194 lines
7.2 KiB
ReStructuredText
194 lines
7.2 KiB
ReStructuredText
.. index:: pair_style exp6/rx
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.. index:: pair_style exp6/rx/kk
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pair_style exp6/rx command
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==========================
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Accelerator Variants: *exp6/rx/kk*
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Syntax
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""""""
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.. code-block:: LAMMPS
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pair_style exp6/rx cutoff ...
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* cutoff = global cutoff for DPD interactions (distance units)
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* weighting = fractional or molecular (optional)
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Examples
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""""""""
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.. code-block:: LAMMPS
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pair_style exp6/rx 10.0
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pair_style exp6/rx 10.0 fractional
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pair_style exp6/rx 10.0 molecular
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pair_coeff * * exp6.params h2o h2o exponent 1.0 1.0 10.0
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pair_coeff * * exp6.params h2o 1fluid exponent 1.0 1.0 10.0
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pair_coeff * * exp6.params 1fluid 1fluid exponent 1.0 1.0 10.0
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pair_coeff * * exp6.params 1fluid 1fluid none 10.0
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pair_coeff * * exp6.params 1fluid 1fluid polynomial filename 10.0
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Description
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"""""""""""
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Style *exp6/rx* is used in reaction DPD simulations, where the
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coarse-grained (CG) particles are composed of *m* species whose
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reaction rate kinetics are determined from a set of *n* reaction rate
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equations through the :doc:`fix rx <fix_rx>` command. The species of
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one CG particle can interact with a species in a neighboring CG
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particle through a site-site interaction potential model. The
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*exp6/rx* style computes an exponential-6 potential given by
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.. math::
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U_{ij}(r) = \frac{\epsilon}{\alpha-6}\{6\exp[\alpha(1-\frac{r_{ij}}{R_{m}})]-\alpha(\frac{R_{m}}{r_{ij}})^6\}
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where the :math:`\epsilon` parameter determines the depth of the
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potential minimum located at :math:`R_m`, and :math:`\alpha` determines
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the softness of the repulsion.
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The coefficients must be defined for each species in a given particle
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type via the :doc:`pair_coeff <pair_coeff>` command as in the examples
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above, where the first argument is the filename that includes the
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exponential-6 parameters for each species. The file includes the
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species tag followed by the :math:`\alpha, \epsilon` and :math:`R_m`
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parameters. The format of the file is described below.
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The second and third arguments specify the site-site interaction
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potential between two species contained within two different
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particles. The species tags must either correspond to the species
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defined in the reaction kinetics files specified with the :doc:`fix rx <fix_rx>` command or they must correspond to the tag "1fluid",
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signifying interaction with a product species mixture determined
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through a one-fluid approximation. The interaction potential is
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weighted by the geometric average of either the mole fraction concentrations
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or the number of molecules associated with the interacting coarse-grained
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particles (see the *fractional* or *molecular* weighting pair style options).
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The coarse-grained potential is stored before and after the
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reaction kinetics solver is applied, where the difference is defined
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to be the internal chemical energy (uChem).
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The fourth argument specifies the type of scaling that will be used
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to scale the EXP-6 parameters as reactions occur. Currently, there
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are three scaling options: *exponent*, *polynomial* and *none*\ .
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Exponent scaling requires two additional arguments for scaling
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the :math:`R_m` and :math:`\epsilon` parameters, respectively. The scaling factor
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is computed by phi\^exponent, where phi is the number of molecules
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represented by the coarse-grain particle and exponent is specified
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as a pair coefficient argument for :math:`R_m` and :math:`\epsilon`, respectively.
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The :math:`R_m` and :math:`\epsilon` parameters are multiplied by the scaling
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factor to give the scaled interaction parameters for the CG particle.
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Polynomial scaling requires a filename to be specified as a pair
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coeff argument. The file contains the coefficients to a fifth order
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polynomial for the :math:`\alpha`, :math:`\epsilon` and :math:`R_m` parameters that depend
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upon phi (the number of molecules represented by the CG particle).
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The format of a polynomial file is provided below.
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The *none* option to the scaling does not have any additional pair coeff
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arguments. This is equivalent to specifying the *exponent* option with
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:math:`R_m` and :math:`\epsilon` exponents of 0.0 and 0.0, respectively.
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The final argument specifies the interaction cutoff (optional).
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----------
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The format of a tabulated file is as follows (without the
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parenthesized comments):
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.. parsed-literal::
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# exponential-6 parameters for various species (one or more comment or blank lines)
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h2o exp6 11.00 0.02 3.50 (species, exp6, alpha, Rm, epsilon)
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no2 exp6 13.60 0.01 3.70
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...
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co2 exp6 13.00 0.03 3.20
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The format of the polynomial scaling file as follows (without the
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parenthesized comments):
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.. parsed-literal::
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# POLYNOMIAL FILE (one or more comment or blank lines)
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# General Functional Form:
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# A\*phi\^5 + B\*phi\^4 + C\*phi\^3 + D\*phi\^2 + E\*phi + F
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#
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# Parameter A B C D E F
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(blank)
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alpha 0.0000 0.00000 0.00008 0.04955 -0.73804 13.63201
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epsilon 0.0000 0.00478 -0.06283 0.24486 -0.33737 2.60097
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rm 0.0001 -0.00118 -0.00253 0.05812 -0.00509 1.50106
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A section begins with a non-blank line whose first character is not a
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"#"; blank lines or lines starting with "#" can be used as comments
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between sections.
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Following a blank line, the next N lines list the species and their
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corresponding parameters. The first argument is the species tag, the
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second argument is the exp6 tag, the third argument is the :math:`\alpha`
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parameter (energy units), the fourth argument is the :math:`\epsilon` parameter
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(energy-distance\^6 units), and the fifth argument is the :math:`R_m` parameter
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(distance units). If a species tag of "1fluid" is listed as a pair
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coefficient, a one-fluid approximation is specified where a
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concentration-dependent combination of the parameters is computed
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through the following equations:
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.. math::
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R_{m}^{3} = & \sum_{a}\sum_{b} x_{a}x_{b}R_{m,ab}^{3} \\
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\epsilon = & \frac{1}{R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\epsilon_{ab}R_{m,ab}^{3} \\
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\alpha = & \frac{1}{\epsilon R_{m}^{3}}\sum_{a}\sum_{b} x_{a}x_{b}\alpha_{ab}\epsilon_{ab}R_{m,ab}^{3}
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where
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.. math::
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\epsilon_{ab} = & \sqrt{\epsilon_{a}\epsilon_{b}} \\
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R_{m,ab} = & \frac{R_{m,a}+R_{m,b}}{2} \\
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\alpha_{ab} = & \sqrt{\alpha_{a}\alpha_{b}}
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and :math:`x_a` and :math:`x_b` are the mole fractions of a and b, respectively, which
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comprise the gas mixture.
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----------
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Mixing, shift, table, tail correction, restart, rRESPA info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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This pair style does not support mixing. Thus, coefficients for all
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I,J pairs must be specified explicitly.
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This style does not support the :doc:`pair_modify <pair_modify>` shift option
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for the energy of the exp() and 1/r\^6 portion of the pair interaction.
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This style does not support the pair_modify tail option for adding long-range
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tail corrections to energy and pressure for the A,C terms in the
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pair interaction.
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----------
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.. include:: accel_styles.rst
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----------
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Restrictions
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""""""""""""
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This command is part of the DPD-REACT package. It is only enabled if
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LAMMPS was built with that package. See the :doc:`Build package <Build_package>` page for more info.
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Related commands
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""""""""""""""""
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:doc:`pair_coeff <pair_coeff>`
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Default
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"""""""
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fractional weighting
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