<p>Define a computation that calculates the temperature of a group of
atoms, after subtracting out a spatially-averaged center-of-mass
velocity field, before computing the kinetic energy. This can be
useful for thermostatting a collection of atoms undergoing a complex
flow, e.g. via a profile-unbiased thermostat (PUT) as described in
<aclass="reference internal"href="fix_nvt_sllod.html#evans"><spanclass="std std-ref">(Evans)</span></a>. A compute of this style can be used by any command
that computes a temperature, e.g. <aclass="reference internal"href="thermo_modify.html"><spanclass="doc">thermo_modify</span></a>,
<p>The <em>xflag</em>, <em>yflag</em>, <em>zflag</em> settings determine which components of
average velocity are subtracted out.</p>
<p>The <em>binstyle</em> setting and its <em>Nx</em>, <em>Ny</em>, <em>Nz</em> arguments determine
how bins are setup to perform spatial averaging. “Bins” can be 1d
slabs, 2d pencils, or 3d bricks depending on which <em>binstyle</em> is used.
The simulation box is partitioned conceptually into <em>Nx</em> by <em>Ny</em> by
<em>Nz</em> bins. Depending on the <em>binstyle</em>, you may only specify one or
two of these values; the others are effectively set to 1 (no binning
in that dimension). For non-orthogonal (triclinic) simulation boxes,
the bins are “tilted” slabs or pencils or bricks that are parallel to
the tilted faces of the box. See the <aclass="reference internal"href="region.html"><spanclass="doc">region prism</span></a>
command for a discussion of the geometry of tilted boxes in LAMMPS.</p>
<p>When a temperature is computed, the center-of-mass velocity for the
set of atoms that are both in the compute group and in the same
spatial bin is calculated. This bias velocity is then subtracted from
the velocities of individual atoms in the bin to yield a thermal
velocity for each atom. Note that if there is only one atom in the
bin, its thermal velocity will thus be 0.0.</p>
<p>After the spatially-averaged velocity field has been subtracted from
each atom, the temperature is calculated by the formula KE = (dim/2 N
- dim*Nx*Ny*Nz) 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. The dim*Nx*Ny*Nz term are degrees of freedom
subtracted to adjust for the removal of the center-of-mass velocity in
each of Nx*Ny*Nz bins, as discussed in the <aclass="reference internal"href="fix_nvt_sllod.html#evans"><spanclass="std std-ref">(Evans)</span></a> paper.</p>
<p>If the <em>out</em> keyword is used with a <em>tensor</em> value, which is the
default, a kinetic energy tensor, stored as a 6-element vector, 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 6 components of the vector are ordered xx,
yy, zz, xy, xz, yz.</p>
<p>If the <em>out</em> keyword is used with a <em>bin</em> value, the count of atoms
and computed temperature for each bin are stored for output, as an
array of values, as described below. The temperature of each bin is
calculated as described above, where the bias velocity is subtracted
and only the remaining thermal velocity of atoms in the bin
contributes to the temperature. See the note below for how the
temperature is normalized by the degrees-of-freedom of atoms in the
bin.</p>
<p>The number of atoms contributing to the temperature is assumed to be
constant for the duration of the run; use the <em>dynamic</em> option of the
<aclass="reference internal"href="compute_modify.html"><spanclass="doc">compute_modify</span></a> command if this is not the case.</p>
<p>The removal of the spatially-averaged velocity field by this fix is
essentially computing the temperature after a “bias” has been removed
from the velocity of the atoms. If this compute is used with a fix
command that performs thermostatting then this bias will be subtracted
from each atom, thermostatting of the remaining thermal velocity will
be performed, and the bias will be added back in. Thermostatting
fixes that work in this way include <aclass="reference internal"href="fix_nh.html"><spanclass="doc">fix nvt</span></a>, <aclass="reference internal"href="fix_temp_rescale.html"><spanclass="doc">fix temp/rescale</span></a>, <aclass="reference internal"href="fix_temp_berendsen.html"><spanclass="doc">fix temp/berendsen</span></a>, and <aclass="reference internal"href="fix_langevin.html"><spanclass="doc">fix langevin</span></a>.</p>
<p>This compute subtracts out degrees-of-freedom due to fixes that
constrain molecular motion, such as <aclass="reference internal"href="fix_shake.html"><spanclass="doc">fix shake</span></a> and
<aclass="reference internal"href="fix_rigid.html"><spanclass="doc">fix rigid</span></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
<em>extra</em> option of the <aclass="reference internal"href="compute_modify.html"><spanclass="doc">compute_modify</span></a> command.</p>
<divclass="admonition note">
<pclass="first admonition-title">Note</p>
<pclass="last">When using the <em>out</em> keyword with a value of <em>bin</em>, the
calculated temperature for each bin does not include the
degrees-of-freedom adjustment described in the preceeding paragraph,
for fixes that constrain molecular motion. It does include the
adjustment due to the <em>extra</em> option, which is applied to each bin.</p>
</div>
<p>See <aclass="reference internal"href="Section_howto.html#howto-16"><spanclass="std std-ref">this howto section</span></a> of the manual for
a discussion of different ways to compute temperature and perform
thermostatting. Using this compute in conjunction with a
thermostatting fix, as explained there, will effectively implement a
profile-unbiased thermostat (PUT), as described in <aclass="reference internal"href="fix_nvt_sllod.html#evans"><spanclass="std std-ref">(Evans)</span></a>.</p>
<p><strong>Output info:</strong></p>
<p>This compute calculates a global scalar (the temperature). Depending
on the setting of the <em>out</em> keyword, it also calculates a global
vector or array. For <em>out</em> = <em>tensor</em>, it calculates a vector of
length 6 (KE tensor), which can be accessed by indices 1-6. For <em>out</em>
= <em>bin</em> it calculates a global array which has 2 columns and N rows,
where N is the number of bins. The first column contains the number
of atoms in that bin. The second contains the temperature of that
bin, calculated as described above. The ordering of rows in the array
is as follows. Bins in x vary fastest, then y, then z. Thus for a
10x10x10 3d array of bins, there will be 1000 rows. The bin with
indices ix,iy,iz = 2,3,4 would map to row M = (iz-1)*10*10 + (iy-1)*10
+ ix = 322, where the rows are numbered from 1 to 1000 and the bin
indices are numbered from 1 to 10 in each dimension.</p>
<p>These values can be used by any command that uses global scalar or
vector or array values from a compute as input. See <aclass="reference internal"href="Section_howto.html#howto-15"><spanclass="std std-ref">this section</span></a> for an overview of LAMMPS output
options.</p>
<p>The scalar value calculated by this compute is “intensive”. The
vector values are “extensive”. The array values are “intensive”.</p>
<p>The scalar value will be in temperature <aclass="reference internal"href="units.html"><spanclass="doc">units</span></a>. The
vector values will be in energy <aclass="reference internal"href="units.html"><spanclass="doc">units</span></a>. The first column
of array values are counts; the values in the second column will be in
temperature <aclass="reference internal"href="units.html"><spanclass="doc">units</span></a>.</p>
</div>
<divclass="section"id="restrictions">
<h2>Restrictions</h2>
<p>You should not use too large a velocity-binning grid, especially in
3d. In the current implementation, the binned velocity averages are
summed across all processors, so this will be inefficient if the grid
is too large, and the operation is performed every timestep, as it
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