179 lines
7.2 KiB
ReStructuredText
179 lines
7.2 KiB
ReStructuredText
.. index:: pair_style ylz
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pair_style ylz command
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===========================
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style ylz cutoff
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* cutoff = global cutoff for interactions (distance units)
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style ylz 2.6
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pair_coeff * * 1.0 1.0 4 3 0.0 2.6
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Description
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"""""""""""
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.. versionadded:: 3Nov2022
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The *ylz* (Yuan-Li-Zhang) style computes an anisotropic interaction
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between pairs of coarse-grained particles considering the relative
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particle orientations. This potential was originally developed as a
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particle-based solvent-free model for biological membranes
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:ref:`(Yuan2010a) <Yuan>`. Unlike :doc:`pair_style gayberne
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<pair_gayberne>`, whose orientation dependence is strictly derived from
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the closest distance between two ellipsoidal rigid bodies, the
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orientation-dependence of this pair style is mathematically defined such
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that the particles can self-assemble into one-particle-thick fluid
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membranes. The potential of this pair style is described by:
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.. math::
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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 ]\\
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where :math:`\mathbf{r}_{i}` and :math:`\mathbf{r}_{j}` are the center
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position vectors of particles i and j, respectively,
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:math:`\mathbf{r}_{ij}=\mathbf{r}_{i}-\mathbf{r}_{j}` is the
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inter-particle distance vector, :math:`r=\left|\mathbf{r}_{ij} \right|`
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and :math:`{\hat{\mathbf{r}}}_{ij}=\mathbf{r}_{ij}/r`. The unit vectors
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:math:`\mathbf{n}_{i}` and :math:`\mathbf{n}_{j}` represent the axes of
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symmetry of particles i and j, respectively, :math:`u_R` and :math:`u_A`
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are the repulsive and attractive potentials, :math:`\phi` is an angular
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function which depends on the relative orientation between pair
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particles, :math:`\mu` is the parameter related to the bending rigidity
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of the membrane, :math:`\beta` is the parameter related to the
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spontaneous curvature, and :math:`\epsilon` is the energy unit,
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respectively. The :math:`\zeta` controls the slope of the attractive
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branch and hence the diffusivity of the particles in the in-plane
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direction of the membrane. :math:`{r}_{c}` is the cutoff radius,
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:math:`r_{min}` is the distance which minimizes the potential energy
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:math:`u_{A}(r)` and :math:`r_{min}=2^{1/6}\sigma`, where :math:`\sigma`
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is the length unit.
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This pair style is suited for solvent-free coarse-grained simulations of
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biological systems involving lipid bilayer membranes, such as vesicle
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shape transformations :ref:`(Yuan2010b) <Yuan>`, nanoparticle
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endocytosis :ref:`(Huang) <Huang>`, modeling of red blood cell membranes
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:ref:`(Fu) <Fu>`, :ref:`(Appshaw) <Appshaw>`, and modeling of cell
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elasticity :ref:`(Becton) <Becton>`.
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Use of this pair style requires the NVE, NVT, or NPT fixes with the
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*asphere* extension (e.g. :doc:`fix nve/asphere <fix_nve_asphere>`) in
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order to integrate particle rotation. Additionally, :doc:`atom_style
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ellipsoid <atom_style>` should be used since it defines the rotational
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state of each particle.
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The following coefficients must be defined for each pair of atoms types
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via the :doc:`pair_coeff <pair_coeff>` command as in the examples above,
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or in the data file or restart files read by the :doc:`read_data
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<read_data>` or :doc:`read_restart <read_restart>` commands, or by
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mixing as described below:
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* :math:`\epsilon` = well depth (energy units)
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* :math:`\sigma` = minimum effective particle radii (distance units)
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* :math:`\zeta` = tuning parameter for the slope of the attractive branch
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* :math:`\mu` = parameter related to bending rigidity
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* :math:`\beta` = parameter related to the spontaneous curvature
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* cutoff (distance units)
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The last coefficient is optional. If not specified, the global
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cutoff specified in the pair_style command is used.
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----------
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Mixing, shift, table, tail correction, restart, rRESPA info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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For atom type pairs I,J and I != J, the epsilon and sigma coefficients
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and cutoff distance for this pair style can be mixed. The default mix
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value is *geometric*\ . See the "pair_modify" command for details.
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The :doc:`pair_modify <pair_modify>` table option is not relevant for
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this pair style.
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This pair style does not support the :doc:`pair_modify <pair_modify>`
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tail option for adding long-range tail corrections to energy and
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pressure.
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This pair style writes its information to :doc:`binary restart files
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<restart>`, so pair_style and pair_coeff commands do not need to be
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specified in an input script that reads a restart file.
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This pair style can only be used via the *pair* keyword of the
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:doc:`run_style respa <run_style>` command. It does not support the
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*inner*, *middle*, *outer* keywords.
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----------
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Restrictions
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""""""""""""
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The *ylz* style is part of the ASPHERE package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package
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<Build_package>` page for more info.
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This pair style requires that atoms store torque and a quaternion to
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represent their orientation, as defined by the :doc:`atom_style
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<atom_style>`. It also requires they store a per-atom :doc:`shape
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<set>`. The particles cannot store a per-particle diameter. To avoid
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being mistakenly considered as point particles, the shape parameters ought
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to be non-spherical, like [1 0.99 0.99]. Unlike the :doc:`resquared
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<pair_resquared>` pair style for which the shape directly determines the
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mathematical expressions of the potential, the shape parameters for this
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pair style is only involved in the computation of the moment of inertia
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and thus only influences the rotational dynamics of individual
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particles.
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This pair style requires that **all** atoms are ellipsoids as defined by
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the :doc:`atom_style ellipsoid <atom_style>` command.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`,
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:doc:`fix nve/asphere <fix_nve_asphere>`,
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:doc:`compute temp/asphere <compute_temp_asphere>`,
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:doc:`pair_style resquared <pair_resquared>`,
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:doc:`pair_style gayberne <pair_gayberne>`
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Default
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"""""""
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none
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----------
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.. _Yuan:
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**(Yuan2010a)** Yuan, Huang, Li, Lykotrafitis, Zhang, Phys. Rev. E, 82, 011905(2010).
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**(Yuan2010b)** Yuan, Huang, Zhang, Soft. Matter, 6, 4571(2010).
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.. _Huang:
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**(Huang)** Huang, Zhang, Yuan, Gao, Zhang, Nano Lett. 13, 4546(2013).
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.. _Fu:
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**(Fu)** Fu, Peng, Yuan, Kfoury, Young, Comput. Phys. Commun, 210, 193-203(2017).
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.. _Appshaw:
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**(Appshaw)** Appshaw, Seddon, Hanna, Soft. Matter,18, 1747(2022).
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.. _Becton:
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**(Becton)** Becton, Averett, Wang, Biomech. Model. Mechanobiology, 18, 425-433(2019).
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