From 907bcd16a84c17d40a30e85915611eab2beb1d7a Mon Sep 17 00:00:00 2001 From: Aidan Thompson Date: Fri, 22 Apr 2022 14:21:57 -0600 Subject: [PATCH] Update compute_temp_profile.rst --- doc/src/compute_temp_profile.rst | 32 +++++++++++++++++--------------- 1 file changed, 17 insertions(+), 15 deletions(-) diff --git a/doc/src/compute_temp_profile.rst b/doc/src/compute_temp_profile.rst index 3f045f2bda..7ccf403eb9 100644 --- a/doc/src/compute_temp_profile.rst +++ b/doc/src/compute_temp_profile.rst @@ -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) ` paper. The extra term defaults to (dim - stream) +velocity in each direction of the *Nx\*Ny\*Nz* bins, as discussed in the +:ref:`(Evans) ` 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 ` 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 ` doc page for a discussion of different ways to compute temperature and perform