235 lines
9.2 KiB
ReStructuredText
235 lines
9.2 KiB
ReStructuredText
.. index:: pair_style resquared
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.. index:: pair_style resquared/gpu
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.. index:: pair_style resquared/omp
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pair_style resquared command
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============================
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Accelerator Variants: *resquared/gpu*, *resquared/omp*
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style resquared 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 resquared 10.0
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pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0
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Description
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"""""""""""
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Style *resquared* computes the RE-squared anisotropic interaction
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:ref:`(Everaers) <Everaers3>`, :ref:`(Babadi) <Babadi>` between pairs of
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ellipsoidal and/or spherical Lennard-Jones particles. For ellipsoidal
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interactions, the potential considers the ellipsoid as being comprised
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of small spheres of size :math:`\sigma`. LJ particles are a single sphere of
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size :math:`\sigma`. The distinction is made to allow the pair style to make
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efficient calculations of ellipsoid/solvent interactions.
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Details for the equations used are given in the references below and
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in `this supplementary document <PDF/pair_resquared_extra.pdf>`_.
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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 ellipsoid <atom_style>` should be used since it defines the
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rotational state and the size and shape of each ellipsoidal particle.
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The following coefficients must be defined for each pair of atoms
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types via the :doc:`pair_coeff <pair_coeff>` command as in the examples
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above, or in the data file or restart files read by the
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:doc:`read_data <read_data>` or :doc:`read_restart <read_restart>`
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commands:
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* A12 = Energy Prefactor/Hamaker constant (energy units)
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* :math:`\sigma` = atomic interaction diameter (distance units)
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* :math:`\epsilon_{i,a}` = relative well depth of type I for side-to-side interactions
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* :math:`\epsilon_{i,b}` = relative well depth of type I for face-to-face interactions
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* :math:`\epsilon_{i,c}` = relative well depth of type I for end-to-end interactions
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* :math:`\epsilon_{j,a}` = relative well depth of type J for side-to-side interactions
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* :math:`\epsilon_{j,b}` = relative well depth of type J for face-to-face interactions
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* :math:`\epsilon_{j,c}` = relative well depth of type J for end-to-end interactions
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* cutoff (distance units)
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The parameters used depend on the type of the interacting particles,
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i.e. ellipsoids or LJ spheres. The type of a particle is determined
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by the diameters specified for its 3 shape parameters. If all 3 shape
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parameters = 0.0, then the particle is treated as an LJ sphere. The
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:math:`\epsilon_{i,*}` or :math:`\epsilon_{j,*}` parameters are ignored
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for LJ spheres. If
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the 3 shape parameters are > 0.0, then the particle is treated as an
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ellipsoid (even if the 3 parameters are equal to each other).
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A12 specifies the energy prefactor which depends on the types of the
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two interacting particles.
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For ellipsoid/ellipsoid interactions, the interaction is computed by
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the formulas in the supplementary document referenced above. A12 is
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the Hamaker constant as described in :ref:`(Everaers) <Everaers3>`. In LJ
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units:
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.. math::
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A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3)^2
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where :math:`\rho` gives the number density of the spherical particles
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composing the ellipsoids and :math:`\epsilon_{\mathrm{LJ}}` determines
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the interaction strength of the spherical particles.
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For ellipsoid/LJ sphere interactions, the interaction is also computed
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by the formulas in the supplementary document referenced above. A12
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has a modified form (see `here <PDF/pair_resquared_extra.pdf>`_ for
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details):
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.. math::
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A_{12} = 4\pi^2\epsilon_{\mathrm{LJ}}(\rho\sigma^3)
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For ellipsoid/LJ sphere interactions, a correction to the distance-
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of-closest approach equation has been implemented to reduce the error
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from two particles of disparate sizes; see `this supplementary document <PDF/pair_resquared_extra.pdf>`_.
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For LJ sphere/LJ sphere interactions, the interaction is computed
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using the standard Lennard-Jones formula, which is much cheaper to
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compute than the ellipsoidal formulas. A12 is used as epsilon in the
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standard LJ formula:
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.. math::
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A_{12} = \epsilon_{\mathrm{LJ}}
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and the specified :math:`\sigma` is used as the :math:`\sigma` in the
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standard LJ formula.
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When one of both of the interacting particles are ellipsoids, then
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:math:`\sigma` specifies the diameter of the continuous distribution of
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constituent particles within each ellipsoid used to model the RE-squared
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potential. Note that this is a different meaning for :math:`\sigma`
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than the :doc:`pair_style gayberne <pair_gayberne>` potential uses.
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The :math:`\epsilon_i` and :math:`\epsilon_j` coefficients are defined
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for atom types, not for pairs of atom types. Thus, in a series of
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pair_coeff commands, they only need to be specified once for each atom
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type.
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Specifically, if any of :math:`\epsilon_{i,a}`, :math:`\epsilon_{i,b}`,
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:math:`\epsilon_{i,c}` are non-zero, the three values are assigned to
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atom type I. If all the :math:`\epsilon_i` values are zero, they are
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ignored. If any of :math:`\epsilon_{j,a}`, :math:`\epsilon_{j,b}`,
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:math:`\epsilon_{j,c}` are non-zero, the three values are assigned to
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atom type J. If all three :math:`\epsilon_i` values are zero, they are
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ignored. Thus the typical way to define the :math:`\epsilon_i` and
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:math:`\epsilon_j` coefficients is to list their values in "pair_coeff
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I J" commands when I = J, but set them to 0.0 when I != J. If you do
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list them when I != J, you should insure they are consistent with their
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values in other pair_coeff commands.
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Note that if this potential is being used as a sub-style of
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:doc:`pair_style hybrid <pair_hybrid>`, and there is no "pair_coeff I I"
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setting made for RE-squared for a particular type I (because I-I
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interactions are computed by another hybrid pair potential), then you
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still need to insure the epsilon a,b,c coefficients are assigned to
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that type in a "pair_coeff I J" command.
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For large uniform molecules it has been shown that the :math:`\epsilon_{*,*}`
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energy parameters are approximately representable in terms of local
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contact curvatures :ref:`(Everaers) <Everaers3>`:
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.. math::
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\epsilon_a = \sigma \cdot { \frac{a}{ b \cdot c } }; \epsilon_b =
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\sigma \cdot { \frac{b}{ a \cdot c } }; \epsilon_c = \sigma \cdot {
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\frac{c}{ a \cdot b } }
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where a, b, and c give the particle diameters.
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The last coefficient is optional. If not specified, the global cutoff
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specified in the pair_style command is used.
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----------
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.. include:: accel_styles.rst
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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 can be mixed, but only for sphere pairs. The
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default mix value is *geometric*\ . See the "pair_modify" command for
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details. Other type pairs cannot be mixed, due to the different
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meanings of the energy prefactors used to calculate the interactions
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and the implicit dependence of the ellipsoid-sphere interaction on the
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equation for the Hamaker constant presented here. Mixing of sigma and
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epsilon followed by calculation of the energy prefactors using the
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equations above is recommended.
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This pair style supports the :doc:`pair_modify <pair_modify>` shift
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option for the energy of the Lennard-Jones portion of the pair
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interaction, but only for sphere-sphere interactions. There is no
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shifting performed for ellipsoidal interactions due to the anisotropic
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dependence of the interaction.
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The :doc:`pair_modify <pair_modify>` table option is not relevant
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for 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 <restart>`, so pair_style and pair_coeff commands do not need
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to be 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 of the :doc:`run_style command <run_style>`.
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----------
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Restrictions
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""""""""""""
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This 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 <Build_package>` doc page for more info.
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This pair style requires that atoms be ellipsoids as defined by the
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:doc:`atom_style ellipsoid <atom_style>` command.
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Particles acted on by the potential can be finite-size aspherical or
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spherical particles, or point particles. Spherical particles have all
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3 of their shape parameters equal to each other. Point particles have
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all 3 of their shape parameters equal to 0.0.
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The distance-of-closest-approach approximation used by LAMMPS becomes
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less accurate when high-aspect ratio ellipsoids are used.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`, :doc:`fix nve/asphere <fix_nve_asphere>`,
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:doc:`compute temp/asphere <compute_temp_asphere>`, :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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.. _Everaers3:
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**(Everaers)** Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
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.. _Babadi:
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**(Babadi)** Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).
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