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Pair ylz docs enhancements

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This commit is contained in:
Mehdi Baghaee
2022-10-25 18:50:37 +08:00
committed by Axel Kohlmeyer
parent 4c176e5afc
commit 371c2d7cbb
2 changed files with 65 additions and 23 deletions
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86
doc/src/pair_ylz.rst
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@ -27,31 +27,47 @@ Description
.. versionadded:: TBD
The *ylz* (Yuan-Li-Zhang) :ref:`(Yuan) <Yuan>` style computes
anisotropic interactions between pairs of particles considering the
relative particle orientations via the formulas
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 the :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 via the formulas
.. 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 bending rigidity, :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 :math:`{r}_{c}`is the cutoff radius. :math:`r_{min}`
is the distance which minimizes the potential energy :math:`u_{A}(r)`and
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.
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.
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>`.
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:
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)
@ -96,10 +112,16 @@ 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.
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 masses,
the shape parameters ought to be non-spherical, like [1 0.99 0.99]. Unlike
the :doc:`pair_style gayberne <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 play a role to 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.
@ -111,7 +133,7 @@ Related commands
:doc:`pair_coeff <pair_coeff>`, :doc:`fix nve/asphere
:doc:<fix_nve_asphere>`, `compute temp/asphere <compute_temp_asphere>`,
:doc::doc:`pair_style resquared <pair_resquared>`, :doc:`pair_style
:doc:gayberne <pair_resquared>`
:doc:gayberne <pair_gayberne>`
Default
"""""""
@ -122,4 +144,22 @@ none
.. _Yuan:
**(Yuan)** Yuan, Huang, Li, Lykotrafitis, Zhang, Phys. Rev. E, 82, 011905(2010).
**(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, Seddonb, Hannaa, Soft. Matter,18, 1747(2022).
.. _Becton:
**(Becton)** Becton, Averett, Wang, Biomech. Model. Mechanobiol, 18, 425-433(2019).

2
doc/utils/sphinx-config/false_positives.txt
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@ -123,6 +123,7 @@ Antonelli
api
Apoorva
Appl
Appshaw
apptainer
Apu
arallel
@ -237,6 +238,7 @@ bcolor
bdiam
bdw
Beckman
Becton
Belak
Bellott
bem