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# fix ave/grid command¶

## Syntax¶

fix ID group-ID ave/grid Nevery Nrepeat Nfreq Nx Ny Nz value1 value2 ... keyword args ...

• ID, group-ID are documented in fix command

• ave/grid = style name of this fix command

• Nevery = use input values every this many timesteps

• Nrepeat = # of times to use input values for calculating averages

• Nfreq = calculate averages every this many timesteps

• Nx, Ny, Nz = grid size in each dimension

• one or more per-atom or per-grid input values can be listed

• per-atom value = vx, vy, vz, fx, fy, fz, density/mass, density/number, mass, temp, c_ID, c_ID[I], f_ID, f_ID[I], v_name

vx,vy,vz,fx,fy,fz,mass = atom attribute (velocity, force component, mass)
density/number, density/mass = number or mass density (per volume)
temp = temperature
c_ID = per-atom vector calculated by a compute with ID
c_ID[I] = Ith column of per-atom array calculated by a compute with ID, I can include wildcard (see below)
f_ID = per-atom vector calculated by a fix with ID
f_ID[I] = Ith column of per-atom array calculated by a fix with ID, I can include wildcard (see below)
v_name = per-atom vector calculated by an atom-style variable with name

• per-grid value = c_ID:gname:dname, c_ID:gname:dname[I], f_ID:gname:dname, f_ID:gname:dname[I]

gname = name of grid defined by compute or fix
dname = name of data field defined by compute or fix
c_ID = per-grid vector calculated by a compute with ID
c_ID[I] = Ith column of per-grid array calculated by a compute with ID, I can include wildcard (see below)
f_ID = per-grid vector calculated by a fix with ID
f_ID[I] = Ith column of per-grid array calculated by a fix with ID, I can include wildcard (see below)

• zero or more keyword/arg pairs may be appended

• keyword = discard or norm or ave or bias or adof or cdof

discard arg = yes or no
yes = discard an atom outside grid in a non-periodic dimension
no = remap an atom outside grid in a non-periodic dimension to first or last grid cell
norm arg = all or sample or none = how output on Nfreq steps is normalized
all = output is sum of atoms across all Nrepeat samples, divided by atom count
sample = output is sum of Nrepeat sample averages, divided by Nrepeat
none = output is sum of Nrepeat sample sums, divided by Nrepeat
ave args = one or running or window M
one = output new average value every Nfreq steps
running = output cumulative average of all previous Nfreq steps
window M = output average of M most recent Nfreq steps
bias arg = bias-ID
bias-ID = ID of a temperature compute that removes a velocity bias for temperature calculation
dof_per_atom = define this many degrees-of-freedom per atom for temperature calculation
cdof value = dof_per_grid_cell
dof_per_grid_cell = add this many degrees-of-freedom per grid_cell for temperature calculation

## Examples¶

fix 1 all ave/grid 10000 1 10000 10 10 10 fx fy fz c_myMSD[*]
fix 1 flow ave/grid 100 10 1000 20 20 30 f_TTM:grid:data


## Description¶

Overlay the 2d or 3d simulation box with a uniformly spaced 2d or 3d grid and use it to either (a) time-average per-atom quantities for the atoms in each grid cell, or to (b) time-average per-grid quantities produced by other computes or fixes. This fix operates in either “per-atom mode” (all input values are per-atom) or in “per-grid mode” (all input values are per-grid). You cannot use both per-atom and per-grid inputs in the same command.

The grid created by this command is distributed; each processor owns the grid points that are within its sub-domain. This is similar to the fix ave/chunk command when it uses chunks from the compute chunk/atom command which are 2d or 3d regular bins. However, the per-bin outputs in that case are global; each processor stores a copy of the entire set of bin data. Thus it more efficient to use the fix ave/grid command when the grid is large and a simulation is run on many processors.

For per-atom mode, only atoms in the specified group contribute to the summing and averaging calculations. For per-grid mode, the specified group is ignored.

The Nevery, Nrepeat, and Nfreq arguments specify on what timesteps the input values will be accessed and contribute to the average. The final averaged quantities are generated on timesteps that are a multiples of Nfreq. The average is over Nrepeat quantities, computed in the preceding portion of the simulation every Nevery timesteps. Nfreq must be a multiple of Nevery and Nevery must be non-zero even if Nrepeat is 1. Also, the timesteps contributing to the average value cannot overlap, i.e. Nrepeat*Nevery can not exceed Nfreq.

For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on timesteps 90,92,94,96,98,100 will be used to compute the final average on timestep 100. Similarly for timesteps 190,192,194,196,198,200 on timestep 200, etc. If Nrepeat=1 and Nfreq = 100, then no time averaging is done; values are simply generated on timesteps 100,200,etc.

In per-atom mode, each input value can also be averaged over the atoms in each grid cell. The way the averaging is done across the Nrepeat timesteps to produce output on the Nfreq timesteps, and across multiple Nfreq outputs, is determined by the norm and ave keyword settings, as discussed below.

The Nx, Ny, and Nz arguments specify the size of the grid that overlays the simulation box. For 2d simulations, Nz must be 1. The Nx, Ny, Nz values can be any positive integer. The grid can be very coarse compared to the particle count, or very fine. If one or more of the values = 1, then bins are 2d planes or 1d slices of the simulation domain. Note that if the total number of grid cells is small, it may be more efficient to use the doc:fix ave/chunk <fix_ave_chunk> command which can treat a grid defined by the compute chunk/atom command as a global grid where each processor owns a copy of all the grid cells. If Nx = Ny = Nz = 1 is used, the same calculation would be more efficiently performed by the doc:fix ave/atom <fix_ave_atom> command.

If the simulation box size or shape changes during a simulation, the grid always conforms to the size/shape of the current simulation box. If one more dimensions have non-periodic shrink-wrapped boundary conditions, as defined by the boundary command, then the grid will extend over the (dynamic) shrink-wrapped extent in each dimension. If the box shape is triclinic, as explained in Howto triclinic, then the grid is also triclinic; each grid cell is a small triclinic cell with the same shape as the simulation box.

In both per-atom and per-grid mode, input values from a compute or fix that produces an array of values (multiple values per atom or per grid point), the bracketed index I can be specified using a wildcard asterisk with the index to effectively specify multiple values. This takes the form “*” or “*n” or “n*” or “m*n”. If N = the number of columns in the array (for mode = vector), then an asterisk with no numeric values means all indices from 1 to N. A leading asterisk means all indices from 1 to n (inclusive). A trailing asterisk means all indices from n to N (inclusive). A middle asterisk means all indices from m to n (inclusive).

Using a wildcard is the same as if the individual columns of the array had been listed one by one. E.g. if there were a compute fft/grid command which produced 3 values for each grid point, these two fix ave/grid commands would be equivalent:

compute myFFT all fft/grid 10 10 10 ...
fix 1 all ave/grid 100 1 100 10 10 10 c_myFFT:grid:data[*]
fix 2 all ave/grid 100 1 100 10 10 10 c_myFFT:grid:data[*][1] c_myFFT:grid:data[*][2] c_myFFT:grid:data[3]


Per-atom mode:

Each specified per-atom value can be an atom attribute (velocity, force component), a number or mass density, a mass or temperature, or the result of a compute or fix or the evaluation of an atom-style variable. In the latter cases, the compute, fix, or variable must produce a per-atom quantity, not a global quantity. Note that the compute property/atom command provides access to any attribute defined and stored by atoms.

The per-atom values of each input vector are summed and averaged independently of the per-atom values in other input vectors.

Computes that produce per-atom quantities are those which have the word atom in their style name. See the doc pages for individual fixes to determine which ones produce per-atom quantities. Variables of style atom are the only ones that can be used with this fix since all other styles of variable produce global quantities.

The atom attribute values (vx,vy,vz,fx,fy,fz,mass) are self-explanatory. As noted above, any other atom attributes can be used as input values to this fix by using the compute property/atom command and then specifying an input value from that compute.

The density/number value means the number density is computed for each grid cell, i.e. number/volume. The density/mass value means the mass density is computed for each grid/cell, i.e. total-mass/volume. The output values are in units of 1/volume or density (mass/volume). See the units command page for the definition of density for each choice of units, e.g. gram/cm^3.

The temp value computes the temperature for each grid cell, by the formula

$\text{KE} = \frac{\text{DOF}}{2} k_B T,$

where KE = total kinetic energy of the atoms in the grid cell ( $$\frac{1}{2} m v^2$$), DOF = the total number of degrees of freedom for all atoms in the grid cell, $$k_B$$ = Boltzmann constant, and $$T$$ = temperature.

The DOF is calculated as N*adof + cdof, where N = number of atoms in the grid cell, adof = degrees of freedom per atom, and cdof = degrees of freedom per grid cell. By default adof = 2 or 3 = dimensionality of system, as set via the dimension command, and cdof = 0.0. This gives the usual formula for temperature.

Note that currently this temperature only includes translational degrees of freedom for each atom. No rotational degrees of freedom are included for finite-size particles. Also no degrees of freedom are subtracted for any velocity bias or constraints that are applied, such as compute temp/partial, or fix shake or fix rigid. This is because those degrees of freedom (e.g. a constrained bond) could apply to sets of atoms that are both inside and outside a specific grid cell, and hence the concept is somewhat ill-defined. In some cases, you can use the adof and cdof keywords to adjust the calculated degrees of freedom appropriately, as explained below.

Also note that a bias can be subtracted from atom velocities before they are used in the above formula for KE, by using the bias keyword. This allows, for example, a thermal temperature to be computed after removal of a flow velocity profile.

Note that the per-grid-cell temperature calculated by this fix and the compute temp/chunk command (using bins) can be different. The compute calculates the temperature for each chunk for a single snapshot. This fix can do that but can also time average those values over many snapshots, or it can compute a temperature as if the atoms in the grid cell on different timesteps were collected together as one set of atoms to calculate their temperature. The compute allows the center-of-mass velocity of each chunk to be subtracted before calculating the temperature; this fix does not.

If a value begins with “c_”, a compute ID must follow which has been previously defined in the input script. If no bracketed integer is appended, the per-atom vector calculated by the compute is used. If a bracketed integer is appended, the Ith column of the per-atom array calculated by the compute is used. Users can also write code for their own compute styles and add them to LAMMPS. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.

If a value begins with “f_”, a fix ID must follow which has been previously defined in the input script. If no bracketed integer is appended, the per-atom vector calculated by the fix is used. If a bracketed integer is appended, the Ith column of the per-atom array calculated by the fix is used. Note that some fixes only produce their values on certain timesteps, which must be compatible with Nevery, else an error results. Users can also write code for their own fix styles and add them to LAMMPS. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.

If a value begins with “v_”, a variable name must follow which has been previously defined in the input script. Variables of style atom can reference thermodynamic keywords and various per-atom attributes, or invoke other computes, fixes, or variables when they are evaluated, so this is a very general means of generating per-atom quantities to average within grid cells.

Per-grid mode:

The attributes that begin with c_ID and f_ID both take colon-separated fields gname and dname. These refer to a grid name and data field name which is defined by the compute or fix. Note that a compute or fix can define one or more grids (of different sizes) and one or more data fields for each of those grids. The sizes of all grids used as values for one instance of this fix must be the same.

The c_ID:gname:dname and c_ID:gname:dname[I] attributes allow per-grid vectors or arrays calculated by a compute to be accessed. The ID in the attribute should be replaced by the actual ID of the compute that has been defined previously in the input script.

If c_ID:gname:dname is used as a attribute, then the per-grid vector calculated by the compute is accessed. If c_ID:gname:dname[I] is used, then I must be in the range from 1-M, which will access the Ith column of the per-grid array with M columns calculated by the compute. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.

The f_ID:gname:dname and f_ID:gname:dname[I] attributes allow per-grid vectors or arrays calculated by a fix to be output. The ID in the attribute should be replaced by the actual ID of the fix that has been defined previously in the input script.

If f_ID:gname:dname is used as a attribute, then the per-grid vector calculated by the fix is printed. If f_ID:gname:dname[I] is used, then I must be in the range from 1-M, which will print the Ith column of the per-grid with M columns calculated by the fix. See the discussion above for how I can be specified with a wildcard asterisk to effectively specify multiple values.

Additional optional keywords also affect the operation of this fix and its outputs. Some are only applicable to per-atom mode. Some are applicable to both per-atom and per-grid mode.

The discard keyword is only applicable to per-atom mode. If a dimension of the system is non-periodic, then grid cells will only span the box dimension (fixed or shrink-wrap boundaries as set by the boundary command command). An atom may thus be slightly outside the range of grid cells on a particular timestep. If discard is set to yes (the default), then the atom will be assigned to the closest grid cell (lowest or highest) in that dimension. If discard is set to no the atom will be ignored.

The norm keyword is only applicable to per-atom mode. In per-grid mode, the norm keyword setting is ignored. The output grid value on an Nfreq timestep is the sum of the grid values in each of the Nrepeat samples, divided by Nrepeat.

In per-atom mode, the norm” keywod affects how averaging is done for the per-grid values that are output on an *Nfreq timestep. Nrepeat samples contribute to the output. The norm keyword has 3 possible settings: all or sample or none. All is the default.

In the formulas that follow, SumI is the sum of a per-atom property over the CountI atoms in a grid cell for a single sample I, where I varies from 1 to N, and N = Nrepeat. These formulas are used for any per-atom input value listed above, except density/number, density/mass, and temp. Those input values are discussed below.

In per-atom mode, for norm all the output grid value on the Nfreq timestep is an average over atoms across the entire Nfreq timescale:

Output = (Sum1 + Sum2 + … + SumN) / (Count1 + Count2 + … + CountN)

In per-atom mode, for norm sample the output grid value on the Nfreq timestep is an average of an average:

Output = (Sum1/Count1 + Sum2/Count2 + … + SumN/CountN) / Nrepeat

In per-atom mode, for norm none the output grid value on the Nfreq timestep is not normalized by the atom counts:

Output = (Sum1 + Sum2 + … SumN) / Nrepeat

For density/number and density/mass, the output value is the same as in the formulas above for norm all and norm sample, except that the result is also divided by the grid cell volume. For norm all, this will be the volume at the final Nfreq timestep. For norm sample, the divide-by-volume is done for each sample, using the grid cell volume at the sample timestep. For norm none, the output is the same as for norm all.

For temp, the output temperature uses the formula for kinetic energy KE listed above, and is normalized similarly to the formulas above for norm all and norm sample, except for the way the degrees of freedom (DOF) are calculated. For norm none, the output is the same as for norm all.

For norm all, the DOF = Nrepeat times cdof plus Count times adof, where Count = (Count1 + Count2 + … + CountN). The cdof and adof keywords are discussed below. The output temperature is computed with all atoms across all samples contributing.

For norm sample, the DOF for a single sample = cdof plus Count times adof, where Count = CountI for a single sample. The output temperature is the average of Nsample temperatures calculated for each sample.

Finally, for all 3 norm settings the output count of atoms per grid cell is:

Output count = (Count1 + Count2 + … CountN) / Nrepeat

This count is the same for all per-atom input values, including density/number, density/mass, and temp.

The ave keyword is applied to both per-atom and per-grid mode. It determines how the per-grid values produced once every Nfreq steps are averaged with values produced on previous steps that were multiples of Nfreq, before they are accessed by another output command.

If the ave setting is one, which is the default, then the grid values produced on Nfreq timesteps are independent of each other; they are output as-is without further averaging.

If the ave setting is running, then the grid values produced on Nfreq timesteps are summed and averaged in a cumulative sense before being output. Each output grid value is thus the average of the grid value produced on that timestep with all preceding values for the same grid value. This running average begins when the fix is defined; it can only be restarted by deleting the fix via the unfix command, or re-defining the fix by re-specifying it.

If the ave setting is window, then the grid values produced on Nfreq timesteps are summed and averaged within a moving “window” of time, so that the last M values for the same grid are used to produce the output. E.g. if M = 3 and Nfreq = 1000, then the grid value output on step 10000 will be the average of the grid values on steps 8000,9000,10000. Outputs on early steps will average over less than M values if they are not available.

The bias, adof, and cdof keywords are only applicable to per-atom mode.

The bias keyword specifies the ID of a temperature compute that removes a “bias” velocity from each atom, specified as bias-ID. It is only used when the temp value is calculated, to compute the thermal temperature of each grid cell after the translational kinetic energy components have been altered in a prescribed way, e.g. to remove a flow velocity profile. See the doc pages for individual computes that calculate a temperature to see which ones implement a bias.

The adof and cdof keywords define the values used in the degree of freedom (DOF) formula described above for temperature calculation for each grid cell. They are only used when the temp value is calculated. They can be used to calculate a more appropriate temperature in some cases. Here are 3 examples:

If grid cells contain some number of water molecules and fix shake is used to make each molecule rigid, then you could calculate a temperature with 6 degrees of freedom (DOF) (3 translational, 3 rotational) per molecule by setting adof to 2.0.

If compute temp/partial is used with the bias keyword to only allow the x component of velocity to contribute to the temperature, then adof = 1.0 would be appropriate.

Using cdof = -2 or -3 (for 2d or 3d simulations) will subtract out 2 or 3 degrees of freedom for each grid cell, similar to how the compute temp command subtracts out 3 DOF for the entire system.

## Restart, fix_modify, output, run start/stop, minimize info¶

No information about this fix is written to binary restart files. None of the fix_modify options are relevant to this fix.

This fix calculates a per-grid array which has one column for each of the specified input values. The units for each column with be in the units for the per-atom or per-grid quantity for the corresponding input value. If the fix is used in per-atom mode, it also calculates a per-grid vector with the count of atoms in each grid cell. The number of rows in the per-grid array and number of values in the per-grid vector (distributed across all processors) is Nx * Ny * Nz.

For access by other commands, the name of the single grid produced by this fix is “grid”. The names of its two per-grid datums are “data” for the per-grid array and “count” for the per-grid vector (if using per-atom values). Both datums can be accessed by various output commands.

In per-atom mode, the per-grid array values calculated by this fix are treated as “intensive”, since they are typically already normalized by the count of atoms in each grid cell.

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

none

## Default¶

The option defaults are discard = yes, norm = all, ave = one, and bias = none.