\(\renewcommand{\AA}{\text{Å}}\)

# pair_style dpd/ext command

Accelerator Variants: dpd/ext/kk dpd/ext/omp

# pair_style dpd/ext/tstat command

Accelerator Variants: dpd/ext/tstat/kk dpd/ext/tstat/omp

## Syntax

    pair_style dpd/ext T cutoff seed
    pair_style dpd/ext/tstat Tstart Tstop cutoff seed

- T = temperature (temperature units)

- Tstart,Tstop = desired temperature at start/end of run (temperature units)

- cutoff = global cutoff for DPD interactions (distance units)

- seed = random # seed (positive integer)

## Examples

    pair_style dpd/ext 1.0 2.5 34387
    pair_coeff 1 1 25.0 4.5 4.5 0.5 0.5 1.2
    pair_coeff 1 2 40.0 4.5 4.5 0.5 0.5 1.2

    pair_style hybrid/overlay lj/cut 2.5 dpd/ext/tstat 1.0 1.0 2.5 34387
    pair_coeff * * lj/cut 1.0 1.0
    pair_coeff * * 4.5 4.5 0.5 0.5 1.2

## Description

The style dpd/ext computes an extended force field for dissipative particle dynamics (DPD) following the exposition in (Groot), (Junghans).

Style dpd/ext/tstat invokes an extended DPD thermostat on pairwise interactions, equivalent to the non-conservative portion of the extended DPD force field. To use dpd/ext/tstat as a thermostat for another pair style, use the pair_style hybrid/overlay command to compute both the desired pair interaction and the thermostat for each pair of particles.

For the style dpd/ext, the force on atom I due to atom J is given as a sum of 3 terms

\[\begin{split}\mathbf{f} = & f^C + f^D + f^R \qquad \qquad r < r_c \\ f^C = & A_{ij} w(r) \hat{\mathbf{r}}_{ij} \\ f^D = & - \gamma_{\parallel} w_{\parallel}^2(r) (\hat{\mathbf{r}}_{ij} \cdot \mathbf{v}_{ij}) \hat{\mathbf{r}}_{ij} - \gamma_{\perp} w_{\perp}^2 (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^\mathrm{T} ) \mathbf{v}_{ij} \\ f^R = & \sigma_{\parallel} w_{\parallel}(r) \frac{\alpha}{\sqrt{\Delta t}} \hat{\mathbf{r}}_{ij} + \sigma_{\perp} w_{\perp} (r) ( \mathbf{I} - \hat{\mathbf{r}}_{ij} \hat{\mathbf{r}}_{ij}^\mathrm{T} ) \frac{\mathbf{\xi}_{ij}}{\sqrt{\Delta t}}\\ w(r) = & 1 - r/r_c \\\end{split}\]

where \(\mathbf{f}^C\) is a conservative force, \(\mathbf{f}^D\) is a dissipative force, and \(\mathbf{f}^R\) is a random force. \(A_{ij}\) is the maximum repulsion between the two atoms, \(\hat{\mathbf{r}}_{ij}\) is a unit vector in the direction \(\mathbf{r}_i - \mathbf{r}_j\), \(\mathbf{v}_{ij} = \mathbf{v}_i - \mathbf{v}_j\) is the vector difference in velocities of the two atoms, \(\alpha\) and \(\mathbf{\xi}_{ij}\) are Gaussian random numbers with zero mean and unit variance, \(\Delta t\) is the timestep, \(w (r) = 1 - r / r_c\) is a weight function for the conservative interactions that varies between 0 and 1, \(r_c\) is the corresponding cutoff, \(w_{\alpha} ( r ) = ( 1 - r / \bar{r}_c )^{s_{\alpha}}\), \(\alpha \equiv ( \parallel, \perp )\), are weight functions with coefficients \(s_\alpha\) that vary between 0 and 1, \(\bar{r}_c\) is the corresponding cutoff, \(\mathbf{I}\) is the unit matrix, \(\sigma_{\alpha} = \sqrt{2 k_B T \gamma_{\alpha}}\), where \(k_B\) is the Boltzmann constant and \(T\) is the temperature in the pair_style command.

For the style dpd/ext/tstat, the force on atom I due to atom J is the same as the above equation, except that the conservative \(\mathbf{f}^C\) term is dropped. Also, during the run, T is set each timestep to a ramped value from Tstart to Tstop.

For the style dpd/ext, the pairwise energy associated with style dpd/ext is only due to the conservative force term \(\mathbf{f}^C\), and is shifted to be zero at the cutoff distance \(r_c\). The pairwise virial is calculated using all three terms. There is no pairwise energy for style dpd/ext/tstat, but the last two terms of the formula contribute the virial.

For the style dpd/ext/tstat, the force on atom I due to atom J is the same as the above equation, except that the conservative \(\mathbf{f}^C\) term is dropped. Also, during the run, T is set each timestep to a ramped value from Tstart to Tstop.

For the style dpd/ext, the pairwise energy associated with style dpd/ext is only due to the conservative force term \(\mathbf{f}^C\), and is shifted to be zero at the cutoff distance \(r_c\). The pairwise virial is calculated using all three terms. There is no pairwise energy for style dpd/ext/tstat, but the last two terms of the formula contribute the virial.

For the style dpd/ext, the following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above:

- A (force units)

- \(\gamma_{\parallel}\) (force/velocity units)

- \(\gamma_{\perp}\) (force/velocity units)

- \(s_{\parallel}\) (unitless)

- \(s_{\perp}\) (unitless)

- \(r_c\) (distance units)

The last coefficient is optional. If not specified, the global DPD cutoff is used. Note that \(\sigma\)’s are set equal to \(\sqrt{2 k_B T \gamma}\), where \(T\) is the temperature set by the pair_style command so it does not need to be specified.

For the style dpd/ext/tstat, the coefficients defined for each pair of atoms types via the pair_coeff command are:

- \(\gamma_{\parallel}\) (force/velocity units)

- \(\gamma_{\perp}\) (force/velocity units)

- \(s_{\parallel}\) (unitless)

- \(s_{\perp}\) (unitless)

- \(r_c\) (distance units)

The last coefficient is optional.

Note

If you are modeling DPD polymer chains, you may want to use the pair_style srp command in conjunction with these pair styles. It is a soft segmental repulsive potential (SRP) that can prevent DPD polymer chains from crossing each other.

Note

The virial calculation for pressure when using these pair styles includes all the components of force listed above, including the random force. Since the random force depends on random numbers, everything that changes the order of atoms in the neighbor list (e.g. different number of MPI ranks or a different neighbor list skin distance) will also change the sequence in which the random numbers are applied and thus the individual forces and therefore also the virial/pressure.

Note

For more consistent time integration and force computation you may consider using fix mvv/dpd instead of fix nve.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

Mixing, shift, table, tail correction, restart, rRESPA info:

The style dpd/ext does not support mixing. Thus, coefficients for all I,J pairs must be specified explicitly.

The pair styles do not support the pair_modify shift option for the energy of the pair interaction. Note that as discussed above, the energy due to the conservative \(\mathbf{f}^C\) term is already shifted to be zero at the cutoff distance \(r_c\).

The pair_modify table option is not relevant for the style dpd/ext.

The style dpd/ext does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure.

The pair styles can only be used via the pair keyword of the run_style respa command. They do not support the inner, middle, and outerkeywords.

The style dpd/ext/tstat 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.

## Restrictions

These styles are part of the DPD-BASIC package. They are only enabled if LAMMPS was built with that package. See the Build package page for more info.

The default frequency for rebuilding neighbor lists is every 10 steps (see the neigh_modify command). This may be too infrequent for style dpd/ext simulations since particles move rapidly and can overlap by large amounts. If this setting yields a non-zero number of say{dangerous} reneighborings (printed at the end of a simulation), you should experiment with forcing reneighboring more often and see if system energies/trajectories change.

The pair styles require to use the comm_modify vel yes command so that velocities are stored by ghost atoms.

The pair styles will not restart exactly when using the read_restart command, though they should provide statistically similar results. This is because the forces they compute depend on atom velocities. See the read_restart command for more details.

## Related commands

pair_style dpd, pair_coeff, fix nvt, fix langevin, pair_style srp, fix mvv/dpd.

Default: none

(Groot) Groot and Warren, J Chem Phys, 107, 4423-35 (1997).

(Junghans) Junghans, Praprotnik and Kremer, Soft Matter 4, 156, 1119-1128 (2008).