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### fix langevin command

Syntax:

    fix ID group-ID langevin Tstart Tstop damp seed keyword values ...

- ID, group-ID are documented in fix command
- langevin = style name of this fix command
- Tstart,Tstop = desired temperature at start/end of run (temperature units)
- Tstart can be a variable (see below)
- damp = damping parameter (time units)
- seed = random number seed to use for white noise (positive integer)
- zero or more keyword/value pairs may be appended
- keyword = angmom or omega or scale or tally or zero

        angmom value = no or scale
          no = 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
        gjf value = no or yes
          no = use standard formulation
          yes = use Gronbech-Jensen/Farago formulation
        omega value = no or yes
          no = do not thermostat rotational degrees of freedom via the angular velocity
          yes = do thermostat rotational degrees of freedom via the angular velocity
        scale values = type ratio
          type = atom type (1-N)
          ratio = factor by which to scale the damping coefficient
        tally value = no or yes
          no = do not tally the energy added/subtracted to atoms
          yes = do tally the energy added/subtracted to atoms
        zero value = no or yes
          no = do not set total random force to zero
          yes = set total random force to zero

Examples:

    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
    fix 1 all langevin 1.0 1.1 100.0 48279 angmom 3.333

Description:

Apply a Langevin thermostat as described in (Schneider) to a group of atoms which models an interaction with a background implicit solvent. Used with fix nve, this command performs Brownian dynamics (BD), since the total force on each atom will have the form:

    F = Fc + Ff + Fr
    Ff = - (m / damp) v
    Fr is proportional to sqrt(Kb T m / (dt damp))

Fc is the conservative force computed via the usual inter-particle interactions (pair_style, bond_style, etc).

The Ff and Fr terms are added by this fix on a per-particle basis. See the pair_style dpd/tstat command for a thermostatting option that adds similar terms on a pairwise basis to pairs of interacting particles.

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.

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 (Dunweg), where a uniform random number is used (instead of a Gaussian random number) for speed.

Note that unless you use the omega or angmom keywords, the thermostat effect of this fix is applied to only the translational degrees of freedom for the particles, which is an important 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 thermostatting takes place; see the description below.

IMPORTANT NOTE: Unlike the fix nvt 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 fix nve 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 fix nvt or fix temp/rescale commands.

See this howto section of the manual for a discussion of different ways to compute temperature and perform thermostatting.

The desired temperature at each timestep is a ramped value during the run from Tstart to Tstop.

Tstart can be specified as an equal-style or atom-style variable. In this case, the Tstop setting is 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 target temperature.

Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent temperature.

Atom-style variables can specify the same formulas as equal-style variables but can also include per-atom values, such as atom coordinates. Thus it is easy to specify a spatially-dependent temperature with optional time-dependence as well.

Like other fixes that perform thermostatting, this fix can be used with compute commands 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 fix_modify command is used to assign a temperature compute to this fix that includes such a bias term. See the doc pages for individual compute commands 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.

The damp 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 units 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 fix viscous command for more details.

The random # seed 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.

The keyword/value option pairs are used in the following ways.

The keyword angmom and omega keywords enable thermostatting of rotational degrees of freedom in addition to the usual translational degrees of freedom. This can only be done for finite-size particles.

A simulation using atom_style sphere defines an omega for finite-size spheres. A simulation using atom_style ellipsoid defines a finite 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 aspherical particles).

The rotational temperature of the particles can be monitored by the compute temp/sphere and compute temp/asphere commands with their rotate options.

For the omega keyword there is also a scale factor of 10.0/3.0 that 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 particles is correct.

For the angmom keyword a similar scale factor is needed which is 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 specified value of the angmom keyword. If your aspherical particles 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 scale factor, the thermostatting effect of the angmom keyword on the rotational temperature of the aspherical particles should still be valid.

The keyword scale 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 fix viscous command, since the damp factor in fix langevin is inversely related to the gamma factor in fix viscous. Also note that the damping factor in fix langevin includes the particle mass in Ff, unlike fix viscous. Thus the mass and size of different atom types should be accounted for in the choice of ratio values.

The keyword tally enables the calculation of the cumulative 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.

The keyword zero can be used to eliminate drift due to the 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 keyword zero is set to yes, the total random force is set exactly 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 momentum will not drift over time.

The keyword gjf can be used to run the Gronbech-Jensen/Farago time-discretization of the Langevin model. The effective random force is composed of the average of two random forces representing half-contributions from the previous and current time intervals. This discretization has been shown to be consistent with the underlying physical model of Langevin dynamics and produces the correct Boltzmann distribution of positions for large timesteps, up to the numerical stability limit. Because the discretized momenta generated by the time integration scheme are not exactly conjugate to the positions, the kinetic energy distribution is systematically lower than the Boltzmann distribution by an amount that grows with the timestep.

Restart, fix_modify, output, run start/stop, minimize info:

No information about this fix is written to binary restart files. 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.

The fix_modify temp option is supported by this fix. You can use it to assign a temperature compute 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.

The fix_modify energy option is supported by this fix to add the energy change induced by Langevin thermostatting to the system's potential energy as part of thermodynamic output. Note that use of this option requires setting the tally keyword to yes.

This fix computes a global scalar which can be accessed by various output commands. 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 tally keyword to yes.

This fix can ramp its target temperature over multiple runs, using the start and stop keywords of the run command. See the run command for details of how to do this.

This fix is not invoked during energy minimization.

Restrictions: none

Related commands:

fix nvt, fix temp/rescale, fix viscous, fix nvt, pair_style dpd/tstat

Default:

The option defaults are angmom = no, omega = no, scale = 1.0 for all types, tally = no, zero = no, gjf = no.

(Dunweg) Dunweg and Paul, Int J of Modern Physics C, 2, 817-27 (1991).

(Schneider) Schneider and Stoll, Phys Rev B, 17, 1302 (1978).

(Gronbech-Jensen) Gronbech-Jensen and Farago, Mol Phys, 111, 983 (2013); Gronbech-Jensen, Hayre, and Farago, arXiv:1303.7011.v2 (2013)