.. index:: pair_style ylz

pair_style ylz command
===========================

Syntax
""""""

.. code-block:: LAMMPS

   pair_style ylz cutoff


* cutoff = global cutoff for interactions (distance units)

Examples
""""""""

.. code-block:: LAMMPS

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


Description
"""""""""""

.. versionadded:: 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
:ref:`(Yuan2010a) <Yuan>`.  Unlike :doc:`pair_style gayberne
<pair_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:

.. math::

   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 ]\\

where :math:`\mathbf{r}_{i}` and :math:`\mathbf{r}_{j}` are the center
position vectors of particles i and j, respectively,
:math:`\mathbf{r}_{ij}=\mathbf{r}_{i}-\mathbf{r}_{j}` is the
inter-particle distance vector, :math:`r=\left|\mathbf{r}_{ij} \right|`
and :math:`{\hat{\mathbf{r}}}_{ij}=\mathbf{r}_{ij}/r`.  The unit vectors
:math:`\mathbf{n}_{i}` and :math:`\mathbf{n}_{j}` represent the axes of
symmetry of particles i and j, respectively, :math:`u_R` and :math:`u_A`
are the repulsive and attractive potentials, :math:`\phi` is an angular
function which depends on the relative orientation between pair
particles, :math:`\mu` is the parameter related to the bending rigidity
of the membrane, :math:`\beta` is the parameter related to the
spontaneous curvature, and :math:`\epsilon` is the energy unit,
respectively.   The :math:`\zeta` controls the slope of the attractive
branch and hence the diffusivity of the particles in the in-plane
direction of the membrane.  :math:`{r}_{c}` is the cutoff radius,
:math:`r_{min}` is the distance which minimizes the potential energy
:math:`u_{A}(r)` and :math:`r_{min}=2^{1/6}\sigma`, where :math:`\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 :ref:`(Yuan2010b) <Yuan>`, nanoparticle
endocytosis :ref:`(Huang) <Huang>`, modeling of red blood cell membranes
:ref:`(Fu) <Fu>`, :ref:`(Appshaw) <Appshaw>`, and modeling of cell
elasticity :ref:`(Becton) <Becton>`.

Use of this pair style requires the NVE, NVT, or NPT fixes with the
*asphere* extension (e.g. :doc:`fix nve/asphere <fix_nve_asphere>`) in
order to integrate particle rotation.  Additionally, :doc:`atom_style
ellipsoid <atom_style>` 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 :doc:`pair_coeff <pair_coeff>` command as in the examples above,
or in the data file or restart files read by the :doc:`read_data
<read_data>` or :doc:`read_restart <read_restart>` commands, or by
mixing as described below:

* :math:`\epsilon` = well depth (energy units)
* :math:`\sigma` = minimum effective particle radii (distance units)
* :math:`\zeta` = tuning parameter for the slope of the attractive branch
* :math:`\mu` = parameter related to bending rigidity
* :math:`\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 :doc:`pair_modify <pair_modify>` table option is not relevant for
this pair style.

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

This pair style writes its information to :doc:`binary restart files
<restart>`, 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
:doc:`run_style respa <run_style>` 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 :doc:`Build package
<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 :doc:`atom_style
<atom_style>`.  It also requires they store a per-atom :doc:`shape
<set>`.  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 :doc:`resquared
<pair_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 :doc:`atom_style ellipsoid <atom_style>` command.


Related commands
""""""""""""""""

:doc:`pair_coeff <pair_coeff>`,
:doc:`fix nve/asphere <fix_nve_asphere>`,
:doc:`compute temp/asphere <compute_temp_asphere>`,
:doc:`pair_style resquared <pair_resquared>`,
:doc:`pair_style gayberne <pair_gayberne>`

Default
"""""""

none

----------

.. _Yuan:

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

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

.. _Huang:

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

.. _Fu:

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

.. _Appshaw:

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

.. _Becton:

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