SquareDensity

class hoomd.md.many_body.SquareDensity(nlist, default_r_cut=None)

Bases: Triplet

Soft force for simulating a van der Waals liquid.

Parameters:

• nlist (hoomd.md.nlist.NeighborList) – Neighbor list

• default_r_cut (float) – Default cutoff radius $[\mathrm{length}]$.

SquareDensity that the square density three-body force should on every particle in the simulation state.

The self energy per particle takes the form:

$$\Psi^{ex} = B (\rho - A)^2$$

which gives a pair-wise additive, three-body force:

$$\vec{f}_{ij} = \left( B (n_i - A) + B (n_j - A) \right) w'_{ij} \vec{e}_{ij}$$

Here, $w_{ij}$ is a quadratic, normalized weighting function,

$$w(x) = \frac{15}{2 \pi r_{c,\mathrm{weight}}^3} (1-r/r_{c,\mathrm{weight}})^2$$

The local density at the location of particle i is defined as

$$n_i = \sum\limits_{j\neq i} w_{ij} \left(\big| \vec r_i - \vec r_j \big|\right)$$

Example:

nl = nlist.Cell()
sqd = md.many_body.SquareDensity(nl, default_r_cut=3.0)
sqd.params[("A", "B")] = dict(A=1.0, B=2.0)
sqd.params[("B", "B")] = dict(A=2.0, B=2.0, default_r_on=1.0)

For further details regarding this multibody potential, see

[1] P. B. Warren, “Vapor-liquid coexistence in many-body dissipative particle dynamics” Phys. Rev. E. Stat. Nonlin. Soft Matter Phys., vol. 68, no. 6 Pt 2, p. 066702, 2003.

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Members inherited from AutotunedObject:

property kernel_parameters

Kernel parameters. Read more...

property is_tuning_complete

Check if kernel parameter tuning is complete. Read more...

tune_kernel_parameters()

Start tuning kernel parameters. Read more...

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Members inherited from Force:

additional_energy

Additional energy term. Read more...

additional_virial

Additional virial tensor term $W_\mathrm{additional}$. Read more...

cpu_local_force_arrays

Local force arrays on the CPU. Read more...

energies

Energy contribution $U_i$ from each particle. Read more...

energy

The potential energy $U$ of the system from this force. Read more...

forces

The force $\vec{F}_i$ applied to each particle. Read more...

gpu_local_force_arrays

Local force arrays on the GPU. Read more...

torques

The torque $\vec{\tau}_i$ applied to each particle. Read more...

virials

Virial tensor contribution $W_i$ from each particle. Read more...

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Members inherited from Triplet:

r_cut

Cuttoff radius beyond which the energy and force are 0. Read more...

nlist

Neighbor list used to compute the triplet potential. Read more...

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Members defined in SquareDensity:

params

The SquareDensity potential parameters. The dictionary has the following keys:

• A (float, required) - $A$ - mean density (default:0) $[\mathrm{length}^{-2}]$ in 2D and $[\mathrm{length}^{-3}]$ in 3D

• B (float, required) - $B$ - coefficient of the harmonic density term $[\mathrm{energy} \cdot \mathrm{length}^4]$ in 2D and $[\mathrm{energy} \cdot \mathrm{length}^6]$ in 3D

Type: TypeParameter [tuple [particle_type, particle_type], dict]