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@ -4,7 +4,9 @@
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.. index:: fix wall/lj1043
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.. index:: fix wall/colloid
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.. index:: fix wall/harmonic
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.. index:: fix wall/lepton
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.. index:: fix wall/morse
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.. index:: fix wall/table
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fix wall/lj93 command
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=====================
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@ -23,20 +25,31 @@ fix wall/colloid command
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fix wall/harmonic command
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=========================
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fix wall/lepton command
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=========================
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fix wall/morse command
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======================
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fix wall/table command
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=========================
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Syntax
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""""""
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.. parsed-literal::
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fix ID group-ID style face args ... keyword value ...
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fix ID group-ID style [tabstyle] [N] face args ... keyword value ...
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* ID, group-ID are documented in :doc:`fix <fix>` command
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* style = *wall/lj93* or *wall/lj126* or *wall/lj1043* or *wall/colloid* or *wall/harmonic* or *wall/morse*
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* style = *wall/lj93* or *wall/lj126* or *wall/lj1043* or *wall/colloid* or *wall/harmonic* or *wall/lepton* or *wall/morse* or *wall/table*
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* tabstyle = *linear* or *spline* = method of table interpolation (only applies to *wall/table*)
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* N = use N values in *linear* or *spline* interpolation (only applies to *wall/table*)
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* one or more face/arg pairs may be appended
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* face = *xlo* or *xhi* or *ylo* or *yhi* or *zlo* or *zhi*
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.. spacer
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* args for styles *lj93* or *lj126* or *lj1043* or *colloid* or *harmonic*
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.. parsed-literal::
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@ -50,7 +63,19 @@ Syntax
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epsilon can be a variable (see below)
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sigma = size factor for wall-particle interaction (distance units)
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sigma can be a variable (see below)
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cutoff = distance from wall at which wall-particle interaction is cut off (distance units)
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cutoff = distance from wall at which wall-particle interactions are cut off (distance units)
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* args for style *lepton*
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.. parsed-literal::
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args = coord expression cutoff
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coord = position of wall = EDGE or constant or variable
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EDGE = current lo or hi edge of simulation box
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constant = number like 0.0 or -30.0 (distance units)
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variable = :doc:`equal-style variable <variable>` like v_x or v_wiggle
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expression = Lepton expression for the potential (energy units)
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cutoff = distance from wall at which wall-particle interactions are cut off (distance units)
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* args for style *morse*
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@ -67,7 +92,20 @@ Syntax
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alpha can be a variable (see below)
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r_0 = distance of the potential minimum from the face of region (distance units)
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r_0 can be a variable (see below)
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cutoff = distance from wall at which wall-particle interaction is cut off (distance units)
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cutoff = distance from wall at which wall-particle interactions are cut off (distance units)
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* args for style *table*
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.. parsed-literal::
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args = coord filename keyword cutoff
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coord = position of wall = EDGE or constant or variable
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EDGE = current lo or hi edge of simulation box
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constant = number like 0.0 or -30.0 (distance units)
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variable = :doc:`equal-style variable <variable>` like v_x or v_wiggle
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filename = file containing tabulated energy and force values
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keyword = section identifier to select a specific table in table file
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cutoff = distance from wall at which wall-particle interactions are cut off (distance units)
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* zero or more keyword/value pairs may be appended
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* keyword = *units* or *fld* or *pbc*
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@ -91,9 +129,13 @@ Examples
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fix wallhi all wall/lj93 xlo -1.0 1.0 1.0 2.5 units box
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fix wallhi all wall/lj93 xhi EDGE 1.0 1.0 2.5
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fix wallhi all wall/harmonic xhi EDGE 100.0 0.0 4.0 units box
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fix wallhi all wall/morse xhi EDGE 1.0 1.0 1.0 2.5 units box
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fix wallhi all wall/lj126 v_wiggle 23.2 1.0 1.0 2.5
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fix zwalls all wall/colloid zlo 0.0 1.0 1.0 0.858 zhi 40.0 1.0 1.0 0.858
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fix xwall mobile wall/table spline 200 EDGE -5.0 walltab.dat HARMONIC 4.0
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fix xwalls mobile wall/lepton xlo -5.0 "k*(r-rc)^2;k=100.0" 4.0 xhi 5.0 "k*(r-rc)^2;k=100.0" 4.0
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Description
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"""""""""""
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@ -103,7 +145,7 @@ wall that interacts with the atoms in the group by generating a force
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on the atom in a direction perpendicular to the wall. The energy of
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wall-particle interactions depends on the style.
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For style *wall/lj93*, the energy E is given by the 9/3 potential:
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For style *wall/lj93*, the energy E is given by the 9-3 Lennard-Jones potential:
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.. math::
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@ -111,7 +153,7 @@ For style *wall/lj93*, the energy E is given by the 9/3 potential:
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\left(\frac{\sigma}{r}\right)^3 \right]
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\qquad r < r_c
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For style *wall/lj126*, the energy E is given by the 12/6 potential:
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For style *wall/lj126*, the energy E is given by the 12-6 Lennard-Jones potential:
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.. math::
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@ -119,7 +161,7 @@ For style *wall/lj126*, the energy E is given by the 12/6 potential:
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\left(\frac{\sigma}{r}\right)^6 \right]
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\qquad r < r_c
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For style *wall/lj1043*, the energy E is given by the 10/4/3 potential:
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For style *wall/lj1043*, the energy E is given by the 10-4-3 Lennard-Jones potential:
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.. math::
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@ -138,8 +180,8 @@ of the :doc:`pair_style colloid <pair_colloid>` potential:
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& \left. - \frac{1}{6} \left(\frac{2R(D+R) + D(D+2R)
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\left[ \ln D - \ln (D+2R) \right]}{D(D+2R)} \right) \right] \qquad r < r_c
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For style *wall/harmonic*, the energy E is given by a harmonic spring
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potential:
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For style *wall/harmonic*, the energy E is given by a repulsive-only harmonic
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spring potential:
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.. math::
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@ -152,6 +194,56 @@ For style *wall/morse*, the energy E is given by a Morse potential:
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E = D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right]
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\qquad r < r_c
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For style *wall/lepton*, the energy E is provided as an Lepton
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expression string using "r" as the distance variable. The `Lepton
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library <https://simtk.org/projects/lepton>`_, that the *wall/lepton*
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style interfaces with, evaluates this expression string at run time to
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compute the wall-particle energy. It also creates an analytical
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representation of the first derivative of this expression with respect
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to "r" and then uses that to compute the force between the wall and
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atoms in the fix group. The Lepton expression must be either enclosed
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in quotes or must not contain any whitespace so that LAMMPS recognizes
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it as a single keyword.
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Optionally, the expression may use "rc" to refer to the cutoff distance
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for the given wall. Further constants in the expression can be defined
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in the same string as additional expressions separated by semi-colons.
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The expression "k*(r-rc)^2;k=100.0" represents a repulsive-only harmonic
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spring as in fix *wall/harmonic* with a force constant *K* (same as
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:math:`\epsilon` above) of 100 energy units. More details on the Lepton
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expression strings are given below.
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For style *wall/table*, the energy E and forces are determined from
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interpolation tables listed in one or more files as a function of
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distance. The interpolation tables are used to evaluate energy and
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forces between particles and the wall similar to how analytic formulas
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are used for the other wall styles.
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The interpolation tables are created as a pre-computation by fitting
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cubic splines to the file values and interpolating energy and force
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values at each of *N* distances. During a simulation, the tables are
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used to interpolate energy and force values as needed for each wall and
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particle separated by a distance *R*\ . The interpolation is done in
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one of two styles: *linear* or *spline*\ .
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For the *linear* style, the distance *R* is used to find the 2
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surrounding table values from which an energy or force is computed by
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linear interpolation.
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For the *spline* style, cubic spline coefficients are computed and
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stored for each of the *N* values in the table, one set of splines for
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energy, another for force. Note that these splines are different than
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the ones used to pre-compute the *N* values. Those splines were fit
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to the *Nfile* values in the tabulated file, where often *Nfile* <
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*N*\ . The distance *R* is used to find the appropriate set of spline
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coefficients which are used to evaluate a cubic polynomial which
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computes the energy or force.
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For each wall a filename and a keyword must be provided as in the
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examples above. The filename specifies a file containing tabulated
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energy and force values. The keyword specifies a section of the file.
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The format of this file is described below.
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In all cases, *r* is the distance from the particle to the wall at
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position *coord*, and :math:`r_c` is the *cutoff* distance at which the
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particle and wall no longer interact. The energy of the wall
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@ -180,11 +272,12 @@ box parameters and timestep and elapsed time. Thus it is easy to
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specify a time-dependent wall position. See examples below.
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For the *wall/lj93* and *wall/lj126* and *wall/lj1043* styles,
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:math:`\epsilon` and :math:`\sigma` are the usual Lennard-Jones parameters, which
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determine the strength and size of the particle as it interacts with
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the wall. Epsilon has energy units. Note that this :math:`\epsilon` and
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:math:`\sigma` may be different than any :math:`\epsilon` or :math:`\sigma` values defined
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for a pair style that computes particle-particle interactions.
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:math:`\epsilon` and :math:`\sigma` are the usual Lennard-Jones
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parameters, which determine the strength and size of the particle as it
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interacts with the wall. Epsilon has energy units. Note that this
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:math:`\epsilon` and :math:`\sigma` may be different than any
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:math:`\epsilon` or :math:`\sigma` values defined for a pair style that
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computes particle-particle interactions.
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The *wall/lj93* interaction is derived by integrating over a 3d
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half-lattice of Lennard-Jones 12/6 particles. The *wall/lj126*
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@ -207,11 +300,11 @@ are the number density of the constituent particles, in the wall and
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colloid respectively, in units of 1/volume.
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The *wall/colloid* interaction is derived by integrating over
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constituent LJ particles of size :math:`\sigma` within the colloid particle
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and a 3d half-lattice of Lennard-Jones 12/6 particles of size :math:`\sigma`
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in the wall. As mentioned in the preceding paragraph, the density of
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particles in the wall and colloid can be different, as specified by
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the :math:`\epsilon` prefactor.
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constituent LJ particles of size :math:`\sigma` within the colloid
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particle and a 3d half-lattice of Lennard-Jones 12/6 particles of size
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:math:`\sigma` in the wall. As mentioned in the preceding paragraph,
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the density of particles in the wall and colloid can be different, as
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specified by the :math:`\epsilon` prefactor.
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For the *wall/harmonic* style, :math:`\epsilon` is effectively the spring
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constant K, and has units (energy/distance\^2). The input parameter
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@ -220,20 +313,21 @@ spring is at the *cutoff*\ . This is a repulsive-only spring since the
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interaction is truncated at the *cutoff*
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For the *wall/morse* style, the three parameters are in this order:
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:math:`D_0` the depth of the potential, :math:`\alpha` the width parameter, and
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:math:`r_0` the location of the minimum. :math:`D_0` has energy units, :math:`\alpha`
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inverse distance units, and :math:`r_0` distance units.
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:math:`D_0` the depth of the potential, :math:`\alpha` the width
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parameter, and :math:`r_0` the location of the minimum. :math:`D_0` has
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energy units, :math:`\alpha` inverse distance units, and :math:`r_0`
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distance units.
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For any wall, the :math:`\epsilon` and/or :math:`\sigma` and/or :math:`\alpha` parameter can
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be specified
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as an :doc:`equal-style variable <variable>`, in which case it should be
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For any wall that supports them, the :math:`\epsilon` and/or
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:math:`\sigma` and/or :math:`\alpha` parameter can be specified as an
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:doc:`equal-style variable <variable>`, in which case it should be
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specified as v_name, where name is the variable name. As with a
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variable wall position, the variable is evaluated each timestep and
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the result becomes the current epsilon or sigma of the wall.
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Equal-style variables can specify formulas with various mathematical
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functions, and include :doc:`thermo_style <thermo_style>` command
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keywords for the simulation box parameters and timestep and elapsed
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time. Thus it is easy to specify a time-dependent wall interaction.
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variable wall position, the variable is evaluated each timestep and the
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result becomes the current epsilon or sigma of the wall. Equal-style
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variables can specify formulas with various mathematical functions, and
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include :doc:`thermo_style <thermo_style>` command keywords for the
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simulation box parameters and timestep and elapsed time. Thus it is
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easy to specify a time-dependent wall interaction.
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.. note::
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@ -266,20 +360,19 @@ define the lattice spacings.
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The *fld* keyword can be used with a *yes* setting to invoke the wall
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constraint before pairwise interactions are computed. This allows an
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implicit FLD model using :doc:`pair_style lubricateU <pair_lubricateU>`
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to include the wall force in its calculations. If the setting is
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*no*, wall forces are imposed after pairwise interactions, in the
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usual manner.
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to include the wall force in its calculations. If the setting is *no*,
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wall forces are imposed after pairwise interactions, in the usual
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manner.
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The *pbc* keyword can be used with a *yes* setting to allow walls to
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be specified in a periodic dimension. See the
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:doc:`boundary <boundary>` command for options on simulation box
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boundaries. The default for *pbc* is *no*, which means the system
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must be non-periodic when using a wall. But you may wish to use a
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periodic box. E.g. to allow some particles to interact with the wall
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via the fix group-ID, and others to pass through it and wrap around a
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periodic box. In this case you should ensure that the wall if
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sufficiently far enough away from the box boundary. If you do not,
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then particles may interact with both the wall and with periodic
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The *pbc* keyword can be used with a *yes* setting to allow walls to be
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specified in a periodic dimension. See the :doc:`boundary <boundary>`
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command for options on simulation box boundaries. The default for *pbc*
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is *no*, which means the system must be non-periodic when using a wall.
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But you may wish to use a periodic box. E.g. to allow some particles to
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interact with the wall via the fix group-ID, and others to pass through
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it and wrap around a periodic box. In this case you should ensure that
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the wall if sufficiently far enough away from the box boundary. If you
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do not, then particles may interact with both the wall and with periodic
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images on the other side of the box, which is probably not what you
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want.
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@ -328,6 +421,57 @@ perturbation on the particles:
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----------
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.. include:: lepton_expression.rst
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----------
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Table file format
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"""""""""""""""""
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Suitable tables for use with fix *wall/table* can be created by the
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Python code in the ``tools/tabulate`` folder of the LAMMPS source code
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distribution.
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The format of a tabulated file is as follows (without the parenthesized
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comments):
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.. parsed-literal::
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# Tabulated wall potential UNITS: real
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HARMONIC (keyword is the first text on a line)
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N 100 FP 200 200
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(blank line)
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1 0.04 1568.16 792.00 (index, distance to wall, energy, force)
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2 0.08 1536.64 784.00
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3 0.12 1505.44 776.00
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...
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99 3.96 0.16 8.00
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100 4.00 0 0
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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. The first line begins with a keyword which identifies
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the section. The line can contain additional text, but the initial text
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must match the argument specified in the fix *wall/table* command. The
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next line lists (in any order) one or more parameters for the table.
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Each parameter is a keyword followed by one or more numeric values.
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The parameter "N" is required and its value is the number of table
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entries that follow. Note that this may be different than the *N*
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specified in the fix *wall/table* command. Let Ntable = *N* in the fix
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command, and Nfile = "N" in the tabulated file. What LAMMPS does is a
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preliminary interpolation by creating splines using the Nfile tabulated
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values as nodal points. It uses these to interpolate as needed to
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generate energy and force values at Ntable different points. The
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resulting tables of length Ntable are then used as described above, when
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computing energy and force for wall-particle interactions. This means that
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if you want the interpolation tables of length Ntable to match exactly
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what is in the tabulated file (with effectively no preliminary
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interpolation), you should set Ntable = Nfile.
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----------
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Restart, fix_modify, output, run start/stop, minimize info
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"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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@ -354,16 +498,15 @@ fix. This allows to set at which level of the :doc:`r-RESPA
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<run_style>` integrator the fix is adding its forces. Default is the
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outermost level.
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This fix computes a global scalar energy and a global vector of
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forces, which can be accessed by various :doc:`output commands
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<Howto_output>`. Note that the scalar energy is the sum of
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interactions with all defined walls. If you want the energy on a
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per-wall basis, you need to use multiple fix wall commands. The
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length of the vector is equal to the number of walls defined by the
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fix. Each vector value is the normal force on a specific wall. Note
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that an outward force on a wall will be a negative value for *lo*
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walls and a positive value for *hi* walls. The scalar and vector
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values calculated by this fix are "extensive".
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This fix computes a global scalar energy and a global vector of forces,
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which can be accessed by various :doc:`output commands <Howto_output>`.
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Note that the scalar energy is the sum of interactions with all defined
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walls. If you want the energy on a per-wall basis, you need to use
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multiple fix wall commands. The length of the vector is equal to the
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number of walls defined by the fix. Each vector value is the normal
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force on a specific wall. Note that an outward force on a wall will be
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a negative value for *lo* walls and a positive value for *hi* walls.
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The scalar and vector values calculated by this fix are "extensive".
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command.
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@ -386,7 +529,11 @@ invoked by the :doc:`minimize <minimize>` command.
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Restrictions
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""""""""""""
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none
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Fix *wall/lepton* is part of the LEPTON package and only enabled if
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LAMMPS was built with this package. See the :doc:`Build package
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|
<Build_package>` page for more info.
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Related commands
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""""""""""""""""
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Axel Kohlmeyer