forked from lijiext/lammps
232 lines
10 KiB
Plaintext
232 lines
10 KiB
Plaintext
"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
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:link(lws,http://lammps.sandia.gov)
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:link(ld,Manual.html)
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:link(lc,Section_commands.html#comm)
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:line
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pair_style gran/hooke command :h3
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pair_style gran/cuda command :h3
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pair_style gran/hooke/history command :h3
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pair_style gran/hertz/history command :h3
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[Syntax:]
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pair_style style Kn Kt gamma_n gamma_t xmu dampflag :pre
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style = {gran/hooke} or {gran/hooke/history} or {gran/hertz/history} :ulb,l
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Kn = elastic constant for normal particle repulsion (force/distance units or pressure units - see discussion below) :l
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Kt = elastic constant for tangential contact (force/distance units or pressure units - see discussion below) :l
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gamma_n = damping coefficient for collisions in normal direction (1/time units or 1/time-distance units - see discussion below) :l
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gamma_t = damping coefficient for collisions in tangential direction (1/time units or 1/time-distance units - see discussion below) :l
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xmu = static yield criterion (unitless fraction between 0.0 and 1.0) :l
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dampflag = 0 or 1 if tangential damping force is excluded or included :l,ule
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IMPORTANT NOTE: Versions of LAMMPS before 9Jan09 had different style
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names for granular force fields. This is to emphasize the fact that
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the Hertzian equation has changed to model polydispersity more
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accurately. A side effect of the change is that the Kn, Kt, gamma_n,
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and gamma_t coefficients in the pair_style command must be specified
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with different values in order to reproduce calculations made with
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earlier versions of LAMMPS, even for monodisperse systems. See the
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NOTE below for details.
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[Examples:]
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pair_style gran/hooke/history 200000.0 NULL 50.0 NULL 0.5 1
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pair_style gran/hooke 200000.0 70000.0 50.0 30.0 0.5 0 :pre
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[Description:]
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The {gran} styles use the following formulas for the frictional force
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between two granular particles, as described in
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"(Brilliantov)"_#Brilliantov, "(Silbert)"_#Silbert, and
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"(Zhang)"_#Zhang, when the distance r between two particles of radii
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Ri and Rj is less than their contact distance d = Ri + Rj. There is
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no force between the particles when r > d.
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The two Hookean styles use this formula:
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:c,image(Eqs/pair_gran_hooke.jpg)
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The Hertzian style uses this formula:
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:c,image(Eqs/pair_gran_hertz.jpg)
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In both equations the first parenthesized term is the normal force
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between the two particles and the second parenthesized term is the
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tangential force. The normal force has 2 terms, a contact force and a
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damping force. The tangential force also has 2 terms: a shear force
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and a damping force. The shear force is a "history" effect that
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accounts for the tangential displacement between the particles for the
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duration of the time they are in contact. This term is included in
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pair styles {hooke/history} and {hertz/history}, but is not included
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in pair style {hooke}. The tangential damping force term is included
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in all three pair styles if {dampflag} is set to 1; it is not included
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if {dampflag} is set to 0.
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The other quantities in the equations are as follows:
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delta = d - r = overlap distance of 2 particles
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Kn = elastic constant for normal contact
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Kt = elastic constant for tangential contact
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gamma_n = viscoelastic damping constant for normal contact
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gamma_t = viscoelastic damping constant for tangential contact
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m_eff = Mi Mj / (Mi + Mj) = effective mass of 2 particles of mass Mi and Mj
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Delta St = tangential displacement vector between 2 spherical particles \
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which is truncated to satisfy a frictional yield criterion
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n_ij = unit vector along the line connecting the centers of the 2 particles
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Vn = normal component of the relative velocity of the 2 particles
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Vt = tangential component of the relative velocity of the 2 particles :ul
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The Kn, Kt, gamma_n, and gamma_t coefficients are specified as
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parameters to the pair_style command. If a NULL is used for Kt, then
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a default value is used where Kt = 2/7 Kn. If a NULL is used for
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gamma_t, then a default value is used where gamma_t = 1/2 gamma_n.
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The interpretation and units for these 4 coefficients are different in
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the Hookean versus Hertzian equations.
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The Hookean model is one where the normal push-back force for two
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overlapping particles is a linear function of the overlap distance.
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Thus the specified Kn is in units of (force/distance). Note that this
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push-back force is independent of absolute particle size (in the
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monodisperse case) and of the relative sizes of the two particles (in
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the polydisperse case). This model also applies to the other terms in
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the force equation so that the specified gamma_n is in units of
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(1/time), Kt is in units of (force/distance), and gamma_t is in units
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of (1/time).
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The Hertzian model is one where the normal push-back force for two
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overlapping particles is proportional to the area of overlap of the
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two particles, and is thus a non-linear function of overlap distance.
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Thus Kn has units of force per area and is thus specified in units of
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(pressure). The effects of absolute particle size (monodispersity)
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and relative size (polydispersity) are captured in the radii-dependent
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pre-factors. When these pre-factors are carried through to the other
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terms in the force equation it means that the specified gamma_n is in
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units of (1/(time*distance)), Kt is in units of (pressure), and
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gamma_t is in units of (1/(time*distance)).
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Note that in the Hookean case, Kn can be thought of as a linear spring
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constant with units of force/distance. In the Hertzian case, Kn is
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like a non-linear spring constant with units of force/area or
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pressure, and as shown in the "(Zhang)"_#Zhang paper, Kn = 4G /
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(3(1-nu)) where nu = the Poisson ratio, G = shear modulus = E /
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(2(1+nu)), and E = Young's modulus. Similarly, Kt = 8G / (2-nu).
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Thus in the Hertzian case Kn and Kt can be set to values that
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corresponds to properties of the material being modeled. This is also
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true in the Hookean case, except that a spring constant must be chosen
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that is appropriate for the absolute size of particles in the model.
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Since relative particle sizes are not accounted for, the Hookean
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styles may not be a suitable model for polydisperse systems.
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IMPORTANT NOTE: In versions of LAMMPS before 9Jan09, the equation for
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Hertzian interactions did not include the sqrt(RiRj/Ri+Rj) term and
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thus was not as accurate for polydisperse systems. For monodisperse
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systems, sqrt(RiRj/Ri+Rj) is a constant factor that effectively scales
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all 4 coefficients: Kn, Kt, gamma_n, gamma_t. Thus you can set the
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values of these 4 coefficients appropriately in the current code to
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reproduce the results of a previous Hertzian monodisperse calculation.
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For example, for the common case of a monodisperse system with
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particles of diameter 1, all 4 of these coefficients should now be set
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2x larger than they were previously.
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Xmu is also specified in the pair_style command and is the upper limit
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of the tangential force through the Coulomb criterion Ft = xmu*Fn,
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where Ft and Fn are the total tangential and normal force components
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in the formulas above. Thus in the Hookean case, the tangential force
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between 2 particles grows according to a tangential spring and
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dash-pot model until Ft/Fn = xmu and is then held at Ft = Fn*xmu until
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the particles lose contact. In the Hertzian case, a similar analogy
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holds, though the spring is no longer linear.
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For granular styles there are no additional coefficients to set for
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each pair of atom types via the "pair_coeff"_pair_coeff.html command.
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All settings are global and are made via the pair_style command.
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However you must still use the "pair_coeff"_pair_coeff.html for all
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pairs of granular atom types. For example the command
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pair_coeff * * :pre
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should be used if all atoms in the simulation interact via a granular
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potential (i.e. one of the pair styles above is used). If a granular
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potential is used as a sub-style of "pair_style
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hybrid"_pair_hybrid.html, then specific atom types can be used in the
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pair_coeff command to determine which atoms interact via a granular
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potential.
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:line
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Styles with a {cuda}, {gpu}, or {opt} suffix are functionally the same
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as the corresponding style without the suffix. They have been
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optimized to run faster, depending on your available hardware, as
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discussed in "this section"_Section_accelerate.html of the manual.
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The accelerated styles take the same arguments and should produce the
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same results, except for round-off and precision issues.
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These accelerated styles are part of the "user-cuda", "gpu", 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 "Making LAMMPS"_Section_start.html#2_3
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section for more info.
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You can specify the accelerated styles explicitly in your input script
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by including their suffix, or you can use the "-suffix command-line
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switch"_Section_start.html#2_6 when you invoke LAMMPS, or you can use
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the "suffix"_suffix.html command in your input script.
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See "this section"_Section_accelerate.html of the manual for more
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instructions on how to use the accelerated styles effectively.
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:line
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[Mixing, shift, table, tail correction, restart, rRESPA info]:
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The "pair_modify"_pair_modify.html mix, shift, table, and tail options
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are not relevant for granular pair styles.
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These pair styles write their information to "binary restart
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files"_restart.html, so a pair_style command does not need to be
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specified in an input script that reads a restart file.
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These pair styles can only be used via the {pair} keyword of the
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"run_style respa"_run_style.html command. They do not support the
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{inner}, {middle}, {outer} keywords.
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:line
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[Restrictions:] none
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All the granular pair styles are part of the "granular" package. It
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is only enabled if LAMMPS was built with that package. See the
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"Making LAMMPS"_Section_start.html#2_3 section for more info.
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These pair styles require that atoms store torque and angular velocity
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(omega) as defined by the "atom_style"_atom_style.html. They also
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require a per-particle radius is stored. The {sphere} atom style does
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all of this.
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This pair style requires you to use the "communicate vel
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yes"_communicate.html option so that velocites are stored by ghost
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atoms.
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[Related commands:]
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"pair_coeff"_pair_coeff.html
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[Default:] none
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:line
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:link(Brilliantov)
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[(Brilliantov)] Brilliantov, Spahn, Hertzsch, Poschel, Phys Rev E, 53,
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p 5382-5392 (1996).
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:link(Silbert)
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[(Silbert)] Silbert, Ertas, Grest, Halsey, Levine, Plimpton, Phys Rev
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E, 64, p 051302 (2001).
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:link(Zhang)
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[(Zhang)] Zhang and Makse, Phys Rev E, 72, p 011301 (2005).
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