YLZ

class hoomd.md.pair.aniso.YLZ(nlist, default_r_cut=None)

Bases: AnisotropicPair

Yuan, Lee, Zhang (YLZ) potential.

Parameters:

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

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

The modulation function $\psi$ creates torques to align the orientation of a pair of particles as function of their axis of symmetry $\mu$ in their local reference frame.

1. A 2,4-Lennard-Jones potential truncated at its minimum $r_{min}$.

2. A cosine potential defined between $r_{min}$ and $r_{cut}$.

$$U(r_{ij},\mu_{i},\mu_{j})= \begin{cases} u\left(r\right)+\left(1-\psi\left(\hat{r}_{ij},\mu_i,\mu_j\right)\right) \epsilon & \text{if }r<r_{min}\\ u(r)\psi\left(\hat{r}_{ij},\mu_i,\mu_j\right)& \text{if }r_{min}<r<r_{cut} \end{cases}$$

$$\mathrm{u}(r)= \begin{cases} \epsilon\lbrack(\frac{r_{min}}{r})^{4}-2(\frac{r_{min}}{r})^{2}\rbrack & \text{if }r<r_{min}\\ -\epsilon\ cos^{2\zeta}(\frac{\pi}{2}\frac{r-r_{min}}{r_{cut}-r_{min}}) & \text{if }r_{min}<r<r_{cut} \end{cases}$$

$$\psi = 1 + \beta(a-1)$$

$$a = \mu_{i}\cdot \mu_{j}-\left(\mu_{i}\cdot\hat{r}_{ij}\right) \left(\mu_{j}\cdot\hat{r}_{ij}\right)+\phi\left(\mu_{i}-\mu_{j} \right)\cdot\hat{r}_{ij}-\phi^2$$

The modulation function $\psi$ introduces torques that align particle orientations with respect to their symmetry axes $\mu$.

The potential was introduced in Hongyan Yuan, Changjin Huang, Ju Li, George Lykotrafitis, and Sulin Zhang 2010.

Example:

ylz = hoomd.md.pair.aniso.YLZ(nlist = neighbor_list,
                                      default_r_cut = 2.6)

ylz_params = {'eps': 1.0, 'phi': 0.0, 'beta': 1.774532,
                'rmin':1.122, 'twozeta': int(4)}

ylz.params.default = ylz_params
ylz.mu.default = (0, 0, 1)
simulation.operations.integrator.forces = [ylz]

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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 YLZ:

params

The YLZ potential parameters unique to each pair of particle types. The dictionary has the following keys:

• params (dict, required)

  • eps (float) - energy parameter $\epsilon$ $[\mathrm{energy}]$

  • phi (float) - parameter related to local curvature $\phi$

  • beta (float) - weight of energy penalty for misoriented particles $\beta$

  • rmin (float) - cutoff where the 4,2 LJ begins $r_{min}$ $[\mathrm{length}]$

  • twozeta (float) - exponent of the cosine potential $2\zeta$

Example:

ylz_params = {'eps': 1.0, 'phi': 0.0, 'beta': 1.774532,
                'rmin':1.12, 'twozeta':int(2)}
ylz.params[('A', 'A')] = ylz_params

mu

$\mu$ - axis of symmetry in the local reference frame (i.e. $(\mu_x, \mu_y, \mu_z)$)

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

Example:

ylz.mu['A'] = (1.0, 0.0, 0.0)