"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

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pair_style dpd/fdt command :h3
pair_style dpd/fdt/energy command :h3

[Syntax:]

pair_style style args :pre

style = {dpd/fdt} or {dpd/fdt/energy}
args = list of arguments for a particular style :ul
  {dpd/fdt} args = T cutoff seed
    T = temperature (temperature units)
    cutoff = global cutoff for DPD interactions (distance units)
    seed = random # seed (positive integer)
  {dpd/fdt/energy} args = cutoff seed
    cutoff = global cutoff for DPD interactions (distance units)
    seed = random # seed (positive integer) :pre

[Examples:]

pair_style dpd/fdt 300.0 2.5 34387
pair_coeff * * 3.0 1.0 2.5 :pre

pair_style dpd/fdt/energy 2.5 34387
pair_coeff * * 3.0 1.0 0.1 2.5 :pre

[Description:]

Styles {dpd/fdt} and {dpd/fdt/energy} compute the force for dissipative
particle dynamics (DPD) simulations.  The {dpd/fdt} style is used to
perform DPD simulations under isothermal and isobaric conditions,
while the {dpd/fdt/energy} style is used to perform DPD simulations
under isoenergetic and isoenthalpic conditions (see "(Lisal)"_#Lisal).
For DPD simulations in general, the force on atom I due to atom J is
given as a sum of 3 terms

:c,image(Eqs/pair_dpd.jpg)

where Fc is a conservative force, Fd is a dissipative force, and Fr is
a random force.  Rij is a unit vector in the direction Ri - Rj, Vij is
the vector difference in velocities of the two atoms = Vi - Vj, alpha
is a Gaussian random number with zero mean and unit variance, dt is
the timestep size, and w(r) is a weighting factor that varies between
0 and 1.  Rc is the cutoff.  The weighting factor, omega_ij, varies
between 0 and 1, and is chosen to have the following functional form:

:c,image(Eqs/pair_dpd_omega.jpg)

Note that alternative definitions of the weighting function exist, but
would have to be implemented as a separate pair style command.

For style {dpd/fdt}, the fluctuation-dissipation theorem defines gamma
to be set equal to sigma*sigma/(2 T), where T is the set point
temperature specified as a pair style parameter in the above examples.
The following coefficients must be defined for each pair of atoms types
via the "pair_coeff"_pair_coeff.html command as in the examples above,
or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html commands:

A (force units)
sigma (force*time^(1/2) units)
cutoff (distance units) :ul

The last coefficient is optional.  If not specified, the global DPD
cutoff is used.

Style {dpd/fdt/energy} is used to perform DPD simulations
under isoenergetic and isoenthalpic conditions.  The fluctuation-dissipation
theorem defines gamma to be set equal to sigma*sigma/(2 dpdTheta), where
dpdTheta is the average internal temperature for the pair. The particle
internal temperature is related to the particle internal energy through
a mesoparticle equation of state (see "fix eos"_fix.html). The
differential internal conductive and mechanical energies are computed
within style {dpd/fdt/energy} as:

:c,image(Eqs/pair_dpd_energy.jpg)

where

:c,image(Eqs/pair_dpd_energy_terms.jpg)

Zeta_ij^q is a second Gaussian random number with zero mean and unit
variance that is used to compute the internal conductive energy. The
fluctuation-dissipation theorem defines alpha*alpha to be set
equal to 2*kB*kappa, where kappa is the mesoparticle thermal
conductivity parameter.   The following coefficients must be defined for
each pair of atoms types via the "pair_coeff"_pair_coeff.html
command as in the examples above, or in the data file or restart files
read by the "read_data"_read_data.html or "read_restart"_read_restart.html
commands:

A (force units)
sigma (force*time^(1/2) units)
kappa (energy*temperature/time units)
cutoff (distance units) :ul

The last coefficient is optional.  If not specified, the global DPD
cutoff is used.

The pairwise energy associated with styles {dpd/fdt} and
{dpd/fdt/energy} is only due to the conservative force term Fc, and is
shifted to be zero at the cutoff distance Rc.  The pairwise virial is
calculated using only the conservative term.

The forces computed through the {dpd/fdt} and {dpd/fdt/energy} styles
can be integrated with the velocity-Verlet integration scheme or the
Shardlow splitting integration scheme described by "(Lisal)"_#Lisal.
In the cases when these pair styles are combined with the
"fix shardlow"_fix_shardlow.html, these pair styles differ from the
other dpd styles in that the dissipative and random forces are split
from the force calculation and are not computed within the pair style.
Thus, only the conservative force is computed by the pair style,
while the stochastic integration of the dissipative and random forces
are handled through the Shardlow splitting algorithm approach.  The
Shardlow splitting algorithm is advantageous, especially when
performing DPD under isoenergetic conditions, as it allows
significantly larger timesteps to be taken.

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[Restrictions:]

These commands are part of the USER-DPD package.  They are only
enabled if LAMMPS was built with that package.  See the "Making
LAMMPS"_Section_start.html#start_3 section for more info.

Pair styles {dpd/fdt} and {dpd/fdt/energy} require use of the
"comm_modify vel yes"_comm_modify.html option so that velocites are
stored by ghost atoms.

Pair style {dpd/fdt/energy} requires "atom_style dpd"_atom_style.html
to be used in order to properly account for the particle internal
energies and temperatures.

[Related commands:]

"pair_coeff"_pair_coeff.html, "fix shardlow"_fix_shardlow.html

[Default:] none

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:link(Lisal)
[(Lisal)] M. Lisal, J.K. Brennan, J. Bonet Avalos, "Dissipative
particle dynamics at isothermal, isobaric, isoenergetic, and
isoenthalpic conditions using Shardlow-like splitting algorithms.",
J. Chem. Phys., 135, 204105 (2011).
