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\documentstyle[12pt]{article}
\begin{document}
\begin{eqnarray}
U_A &=& - \frac{A}{6} \left[
\frac{2 a_1 a_2}{r^2-\left(a_1+a_2\right)^2}
+ \frac{2 a_1 a_2}{r^2 - \left(a_1 - a_2\right)^2}
+ \mathrm{ln}
\left(
\frac{r^2-\left(a_1+a_2\right)^2}{r^2-\left(a_1-a_2\right)^2}
\right)
\right] \nonumber \\
\nonumber \\
U_R &=& \frac{A}{37800} \frac{\sigma^6}{r}
\left[ \frac{}{} \right. \nonumber \\
&&\qquad \frac{r^2-7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
{\left(r-a_1-a_2\right)^7} \nonumber \\
&&\qquad +\frac{r^2+7r\left(a_1+a_2\right)+6\left(a_1^2+7a_1a_2+a_2^2\right)}
{\left(r+a_1+a_2\right)^7} \nonumber \\
&&\qquad -\frac{r^2+7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
{\left(r+a_1-a_2\right)^7} \nonumber \\
&&\qquad \left. -\frac{r^2-7r\left(a_1-a_2\right)+6\left(a_1^2-7a_1a_2+a_2^2\right)}
{\left(r-a_1+a_2\right)^7}
\right] \nonumber \\
\nonumber \\
U &=& U_A + U_R, \qquad r < r_c \nonumber
\end{eqnarray}
\end{document}

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\documentstyle[12pt]{article}
\begin{document}
\begin{eqnarray}
U &=& \frac{2 ~ a^3 ~ \sigma^3 ~ A}{9 \left( a^2 - r^2 \right)^3}
\left[ 1 - \frac{\left(5 ~ a^6+45~a^4~r^2+63~a^2~r^4+15~r^6\right) \sigma^6}
{15 \left(a-r\right)^6 \left( a+r \right)^6} \right], ~~ r < r_c \nonumber
\end{eqnarray}
\end{document}

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\documentstyle[12pt]{article}
\begin{document}
\begin{eqnarray}
U &=& \frac{A}{36} \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{ \sigma}{r} \right)^6 \right], ~~ r < r_c \nonumber
\end{eqnarray}
\end{document}

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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] \\
E_{qq} & = & \frac{q_i q_j}{r} \\
E_{qp} & = & \frac{q}{r^3} (p \bullet \vec{r}) \\
E_{pp} & = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) -
\frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})
\end{eqnarray*}
\begin{eqnarray*}
F_{qq} & = & \frac{q_i q_j}{r^3} \vec{r} \\
F_{qp} & = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5}
(\vec{p} \bullet \vec{r}) \vec{r} \\
F_{pp} & = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
\frac{15}{r^7} (\vec{p_i} \bullet \vec{r})
(\vec{p_j} \bullet \vec{r}) \vec{r} +
\frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} +
(\vec{p_i} \bullet \vec{r}) \vec{p_j} \right]
\end{eqnarray*}
\begin{eqnarray*}
T_{pq} = T_{ij} & = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
T_{pp} = T_{ij} & = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) +
\frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
(\vec{p_i} \times \vec{r}) \\
T_{pp} = T_{ji} & = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) +
\frac{3}{r^5} (\vec{p_i} \bullet \vec{r})
(\vec{p_j} \times \vec{r}) \\
\end{eqnarray*}
\end{document}

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<HTML>
<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>
<HR>
<H3>compute temp/deform command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID temp/deform
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>temp/deform = style name of this compute command
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute myTemp all temp/deform myDeform
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the temperature of a group of
atoms, after subtracting out a streaming velocity induced by the
simulation box changing size and/or shape, for example in a
non-equilibrium MD (NEMD) simulation. The size/shape change is
induced by use of the <A HREF = "fix_deform.html">fix deform</A> command. A compute
of this style is created by the <A HREF = "fix_nvt_sllod.html">fix nvt/sllod</A>
command to compute the thermal temperature of atoms for thermostatting
purposes. A compute of this style can also be used by any command
that computes a temperature, e.g. <A HREF = "thermo_modify.html">thermo_modify</A>,
<A HREF = "fix_temp_rescale.html">fix temp/rescale</A>, <A HREF = "fix_npt.html">fix npt</A>, etc.
</P>
<P>The deformation fix changes the box size and/or shape over time, so
each point in the simulation box can be thought of as having a
"streaming" velocity. For example, if the box is being sheared in x,
relative to y, then points at the bottom of the box (low y) have a
small x velocity, while points at the top of the box (hi y) have a
large x velocity. This position-dependent streaming velocity is
subtracted from each atom's actual velocity to yield a thermal
velocity which is used to compute the temperature.
</P>
<P>IMPORTANT NOTE: <A HREF = "fix_deform.html">Fix deform</A> has an option for
remapping either atom coordinates or velocities to the changing
simulation box. To use this compute, the fix should NOT remap atom
positions, but rather should let atoms respond to the changing box by
adjusting their own velocities (or let fix deform remap the atom
velocities). If the fix does remap atom positions, their velocity is
not changed, and thus they do not have the streaming velocity assumed
by this compute. LAMMPS will warn you if this setting is not
consistent.
</P>
<P>The temperature is calculated by the formula KE = dim/2 N k T, where
KE = total kinetic energy of the group of atoms (sum of 1/2 m v^2),
dim = 2 or 3 = dimensionality of the simulation, N = number of atoms
in the group, k = Boltzmann constant, and T = temperature. Note that
v in the kinetic energy formula is the atom's thermal velocity.
</P>
<P>A 6-component kinetic energy tensor is also calculated by this compute
for use in the computation of a pressure tensor. The formula for the
components of the tensor is the same as the above formula, except that
v^2 is replaced by vx * vy for the xy component, etc.
</P>
<P>The number of atoms contributing to the temperature is assumed to be
constant for the duration of the run; use the <I>dynamic</I> option of the
<A HREF = "compute_modify.html">compute_modify</A> command if this is not the case.
</P>
<P>This compute subtracts out degrees-of-freedom due to fixes that
constrain molecular motion, such as <A HREF = "fix_shake.html">fix shake</A> and
<A HREF = "fix_rigid.html">fix rigid</A>. This means the temperature of groups of
atoms that include these constraints will be computed correctly. If
needed, the subtracted degrees-of-freedom can be altered using the
<I>extra</I> option of the <A HREF = "compute_modify.html">compute_modify</A> command.
</P>
<P><B>Restrictions:</B> none
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute_temp_ramp.html">compute temp/ramp</A>, <A HREF = "fix_deform.html">fix
deform</A>, <A HREF = "fix_nvt_sllod.html">fix nvt/sllod</A>
</P>
<P><B>Default:</B> none
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
compute temp/deform command :h3
[Syntax:]
compute ID group-ID temp/deform :pre
ID, group-ID are documented in "compute"_compute.html command
temp/deform = style name of this compute command :ul
[Examples:]
compute myTemp all temp/deform myDeform :pre
[Description:]
Define a computation that calculates the temperature of a group of
atoms, after subtracting out a streaming velocity induced by the
simulation box changing size and/or shape, for example in a
non-equilibrium MD (NEMD) simulation. The size/shape change is
induced by use of the "fix deform"_fix_deform.html command. A compute
of this style is created by the "fix nvt/sllod"_fix_nvt_sllod.html
command to compute the thermal temperature of atoms for thermostatting
purposes. A compute of this style can also be used by any command
that computes a temperature, e.g. "thermo_modify"_thermo_modify.html,
"fix temp/rescale"_fix_temp_rescale.html, "fix npt"_fix_npt.html, etc.
The deformation fix changes the box size and/or shape over time, so
each point in the simulation box can be thought of as having a
"streaming" velocity. For example, if the box is being sheared in x,
relative to y, then points at the bottom of the box (low y) have a
small x velocity, while points at the top of the box (hi y) have a
large x velocity. This position-dependent streaming velocity is
subtracted from each atom's actual velocity to yield a thermal
velocity which is used to compute the temperature.
IMPORTANT NOTE: "Fix deform"_fix_deform.html has an option for
remapping either atom coordinates or velocities to the changing
simulation box. To use this compute, the fix should NOT remap atom
positions, but rather should let atoms respond to the changing box by
adjusting their own velocities (or let fix deform remap the atom
velocities). If the fix does remap atom positions, their velocity is
not changed, and thus they do not have the streaming velocity assumed
by this compute. LAMMPS will warn you if this setting is not
consistent.
The temperature is calculated by the formula KE = dim/2 N k T, where
KE = total kinetic energy of the group of atoms (sum of 1/2 m v^2),
dim = 2 or 3 = dimensionality of the simulation, N = number of atoms
in the group, k = Boltzmann constant, and T = temperature. Note that
v in the kinetic energy formula is the atom's thermal velocity.
A 6-component kinetic energy tensor is also calculated by this compute
for use in the computation of a pressure tensor. The formula for the
components of the tensor is the same as the above formula, except that
v^2 is replaced by vx * vy for the xy component, etc.
The number of atoms contributing to the temperature is assumed to be
constant for the duration of the run; use the {dynamic} option of the
"compute_modify"_compute_modify.html command if this is not the case.
This compute subtracts out degrees-of-freedom due to fixes that
constrain molecular motion, such as "fix shake"_fix_shake.html and
"fix rigid"_fix_rigid.html. This means the temperature of groups of
atoms that include these constraints will be computed correctly. If
needed, the subtracted degrees-of-freedom can be altered using the
{extra} option of the "compute_modify"_compute_modify.html command.
[Restrictions:] none
[Related commands:]
"compute temp/ramp"_compute_temp_ramp.html, "fix
deform"_fix_deform.html, "fix nvt/sllod"_fix_nvt_sllod.html
[Default:] none

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<HTML>
<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>
<HR>
<H3>compute temp/dipole command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>compute ID group-ID temp/dipole
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
<LI>temp/dipole = style name of this compute command
</UL>
<P><B>Examples:</B>
</P>
<PRE>compute 1 all temp/dipole
compute myTemp mobile temp/dipole
</PRE>
<P><B>Description:</B>
</P>
<P>Define a computation that calculates the temperature of a group of
particles that include a point dipole. The computation is similar to
<A HREF = "compute_temp.html">compute_temp</A>, however, additional degrees of
freedom are inlclude to account for the rotational state of the
particles. The associated kinetic energy includes a rotational term
KE_rotational = 1/2 I w^2, where I is the moment of inertia and w is
the angular velocity.
</P>
<P><B>Restrictions:</B>
</P>
<P>Can only be used if LAMMPS was built with the "dipole" package.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "compute_temp.html">compute temp</A>
</P>
<P><B>Default:</B> none
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
compute temp/dipole command :h3
[Syntax:]
compute ID group-ID temp/dipole :pre
ID, group-ID are documented in "compute"_compute.html command
temp/dipole = style name of this compute command :ul
[Examples:]
compute 1 all temp/dipole
compute myTemp mobile temp/dipole :pre
[Description:]
Define a computation that calculates the temperature of a group of
particles that include a point dipole. The computation is similar to
"compute_temp"_compute_temp.html, however, additional degrees of
freedom are inlclude to account for the rotational state of the
particles. The associated kinetic energy includes a rotational term
KE_rotational = 1/2 I w^2, where I is the moment of inertia and w is
the angular velocity.
[Restrictions:]
Can only be used if LAMMPS was built with the "dipole" package.
[Related commands:]
"compute temp"_compute_temp.html
[Default:] none

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<HTML>
<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>
<HR>
<H3>fix deform command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID deform N parameter args ... keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>deform = style name of this fix command
<LI>N = perform box deformation every this many timesteps
<LI>one or more parameter/arg pairs may be appended
<PRE>parameter = <I>x</I> or <I>y</I> or <I>z</I> or <I>xy</I> or <I>xz</I> or <I>yz</I>
<I>x</I>, <I>y</I>, <I>z</I> args = style value(s)
style = <I>final</I> or <I>delta</I> or <I>scale</I> or <I>vel</I> or <I>rate</I> or <I>volume</I>
<I>final</I> values = lo hi
lo hi = box boundaries at end of run (distance units)
<I>delta</I> values = dlo dhi
dlo dhi = change in box boundaries at end of run (distance units)
<I>scale</I> values = factor
factor = multiplicative factor for change in box length at end of run
<I>vel</I> value = V
V = change box length at this velocity (distance/time units),
effectively an engineering strain rate
<I>rate</I> value = R
R = true strain rate (1/time units)
<I>volume</I> value = none = adjust this dim to preserve volume of system
<I>xy</I>, <I>xz</I>, <I>yz</I> args = style value
style = <I>final</I> or <I>delta</I> or <I>vel</I> or <I>rate</I>
<I>final</I> value = tilt
tilt = tilt factor at end of run (distance units)
<I>delta</I> value = dtilt
dtilt = change in tilt factor at end of run (distance units)
<I>vel</I> value = V
V = change tilt factor at this velocity (distance/time units),
effectively an engineering shear strain rate
<I>rate</I> value = R
R = true shear strain rate (1/time units)
</PRE>
<LI>zero or more keyword/value pairs may be appended to the args
<LI>keyword = <I>remap</I> or <I>units</I>
<PRE> <I>remap</I> value = <I>x</I> or <I>v</I> or <I>none</I>
x = remap coords of atoms in group into deforming box
v = remap velocities of all atoms when they cross periodic boundaries
none = no remapping of x or v
<I>units</I> value = <I>lattice</I> or <I>box</I>
lattice = distances are defined in lattice units
box = distances are defined in simulation box units
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all deform x final 0.0 9.0 z final 0.0 5.0 units box
fix 1 all deform x rate 0.1 y volume z volume
fix 1 all deform xy rate 0.001 remap v
fix 1 all deform y delta 0.5 xz vel 1.0
</PRE>
<P><B>Description:</B>
</P>
<P>Change the volume and/or shape of the simulation box during a dynamics
run. Orthogonal simulation boxes have 3 adjustable parameters
(x,y,z). Triclinic (non-orthogonal) simulation boxes have 6
adjustable parameters (x,y,z,xy,xz,yz). Any or all of them can be
adjusted independently and simultaneously by this command. This fix
can be used to perform non-equilibrium MD (NEMD) simulations of a
continuously strained system. See the <A HREF = "fix_nvt_sllod.html">fix
nvt/sllod</A> and <A HREF = "compute_temp_deform.html">compute
temp/deform</A> commands for more details.
</P>
<P>Any parameter varied by this command must refer to a periodic
dimension - see the <A HREF = "boundary.html">boundary</A> command. For parameters
"xy", "xz", and "yz" this means both affected dimensions must be
periodic, e.g. x and y for "xy". Dimensions not varied by this
command can be periodic or non-periodic. Unspecified dimensions can
also be controlled by a <A HREF = "fix_npt.html">fix npt</A> or <A HREF = "fix_nph.html">fix
nph</A> command.
</P>
<P>The size and shape of the initial simulation box at the beginning of a
run are specified by the <A HREF = "create_box.html">create_box</A> or
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A> command
used to setup the simulation, or they are the values from the end of
the previous run. The <A HREF = "create_box.html">create_box</A>, <A HREF = "read_data.html">read
data</A>, and <A HREF = "read_restart.html">read_restart</A> commands
also specify whether the simulation box is orthogonal or triclinic and
explain the meaning of the xy,xz,yz tilt factors. If fix deform
changes the xy,xz,yz tilt factors, then the simulation box must be
triclinic, even if its initial tilt factors are 0.0.
</P>
<P>As described below, the desired simulation box size and shape at the
end of the run are determined by the parameters of the fix deform
command. Every Nth timestep during the run, the simulation box is
expanded, contracted, or tilted to ramped values between the initial
and final values. The <A HREF = "run.html">run</A> command documents how to make
the ramping take place across multiple runs.
</P>
<HR>
<P>For the <I>x</I>, <I>y</I>, and <I>z</I> parameters, this is the meaning of their
styles and values.
</P>
<P>The <I>final</I>, <I>delta</I>, <I>scale</I>, and <I>vel</I> styles all change the
specified dimension of the box via "constant displacement" which is
effectively a "constant engineering strain rate". This means the box
dimension changes linearly with time from its initial to final value.
</P>
<P>For style <I>final</I>, the final lo and hi box boundaries of a dimension
are specified. The values can be in lattice or box distance units.
See the discsussion of the units keyword below.
</P>
<P>For style <I>delta</I>, plus or minus changes in the lo/hi box boundaries
of a dimension are specified. The values can be in lattice or box
distance units. See the discsussion of the units keyword below.
</P>
<P>For style <I>scale</I>, a multiplicative factor to apply to the box length
of a dimension is specified. For example, if the initial box length
is 10, and the factor is 1.1, then the final box length will be 11. A
factor less than 1.0 means compression.
</P>
<P>For style <I>vel</I>, a velocity at which the box length changes is
specified in units of distance/time. This is effectively an
"engineering strain rate", where rate = V/L0 and L0 is the initial box
length. The distance can be in lattice or box distance units. See
the discussion of the units keyword below. For example, if the
initial box length is 100 Angstroms, and V is 10 Angstroms/psec,
then after 10 psec, the box length will have doubled. After 20 psec,
it will have tripled.
</P>
<P>The <I>rate</I> style changes a dimension of the box at a "true constant
strain rate". Note that this is not an "engineering strain rate", as
the other styles are. Rather, for a "true" rate, the rate of change
is constant, which means the box dimension changes non-linearly with
time from its initial to final value. The units of the specified
strain rate are 1/time. See the <A HREF = "units.html">units</A> command for the
time units associated with different choices of simulation units,
e.g. picoseconds for "metal" units). Thus if the <I>rate</I> R is 0.01 and
time units are picoseconds, this means the box length will increase by
1% every picosecond. R = 1 or 2 means the box length will double or
triple every picosecond. R = -0.1 means the box length will shrink by
10% every picosecond. Note that for a "true" rate the change is
continuous, so running with R = 1 for 10 picoseconds does not expand
the box length by a factor of 10, but by a factor of 1024 since it
doubles every picosecond.
</P>
<P>Note that to change the volume (or cross-sectional area) of the
simulation box at a constant rate, you can change multiple dimensions
via <I>rate</I>. E.g. to double the box volume every picosecond, you could
set "x rate M", "y rate M", "z rate M", with M = pow(2,1/3) - 1 =
1.26, since if each box dimension grows by 26%, the box volume
doubles.
</P>
<P>The <I>volume</I> style changes the specified dimension in such a way that
the box volume remains constant while other box dimensions are changed
explicitly via the styles discussed above. For example, "x scale 1.1
y scale 1.1 z volume" will shrink the z box length as the x,y box
lengths increase, to keep the volume constant (product of x,y,z
lengths). If "x scale 1.1 z volume" is specified and parameter <I>y</I> is
unspecified, then the z box length will shrink as x increases to keep
the product of x,z lengths constant. If "x scale 1.1 y volume z
volume" is specified, then both the y,z box lengths will shrink as x
increases to keep the volume constant (product of x,y,z lengths). In
this case, the y,z box lengths shrink so as to keep their relative
aspect ratio constant.
</P>
<P>For solids or liquids, note that when one dimension of the box is
expanded via fix deform (i.e. tensile strain), it may be physically
undesirable to hold the other 2 box lengths constant (unspecified by
fix deform) since that implies a density change. Using the <I>volume</I>
style for those 2 dimensions to keep the box volume constant may make
more physical sense, but may also not be correct for materials and
potentials whose Poisson ratio is not 0.5. An alternative is to use
<A HREF = "fix_npt.html">fix npt aniso</A> with zero applied pressure on those 2
dimensions, so that they respond to the tensile strain dynamically.
</P>
<P>For the <I>scale</I>, <I>vel</I>, <I>rate</I>, and <I>volume</I> styles, the box length is
expanded or compressed around its mid point.
</P>
<HR>
<P>For the <I>xy</I>, <I>xz</I>, and <I>yz</I> parameters, this is the meaning of their
styles and values. Note that changing the tilt factors of a triclinic
box does not change its volume.
</P>
<P>For style <I>final</I>, the final tilt factor is specified. The value
can be in lattice or box distance units. See the discussion of the
units keyword below.
</P>
<P>For style <I>delta</I>, a plus or minus change in the tilt factor is
specified. The value can be in lattice or box distance units. See
the discsussion of the units keyword below.
</P>
<P>For style <I>vel</I>, a velocity at which the tilt factor changes is
specified in units of distance/time. This is effectively an
"engineering shear strain rate", where rate = V/L0 and L0 is the
initial box length perpendicular to the direction of shear. The
distance can be in lattice or box distance units. See the discsussion
of the units keyword below. For example, if the initial tilt factor
is 5 Angstroms, and the V is 10 Angstroms/psec, then after 1 psec, the
tilt factor will be 15 Angstroms. After 2 psec, it will be 25
Angstroms.
</P>
<P>The <I>rate</I> style changes a tilt factor at a "true constant shear
strain rate". Note that this is not an "engineering shear strain
rate", as the other styles are. Rather, for a "true" rate, the rate
of change is constant, which means the tilt factor changes
non-linearly with time from its initial to final value. The units of
shear strain rate are 1/time. See the <A HREF = "units.html">units</A> command for
the time units associated with different choices of simulation units,
e.g. picoseconds for "metal" units). Thus if the <I>rate</I> R is 0.01 and
time units are picoseconds, this means the tilt factor will increase
by 1% every picosecond. R = 1 or 2 means the tilt factor will double
or triple every picosecond. R = -0.1 means the tilt factor will
shrink by 10% every picosecond. Note that the change is continuous,
so running with R = 1 for 10 picoseconds does not change the tilt
factor by a factor of 10, but by a factor of 1024 since it doubles
every picosecond. Also note, that the initial tilt factor must be
non-zero to use the <I>rate</I> option.
</P>
<P>Note that shear strain is defined as the tilt factor divided by the
perpendicular box length. The <I>rate</I> style controls the tilt factor,
but assumes the perpendicular box length remains constant. If this is
not the case (e.g. it changes due to another fix deform parameter),
then this effect on the shear strain is ignored.
</P>
<P>All of these styles change the xy, xz, yz tilt factors during a
simulation. In LAMMPS, tilt factors (xy,xz,yz) for triclinic boxes
are always bounded by half the distance of the parallel box length.
For example, if xlo = 2 and xhi = 12, then the x box length is 10 and
the xy tilt factor must be between -5 and 5. Similarly, both xz and
yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2. Note that this is
not a limitation, since if the maximum tilt factor is 5 (as in this
example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
... are all equivalent.
</P>
<P>To obey this constraint and allow for large shear deformations to be
applied via the <I>xy</I>, <I>xz</I>, or <I>yz</I> parameters, the folloiwng
algorithm is used. If <I>prd</I> is the associated parallel box length (10
in the example above), then if the tilt factor exceeds the accepted
range of -5 to 5 during the simulation, then the box is re-shaped to
the other limit (an equivalent box) and the simulation continues.
Thus for this example, if the initial xy tilt factor was 0.0 and "xy
final 100.0" was specified, then during the simulation the xy tilt
factor would increase from 0.0 to 5.0, the box would be re-shaped so
that the tilt factor becomes -5.0, the tilt factor would increase from
-5.0 to 5.0, the box would be re-shaped again, etc. The re-shaping
would occur 10 times and the final tilt factor at the end of the
simulation would be 0.0. During each re-shaping event, atoms are
remapped into the new box in the appropriate manner.
</P>
<HR>
<P>Each time the box size or shape is changed, the <I>remap</I> keyword
determines whether atom positions are re-mapped to the new box. If
<I>remap</I> is set to <I>x</I> (the default), atoms in the fix group are
re-mapped; otherwise they are not. If <I>remap</I> is set to <I>v</I>, then any
atom in the fix group that crosses a periodic boundary will have a
delta added to its velocity equal to the difference in velocities
between the lo and hi boundaries. Note that this velocity difference
can include tilt components, e.g. a delta in the x velocity when an
atom crosses the y periodic boundary. If <I>remap</I> is set to <I>none</I>,
then neither of these remappings take place.
</P>
<P>IMPORTANT NOTE: When non-equilibrium MD (NEMD) simulations are
performed using this fix, the option "remap v" should normally be
used. This is because <A HREF = "fix_nvt_sllod.html">fix nvt/sllod</A> adjusts the
atom positions and velocities to provide a velocity profile that
matches the changing box size/shape. Thus atom coordinates should NOT
be remapped by fix deform, but velocities SHOULD be when atoms cross
periodic boundaries, since when atoms cross periodic boundaries since
that is consistent with maintaining the velocity profile created by
fix nvt/sllod. LAMMPS will warn you if this settings is not
consistent.
</P>
<P>The <I>units</I> keyword determines the meaning of the distance units used
to define various arguments. A <I>box</I> value selects standard distance
units as defined by the <A HREF = "units.html">units</A> command, e.g. Angstroms for
units = real or metal. A <I>lattice</I> value means the distance units are
in lattice spacings. The <A HREF = "lattice.html">lattice</A> command must have
been previously used to define the lattice spacing. Note that the
units choice also affects the <I>vel</I> style parameters since it is
defined in terms of distance/time.
</P>
<HR>
<P><B>Restrictions:</B>
</P>
<P>Any box dimension varied by this fix must be periodic.
</P>
<P><B>Related commands:</B> none
</P>
<P><B>Default:</B>
</P>
<P>The option defaults are remap = x and units = lattice.
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
fix deform command :h3
[Syntax:]
fix ID group-ID deform N parameter args ... keyword value ... :pre
ID, group-ID are documented in "fix"_fix.html command :ulb,l
deform = style name of this fix command :l
N = perform box deformation every this many timesteps :l
one or more parameter/arg pairs may be appended :l
parameter = {x} or {y} or {z} or {xy} or {xz} or {yz}
{x}, {y}, {z} args = style value(s)
style = {final} or {delta} or {scale} or {vel} or {rate} or {volume}
{final} values = lo hi
lo hi = box boundaries at end of run (distance units)
{delta} values = dlo dhi
dlo dhi = change in box boundaries at end of run (distance units)
{scale} values = factor
factor = multiplicative factor for change in box length at end of run
{vel} value = V
V = change box length at this velocity (distance/time units),
effectively an engineering strain rate
{rate} value = R
R = true strain rate (1/time units)
{volume} value = none = adjust this dim to preserve volume of system
{xy}, {xz}, {yz} args = style value
style = {final} or {delta} or {vel} or {rate}
{final} value = tilt
tilt = tilt factor at end of run (distance units)
{delta} value = dtilt
dtilt = change in tilt factor at end of run (distance units)
{vel} value = V
V = change tilt factor at this velocity (distance/time units),
effectively an engineering shear strain rate
{rate} value = R
R = true shear strain rate (1/time units) :pre
zero or more keyword/value pairs may be appended to the args :l
keyword = {remap} or {units} :l
{remap} value = {x} or {v} or {none}
x = remap coords of atoms in group into deforming box
v = remap velocities of all atoms when they cross periodic boundaries
none = no remapping of x or v
{units} value = {lattice} or {box}
lattice = distances are defined in lattice units
box = distances are defined in simulation box units :pre
:ule
[Examples:]
fix 1 all deform x final 0.0 9.0 z final 0.0 5.0 units box
fix 1 all deform x rate 0.1 y volume z volume
fix 1 all deform xy rate 0.001 remap v
fix 1 all deform y delta 0.5 xz vel 1.0 :pre
[Description:]
Change the volume and/or shape of the simulation box during a dynamics
run. Orthogonal simulation boxes have 3 adjustable parameters
(x,y,z). Triclinic (non-orthogonal) simulation boxes have 6
adjustable parameters (x,y,z,xy,xz,yz). Any or all of them can be
adjusted independently and simultaneously by this command. This fix
can be used to perform non-equilibrium MD (NEMD) simulations of a
continuously strained system. See the "fix
nvt/sllod"_fix_nvt_sllod.html and "compute
temp/deform"_compute_temp_deform.html commands for more details.
Any parameter varied by this command must refer to a periodic
dimension - see the "boundary"_boundary.html command. For parameters
"xy", "xz", and "yz" this means both affected dimensions must be
periodic, e.g. x and y for "xy". Dimensions not varied by this
command can be periodic or non-periodic. Unspecified dimensions can
also be controlled by a "fix npt"_fix_npt.html or "fix
nph"_fix_nph.html command.
The size and shape of the initial simulation box at the beginning of a
run are specified by the "create_box"_create_box.html or
"read_data"_read_data.html or "read_restart"_read_restart.html command
used to setup the simulation, or they are the values from the end of
the previous run. The "create_box"_create_box.html, "read
data"_read_data.html, and "read_restart"_read_restart.html commands
also specify whether the simulation box is orthogonal or triclinic and
explain the meaning of the xy,xz,yz tilt factors. If fix deform
changes the xy,xz,yz tilt factors, then the simulation box must be
triclinic, even if its initial tilt factors are 0.0.
As described below, the desired simulation box size and shape at the
end of the run are determined by the parameters of the fix deform
command. Every Nth timestep during the run, the simulation box is
expanded, contracted, or tilted to ramped values between the initial
and final values. The "run"_run.html command documents how to make
the ramping take place across multiple runs.
:line
For the {x}, {y}, and {z} parameters, this is the meaning of their
styles and values.
The {final}, {delta}, {scale}, and {vel} styles all change the
specified dimension of the box via "constant displacement" which is
effectively a "constant engineering strain rate". This means the box
dimension changes linearly with time from its initial to final value.
For style {final}, the final lo and hi box boundaries of a dimension
are specified. The values can be in lattice or box distance units.
See the discsussion of the units keyword below.
For style {delta}, plus or minus changes in the lo/hi box boundaries
of a dimension are specified. The values can be in lattice or box
distance units. See the discsussion of the units keyword below.
For style {scale}, a multiplicative factor to apply to the box length
of a dimension is specified. For example, if the initial box length
is 10, and the factor is 1.1, then the final box length will be 11. A
factor less than 1.0 means compression.
For style {vel}, a velocity at which the box length changes is
specified in units of distance/time. This is effectively an
"engineering strain rate", where rate = V/L0 and L0 is the initial box
length. The distance can be in lattice or box distance units. See
the discussion of the units keyword below. For example, if the
initial box length is 100 Angstroms, and V is 10 Angstroms/psec,
then after 10 psec, the box length will have doubled. After 20 psec,
it will have tripled.
The {rate} style changes a dimension of the box at a "true constant
strain rate". Note that this is not an "engineering strain rate", as
the other styles are. Rather, for a "true" rate, the rate of change
is constant, which means the box dimension changes non-linearly with
time from its initial to final value. The units of the specified
strain rate are 1/time. See the "units"_units.html command for the
time units associated with different choices of simulation units,
e.g. picoseconds for "metal" units). Thus if the {rate} R is 0.01 and
time units are picoseconds, this means the box length will increase by
1% every picosecond. R = 1 or 2 means the box length will double or
triple every picosecond. R = -0.1 means the box length will shrink by
10% every picosecond. Note that for a "true" rate the change is
continuous, so running with R = 1 for 10 picoseconds does not expand
the box length by a factor of 10, but by a factor of 1024 since it
doubles every picosecond.
Note that to change the volume (or cross-sectional area) of the
simulation box at a constant rate, you can change multiple dimensions
via {rate}. E.g. to double the box volume every picosecond, you could
set "x rate M", "y rate M", "z rate M", with M = pow(2,1/3) - 1 =
1.26, since if each box dimension grows by 26%, the box volume
doubles.
The {volume} style changes the specified dimension in such a way that
the box volume remains constant while other box dimensions are changed
explicitly via the styles discussed above. For example, "x scale 1.1
y scale 1.1 z volume" will shrink the z box length as the x,y box
lengths increase, to keep the volume constant (product of x,y,z
lengths). If "x scale 1.1 z volume" is specified and parameter {y} is
unspecified, then the z box length will shrink as x increases to keep
the product of x,z lengths constant. If "x scale 1.1 y volume z
volume" is specified, then both the y,z box lengths will shrink as x
increases to keep the volume constant (product of x,y,z lengths). In
this case, the y,z box lengths shrink so as to keep their relative
aspect ratio constant.
For solids or liquids, note that when one dimension of the box is
expanded via fix deform (i.e. tensile strain), it may be physically
undesirable to hold the other 2 box lengths constant (unspecified by
fix deform) since that implies a density change. Using the {volume}
style for those 2 dimensions to keep the box volume constant may make
more physical sense, but may also not be correct for materials and
potentials whose Poisson ratio is not 0.5. An alternative is to use
"fix npt aniso"_fix_npt.html with zero applied pressure on those 2
dimensions, so that they respond to the tensile strain dynamically.
For the {scale}, {vel}, {rate}, and {volume} styles, the box length is
expanded or compressed around its mid point.
:line
For the {xy}, {xz}, and {yz} parameters, this is the meaning of their
styles and values. Note that changing the tilt factors of a triclinic
box does not change its volume.
For style {final}, the final tilt factor is specified. The value
can be in lattice or box distance units. See the discussion of the
units keyword below.
For style {delta}, a plus or minus change in the tilt factor is
specified. The value can be in lattice or box distance units. See
the discsussion of the units keyword below.
For style {vel}, a velocity at which the tilt factor changes is
specified in units of distance/time. This is effectively an
"engineering shear strain rate", where rate = V/L0 and L0 is the
initial box length perpendicular to the direction of shear. The
distance can be in lattice or box distance units. See the discsussion
of the units keyword below. For example, if the initial tilt factor
is 5 Angstroms, and the V is 10 Angstroms/psec, then after 1 psec, the
tilt factor will be 15 Angstroms. After 2 psec, it will be 25
Angstroms.
The {rate} style changes a tilt factor at a "true constant shear
strain rate". Note that this is not an "engineering shear strain
rate", as the other styles are. Rather, for a "true" rate, the rate
of change is constant, which means the tilt factor changes
non-linearly with time from its initial to final value. The units of
shear strain rate are 1/time. See the "units"_units.html command for
the time units associated with different choices of simulation units,
e.g. picoseconds for "metal" units). Thus if the {rate} R is 0.01 and
time units are picoseconds, this means the tilt factor will increase
by 1% every picosecond. R = 1 or 2 means the tilt factor will double
or triple every picosecond. R = -0.1 means the tilt factor will
shrink by 10% every picosecond. Note that the change is continuous,
so running with R = 1 for 10 picoseconds does not change the tilt
factor by a factor of 10, but by a factor of 1024 since it doubles
every picosecond. Also note, that the initial tilt factor must be
non-zero to use the {rate} option.
Note that shear strain is defined as the tilt factor divided by the
perpendicular box length. The {rate} style controls the tilt factor,
but assumes the perpendicular box length remains constant. If this is
not the case (e.g. it changes due to another fix deform parameter),
then this effect on the shear strain is ignored.
All of these styles change the xy, xz, yz tilt factors during a
simulation. In LAMMPS, tilt factors (xy,xz,yz) for triclinic boxes
are always bounded by half the distance of the parallel box length.
For example, if xlo = 2 and xhi = 12, then the x box length is 10 and
the xy tilt factor must be between -5 and 5. Similarly, both xz and
yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2. Note that this is
not a limitation, since if the maximum tilt factor is 5 (as in this
example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
... are all equivalent.
To obey this constraint and allow for large shear deformations to be
applied via the {xy}, {xz}, or {yz} parameters, the folloiwng
algorithm is used. If {prd} is the associated parallel box length (10
in the example above), then if the tilt factor exceeds the accepted
range of -5 to 5 during the simulation, then the box is re-shaped to
the other limit (an equivalent box) and the simulation continues.
Thus for this example, if the initial xy tilt factor was 0.0 and "xy
final 100.0" was specified, then during the simulation the xy tilt
factor would increase from 0.0 to 5.0, the box would be re-shaped so
that the tilt factor becomes -5.0, the tilt factor would increase from
-5.0 to 5.0, the box would be re-shaped again, etc. The re-shaping
would occur 10 times and the final tilt factor at the end of the
simulation would be 0.0. During each re-shaping event, atoms are
remapped into the new box in the appropriate manner.
:line
Each time the box size or shape is changed, the {remap} keyword
determines whether atom positions are re-mapped to the new box. If
{remap} is set to {x} (the default), atoms in the fix group are
re-mapped; otherwise they are not. If {remap} is set to {v}, then any
atom in the fix group that crosses a periodic boundary will have a
delta added to its velocity equal to the difference in velocities
between the lo and hi boundaries. Note that this velocity difference
can include tilt components, e.g. a delta in the x velocity when an
atom crosses the y periodic boundary. If {remap} is set to {none},
then neither of these remappings take place.
IMPORTANT NOTE: When non-equilibrium MD (NEMD) simulations are
performed using this fix, the option "remap v" should normally be
used. This is because "fix nvt/sllod"_fix_nvt_sllod.html adjusts the
atom positions and velocities to provide a velocity profile that
matches the changing box size/shape. Thus atom coordinates should NOT
be remapped by fix deform, but velocities SHOULD be when atoms cross
periodic boundaries, since when atoms cross periodic boundaries since
that is consistent with maintaining the velocity profile created by
fix nvt/sllod. LAMMPS will warn you if this settings is not
consistent.
The {units} keyword determines the meaning of the distance units used
to define various arguments. A {box} value selects standard distance
units as defined by the "units"_units.html command, e.g. Angstroms for
units = real or metal. A {lattice} value means the distance units are
in lattice spacings. The "lattice"_lattice.html command must have
been previously used to define the lattice spacing. Note that the
units choice also affects the {vel} style parameters since it is
defined in terms of distance/time.
:line
[Restrictions:]
Any box dimension varied by this fix must be periodic.
[Related commands:] none
[Default:]
The option defaults are remap = x and units = lattice.

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<HTML>
<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>
<HR>
<H3>fix npt/asphere command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID npt/asphere Tstart Tstop Tdamp p-style args keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>npt/asphere = style name of this fix command
<LI>Tstart,Tstop = desired temperature at start/end of run
<LI>Tdamp = temperature damping parameter (time units)
<LI>p-style = <I>xyz</I> or <I>xy</I> or <I>yz</I> or <I>xz</I> or <I>aniso</I>
<PRE> <I>xyz</I> args = Pstart Pstop Pdamp
Pstart,Pstop = desired pressure at start/end of run (pressure units)
Pdamp = pressure damping parameter (time units)
<I>xy</I> or <I>yz</I> or <I>xz</I> or <I>aniso</I> args = Px_start Px_stop Py_start Py_stop Pz_start Pz_stop Pdamp
Px_start,Px_stop,... = desired pressure in x,y,z at start/end of run (pressure units)
Pdamp = pressure damping parameter (time units)
</PRE>
<LI>zero or more keyword/value pairs may be appended to the args
<LI>keyword = <I>drag</I> or <I>dilate</I>
<PRE> <I>drag</I> value = drag factor added to barostat/thermostat (0.0 = no drag)
<I>dilate</I> value = <I>all</I> or <I>partial</I>
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all npt/asphere 300.0 300.0 100.0 xyz 0.0 0.0 1000.0
fix 2 all npt/asphere 300.0 300.0 100.0 xz 5.0 5.0 NULL NULL 5.0 5.0 1000.0
fix 2 all npt/asphere 300.0 300.0 100.0 xz 5.0 5.0 NULL NULL 5.0 5.0 1000.0 drag 0.2
fix 2 water npt/asphere 300.0 300.0 100.0 aniso 0.0 0.0 0.0 0.0 NULL NULL 1000.0 dilate partial
</PRE>
<P><B>Description:</B>
</P>
<P>Perform constant NPT integration to update positions, velocities,
and angular velocity each timestep for aspherical or ellipsoidal
particles in the group using a Nose/Hoover temperature
thermostat and Nose/Hoover pressure barostat. P is pressure; T is
temperature. This creates a system trajectory consistent with the
isothermal-isobaric ensemble.
</P>
<P>The desired temperature at each timestep is a ramped value during the
run from <I>Tstart</I> to <I>Tstop</I>. The <A HREF = "run.html">run</A> command documents
how to make the ramping take place across multiple runs. The <I>Tdamp</I>
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the <A HREF = "units.html">units</A> command).
</P>
<P>The particles in the fix group are the only ones whose velocities and
positions are updated by the velocity/position update portion of the
NPT integration.
</P>
<P>Regardless of what particles are in the fix group, a global pressure is
computed for all particles. Similarly, when the size of the simulation
box is changed, all particles are re-scaled to new positions, unless the
keyword <I>dilate</I> is specified with a value of <I>partial</I>, in which case
only the particles in the fix group are re-scaled. The latter can be
useful for leaving the coordinates of particles in a solid substrate
unchanged and controlling the pressure of a surrounding fluid.
</P>
<HR>
<P>The pressure can be controlled in one of several styles, as specified
by the <I>p-style</I> argument. In each case, the desired pressure at each
timestep is a ramped value during the run from the starting value to
the end value. The <A HREF = "run.html">run</A> command documents how to make the
ramping take place across multiple runs.
</P>
<P>Style <I>xyz</I> means couple all 3 dimensions together when pressure is
computed (isotropic pressure), and dilate/contract the 3 dimensions
together.
</P>
<P>Styles <I>xy</I> or <I>yz</I> or <I>xz</I> means that the 2 specified dimensions are
coupled together, both for pressure computation and for
dilation/contraction. The 3rd dimension dilates/contracts
independently, using its pressure component as the driving force.
</P>
<P>For style <I>aniso</I>, all 3 dimensions dilate/contract independently
using their individual pressure components as the 3 driving forces.
</P>
<P>For any of the styles except <I>xyz</I>, any of the independent pressure
components (e.g. z in <I>xy</I>, or any dimension in <I>aniso</I>) can have
their target pressures (both start and stop values) specified as NULL.
This means that no pressure control is applied to that dimension so
that the box dimension remains unchanged.
</P>
<P>In some cases (e.g. for solids) the pressure (volume) and/or
temperature of the system can oscillate undesirably when a Nose/Hoover
barostat and thermostat is applied. The optional <I>drag</I> keyword will
damp these oscillations, although it alters the Nose/Hoover equations.
A value of 0.0 (no drag) leaves the Nose/Hoover formalism unchanged.
A non-zero value adds a drag term; the larger the value specified, the
greater the damping effect. Performing a short run and monitoring the
pressure and temperature is the best way to determine if the drag term
is working. Typically a value between 0.2 to 2.0 is sufficient to
damp oscillations after a few periods.
</P>
<P>For all pressure styles, the simulation box stays rectangular in
shape. Parinello-Rahman boundary conditions (tilted box) are not
implemented in LAMMPS.
</P>
<P>For all styles, the <I>Pdamp</I> parameter operates like the <I>Tdamp</I>
parameter, determining the time scale on which pressure is relaxed.
For example, a value of 1000.0 means to relax the pressure in a
timespan of (roughly) 1000 time units (tau or fmsec or psec - see the
<A HREF = "units.html">units</A> command).
</P>
<HR>
<P>This fix computes a temperature and pressure each timestep. To do
this, the fix creates its own computes of style "temp/asphere" and
"pressure", as if these commands had been issued:
</P>
<PRE>compute fix-ID_temp group-ID temp/asphere
compute fix-ID_press group-ID pressure fix-ID_temp
</PRE>
<P>See the <A HREF = "compute_temp_asphere.html">compute temp/asphere</A> and <A HREF = "compute_pressure.html">compute
pressure</A> commands for details. Note that the
IDs of the new computes are the fix-ID with underscore + "temp" or
"press" appended and the group for the new computes is the same as the
fix group.
</P>
<P>Note that these are NOT the computes used by thermodynamic output (see
the <A HREF = "thermo_style.html">thermo_style</A> command) with ID = <I>thermo_temp</I>
and <I>thermo_press</I>. This means you can change the attributes of this
fix's temperature or pressure via the
<A HREF = "compute_modify.html">compute_modify</A> command or print this temperature
or pressure during thermodyanmic output via the <A HREF = "thermo_style.html">thermo_style
custom</A> command using the appropriate compute-ID.
It also means that changing attributes of <I>thermo_temp</I> or
<I>thermo_press</I> will have no effect on this fix. Alternatively, you
can directly assign a new compute (for calculating temeperature or
pressure) that you have defined to this fix via the
<A HREF = "fix_modify.html">fix_modify</A> command. If you do this, note that the
kinetic energy derived from T should be consistent with the virial
term computed using all particles. LAMMPS will warn you if you choose
to compute temperature on a subset of particles.
</P>
<P>This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the <A HREF = "fix_modify.html">fix_modify energy</A> option. The contribution can
also be printed by itself via the keyword <I>f_fix-ID</I> in the
<A HREF = "thermo_style.html">thermo_style custom</A> command.
</P>
<P><B>Restrictions:</B>
</P>
<P>Can only be used if LAMMPS was built with the "asphere" package.
</P>
<P>Any dimension being adjusted by this fix must be periodic. A
dimension whose target pressures are specified as NULL can be
non-periodic or periodic.
</P>
<P>The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_npt.html">fix npt</A>, <A HREF = "fix_nve_asphere.html">fix nve_asphere</A>,
<A HREF = "fix_modify.html">fix_modify</A>
</P>
<P><B>Default:</B>
</P>
<P>The keyword defaults are drag = 0.0 and dilate = all.
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
fix npt/asphere command :h3
[Syntax:]
fix ID group-ID npt/asphere Tstart Tstop Tdamp p-style args keyword value ... :pre
ID, group-ID are documented in "fix"_fix.html command :ulb,l
npt/asphere = style name of this fix command :l
Tstart,Tstop = desired temperature at start/end of run :l
Tdamp = temperature damping parameter (time units) :l
p-style = {xyz} or {xy} or {yz} or {xz} or {aniso} :l
{xyz} args = Pstart Pstop Pdamp
Pstart,Pstop = desired pressure at start/end of run (pressure units)
Pdamp = pressure damping parameter (time units)
{xy} or {yz} or {xz} or {aniso} args = Px_start Px_stop Py_start Py_stop Pz_start Pz_stop Pdamp
Px_start,Px_stop,... = desired pressure in x,y,z at start/end of run (pressure units)
Pdamp = pressure damping parameter (time units) :pre
zero or more keyword/value pairs may be appended to the args :l
keyword = {drag} or {dilate} :l
{drag} value = drag factor added to barostat/thermostat (0.0 = no drag)
{dilate} value = {all} or {partial} :pre
:ule
[Examples:]
fix 1 all npt/asphere 300.0 300.0 100.0 xyz 0.0 0.0 1000.0
fix 2 all npt/asphere 300.0 300.0 100.0 xz 5.0 5.0 NULL NULL 5.0 5.0 1000.0
fix 2 all npt/asphere 300.0 300.0 100.0 xz 5.0 5.0 NULL NULL 5.0 5.0 1000.0 drag 0.2
fix 2 water npt/asphere 300.0 300.0 100.0 aniso 0.0 0.0 0.0 0.0 NULL NULL 1000.0 dilate partial :pre
[Description:]
Perform constant NPT integration to update positions, velocities,
and angular velocity each timestep for aspherical or ellipsoidal
particles in the group using a Nose/Hoover temperature
thermostat and Nose/Hoover pressure barostat. P is pressure; T is
temperature. This creates a system trajectory consistent with the
isothermal-isobaric ensemble.
The desired temperature at each timestep is a ramped value during the
run from {Tstart} to {Tstop}. The "run"_run.html command documents
how to make the ramping take place across multiple runs. The {Tdamp}
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the "units"_units.html command).
The particles in the fix group are the only ones whose velocities and
positions are updated by the velocity/position update portion of the
NPT integration.
Regardless of what particles are in the fix group, a global pressure is
computed for all particles. Similarly, when the size of the simulation
box is changed, all particles are re-scaled to new positions, unless the
keyword {dilate} is specified with a value of {partial}, in which case
only the particles in the fix group are re-scaled. The latter can be
useful for leaving the coordinates of particles in a solid substrate
unchanged and controlling the pressure of a surrounding fluid.
:line
The pressure can be controlled in one of several styles, as specified
by the {p-style} argument. In each case, the desired pressure at each
timestep is a ramped value during the run from the starting value to
the end value. The "run"_run.html command documents how to make the
ramping take place across multiple runs.
Style {xyz} means couple all 3 dimensions together when pressure is
computed (isotropic pressure), and dilate/contract the 3 dimensions
together.
Styles {xy} or {yz} or {xz} means that the 2 specified dimensions are
coupled together, both for pressure computation and for
dilation/contraction. The 3rd dimension dilates/contracts
independently, using its pressure component as the driving force.
For style {aniso}, all 3 dimensions dilate/contract independently
using their individual pressure components as the 3 driving forces.
For any of the styles except {xyz}, any of the independent pressure
components (e.g. z in {xy}, or any dimension in {aniso}) can have
their target pressures (both start and stop values) specified as NULL.
This means that no pressure control is applied to that dimension so
that the box dimension remains unchanged.
In some cases (e.g. for solids) the pressure (volume) and/or
temperature of the system can oscillate undesirably when a Nose/Hoover
barostat and thermostat is applied. The optional {drag} keyword will
damp these oscillations, although it alters the Nose/Hoover equations.
A value of 0.0 (no drag) leaves the Nose/Hoover formalism unchanged.
A non-zero value adds a drag term; the larger the value specified, the
greater the damping effect. Performing a short run and monitoring the
pressure and temperature is the best way to determine if the drag term
is working. Typically a value between 0.2 to 2.0 is sufficient to
damp oscillations after a few periods.
For all pressure styles, the simulation box stays rectangular in
shape. Parinello-Rahman boundary conditions (tilted box) are not
implemented in LAMMPS.
For all styles, the {Pdamp} parameter operates like the {Tdamp}
parameter, determining the time scale on which pressure is relaxed.
For example, a value of 1000.0 means to relax the pressure in a
timespan of (roughly) 1000 time units (tau or fmsec or psec - see the
"units"_units.html command).
:line
This fix computes a temperature and pressure each timestep. To do
this, the fix creates its own computes of style "temp/asphere" and
"pressure", as if these commands had been issued:
compute fix-ID_temp group-ID temp/asphere
compute fix-ID_press group-ID pressure fix-ID_temp :pre
See the "compute temp/asphere"_compute_temp_asphere.html and "compute
pressure"_compute_pressure.html commands for details. Note that the
IDs of the new computes are the fix-ID with underscore + "temp" or
"press" appended and the group for the new computes is the same as the
fix group.
Note that these are NOT the computes used by thermodynamic output (see
the "thermo_style"_thermo_style.html command) with ID = {thermo_temp}
and {thermo_press}. This means you can change the attributes of this
fix's temperature or pressure via the
"compute_modify"_compute_modify.html command or print this temperature
or pressure during thermodyanmic output via the "thermo_style
custom"_thermo_style.html command using the appropriate compute-ID.
It also means that changing attributes of {thermo_temp} or
{thermo_press} will have no effect on this fix. Alternatively, you
can directly assign a new compute (for calculating temeperature or
pressure) that you have defined to this fix via the
"fix_modify"_fix_modify.html command. If you do this, note that the
kinetic energy derived from T should be consistent with the virial
term computed using all particles. LAMMPS will warn you if you choose
to compute temperature on a subset of particles.
This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the "fix_modify energy"_fix_modify.html option. The contribution can
also be printed by itself via the keyword {f_fix-ID} in the
"thermo_style custom"_thermo_style.html command.
[Restrictions:]
Can only be used if LAMMPS was built with the "asphere" package.
Any dimension being adjusted by this fix must be periodic. A
dimension whose target pressures are specified as NULL can be
non-periodic or periodic.
The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
[Related commands:]
"fix npt"_fix_npt.html, "fix nve_asphere"_fix_nve_asphere.html,
"fix_modify"_fix_modify.html
[Default:]
The keyword defaults are drag = 0.0 and dilate = all.

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<HTML>
<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>
<HR>
<H3>fix nve/dipole command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID nve/dipole
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>nve/dipole = style name of this fix command
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all nve/dipole
</PRE>
<P><B>Description:</B>
</P>
<P>Perform constant NVE updates of position, velocity, orientation, and
angular velocity for particles with point dipole moments in the group
each timestep. V is volume; E is energy. This creates a system
trajectory consistent with the microcanonical ensemble.
</P>
<P><B>Restrictions:</B>
</P>
<P>Can only be used if LAMMPS was built with the "dipole" package.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_nve.html">fix nve</A>
</P>
<P><B>Default:</B> none
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
fix nve/dipole command :h3
[Syntax:]
fix ID group-ID nve/dipole :pre
ID, group-ID are documented in "fix"_fix.html command
nve/dipole = style name of this fix command :ul
[Examples:]
fix 1 all nve/dipole :pre
[Description:]
Perform constant NVE updates of position, velocity, orientation, and
angular velocity for particles with point dipole moments in the group
each timestep. V is volume; E is energy. This creates a system
trajectory consistent with the microcanonical ensemble.
[Restrictions:]
Can only be used if LAMMPS was built with the "dipole" package.
[Related commands:]
"fix nve"_fix_nve.html
[Default:] none

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<HTML>
<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>
<HR>
<H3>fix nvt/asphere command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID nvt/asphere Tstart Tstop Tdamp keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>nvt/asphere = style name of this fix command
<LI>Tstart,Tstop = desired temperature at start/end of run
<LI>Tdamp = temperature damping parameter (time units)
<LI>zero or more keyword/value pairs may be appended to the args
<LI>keyword = <I>drag</I>
<PRE> <I>drag</I> value = drag factor added to thermostat (0.0 = no drag)
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all nvt/asphere 300.0 300.0 100.0
fix 1 all nvt/asphere 300.0 300.0 100.0 drag 0.2
</PRE>
<P><B>Description:</B>
</P>
<P>Perform constant NVT integration to update positions, velocities,
and angular velocities each timestep for aspherical or ellipsoidal
particles in the group using a Nose/Hoover temperature thermostat.
V is volume; T is temperature. This creates a system trajectory
consistent with the canonical ensemble.
</P>
<P>The desired temperature at each timestep is a ramped value during the
run from <I>Tstart</I> to <I>Tstop</I>. The <A HREF = "run.html">run</A> command documents
how to make the ramping take place across multiple runs. The <I>Tdamp</I>
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the <A HREF = "units.html">units</A> command).
</P>
<P>In some cases (e.g. for solids) the temperature of the system can
oscillate undesirably when a Nose/Hoover thermostat is applied. The
optional <I>drag</I> keyword will damp these oscillations, although it
alters the Nose/Hoover equations. A value of 0.0 (no drag) leaves the
Nose/Hoover formalism unchanged. A non-zero value adds a drag term;
the larger the value specified, the greater the damping effect.
Performing a short run and monitoring the temperature is the best way
to determine if the drag term is working. Typically a value between
0.2 to 2.0 is sufficient to damp oscillations after a few periods.
</P>
<P>This fix computes a temperature each timestep. To do this, the fix
creates its own compute of style "temp/asphere", as if this command
had been issued:
</P>
<PRE>compute fix-ID_temp group-ID temp/asphere
</PRE>
<P>See the <A HREF = "compute_temp_asphere.html">compute temp/asphere</A> command for
details. Note that the ID of the new compute is the fix-ID with
underscore + "temp" appended and the group for the new compute is
the same as the fix group.
</P>
<P>Note that this is NOT the compute used by thermodynamic output (see
the <A HREF = "thermo_style.html">thermo_style</A> command) with ID = <I>thermo_temp</I>.
This means you can change the attributes of this fix's temperature
(e.g. its degrees-of-freedom) via the
<A HREF = "compute_modify.html">compute_modify</A> command or print this temperature
during thermodyanmic output via the <A HREF = "thermo_style.html">thermo_style
custom</A> command using the appropriate compute-ID.
It also means that changing attributes of <I>thermo_temp</I> will have no
effect on this fix. Alternatively, you can directly assign a new
compute (for calculating temeperature) that you have defined to this
fix via the <A HREF = "fix_modify.html">fix_modify</A> command.
</P>
<P>This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the <A HREF = "fix_modify.html">fix_modify energy</A> option. The contribution can
also be printed by itself via the keyword <I>f_fix-ID</I> in the
<A HREF = "thermo_style.html">thermo_style custom</A> command.
</P>
<P><B>Restrictions:</B>
</P>
<P>Can only be used if LAMMPS was built with the "asphere" package.
</P>
<P>The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_nvt.html">fix nvt</A>, <A HREF = "fix_nve_asphere.html">fix nve_asphere</A>, <A HREF = "fix_npt_asphere.html">fix
npt_asphere</A>, <A HREF = "fix_modify.html">fix_modify</A>
</P>
<P><B>Default:</B>
</P>
<P>The keyword defaults are drag = 0.0.
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
fix nvt/asphere command :h3
[Syntax:]
fix ID group-ID nvt/asphere Tstart Tstop Tdamp keyword value ... :pre
ID, group-ID are documented in "fix"_fix.html command :ulb,l
nvt/asphere = style name of this fix command :l
Tstart,Tstop = desired temperature at start/end of run :l
Tdamp = temperature damping parameter (time units) :l
zero or more keyword/value pairs may be appended to the args :l
keyword = {drag} :l
{drag} value = drag factor added to thermostat (0.0 = no drag) :pre
:ule
[Examples:]
fix 1 all nvt/asphere 300.0 300.0 100.0
fix 1 all nvt/asphere 300.0 300.0 100.0 drag 0.2 :pre
[Description:]
Perform constant NVT integration to update positions, velocities,
and angular velocities each timestep for aspherical or ellipsoidal
particles in the group using a Nose/Hoover temperature thermostat.
V is volume; T is temperature. This creates a system trajectory
consistent with the canonical ensemble.
The desired temperature at each timestep is a ramped value during the
run from {Tstart} to {Tstop}. The "run"_run.html command documents
how to make the ramping take place across multiple runs. The {Tdamp}
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the "units"_units.html command).
In some cases (e.g. for solids) the temperature of the system can
oscillate undesirably when a Nose/Hoover thermostat is applied. The
optional {drag} keyword will damp these oscillations, although it
alters the Nose/Hoover equations. A value of 0.0 (no drag) leaves the
Nose/Hoover formalism unchanged. A non-zero value adds a drag term;
the larger the value specified, the greater the damping effect.
Performing a short run and monitoring the temperature is the best way
to determine if the drag term is working. Typically a value between
0.2 to 2.0 is sufficient to damp oscillations after a few periods.
This fix computes a temperature each timestep. To do this, the fix
creates its own compute of style "temp/asphere", as if this command
had been issued:
compute fix-ID_temp group-ID temp/asphere :pre
See the "compute temp/asphere"_compute_temp_asphere.html command for
details. Note that the ID of the new compute is the fix-ID with
underscore + "temp" appended and the group for the new compute is
the same as the fix group.
Note that this is NOT the compute used by thermodynamic output (see
the "thermo_style"_thermo_style.html command) with ID = {thermo_temp}.
This means you can change the attributes of this fix's temperature
(e.g. its degrees-of-freedom) via the
"compute_modify"_compute_modify.html command or print this temperature
during thermodyanmic output via the "thermo_style
custom"_thermo_style.html command using the appropriate compute-ID.
It also means that changing attributes of {thermo_temp} will have no
effect on this fix. Alternatively, you can directly assign a new
compute (for calculating temeperature) that you have defined to this
fix via the "fix_modify"_fix_modify.html command.
This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the "fix_modify energy"_fix_modify.html option. The contribution can
also be printed by itself via the keyword {f_fix-ID} in the
"thermo_style custom"_thermo_style.html command.
[Restrictions:]
Can only be used if LAMMPS was built with the "asphere" package.
The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
[Related commands:]
"fix nvt"_fix_nvt.html, "fix nve_asphere"_fix_nve_asphere.html, "fix
npt_asphere"_fix_npt_asphere.html, "fix_modify"_fix_modify.html
[Default:]
The keyword defaults are drag = 0.0.

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<HTML>
<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>
<HR>
<H3>fix nvt/sllod command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>fix ID group-ID nvt/sllod Tstart Tstop Tdamp keyword value ...
</PRE>
<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
<LI>nvt/sllod = style name of this fix command
<LI>Tstart,Tstop = desired temperature at start/end of run
<LI>Tdamp = temperature damping parameter (time units)
<LI>zero or more keyword/value pairs may be appended to the args
<LI>keyword = <I>drag</I>
<PRE> <I>drag</I> value = drag factor added to thermostat (0.0 = no drag)
</PRE>
</UL>
<P><B>Examples:</B>
</P>
<PRE>fix 1 all nvt/sllod 300.0 300.0 100.0
fix 1 all nvt/sllod 300.0 300.0 100.0 drag 0.2
</PRE>
<P><B>Description:</B>
</P>
<P>Perform constant NVT integration to update positions and velocities
each timestep for atoms in the group using a Nose/Hoover temperature
thermostat. V is volume; T is temperature. This creates a system
trajectory consistent with the canonical ensemble.
</P>
<P>This thermostat is used for a simulation box that is changing size
and/or shape, for example in a non-equilibrium MD (NEMD) simulation.
The size/shape change is induced by use of the <A HREF = "fix_deform.html">fix
deform</A> command, so each point in the simulation box
can be thought of as having a "streaming" velocity. This
position-dependent streaming velocity is subtracted from each atom's
actual velocity to yield a thermal velocity which is used for
temperature computation and thermostatting. For example, if the box
is being sheared in x, relative to y, then points at the bottom of the
box (low y) have a small x velocity, while points at the top of the
box (hi y) have a large x velocity. These velocities do not
contribute to the thermal "temperature" of the atom.
</P>
<P>IMPORTANT NOTE: <A HREF = "fix_deform.html">Fix deform</A> has an option for
remapping either atom coordinates or velocities to the changing
simulation box. To use fix nvt/sllod, fix deform should NOT remap
atom positions, because fix nvt/sllod adjusts the atom positions and
velocities to create a velocity profile that matches the changing box
size/shape. Fix deform SHOUDLD remap atom velocities when atoms cross
periodic boundaries since that is consistent with maintaining the
velocity profile created by fix nvt/sllod. LAMMPS will warn you if
this setting is not consistent.
</P>
<P>The SLLOD equations of motion coupled to a Nose/Hoover thermostat are
discussed in <A HREF = "#Tuckerman">(Tuckerman)</A> (eqs 4 and 5), which is what is
implemented in LAMMPS in a velocity Verlet formulation.
</P>
<P>The desired temperature at each timestep is a ramped value during the
run from <I>Tstart</I> to <I>Tstop</I>. The <A HREF = "run.html">run</A> command documents
how to make the ramping take place across multiple runs. The <I>Tdamp</I>
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the <A HREF = "units.html">units</A> command).
</P>
<P>In some cases (e.g. for solids) the temperature of the system can
oscillate undesirably when a Nose/Hoover thermostat is applied. The
optional <I>drag</I> keyword will damp these oscillations, although it
alters the Nose/Hoover equations. A value of 0.0 (no drag) leaves the
Nose/Hoover formalism unchanged. A non-zero value adds a drag term;
the larger the value specified, the greater the damping effect.
Performing a short run and monitoring the temperature is the best way
to determine if the drag term is working. Typically a value between
0.2 to 2.0 is sufficient to damp oscillations after a few periods.
</P>
<P>This fix computes a temperature each timestep. To do this, the fix
creates its own compute of style "temp/deform", as if this command had
been issued:
</P>
<PRE>compute fix-ID_temp group-ID temp/deform
</PRE>
<P>See the <A HREF = "compute_temp_deform.html">compute temp/deform</A> command for
details. Note that the ID of the new compute is the fix-ID with
underscore + "temp" appended and the group for the new compute is the
same as the fix group.
</P>
<P>Note that this is NOT the compute used by thermodynamic output (see
the <A HREF = "thermo_style.html">thermo_style</A> command) with ID = <I>thermo_temp</I>.
This means you can change the attributes of this fix's temperature
(e.g. its degrees-of-freedom) via the
<A HREF = "compute_modify.html">compute_modify</A> command or print this temperature
during thermodyanmic output via the <A HREF = "thermo_style.html">thermo_style
custom</A> command using the appropriate compute-ID.
It also means that changing attributes of <I>thermo_temp</I> will have no
effect on this fix. Alternatively, you can directly assign a new
compute (for calculating temeperature) that you have defined to this
fix via the <A HREF = "fix_modify.html">fix_modify</A> command.
</P>
<P>This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the <A HREF = "fix_modify.html">fix_modify energy</A> option. The contribution can
also be printed by itself via the keyword <I>f_fix-ID</I> in the
<A HREF = "thermo_style.html">thermo_style custom</A> command.
</P>
<P><B>Restrictions:</B>
</P>
<P>The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "fix_nve.html">fix nve</A>, <A HREF = "fix_npt.html">fix npt</A>, <A HREF = "fix_npt.html">fix
npt</A>, <A HREF = "fix_temp_rescale.html">fix temp/rescale</A>, <A HREF = "fix_langevin.html">fix
langevin</A>, <A HREF = "fix_modify.html">fix_modify</A>,
<A HREF = "temperature.html">temperature</A>
</P>
<P><B>Default:</B>
</P>
<P>The keyword defaults are drag = 0.0.
</P>
<HR>
<A NAME = "Tuckerman"></A>
<P><B>(Tuckerman)</B> Tuckerman, Mundy, Balasubramanian, Klein, J Chem Phys,
106, 5615 (1997).
</P>
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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
fix nvt/sllod command :h3
[Syntax:]
fix ID group-ID nvt/sllod Tstart Tstop Tdamp keyword value ... :pre
ID, group-ID are documented in "fix"_fix.html command :ulb,l
nvt/sllod = style name of this fix command :l
Tstart,Tstop = desired temperature at start/end of run :l
Tdamp = temperature damping parameter (time units) :l
zero or more keyword/value pairs may be appended to the args :l
keyword = {drag} :l
{drag} value = drag factor added to thermostat (0.0 = no drag) :pre
:ule
[Examples:]
fix 1 all nvt/sllod 300.0 300.0 100.0
fix 1 all nvt/sllod 300.0 300.0 100.0 drag 0.2 :pre
[Description:]
Perform constant NVT integration to update positions and velocities
each timestep for atoms in the group using a Nose/Hoover temperature
thermostat. V is volume; T is temperature. This creates a system
trajectory consistent with the canonical ensemble.
This thermostat is used for a simulation box that is changing size
and/or shape, for example in a non-equilibrium MD (NEMD) simulation.
The size/shape change is induced by use of the "fix
deform"_fix_deform.html command, so each point in the simulation box
can be thought of as having a "streaming" velocity. This
position-dependent streaming velocity is subtracted from each atom's
actual velocity to yield a thermal velocity which is used for
temperature computation and thermostatting. For example, if the box
is being sheared in x, relative to y, then points at the bottom of the
box (low y) have a small x velocity, while points at the top of the
box (hi y) have a large x velocity. These velocities do not
contribute to the thermal "temperature" of the atom.
IMPORTANT NOTE: "Fix deform"_fix_deform.html has an option for
remapping either atom coordinates or velocities to the changing
simulation box. To use fix nvt/sllod, fix deform should NOT remap
atom positions, because fix nvt/sllod adjusts the atom positions and
velocities to create a velocity profile that matches the changing box
size/shape. Fix deform SHOUDLD remap atom velocities when atoms cross
periodic boundaries since that is consistent with maintaining the
velocity profile created by fix nvt/sllod. LAMMPS will warn you if
this setting is not consistent.
The SLLOD equations of motion coupled to a Nose/Hoover thermostat are
discussed in "(Tuckerman)"_#Tuckerman (eqs 4 and 5), which is what is
implemented in LAMMPS in a velocity Verlet formulation.
The desired temperature at each timestep is a ramped value during the
run from {Tstart} to {Tstop}. The "run"_run.html command documents
how to make the ramping take place across multiple runs. The {Tdamp}
parameter is specified in time units and determines how rapidly the
temperature is relaxed. For example, a value of 100.0 means to relax
the temperature in a timespan of (roughly) 100 time units (tau or
fmsec or psec - see the "units"_units.html command).
In some cases (e.g. for solids) the temperature of the system can
oscillate undesirably when a Nose/Hoover thermostat is applied. The
optional {drag} keyword will damp these oscillations, although it
alters the Nose/Hoover equations. A value of 0.0 (no drag) leaves the
Nose/Hoover formalism unchanged. A non-zero value adds a drag term;
the larger the value specified, the greater the damping effect.
Performing a short run and monitoring the temperature is the best way
to determine if the drag term is working. Typically a value between
0.2 to 2.0 is sufficient to damp oscillations after a few periods.
This fix computes a temperature each timestep. To do this, the fix
creates its own compute of style "temp/deform", as if this command had
been issued:
compute fix-ID_temp group-ID temp/deform :pre
See the "compute temp/deform"_compute_temp_deform.html command for
details. Note that the ID of the new compute is the fix-ID with
underscore + "temp" appended and the group for the new compute is the
same as the fix group.
Note that this is NOT the compute used by thermodynamic output (see
the "thermo_style"_thermo_style.html command) with ID = {thermo_temp}.
This means you can change the attributes of this fix's temperature
(e.g. its degrees-of-freedom) via the
"compute_modify"_compute_modify.html command or print this temperature
during thermodyanmic output via the "thermo_style
custom"_thermo_style.html command using the appropriate compute-ID.
It also means that changing attributes of {thermo_temp} will have no
effect on this fix. Alternatively, you can directly assign a new
compute (for calculating temeperature) that you have defined to this
fix via the "fix_modify"_fix_modify.html command.
This fix makes a contribution to the potential energy of the system
that can be included in thermodynamic output of potential energy using
the "fix_modify energy"_fix_modify.html option. The contribution can
also be printed by itself via the keyword {f_fix-ID} in the
"thermo_style custom"_thermo_style.html command.
[Restrictions:]
The final Tstop cannot be 0.0 since it would make the target T = 0.0
at some timestep during the simulation which is not allowed in
the Nose/Hoover formulation.
[Related commands:]
"fix nve"_fix_nve.html, "fix npt"_fix_npt.html, "fix
npt"_fix_npt.html, "fix temp/rescale"_fix_temp_rescale.html, "fix
langevin"_fix_langevin.html, "fix_modify"_fix_modify.html,
"temperature"_temperature.html
[Default:]
The keyword defaults are drag = 0.0.
:line
:link(Tuckerman)
[(Tuckerman)] Tuckerman, Mundy, Balasubramanian, Klein, J Chem Phys,
106, 5615 (1997).

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<HTML>
<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>
<HR>
<H3>pair_style colloid command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style colloid cutoff
</PRE>
<UL><LI>cutoff = global cutoff for colloidal interactions (distance units)
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style colloid 10.0
pair_coeff * * 25 1.0 10.0 10.0
pair_coeff 1 1 144 1.0 0.0 0.0 3.0
pair_coeff 1 2 75.398 1.0 0.0 10.0 9.0
pair_coeff 2 2 39.478 1.0 10.0 10.0 25.0
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>colloid</I> computes pairwise interactions between large colloidal
particles and small solvent particles using 3 formulas. A colloidal
particle has a size > sigma; a solvent particle is the usual
Lennard-Jones particle of size sigma.
</P>
<P>The colloid-colloid interaction energy is given by
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_cc.jpg">
</CENTER>
<P>A is the Hamaker constant, a1 and a2 are the radii of the two
colloidal particles, and Rc is the cutoff. This equation results from
describing each colloidal particle as an integrated collection of
Lennard-Jones particles of size sigma and is derived in
<A HREF = "#Everaers">(Everaers)</A>.
</P>
<P>The colloid-solvent interaction energy is given by
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_cs.jpg">
</CENTER>
<P>A is the Hamaker constant, a is the radius of the colloidal particle,
and Rc is the cutoff. This formula is derived from the
colloid-colloid interaction, letting one of the particle sizes go to
zero.
</P>
<P>The solvent-solvent interaction energy is given by the usual
Lennard-Jones formula
</P>
<CENTER><IMG SRC = "Eqs/pair_colloid_ss.jpg">
</CENTER>
<P>which results from letting both particle sizes go to zero.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>A (energy units)
<LI>sigma (distance units)
<LI>d1 (distance units)
<LI>d2 (distance units)
<LI>cutoff (distance units)
</UL>
<P>A is the energy prefactor and should typically be set as follows:
</P>
<UL><LI>A_cc = colloid/colloid = 4 pi^2 = 39.5
<LI>A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
<LI>A_cs = colloid/solvent = sqrt(A_cc*A_ss)
</UL>
<P>Sigma is the size of the solvent particle or the constituent particles
integrated over in the colloidal particle and should typically be set
as follows:
</P>
<UL><LI>Sigma_cc = colloid/colloid = 1.0
<LI>Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
<LI>Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma
</UL>
<P>Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
1.0.
</P>
<P>D1 and d2 are particle diameters, so that d1 = 2*a1 and d2 = 2*a2 in
the formulas above. Both d1 and d2 must be values >= 0. If d1 > 0
and d2 > 0, then the pair interacts via the colloid-colloid formula
above. If d1 = 0 and d2 = 0, then the pair interacts via the
solvent-solvent formula. I.e. a d value of 0 is a Lennard-Jones
particle of size sigma. If either d1 = 0 or d2 = 0 and the other is
larger, then the pair interacts via the colloid-solvent formula.
</P>
<P>Note that the diameter of a particular particle type may appear in
multiple pair_coeff commands, as it interacts with other particle
types. You should insure the particle diameter is specified
consistently each time it appears.
</P>
<P>The last coefficient is optional. If not specified, the global cutoff
specified in the pair_style command is used. However, you typically
want different cutoffs for interactions between different particle
sizes. E.g. if colloidal particles of diameter 10 are used with
solvent particles of diameter 1, then a solvent-solvent cutoff of 2.5
would correspond to a colloid-colloid cutoff of 25. A good
rule-of-thumb is to use a colloid-solvent cutoff that is half the big
diamter + 4 times the small diamter. I.e. 9 = 5 + 4 for the
colloid-solvent cutoff in this case.
</P>
<P>If a pair_coeff command is not specified for I != J, then the
coefficients are mixed according the mixing rules defined by the
<A HREF = "pair_modify.html">pair_modify</A> command. The prefactor A is mixed like
the Lennard-Jones epsilon; sigma,d1,d2 are all mixed like the
Lennard-Jones sigma.
</P>
<P><B>Restrictions:</B>
</P>
<P>The <I>colloid</I> style is part of the "colloid" package. It is only
enabled if LAMMPS was built with that package. See the <A HREF = "Section_start.html#2_3">Making
LAMMPS</A> section for more info.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Everaers"></A>
<P><B>(Everaers)</B> Everaers, Ejtehadi, Phys Rev E, 67, 041710 (2003).
</P>
</HTML>

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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
pair_style colloid command :h3
[Syntax:]
pair_style colloid cutoff :pre
cutoff = global cutoff for colloidal interactions (distance units) :ul
[Examples:]
pair_style colloid 10.0
pair_coeff * * 25 1.0 10.0 10.0
pair_coeff 1 1 144 1.0 0.0 0.0 3.0
pair_coeff 1 2 75.398 1.0 0.0 10.0 9.0
pair_coeff 2 2 39.478 1.0 10.0 10.0 25.0 :pre
[Description:]
Style {colloid} computes pairwise interactions between large colloidal
particles and small solvent particles using 3 formulas. A colloidal
particle has a size > sigma; a solvent particle is the usual
Lennard-Jones particle of size sigma.
The colloid-colloid interaction energy is given by
:c,image(Eqs/pair_colloid_cc.jpg)
A is the Hamaker constant, a1 and a2 are the radii of the two
colloidal particles, and Rc is the cutoff. This equation results from
describing each colloidal particle as an integrated collection of
Lennard-Jones particles of size sigma and is derived in
"(Everaers)"_#Everaers.
The colloid-solvent interaction energy is given by
:c,image(Eqs/pair_colloid_cs.jpg)
A is the Hamaker constant, a is the radius of the colloidal particle,
and Rc is the cutoff. This formula is derived from the
colloid-colloid interaction, letting one of the particle sizes go to
zero.
The solvent-solvent interaction energy is given by the usual
Lennard-Jones formula
:c,image(Eqs/pair_colloid_ss.jpg)
which results from letting both particle sizes go to zero.
The following coefficients must be defined for each pair of atoms
types via the "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands:
A (energy units)
sigma (distance units)
d1 (distance units)
d2 (distance units)
cutoff (distance units) :ul
A is the energy prefactor and should typically be set as follows:
A_cc = colloid/colloid = 4 pi^2 = 39.5
A_ss = solvent/solvent = 144 (assuming epsilon = 1, so that 144/36 = 4)
A_cs = colloid/solvent = sqrt(A_cc*A_ss) :ul
Sigma is the size of the solvent particle or the constituent particles
integrated over in the colloidal particle and should typically be set
as follows:
Sigma_cc = colloid/colloid = 1.0
Sigma_ss = solvent/solvent = 1.0 or whatever size the solvent particle is
Sigma_cs = colloid/solvent = arithmetic mixing between colloid sigma and solvent sigma :ul
Thus typically Sigma_cs = 1.0, unless the solvent particle's size !=
1.0.
D1 and d2 are particle diameters, so that d1 = 2*a1 and d2 = 2*a2 in
the formulas above. Both d1 and d2 must be values >= 0. If d1 > 0
and d2 > 0, then the pair interacts via the colloid-colloid formula
above. If d1 = 0 and d2 = 0, then the pair interacts via the
solvent-solvent formula. I.e. a d value of 0 is a Lennard-Jones
particle of size sigma. If either d1 = 0 or d2 = 0 and the other is
larger, then the pair interacts via the colloid-solvent formula.
Note that the diameter of a particular particle type may appear in
multiple pair_coeff commands, as it interacts with other particle
types. You should insure the particle diameter is specified
consistently each time it appears.
The last coefficient is optional. If not specified, the global cutoff
specified in the pair_style command is used. However, you typically
want different cutoffs for interactions between different particle
sizes. E.g. if colloidal particles of diameter 10 are used with
solvent particles of diameter 1, then a solvent-solvent cutoff of 2.5
would correspond to a colloid-colloid cutoff of 25. A good
rule-of-thumb is to use a colloid-solvent cutoff that is half the big
diamter + 4 times the small diamter. I.e. 9 = 5 + 4 for the
colloid-solvent cutoff in this case.
If a pair_coeff command is not specified for I != J, then the
coefficients are mixed according the mixing rules defined by the
"pair_modify"_pair_modify.html command. The prefactor A is mixed like
the Lennard-Jones epsilon; sigma,d1,d2 are all mixed like the
Lennard-Jones sigma.
[Restrictions:]
The {colloid} style is part of the "colloid" package. It is only
enabled if LAMMPS was built with that package. See the "Making
LAMMPS"_Section_start.html#2_3 section for more info.
[Related commands:]
"pair_coeff"_pair_coeff.html
[Default:] none
:line
:link(Everaers)
[(Everaers)] Everaers, Ejtehadi, Phys Rev E, 67, 041710 (2003).

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<HTML>
<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>
<HR>
<H3>pair_style dipole/cut command
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style dipole/cut cutoff (cutoff2)
</PRE>
<UL><LI>cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
<LI>cutoff2 = global cutoff for Coulombic (optional) (distance units)
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style dipole/cut 10.0
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>dipole/cut</I> computes interactions bewteen pairs of particles
that each have a charge and/or a point dipole moment. In addition to
the usual Lennard-Jones interaction between the particles (Elj) the
charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole (Epp)
interactions are computed by these formulas for the energy (E), force
(F), and torque (T) between particles I and J.
</P>
<CENTER><IMG SRC = "Eqs/pair_dipole.jpg">
</CENTER>
<P>where qi and qj are the charges on the two particles, pi and pj are
the dipole moment vectors of the two particles, r is their separation
distance, and the vector r = Ri - Rj is the separation vector between
the two particles. Note that Eqq and Fqq are simply Coulombic energy
and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. These formulas are discussed in
<A HREF = "#Allen">(Allen)</A> and in <A HREF = "#Toukmaji">(Toukmaji)</A>.
</P>
<P>If one cutoff is specified in the pair_style command, it is used for
both the LJ and Coulombic (q,p) terms. If two cutoffs are specified,
they are used as cutoffs for the LJ and Coulombic (q,p) terms
respectively.
</P>
<P>Use of this pair style requires the use of the <A HREF = "fix_nve_dipole.html">fix
nve/dipole</A> command to integrate rotation of the
dipole moments. Additionally, <A HREF = "atom_style.html">atom_style dipole</A>
should be used since it defines the point dipoles and their rotational
state. The magnitude of the dipole moment for each type of particle
can be defined by the <A HREF = "dipole.html">dipole</A> command or in the "Dipoles"
section of the data file read in by the <A HREF = "read_data.html">read_data</A>
command. Their initial orientation can be defined by the <A HREF = "set.html">set
dipole</A> command or in the "Atoms" section of the data file.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>epsilon (energy units)
<LI>sigma (distance units)
<LI>cutoff1 (distance units)
<LI>cutoff2 (distance units)
</UL>
<P>The latter 2 coefficients are optional. If not specified, the global
LJ and Coulombic cutoffs specified in the pair_style command are used.
If only one cutoff is specified, it is used as the cutoff for both LJ
and Coulombic interactions for this type pair. If both coefficients
are specified, they are used as the LJ and Coulombic cutoffs for this
type pair.
</P>
<P><B>Restrictions:</B>
</P>
<P>Can only be used if LAMMPS was built with the "dipole" package.
</P>
<P>The use of this potential requires additional fixes as described
above.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "fix_nve_dipole.html">fix nve/dipole</A>,
<A HREF = "compute_temp_dipole.html">compute temp/dipole</A>
</P>
<P><B>Default:</B> none
</P>
<HR>
<A NAME = "Allen"></A>
<P><B>(Allen)</B> Allen and Tildesley, Computer Simulation of Liquids,
Clarendon Press, Oxford, 1987.
</P>
<A NAME = "Toukmaji"></A>
<P><B>(Toukmaji)</B> Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
10913 (2000).
</P>
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"LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc :c
:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)
:line
pair_style dipole/cut command :h3
[Syntax:]
pair_style dipole/cut cutoff (cutoff2) :pre
cutoff = global cutoff LJ (and Coulombic if only 1 arg) (distance units)
cutoff2 = global cutoff for Coulombic (optional) (distance units) :ul
[Examples:]
pair_style dipole/cut 10.0
pair_coeff * * 1.0 1.0
pair_coeff 2 3 1.0 1.0 2.5 4.0 :pre
[Description:]
Style {dipole/cut} computes interactions bewteen pairs of particles
that each have a charge and/or a point dipole moment. In addition to
the usual Lennard-Jones interaction between the particles (Elj) the
charge-charge (Eqq), charge-dipole (Eqp), and dipole-dipole (Epp)
interactions are computed by these formulas for the energy (E), force
(F), and torque (T) between particles I and J.
:c,image(Eqs/pair_dipole.jpg)
where qi and qj are the charges on the two particles, pi and pj are
the dipole moment vectors of the two particles, r is their separation
distance, and the vector r = Ri - Rj is the separation vector between
the two particles. Note that Eqq and Fqq are simply Coulombic energy
and force, Fij = -Fji as symmetric forces, and Tij != -Tji since the
torques do not act symmetrically. These formulas are discussed in
"(Allen)"_#Allen and in "(Toukmaji)"_#Toukmaji.
If one cutoff is specified in the pair_style command, it is used for
both the LJ and Coulombic (q,p) terms. If two cutoffs are specified,
they are used as cutoffs for the LJ and Coulombic (q,p) terms
respectively.
Use of this pair style requires the use of the "fix
nve/dipole"_fix_nve_dipole.html command to integrate rotation of the
dipole moments. Additionally, "atom_style dipole"_atom_style.html
should be used since it defines the point dipoles and their rotational
state. The magnitude of the dipole moment for each type of particle
can be defined by the "dipole"_dipole.html command or in the "Dipoles"
section of the data file read in by the "read_data"_read_data.html
command. Their initial orientation can be defined by the "set
dipole"_set.html command or in the "Atoms" section of the data file.
The following coefficients must be defined for each pair of atoms
types via the "pair_coeff"_pair_coeff.html command as in the examples
above, or in the data file or restart files read by the
"read_data"_read_data.html or "read_restart"_read_restart.html
commands:
epsilon (energy units)
sigma (distance units)
cutoff1 (distance units)
cutoff2 (distance units) :ul
The latter 2 coefficients are optional. If not specified, the global
LJ and Coulombic cutoffs specified in the pair_style command are used.
If only one cutoff is specified, it is used as the cutoff for both LJ
and Coulombic interactions for this type pair. If both coefficients
are specified, they are used as the LJ and Coulombic cutoffs for this
type pair.
[Restrictions:]
Can only be used if LAMMPS was built with the "dipole" package.
The use of this potential requires additional fixes as described
above.
[Related commands:]
"pair_coeff"_pair_coeff.html, "fix nve/dipole"_fix_nve_dipole.html,
"compute temp/dipole"_compute_temp_dipole.html
[Default:] none
:line
:link(Allen)
[(Allen)] Allen and Tildesley, Computer Simulation of Liquids,
Clarendon Press, Oxford, 1987.
:link(Toukmaji)
[(Toukmaji)] Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113,
10913 (2000).