and sigma are the LJ parameters for the constituent LJ
particles. Rho_wall and rho_colloid are the number density of the
constituent particles, in the wall and colloid respectively, in units
of 1/volume.</p>
<p>The <em>wall/colloid</em> interaction is derived by integrating over
constituent LJ particles of size <em>sigma</em> within the colloid particle
and a 3d half-lattice of Lennard-Jones 12/6 particles of size <em>sigma</em>
in the wall. As mentioned in the preceeding paragraph, the density of
particles in the wall and colloid can be different, as specified by
the <em>epsilon</em> pre-factor.</p>
<p>For the <em>wall/harmonic</em> style, <em>epsilon</em> is effectively the spring
constant K, and has units (energy/distance^2). The input parameter
<em>sigma</em> is ignored. The minimum energy position of the harmonic
spring is at the <em>cutoff</em>. This is a repulsive-only spring since the
interaction is truncated at the <em>cutoff</em></p>
<p>For any wall, the <em>epsilon</em> and/or <em>sigma</em> parameter can be specified
as an <a class="reference internal" href="variable.html"><span class="doc">equal-style variable</span></a>, in which case it should be
specified as v_name, where name is the variable name. As with a
variable wall position, the variable is evaluated each timestep and
the result becomes the current epsilon or sigma of the wall.
Equal-style variables can specify formulas with various mathematical
functions, and include <a class="reference internal" href="thermo_style.html"><span class="doc">thermo_style</span></a> command
keywords for the simulation box parameters and timestep and elapsed
time. Thus it is easy to specify a time-dependent wall interaction.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">For all of the styles, you must insure that r is always > 0 for
all particles in the group, or LAMMPS will generate an error. This
means you cannot start your simulation with particles at the wall
position <em>coord</em> (r = 0) or with particles on the wrong side of the
wall (r < 0). For the <em>wall/lj93</em> and <em>wall/lj126</em> styles, the energy
of the wall/particle interaction (and hence the force on the particle)
blows up as r -> 0. The <em>wall/colloid</em> style is even more
restrictive, since the energy blows up as D = r-R -> 0. This means
the finite-size particles of radius R must be a distance larger than R
from the wall position <em>coord</em>. The <em>harmonic</em> style is a softer
potential and does not blow up as r -> 0, but you must use a large
enough <em>epsilon</em> that particles always reamin on the correct side of
the wall (r > 0).</p>
</div>
<p>The <em>units</em> keyword determines the meaning of the distance units used
to define a wall position, but only when a numeric constant or
variable is used. It is not relevant when EDGE is used to specify a
face position. In the variable case, the variable is assumed to
produce a value compatible with the <em>units</em> setting you specify.</p>
<p>A <em>box</em> value selects standard distance units as defined by the
<a class="reference internal" href="units.html"><span class="doc">units</span></a> command, e.g. Angstroms for units = real or metal.
A <em>lattice</em> value means the distance units are in lattice spacings.
The <a class="reference internal" href="lattice.html"><span class="doc">lattice</span></a> command must have been previously used to
define the lattice spacings.</p>
<p>The <em>fld</em> keyword can be used with a <em>yes</em> setting to invoke the wall
constraint before pairwise interactions are computed. This allows an
implicit FLD model using <a class="reference internal" href="pair_lubricateU.html"><span class="doc">pair_style lubricateU</span></a>
to include the wall force in its calculations. If the setting is
<em>no</em>, wall forces are imposed after pairwise interactions, in the
usual manner.</p>
<p>The <em>pbc</em> keyword can be used with a <em>yes</em> setting to allow walls to
be specified in a periodic dimension. See the
<a class="reference internal" href="boundary.html"><span class="doc">boundary</span></a> command for options on simulation box
boundaries. The default for <em>pbc</em> is <em>no</em>, which means the system
must be non-periodic when using a wall. But you may wish to use a
periodic box. E.g. to allow some particles to interact with the wall
via the fix group-ID, and others to pass through it and wrap around a
periodic box. In this case you should insure that the wall if
sufficiently far enough away from the box boundary. If you do not,
then particles may interact with both the wall and with periodic
images on the other side of the box, which is probably not what you
want.</p>
<hr class="docutils" />
<p>Here are examples of variable definitions that move the wall position
in a time-dependent fashion using equal-style
<a class="reference internal" href="variable.html"><span class="doc">variables</span></a>. The wall interaction parameters (epsilon,
sigma) could be varied with additional variable definitions.</p>
<pre class="literal-block">
variable ramp equal ramp(0,10)
fix 1 all wall xlo v_ramp 1.0 1.0 2.5
</pre>
<pre class="literal-block">
variable linear equal vdisplace(0,20)
fix 1 all wall xlo v_linear 1.0 1.0 2.5
</pre>
<pre class="literal-block">
variable wiggle equal swiggle(0.0,5.0,3.0)
fix 1 all wall xlo v_wiggle 1.0 1.0 2.5
</pre>
<pre class="literal-block">
variable wiggle equal cwiggle(0.0,5.0,3.0)
fix 1 all wall xlo v_wiggle 1.0 1.0 2.5
</pre>
<p>The ramp(lo,hi) function adjusts the wall position linearly from lo to
hi over the course of a run. The vdisplace(c0,velocity) function does
something similar using the equation position = c0 + velocity*delta,
where delta is the elapsed time.</p>
<p>The swiggle(c0,A,period) function causes the wall position to
oscillate sinusoidally according to this equation, where omega = 2 PI
/ period:</p>
<pre class="literal-block">
position = c0 + A sin(omega*delta)
</pre>
<p>The cwiggle(c0,A,period) function causes the wall position to
oscillate sinusoidally according to this equation, which will have an
initial wall velocity of 0.0, and thus may impose a gentler
perturbation on the particles:</p>
<pre class="literal-block">
position = c0 + A (1 - cos(omega*delta))
</pre>
<hr class="docutils" />
<p><strong>Restart, fix_modify, output, run start/stop, minimize info:</strong></p>
<p>No information about this fix is written to <a class="reference internal" href="restart.html"><span class="doc">binary restart files</span></a>.</p>
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>energy</em> option is supported by this
fix to add the energy of interaction between atoms and each wall to
the system’s potential energy as part of <a class="reference internal" href="thermo_style.html"><span class="doc">thermodynamic output</span></a>.</p>
<p>The <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>respa</em> option is supported by this
fix. This allows to set at which level of the <a class="reference internal" href="run_style.html"><span class="doc">r-RESPA</span></a>
integrator the fix is adding its forces. Default is the outermost level.</p>
<p>This fix computes a global scalar energy and a global vector of
forces, which can be accessed by various <a class="reference internal" href="Section_howto.html#howto-15"><span class="std std-ref">output commands</span></a>. Note that the scalar energy is
the sum of interactions with all defined walls. If you want the
energy on a per-wall basis, you need to use multiple fix wall
commands. The length of the vector is equal to the number of walls
defined by the fix. Each vector value is the normal force on a
specific wall. Note that an outward force on a wall will be a
negative value for <em>lo</em> walls and a positive value for <em>hi</em> walls.
The scalar and vector values calculated by this fix are “extensive”.</p>
<p>No parameter of this fix can be used with the <em>start/stop</em> keywords of
the <a class="reference internal" href="run.html"><span class="doc">run</span></a> command.</p>
<p>The forces due to this fix are imposed during an energy minimization,
invoked by the <a class="reference internal" href="minimize.html"><span class="doc">minimize</span></a> command.</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">If you want the atom/wall interaction energy to be included in
the total potential energy of the system (the quantity being
minimized), you MUST enable the <a class="reference internal" href="fix_modify.html"><span class="doc">fix_modify</span></a> <em>energy</em>
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