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Update compute_temp_profile.rst

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Aidan Thompson
2022-04-22 14:21:57 -06:00
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parent a3e204a99d
commit 907bcd16a8
1 changed files with 17 additions and 15 deletions
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doc/src/compute_temp_profile.rst
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@ -77,17 +77,17 @@ bin, its thermal velocity will thus be 0.0.
After the spatially-averaged velocity field has been subtracted from
each atom, the temperature is calculated by the formula
KE = (dim\*N - stream\*Nx\*Ny\*Nz - extra ) k T/2, 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, stream = 0, 1, 2 or 3 for
streaming velocity subtracted in 0, 1, 2 or 3 dimensions, extra = extra
degrees-of-freedom, N = number of atoms in the group, k = Boltzmann
constant, and T = temperature. The stream\*Nx\*Ny\*Nz term is degrees
*KE* = (*dim\*N* - *Ns\*Nx\*Ny\*Nz* - *extra* ) *k* *T*/2, 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, *Ns* = 0, 1, 2 or 3 for
streaming velocity subtracted in 0, 1, 2 or 3 dimensions, *extra* = extra
degrees-of-freedom, *N* = number of atoms in the group, *k* = Boltzmann
constant, and *T* = temperature. The *Ns\*Nx\*Ny\*Nz* term is degrees
of freedom subtracted to adjust for the removal of the center-of-mass
velocity in each direction of the Nx\*Ny\*Nz bins, as discussed in the
:ref:`(Evans) <Evans1>` paper. The extra term defaults to (dim - stream)
velocity in each direction of the *Nx\*Ny\*Nz* bins, as discussed in the
:ref:`(Evans) <Evans1>` paper. The extra term defaults to (*dim* - *Ns*)
and accounts for overall conservation of center-of-mass velocity across
the group in directions where streaming velocity is not subtracted. This
the group in directions where streaming velocity is *not* subtracted. This
can be altered using the *extra* option of the
:doc:`compute_modify <compute_modify>` command.
@ -95,9 +95,9 @@ If the *out* keyword is used with a *tensor* 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.
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.*
If the *out* keyword is used with a *bin* value, the count of atoms
and computed temperature for each bin are stored for output, as an
@ -133,10 +133,12 @@ needed, the subtracted degrees-of-freedom can be altered using the
calculated temperature for each bin includes the degrees-of-freedom
adjustment described in the preceding paragraph for fixes that
constrain molecular motion, as well as the adjustment due to
the *extra* option (which defaults to dim - stream as described above),
the *extra* option (which defaults to *dim* - *Ns* as described above),
by fractionally applying them based on the fraction of atoms in each
bin, so that the degrees-of-freedom summed over all bins is consistent
with the degrees-of-freedom in the scalar temperature calculation.
bin. As a result, the bin degrees-of-freedom summed over all bins exactly
equals the degrees-of-freedom used in the scalar temperature calculation,
:math:`\Sigma N_{DOF_i} = N_{DOF}` and the corresponding relation for temperature
is also satisfied :math:`\Sigma N_{DOF_i} T_i = N_{DOF} T`
See the :doc:`Howto thermostat <Howto_thermostat>` doc page for a
discussion of different ways to compute temperature and perform