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### fix ave/spatial command

Syntax:

    fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta style arg keyword args ...

- ID, group-ID are documented in fix command
- ave/spatial = style name of this fix command
- Nevery = calculate property every this many timesteps
- Nrepeat = # of times to repeat the Nevery calculation before averaging
- Nfreq = timestep frequency at which the average value is computed
- dim = x or y or z
- origin = lower or center or upper or coordinate value (distance units)
- delta = thickness of spatial layers in dim (distance units)
- style = density or compute or fix

        density arg = mass or number
          mass = calculate mass density
          number = calculate number density
        compute arg = compute-ID that stores or calculates per-atom quantities
        fix arg = fix-ID that stores or calculates per-atom quantities

- zero or more keyword/arg pairs may be appended
- keyword = norm or units or file or ave

        units arg = box or lattice or reduced
        norm arg = all or sample
        file arg = filename
          filename = file to write results to
        ave args = one or running or window M
          one = output new average value every Nfreq steps
          running = output cummulative average of all previous Nfreq steps
          window M = output average of M most recent Nfreq steps

Examples:

    fix 1 all ave/spatial 10000 1 10000 z lower 0.02 compute myCentro units reduced
    fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 compute Vx norm sample file vel.profile
    fix 1 flow ave/spatial 100 5 1000 y 0.0 2.5 density mass ave running

Description:

Calculate one or more instantaneous per-atom quantities every few timesteps, average them by layer in a chosen dimension and over a longer timescale. The resulting averages can be used by other output commands such as thermo_style custom, and also written to a file.

This fix can be used to spatially average per-atom properties (velocity, force) or per-atom quantities calculated by a compute (energy, stress) or by another fix (see the fix ave/atom command) or by a variable via an equation you define (see the compute variable/atom command).

For style density, the number of atoms in each layer is counted, either by mass or by number. The compute style allows specification of a compute which will be invoked to calculate the desired property. The compute can be previously defined in the input script or it can be a compute defined by a dump custom command.

For style compute, the fix ave/spatial command accesses the per-atom scalar or vector values stored by the compute. Thus it must be a "per-atom" compute with the word "atom" in its style name, rather than a "global" compute. See the fix ave/time command if you wish to time-average a global quantity calculated by a compute without the word atom in its style name, e.g. a compute that calculates a temperature or pressure.

See the compute command for a list of pre-defined per-atom computes. Two special computes of note are as follows. The compute attribute/atom command selects one or more atom attributes like vx or fz. The "compute variable/atom" style can calculate a value for an atom that can be specified by a variable atom equation. Users can also write code for their own per-atom compute styles and add them to LAMMPS. Note that the dump custom command can also be used to directly output quantities calculated by a per-atom compute in a per-atom fashion.

For style fix, the fix ave/spatial command accesses the per-atom scalar or vector values stored by another fix. The fix ave/atom command is an example of such a fix.

The Nevery, Nrepeat, and Nfreq arguments specify on what timesteps the per-atom property will be evaluated in order to contribute to the average. The final averaged values are computed every Nfreq timesteps. The average is over Nrepeat values, computed in the preceeding 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.

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. Similary for timesteps 190,192,194,196,198,200 on timestep 200, etc.

The per-atom property is also averaged over atoms in each layer, where the layers are in a particular dim and have a thickness given by delta. Every Nfreq steps, when an averaging is being performed and the per-atom property is calculated for the first time, the number of layers and the layer boundaries are computed. Thus if the simlation box changes size during a simulation, the number of layers and their boundaries may also change. Layers are defined relative to a specified origin, which may be the lower/upper edge of the box (in dim) or its center point, or a specified coordinate value. Starting at the origin, sufficient layers are created in both directions to completely cover the box. On subsequent timesteps every atom is mapped to one of the layers. Atoms beyond the lowermost/uppermost layer are counted in the first/last layer.

For orthogonal simulation boxes, the layers are "slices" aligned with the xyz coordinate axes. For non-orthogonal (triclinic) simulation boxes, the layers are "tilted slices" 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. As described there, a tilted simulation box has edge vectors a,b,c. In that nomenclature, layers in the x dimension have faces with normals in the "b" cross "c" direction. Layers in y have faces normal to the "a" cross "c" direction. And layers in z have faces normal to the "a" cross "b" direction. Note that in order to define the thickness and position of these tilted layers in an unambiguous fashion, the units option must be set to reduced when using a non-orthogonal simulation box, as discussed below.

For the compute and fix keywords, the per-atom calculation performed by the compute or fix is on the group defined by that command. However, only atoms in the fix group are included in the layer averaging.

Note that some computes perform costly calculations, involving the creation or use of neighbor lists. If the compute is invoked too often by fix ave/spatial, it can slow down a simulation.

Additional optional keywords also affect the operation of this fix.

The units keyword determines the meaning of the distance units used for the layer thickness delta and for origin if it is a coordinate value. For orthogonal simulation boxes, any of the 3 options may be used. For non-orthogonal (triclinic) simulation boxes, only the reduced option may be used.

A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacing. A reduced value means normalized unitless values between 0 and 1, which represent the lower and upper faces of the simulation box respectively. Thus an origin value of 0.5 means the center of the box in any dimension. A delta value of 0.1 means 10 layers span the box in any dimension.

Consider a non-orthogonal box, with layers in the x dimension. No matter how the box is tilted, an origin of 0.0 means start layers at the lower "b" cross "c" plane of the simulation box and an origin of 1.0 means to start layers at the upper "b" cross "c" face of the box. A delta value of 0.1 means there will be 10 layers from 0.0 to 1.0, regardless of the current size or shape of the simulation box.

The norm keyword affects how time-averaging is done within for the output produced every Nfreq timesteps. For an all setting, a layer quantity is summed over all atoms in all Nrepeat samples, as is the count of atoms in the layer. The printed value for the layer is Total-quantity / Total-count. In other words it is an average over the entire Nfreq timescale.

For a sample setting, the quantity is summed over atoms for only a single sample, as is the count, and a "average sample value" is computed, i.e. Sample-quantity / Sample-count. The printed value for the layer is the average of the Nrepeat "average sample values", In other words it is an average of an average.

The file keyword allows a filename to be specified. Every Nfreq timesteps, layer info will be written to a text file in the following format. A line with the timestep and number of layers is written. Then one line per layer is written, containing the layer ID (1-N), the coordinate of the center of the layer, the number of atoms in the layer, and one or more calculated values. The number of atoms and the value(s) are average quantities. If the value of the units keyword is box or lattice, the "coord" is printed in box units. If the value of the units keyword is reduced, the "coord" is printed in reduced units (0-1).

If the style is density, or the style is compute or fix with a compute/fix that calculates a single quantity per atom, then a single value will be printed for each layer. If the style is compute or fix with a compute/fix that calculates N quantities per atom, then N values per line will be written, each of them averaged independently.

The ave keyword determines how the layer values produced every Nfreq steps are averaged with layer values produced on previous steps that were multiples of Nfreq, before they are accessed by another output command or written to a file.

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

If the ave setting is running, then the layer values produced on timesteps that are multiples of Nfreq are summed and averaged in a cummulative sense before being output. Each output layer value is thus the average of the layer value produced on that timestep with all preceeding values for the same layer. 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 layer values produced on timesteps that are multiples of Nfreq are summed and averaged within a moving "window" of time, so that the last M values for the same layer are used to produce the output. E.g. if M = 3 and Nfreq = 1000, then the output on step 10000 will be the average of the individual layer values on steps 8000,9000,10000. Outputs on early steps will average over less than M values if they are not available.

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 computes a vector of quantities which can be accessed by various output commands. The values should only be accessed on timesteps that are multiples of Nfreq since that is when averaging is complete. The vector is of length N = nlayers*nvalues where nvalues is the number of per-atom quantities produced by the compute or fix that fix ave/spatial accesses. Nvalues = 1 if the style is density. If nvalues > 1 and vector value N is accessed by another output command, then the average quantity for the Ith layer and Jth value in that layer is accessed, where I = N / nvalues + 1 and J = N % nvalues + 1.

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.

Restrictions:

When the ave keyword is set to running or window then the number of layers must remain the same during the simulation, so that the appropriate averaging can be done. This will be the case if the simulation box size doesn't change or if the units keyword is set to reduced.

Related commands:

compute, fix ave/time

Default:

The option defaults are units = lattice, norm = all, no file output, and ave = one.