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244 lines
11 KiB
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<H3>pair_style resquared command
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</H3>
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<H3>pair_style resquared/gpu command
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</H3>
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<H3>pair_style resquared/omp command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>pair_style resquared cutoff
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</PRE>
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<UL><LI>cutoff = global cutoff for interactions (distance units)
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>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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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Style <I>resquared</I> computes the RE-squared anisotropic interaction
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<A HREF = "#Everaers">(Everaers)</A>, <A HREF = "#Babadi">(Babadi)</A> 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 sigma. LJ particles are a single sphere of
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size 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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</P>
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<P>Details for the equations used are given in the references below and
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in <A HREF = "PDF/pair_resquared_extra.pdf">this supplementary document</A>.
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</P>
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<P>Use of this pair style requires the NVE, NVT, or NPT fixes with the
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<I>asphere</I> extension (e.g. <A HREF = "fix_nve_asphere.html">fix nve/asphere</A>) in
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order to integrate particle rotation. Additionally, <A HREF = "atom_style.html">atom_style
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ellipsoid</A> 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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</P>
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<P>The following coefficients must be defined for each pair of atoms
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types via the <A HREF = "pair_coeff.html">pair_coeff</A> 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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<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
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commands:
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</P>
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<UL><LI>A12 = Energy Prefactor/Hamaker constant (energy units)
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<LI>sigma = atomic interaction diameter (distance units)
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<LI>epsilon_i_a = relative well depth of type I for side-to-side interactions
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<LI>epsilon_i_b = relative well depth of type I for face-to-face interactions
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<LI>epsilon_i_c = relative well depth of type I for end-to-end interactions
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<LI>epsilon_j_a = relative well depth of type J for side-to-side interactions
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<LI>epsilon_j_b = relative well depth of type J for face-to-face interactions
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<LI>epsilon_j_c = relative well depth of type J for end-to-end interactions
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<LI>cutoff (distance units)
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</UL>
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<P>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 paramters. 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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epsilon_i_* or epsilon_j_* parameters are ignored for LJ spheres. If
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the 3 shape paraemters 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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</P>
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<P>A12 specifies the energy prefactor which depends on the types of the
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two interacting particles.
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</P>
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<P>For ellipsoid/ellipsoid interactions, the interaction is computed by
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the formulas in the supplementary docuement referenced above. A12 is
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the Hamaker constant as described in <A HREF = "#Everaers">(Everaers)</A>. In LJ
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units:
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</P>
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<CENTER><IMG SRC = "Eqs/pair_resquared.jpg">
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</CENTER>
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<P>where rho gives the number density of the spherical particles
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composing the ellipsoids and epsilon_LJ determines the interaction
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strength of the spherical particles.
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</P>
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<P>For ellipsoid/LJ sphere interactions, the interaction is also computed
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by the formulas in the supplementary docuement referenced above. A12
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has a modifed form (see <A HREF = "PDF/pair_resquared_extra.pdf">here</A> for
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details):
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</P>
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<CENTER><IMG SRC = "Eqs/pair_resquared2.jpg">
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</CENTER>
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<P>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 <A HREF = "PDF/pair_resquared_extra.pdf">this supplementary
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document</A>.
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</P>
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<P>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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</P>
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<CENTER><IMG SRC = "Eqs/pair_resquared3.jpg">
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</CENTER>
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<P>and the specified <I>sigma</I> is used as the sigma in the standard LJ
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formula.
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</P>
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<P>When one of both of the interacting particles are ellipsoids, then
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<I>sigma</I> specifies the diameter of the continuous distribution of
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constituent particles within each ellipsoid used to model the
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RE-squared potential. Note that this is a different meaning for
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<I>sigma</I> than the <A HREF = "pair_gayberne.html">pair_style gayberne</A> potential
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uses.
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</P>
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<P>The epsilon_i and epsilon_j coefficients are defined for atom types,
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not for pairs of atom types. Thus, in a series of pair_coeff
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commands, they only need to be specified once for each atom type.
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</P>
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<P>Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
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non-zero, the three values are assigned to atom type I. If all the
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epsilon_i values are zero, they are ignored. If any of epsilon_j_a,
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epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
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to atom type J. If all three epsilon_i values are zero, they are
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ignored. Thus the typical way to define the epsilon_i and epsilon_j
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coefficients is to list their values in "pair_coeff I J" commands when
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I = J, but set them to 0.0 when I != J. If you do list them when I !=
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J, you should insure they are consistent with their values in other
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pair_coeff commands.
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</P>
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<P>Note that if this potential is being used as a sub-style of
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<A HREF = "pair_hybrid.html">pair_style hybrid</A>, 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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</P>
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<P>For large uniform molecules it has been shown that the epsilon_*_*
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energy parameters are approximately representable in terms of local
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contact curvatures <A HREF = "#Everaers">(Everaers)</A>:
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</P>
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<CENTER><IMG SRC = "Eqs/pair_resquared4.jpg">
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</CENTER>
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<P>where a, b, and c give the particle diameters.
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</P>
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<P>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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</P>
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<HR>
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<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
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the same as the corresponding style without the suffix. They have
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been optimized to run faster, depending on your available hardware, as
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discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
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manual. The accelerated styles take the same arguments and should
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produce the same results, except for round-off and precision issues.
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</P>
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<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
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packages, respectively. They are only enabled if LAMMPS was built with
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those packages. See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
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section for more info.
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</P>
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<P>You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
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switch</A> when you invoke LAMMPS, or you can
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use the <A HREF = "suffix.html">suffix</A> command in your input script.
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</P>
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<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
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more instructions on how to use the accelerated styles effectively.
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</P>
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<HR>
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<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
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</P>
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<P>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 <I>geometric</I>. 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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</P>
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<P>This pair styles supports the <A HREF = "pair_modify.html">pair_modify</A> 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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</P>
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<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
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for this pair style.
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</P>
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<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
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tail option for adding long-range tail corrections to energy and
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pressure.
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</P>
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<P>This pair style writes its information to <A HREF = "restart.html">binary restart
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files</A>, 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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</P>
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<P>This pair style can only be used via the <I>pair</I> keyword of the
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<A HREF = "run_style.html">run_style respa</A> command. It does not support the
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<I>inner</I>, <I>middle</I>, <I>outer</I> keywords of the <A HREF = "run_style.html">run_style
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command</A>.
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</P>
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<HR>
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<P><B>Restrictions:</B>
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</P>
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<P>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 <A HREF = "Section_start.html#start_3">Making
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LAMMPS</A> section for more info.
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</P>
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<P>This pair style requires that atoms be ellipsoids as defined by the
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<A HREF = "atom_style.html">atom_style ellipsoid</A> command.
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</P>
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<P>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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</P>
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<P>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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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "fix_nve_asphere.html">fix nve/asphere</A>,
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<A HREF = "compute_temp_asphere.html">compute temp/asphere</A>, <A HREF = "pair_gayberne.html">pair_style
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gayberne</A>
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</P>
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<P><B>Default:</B> none
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</P>
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<HR>
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<A NAME = "Everaers"></A>
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<P><B>(Everaers)</B> Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
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</P>
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<A NAME = "Babadi"></A>
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<P><B>(Berardi)</B> Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).
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</P>
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</HTML>
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