" > < span > -suffix command-line switch< / span > < / a > when you invoke LAMMPS, or you can
use the < a class = "reference internal" href = "suffix.html" > < em > suffix< / em > < / a > command in your input script.< / p >
< p > See < a class = "reference internal" href = "Section_accelerate.html" > < em > Section_accelerate< / em > < / a > of the manual for
more instructions on how to use the accelerated styles effectively.< / p >
< / div >
< hr class = "docutils" / >
< div class = "section" id = "restart-fix-modify-output-run-start-stop-minimize-info" >
< h2 > Restart, fix_modify, output, run start/stop, minimize info< a class = "headerlink" href = "#restart-fix-modify-output-run-start-stop-minimize-info" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > No information about this fix is written to < a class = "reference internal" href = "restart.html" > < em > binary restart files< / em > < / a > . Because the state of the random number generator
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
if no restart had taken place. However, in a statistical sense, a
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restarted simulation should produce the same behavior.< / p >
< p > The < a class = "reference internal" href = "fix_modify.html" > < em > fix_modify< / em > < / a > < em > temp< / em > option is supported by this
fix. You can use it to assign a temperature < a class = "reference internal" href = "compute.html" > < em > compute< / em > < / a >
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you have defined to this fix which will be used in its thermostatting
procedure, as described above. For consistency, the group used by
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this fix and by the compute should be the same.< / p >
< p > The < a class = "reference internal" href = "fix_modify.html" > < em > fix_modify< / em > < / a > < em > energy< / em > 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 class = "reference internal" href = "thermo_style.html" > < em > thermodynamic output< / em > < / a > . Note that use of this option requires
setting the < em > tally< / em > keyword to < em > yes< / em > .< / p >
< p > This fix computes a global scalar which can be accessed by various
< a class = "reference internal" href = "Section_howto.html#howto-15" > < span > output commands< / span > < / 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
quantity requires setting the < em > tally< / em > keyword to < em > yes< / em > .< / p >
< p > This fix can ramp its target temperature over multiple runs, using the
< em > start< / em > and < em > stop< / em > keywords of the < a class = "reference internal" href = "run.html" > < em > run< / em > < / a > command. See the
< a class = "reference internal" href = "run.html" > < em > run< / em > < / a > command for details of how to do this.< / p >
< p > This fix is not invoked during < a class = "reference internal" href = "minimize.html" > < em > energy minimization< / em > < / a > .< / p >
< / div >
< div class = "section" id = "restrictions" >
< h2 > Restrictions< a class = "headerlink" href = "#restrictions" title = "Permalink to this headline" > ¶< / a > < / h2 >
< blockquote >
< div > none< / div > < / blockquote >
< / 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_nh.html" > < em > fix nvt< / em > < / a > , < a class = "reference internal" href = "fix_temp_rescale.html" > < em > fix temp/rescale< / em > < / a > , < a class = "reference internal" href = "fix_viscous.html" > < em > fix viscous< / em > < / a > , < a class = "reference internal" href = "fix_nh.html" > < em > fix nvt< / em > < / a > , < a class = "reference internal" href = "pair_dpd.html" > < em > pair_style dpd/tstat< / em > < / a > < / p >
< / div >
< div class = "section" id = "default" >
< h2 > Default< a class = "headerlink" href = "#default" title = "Permalink to this headline" > ¶< / a > < / h2 >
< p > The option defaults are angmom = no, omega = no, scale = 1.0 for all
types, tally = no, zero = no, gjf = no.< / p >
< hr class = "docutils" / >
< p id = "dunweg" > < strong > (Dunweg)< / strong > Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).< / p >
< p id = "schneider" > < strong > (Schneider)< / strong > Schneider and Stoll, Phys Rev B, 17, 1302 (1978).< / p >
< p id = "gronbech-jensen" > < strong > (Gronbech-Jensen)< / strong > Gronbech-Jensen and Farago, Mol Phys, 111, 983
(2013); Gronbech-Jensen, Hayre, and Farago, Comp Phys Comm,
185, 524 (2014)< / p >
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