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fix_wall_region.html
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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>
</CENTER>
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<H3>fix wall/region command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID wall/region region-ID style epsilon sigma cutoff
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>wall/region = style name of this fix command
<LI>region-ID = region whose boundary will act as wall
<LI>style = <I>lj93</I> or <I>lj126</I> or <I>colloid</I> or <I>harmonic</I>
<LI>epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)
<LI>sigma = size factor for wall-particle interaction (distance units)
<LI>cutoff = distance from wall at which wall-particle interaction is cut off (distance units)
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix wall all wall/region mySphere lj93 1.0 1.0 2.5
</PRE>
<P><B>Description:</B>
</P>
<P>Treat the surface of the geometric region defined by the <I>region-ID</I>
as a bounding wall which interacts with nearby particles according to
the specified style. The distance between a particle and the surface
is the distance to the nearest point on the surface and the force the
wall exerts on the particle is along the direction between that point
and the particle, which is the direction normal to the surface at that
point. Note that if the region surface is comprised of multiple
"faces", then each face can exert a force on the particle if it is
close enough. E.g. for <A HREF = "region.html">region_style block</A>, a particle
in the interior, near a corner of the block, could feel wall forces
from 1, 2, or 3 faces of the block.
</P>
<P>Regions are defined using the <A HREF = "region.html">region</A> command. Note that
the region volume can be interior or exterior to the bounding surface,
which will determine in which direction the surface interacts with
particles, i.e. the direction of the surface normal. Regions can
either be primitive shapes (block, sphere, cylinder, etc) or
combinations of primitive shapes specified via the <I>union</I> or
<I>intersect</I> region styles. These latter styles can be used to
construct particle containers with complex shapes. Regions can also
change over time via the <A HREF = "region.html">region</A> command keywords (move)
and <I>rotate</I>. If such a region is used with this fix, then the of
region surface will move over time in the corresponding manner.
</P>
<P>IMPORTANT NOTE: As discussed on the <A HREF = "region.html">region</A> command doc
page, regions in LAMMPS do not get wrapped across periodic boundaries.
It is up to you to insure that periodic or non-periodic boundaries are
specified appropriately via the <A HREF = "boundary.html">boundary</A> command when
using a region as a wall that bounds particle motion. This also means
that if you embed a region in your simulation box and want it to
repulse particles from its surface (using the "side out" option in the
<A HREF = "region.html">region</A> command), that its repulsive force will not be
felt across a periodic boundary.
</P>
<P>IMPORTANT NOTE: For primitive regions with sharp corners and/or edges
(e.g. a block or cylinder), wall/particle forces are computed
accurately for both interior and exterior regions. For <I>union</I> and
<I>intersect</I> regions, additional sharp corners and edges may be present
due to the intersection of the surfaces of 2 or more primitive
volumes. These corners and edges can be of two types: concave or
convex. Concave points/edges are like the corners of a cube as seen
by particles in the interior of a cube. Wall/particle forces around
these features are computed correctly. Convex points/edges are like
the corners of a cube as seen by particles exterior to the cube,
i.e. the points jut into the volume where particles are present.
LAMMPS does NOT compute the location of these convex points directly,
and hence wall/particle forces in the cutoff volume around these
points suffer from inaccuracies. The basic problem is that the
outward normal of the surface is not continuous at these points. This
can cause particles to feel no force (they don't "see" the wall) when
in one location, then move a distance epsilon, and suddenly feel a
large force because they now "see" the wall. In a worst-case
scenario, this can blow particles out of the simulation box. Thus, as
a general rule you should not use the fix wall/region command with
<I>union</I> or <I>interesect</I> regions that have convex points or edges.
</P>
<P>IMPORTANT NOTE: Similarly, you should not define <I>union</I> or
<I>intersert</I> regions for use with this command that share a common
face, even if the face is smooth. E.g. two regions of style block in
a <I>union</I> region, where the two blocks have the same face. This is
because LAMMPS discards points that are part of multiple sub-regions
when calculating wall/particle interactions, to avoid double-counting
the interaction. Having two coincident faces could cause the face to
become invisible to the particles. The solution is to make the two
faces differ by epsilon in their position.
</P>
<P>The energy of wall-particle interactions depends on the specified
style.
</P>
<P>For style <I>lj93</I>, the energy E is given by the 9/3 potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_lj93.jpg">
</CENTER>
<P>For style <I>lj126</I>, the energy E is given by the 12/6 potential:
</P>
<CENTER><IMG SRC = "Eqs/pair_lj.jpg">
</CENTER>
<P>For style <I>colloid</I>, the energy E is given by an integrated form of
the <A HREF = "pair_colloid.html">pair_style colloid</A> potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_colloid.jpg">
</CENTER>
<P>For style <I>wall/harmonic</I>, the energy E is given by a harmonic spring
potential:
</P>
<CENTER><IMG SRC = "Eqs/fix_wall_harmonic.jpg">
</CENTER>
<P>In all cases, <I>r</I> is the distance from the particle to the region
surface, and Rc is the <I>cutoff</I> distance at which the particle and
surface no longer interact. The energy of the wall potential is
shifted so that the wall-particle interaction energy is 0.0 at the
cutoff distance.
</P>
<P>For the <I>lj93</I> and <I>lj126</I> styles, <I>epsilon</I> and <I>sigma</I> are the usual
Lennard-Jones parameters, which determine the strength and size of the
particle as it interacts with the wall. Epsilon has energy units.
Note that this <I>epsilon</I> and <I>sigma</I> may be different than any
<I>epsilon</I> or <I>sigma</I> values defined for a pair style that computes
particle-particle interactions.
</P>
<P>The <I>lj93</I> interaction is derived by integrating over a 3d
half-lattice of Lennard-Jones 12/6 particles. The <I>lj126</I> interaction
is effectively a harder, more repulsive wall interaction.
</P>
<P>For the <I>colloid</I> style, <I>epsilon</I> is effectively a Hamaker constant
with energy units for the colloid-wall interaction, <I>R</I> is the radius
of the colloid particle, <I>D</I> is the distance from the surface of the
colloid particle to the wall (r-R), and <I>sigma</I> is the size of a
constituent LJ particle inside the colloid particle. Note that the
cutoff distance Rc in this case is the distance from the colloid
particle center to the wall.
</P>
<P>The <I>colloid</I> interaction is derived by integrating over constituent
LJ particles of size <I>sigma</I> within the colloid particle and a 3d
half-lattice of Lennard-Jones 12/6 particles of size <I>sigma</I> in the
wall.
</P>
<P>For the <I>wall/harmonic</I> style, <I>epsilon</I> is effectively the spring
constant K, and has units (energy/distance^2). The input parameter
<I>sigma</I> is ignored. The minimum energy position of the harmonic
spring is at the <I>cutoff</I>. This is a repulsive-only spring since the
interaction is truncated at the <I>cutoff</I>
</P>
<P>IMPORTANT NOTE: 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 on
the region surface (r = 0) or with particles on the wrong side of the
region surface (r < 0). For the <I>wall/lj93</I> and <I>wall/lj126</I> styles,
the energy of the wall/particle interaction (and hence the force on
the particle) blows up as r -> 0. The <I>wall/colloid</I> 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 region surface. The <I>harmonic</I> style is a softer
potential and does not blow up as r -> 0, but you must use a large
enough <I>epsilon</I> that particles always reamin on the correct side of
the region surface (r > 0).
</P>
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
</P>
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
files</A>.
</P>
<P>The <A HREF = "fix_modify.html">fix_modify</A> <I>energy</I> option is supported by this
fix to add the energy of interaction between atoms and the wall to the
system's potential energy as part of <A HREF = "thermo_style.html">thermodynamic
output</A>.
</P>
<P>This fix computes a global scalar energy and a global 3-length vector
of forces, which can be accessed by various <A HREF = "Section_howto.html#howto_15">output
commands</A>. The scalar energy is the sum
of energy interactions for all particles interacting with the wall
represented by the region surface. The 3 vector quantities are the
x,y,z components of the total force acting on the wall due to the
particles. The scalar and vector values calculated by this fix are
"extensive".
</P>
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
the <A HREF = "run.html">run</A> command.
</P>
<P>The forces due to this fix are imposed during an energy minimization,
invoked by the <A HREF = "minimize.html">minimize</A> command.
</P>
<P>IMPORTANT NOTE: 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 HREF = "fix_modify.html">fix_modify</A>
<I>energy</I> option for this fix.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_wall.html">fix wall/lj93</A>,
<A HREF = "fix_wall.html">fix wall/lj126</A>,
<A HREF = "fix_wall.html">fix wall/colloid</A>,
<A HREF = "fix_wall_gran.html">fix wall/gran</A>
</P>
<P><B>Default:</B> none
</P>
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