\(\renewcommand{\AA}{\text{Å}}\)

# pair_style ylz command

## Syntax

    pair_style ylz cutoff

- cutoff = global cutoff for interactions (distance units)

## Examples

    pair_style   ylz  2.6
    pair_coeff   *  *  1.0  1.0  4  3  0.0  2.6

## Description

Added in version 3Nov2022.

The ylz (Yuan-Li-Zhang) style computes an anisotropic interaction between pairs of coarse-grained particles considering the relative particle orientations. This potential was originally developed as a particle-based solvent-free model for biological membranes (Yuan2010a). Unlike pair_style gayberne, whose orientation dependence is strictly derived from the closest distance between two ellipsoidal rigid bodies, the orientation-dependence of this pair style is mathematically defined such that the particles can self-assemble into one-particle-thick fluid membranes. The potential of this pair style is described by:

\[\begin{split}U ( \mathbf{r}_{ij}, \mathbf{n}_i, \mathbf{n}_j ) =\left\{\begin{matrix} {u}_R(r)+\left [ 1-\phi (\mathbf{\hat{r}}_{ij}, \mathbf{n}_i, \mathbf{n}_j ) \right ]\epsilon, ~~ r<{r}_{min} \\ {u}_A(r)\phi (\mathbf{\hat{r}}_{ij}, \mathbf{n}_i, \mathbf{n}_j ),~~ {r}_{min}<r<{r}_{c} \\ \end{matrix}\right.\\\\ \phi (\mathbf{\hat{r}}_{ij}, \mathbf{n}_i, \mathbf{n}_j )=1+\left [ \mu (a(\mathbf{\hat{r}}_{ij}, \mathbf{n}_i, \mathbf{n}_j )-1) \right ] \\\\a(\mathbf{\hat{r}}_{ij}, \mathbf{n}_i, \mathbf{n}_j )=(\mathbf{n}_i\times\mathbf{\hat{r}}_{ij} )\cdot (\mathbf{n}_j\times\mathbf{\hat{r}}_{ij} )+{\beta}(\mathbf{n}_i-\mathbf{n}_j)\cdot \mathbf{\hat{r}}_{ij}-\beta^{2}\\\\ {u}_R(r)=\epsilon \left [ \left ( \frac{{r}_{min}}{r} \right )^{4}-2\left ( \frac{{r}_{min}}{r}\right )^{2} \right ] \\\\ {u}_A(r)=-\epsilon\;cos^{2\zeta }\left [ \frac{\pi}{2}\frac{\left ( {r}-{r}_{min} \right )}{\left ( {r}_{c}-{r}_{min} \right )} \right ]\\\end{split}\]

where \(\mathbf{r}_{i}\) and \(\mathbf{r}_{j}\) are the center position vectors of particles i and j, respectively, \(\mathbf{r}_{ij}=\mathbf{r}_{i}-\mathbf{r}_{j}\) is the inter-particle distance vector, \(r=\left|\mathbf{r}_{ij} \right|\) and \({\hat{\mathbf{r}}}_{ij}=\mathbf{r}_{ij}/r\). The unit vectors \(\mathbf{n}_{i}\) and \(\mathbf{n}_{j}\) represent the axes of symmetry of particles i and j, respectively, \(u_R\) and \(u_A\) are the repulsive and attractive potentials, \(\phi\) is an angular function which depends on the relative orientation between pair particles, \(\mu\) is the parameter related to the bending rigidity of the membrane, \(\beta\) is the parameter related to the spontaneous curvature, and \(\epsilon\) is the energy unit, respectively. The \(\zeta\) controls the slope of the attractive branch and hence the diffusivity of the particles in the in-plane direction of the membrane. \({r}_{c}\) is the cutoff radius, \(r_{min}\) is the distance which minimizes the potential energy \(u_{A}(r)\) and \(r_{min}=2^{1/6}\sigma\), where \(\sigma\) is the length unit.

This pair style is suited for solvent-free coarse-grained simulations of biological systems involving lipid bilayer membranes, such as vesicle shape transformations (Yuan2010b), nanoparticle endocytosis (Huang), modeling of red blood cell membranes (Fu), (Appshaw), and modeling of cell elasticity (Becton).

Use of this pair style requires the NVE, NVT, or NPT fixes with the asphere extension (e.g. fix nve/asphere) in order to integrate particle rotation. Additionally, atom_style ellipsoid should be used since it defines the rotational state of each particle.

The following coefficients must be defined for each pair of atoms types via the pair_coeff command as in the examples above, or in the data file or restart files read by the read_data or read_restart commands, or by mixing as described below:

- \(\epsilon\) = well depth (energy units)

- \(\sigma\) = minimum effective particle radii (distance units)

- \(\zeta\) = tuning parameter for the slope of the attractive branch

- \(\mu\) = parameter related to bending rigidity

- \(\beta\) = parameter related to the spontaneous curvature

- cutoff (distance units)

The last coefficient is optional. If not specified, the global cutoff specified in the pair_style command is used.

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

For atom type pairs I,J and I != J, the epsilon and sigma coefficients and cutoff distance for this pair style can be mixed. The default mix value is geometric. See the “pair_modify” command for details.

The pair_modify table option is not relevant for this pair style.

This pair style does not support the pair_modify tail option for adding long-range tail corrections to energy and pressure.

This pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file.

This pair style can only be used via the pair keyword of the run_style respa command. It does not support the inner, middle, outer keywords.

## Restrictions

The ylz style is part of the ASPHERE package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

This pair style requires that atoms store torque and a quaternion to represent their orientation, as defined by the atom_style. It also requires they store a per-atom shape. The particles cannot store a per-particle diameter. To avoid being mistakenly considered as point particles, the shape parameters ought to be non-spherical, like [1 0.99 0.99]. Unlike the resquared pair style for which the shape directly determines the mathematical expressions of the potential, the shape parameters for this pair style is only involved in the computation of the moment of inertia and thus only influences the rotational dynamics of individual particles.

This pair style requires that all atoms are ellipsoids as defined by the atom_style ellipsoid command.

## Related commands

pair_coeff, fix nve/asphere, compute temp/asphere, pair_style resquared, pair_style gayberne

## Default

none

(Yuan2010a) Yuan, Huang, Li, Lykotrafitis, Zhang, Phys. Rev. E, 82, 011905(2010).

(Yuan2010b) Yuan, Huang, Zhang, Soft. Matter, 6, 4571(2010).

(Huang) Huang, Zhang, Yuan, Gao, Zhang, Nano Lett. 13, 4546(2013).

(Fu) Fu, Peng, Yuan, Kfoury, Young, Comput. Phys. Commun, 210, 193-203(2017).

(Appshaw) Appshaw, Seddon, Hanna, Soft. Matter,18, 1747(2022).

(Becton) Becton, Averett, Wang, Biomech. Model. Mechanobiology, 18, 425-433(2019).