Fourier

class hoomd.md.pair.Fourier(nlist, default_r_cut=None, default_r_on=0.0, mode='none')

Bases: Pair

Fourier pair force.

Parameters:

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

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

• default_r_on (float) – Default turn-on radius $[\mathrm{length}]$.

• mode (str) – Energy shifting/smoothing mode.

Fourier computes the Fourier pair force on every particle in the simulation state:

$$U(r) = \frac{1}{r^{12}} + \frac{1}{r^2}\sum_{n=1}^4 \left[ a_n cos \left( \frac{n \pi r}{r_{cut}} \right) + b_n sin \left( \frac{n \pi r}{r_{cut}} \right) \right]$$

where

$$\begin{split} a_1 &= \sum_{n=2}^4 (-1)^n a_n \\ b_1 &= \sum_{n=2}^4 n (-1)^n b_n \\ \end{split}$$

enforce $U(r_\mathrm{cut}) = 0$.

Example:

nl = nlist.Cell()
fourier = pair.Fourier(default_r_cut=3.0, nlist=nl)
fourier.params[('A', 'A')] = dict(a=[a2,a3,a4], b=[b2,b3,b4])

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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 Pair:

nlist

Neighbor list used to compute the pair force. Read more...

mode

Energy smoothing/cutoff mode. Read more...

r_cut

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

r_on

Radius at which the XPLOR smoothing function starts. Read more...

compute_energy()

Compute the energy between two sets of particles. Read more...

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Members defined in Fourier:

params

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

• a (float, required) - array of 3 values corresponding to a2, a3 and a4 in the Fourier series $[\mathrm{dimensionless}]$

• b (float, required) - array of 3 values corresponding to b2, b3 and b4 in the Fourier series $[\mathrm{dimensionless}]$

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