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# compute temp/profile command

## Syntax

    compute ID group-ID temp/profile xflag yflag zflag binstyle args

- ID, group-ID are documented in compute command

- temp/profile = style name of this compute command

- xflag,yflag,zflag = 0/1 for whether to exclude/include this dimension

- binstyle = x or y or z or xy or yz or xz or xyz

      x arg = Nx
      y arg = Ny
      z arg = Nz
      xy args = Nx Ny
      yz args = Ny Nz
      xz args = Nx Nz
      xyz args = Nx Ny Nz
        Nx, Ny, Nz = number of velocity bins in x, y, z dimensions

- zero or more keyword/value pairs may be appended

- keyword = out

      out value = tensor or bin

## Examples

    compute myTemp flow temp/profile 1 1 1 x 10
    compute myTemp flow temp/profile 1 1 1 x 10 out bin
    compute myTemp flow temp/profile 0 1 1 xyz 20 20 20

## Description

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 (Evans)). A compute of this style can be used by any command that computes a temperature (e.g. thermo_modify, fix temp/rescale, fix npt).

The xflag, yflag, zflag settings determine which components of average velocity are subtracted out.

The binstyle setting and its Nx, Ny, Nz arguments determine how bins are setup to perform spatial averaging. “Bins” can be 1d slabs, 2d pencils, or 3d bricks depending on which binstyle is used. The simulation box is partitioned conceptually into Nx \(\times\) Ny \(\times\) Nz bins. Depending on the binstyle, 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 region prism command for a discussion of the geometry of tilted boxes in LAMMPS.

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.

After the spatially-averaged velocity field has been subtracted from each atom, the temperature is calculated by the formula

\[\text{KE} = \left( \frac{\text{dim}}{N} - N_s N_x N_y N_z - \text{extra} \right) \frac{k_B T}{2},\]

where KE is the total kinetic energy of the group of atoms (sum of \(\frac12 m v^2\); dim = 2 or 3 is the dimensionality of the simulation; \(N_s =\) 0, 1, 2, or 3 for streaming velocity subtracted in 0, 1, 2, or 3 dimensions, respectively; extra is the number of extra degrees of freedom; N is the number of atoms in the group; \(k_B\) is the Boltzmann constant, and \(T\) is the absolute temperature. The \(N_s N_x N_y N_z\) term is the number of 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 (Evans) paper. The extra term defaults to \(\text{dim} - N_s\) and accounts for overall conservation of center-of-mass velocity across the group in directions where streaming velocity is not subtracted. This can be altered using the extra option of the compute_modify command.

If the out keyword is used with a tensor value, which is the default, then a symmetric tensor, stored as a six-element vector, is also calculated by this compute for use in the computation of a pressure tensor by the compute pressue command. The formula for the components of the tensor is the same as the above expression for \(E_\mathrm{kin}\), except that the 1/2 factor is NOT included and the \(v_i^2\) is replaced by \(v_{i,x} v_{i,y}\) for the \(xy\) component, and so on. Note that because it lacks the 1/2 factor, these tensor components are twice those of the traditional kinetic energy tensor. The six 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 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.

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 command if this is not the case.

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 fix nvt, fix temp/rescale, fix temp/berendsen, and fix langevin.

This compute subtracts out degrees-of-freedom due to fixes that constrain molecular motion, such as fix shake and fix rigid. 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 command.

Note

When using the out keyword with a value of bin, 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 - Ns as described above), by fractionally applying them based on the fraction of atoms in each 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, \(\Sigma N_{\text{DOF}_i} = N_\text{DOF}\) and the corresponding relation for temperature is also satisfied (\(\Sigma N_{\text{DOF}_i} T_i = N_\text{DOF} T\)). These relations will break down in cases for which the adjustment exceeds the actual number of degrees of freedom in a bin. This could happen if a bin is empty or in situations in which rigid molecules are non-uniformly distributed, in which case the reported temperature within a bin may not be accurate.

See the Howto thermostat page 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 (Evans).

## Output info

This compute calculates a global scalar (the temperature). Depending on the setting of the out keyword, it also calculates a global vector or array. For out = tensor, it calculates a vector of length 6 (symmetric tensor), which can be accessed by indices 1–6. For out = bin 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 \(10\times 10\times 10\) 3d array of bins, there will be 1000 rows. The bin with indices \((i_x,i_y,i_z) = (2,3,4)\) would map to row \(M = 10^2(i_z-1) + 10(i_y-1) + i_x = 322\), where the rows are numbered from 1 to 1000 and the bin indices are numbered from 1 to 10 in each dimension.

These values can be used by any command that uses global scalar or vector or array values from a compute as input. See the Howto output page for an overview of LAMMPS output options.

The scalar value calculated by this compute is “intensive”. The vector values are “extensive”. The array values are “intensive”.

The scalar value us in temperature units. The vector values are in energy units. The first column of array values are counts; the values in the second column will be in temperature units.

## Restrictions

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 will be for most thermostats.

## Related commands

compute temp, compute temp/ramp, compute temp/deform, compute pressure

## Default

The option default is out = tensor.

(Evans) Evans and Morriss, Phys Rev Lett, 56, 2172-2175 (1986).