\(\renewcommand{\AA}{\text{Å}}\)

# region command

Accelerator Variants: block/kk, sphere/kk

## Syntax

    region ID style args keyword arg ...

- ID = user-assigned name for the region

- style = delete or block or cone or cylinder or ellipsoid or plane or prism or sphere or union or intersect

      delete = no args
      block args = xlo xhi ylo yhi zlo zhi
        xlo,xhi,ylo,yhi,zlo,zhi = bounds of block in all dimensions (distance units)
          xlo,xhi,ylo,yhi,zlo,zhi can be a variable (see below)
      cone args = dim c1 c2 radlo radhi lo hi
        dim = x or y or z = axis of cone
        c1,c2 = coords of cone axis in other 2 dimensions (distance units)
        radlo,radhi = cone radii at lo and hi end (distance units)
        lo,hi = bounds of cone in dim (distance units)
          c1,c2,radlo,radhi,lo,hi can be a variable (see below)
      cylinder args = dim c1 c2 radius lo hi
        dim = x or y or z = axis of cylinder
        c1,c2 = coords of cylinder axis in other 2 dimensions (distance units)
        radius = cylinder radius (distance units)
          c1,c2, and radius can be a variable (see below)
        lo,hi = bounds of cylinder in dim (distance units)
      ellipsoid args = x y z a b c
        x,y,z = center of ellipsoid (distance units)
        a,b,c = half the length of the principal axes of the ellipsoid (distance units)
          x,y,z,a,b and c can be a variable (see below)
      plane args = px py pz nx ny nz
        px,py,pz = point on the plane (distance units)
        nx,ny,nz = direction normal to plane (distance units)
          px,py,pz,nx,ny,nz can be a variable (see below)
      prism args = xlo xhi ylo yhi zlo zhi xy xz yz
        xlo,xhi,ylo,yhi,zlo,zhi = bounds of untilted prism (distance units)
        xy = distance to tilt y in x direction (distance units)
        xz = distance to tilt z in x direction (distance units)
        yz = distance to tilt z in y direction (distance units)
          xlo,xhi,ylo,yhi,zlo,zhi,xy,xz,yz can be a variable (see below)
      sphere args = x y z radius
        x,y,z = center of sphere (distance units)
        radius = radius of sphere (distance units)
          x,y,z, and radius can be a variable (see below)
      union args = N reg-ID1 reg-ID2 ...
        N = # of regions to follow, must be 2 or greater
        reg-ID1,reg-ID2, ... = IDs of regions to join together
      intersect args = N reg-ID1 reg-ID2 ...
        N = # of regions to follow, must be 2 or greater
        reg-ID1,reg-ID2, ... = IDs of regions to intersect

- zero or more keyword/arg pairs may be appended

- keyword = side or units or move or rotate or open

      side value = in or out
        in = the region is inside the specified geometry
        out = the region is outside the specified geometry
      units value = lattice or box
        lattice = the geometry is defined in lattice units
        box = the geometry is defined in simulation box units
      move args = v_x v_y v_z
        v_x,v_y,v_z = equal-style variables for x,y,z displacement of region over time (distance units)
      rotate args = v_theta Px Py Pz Rx Ry Rz
        v_theta = equal-style variable for rotaton of region over time (in radians)
        Px,Py,Pz = origin for axis of rotation (distance units)
        Rx,Ry,Rz = axis of rotation vector
      open value = integer from 1-6 corresponding to face index (see below)

- accelerated styles (with same args) = block/kk, sphere/kk

## Examples

    region 1 block -3.0 5.0 INF 10.0 INF INF
    region 2 sphere 0.0 0.0 0.0 5 side out
    region void cylinder y 2 3 5 -5.0 EDGE units box
    region 1 prism 0 10 0 10 0 10 2 0 0
    region outside union 4 side1 side2 side3 side4
    region 2 sphere 0.0 0.0 0.0 5 side out move v_left v_up NULL
    region openbox block 0 10 0 10 0 10 open 5 open 6 units box
    region funnel cone z 10 10 2 5 0 10 open 1 units box

## Description

This command defines a geometric region of space. Various other commands use regions. For example, the region can be filled with atoms via the create_atoms command. Or a bounding box around the region, can be used to define the simulation box via the create_box command. Or the atoms in the region can be identified as a group via the group command, or deleted via the delete_atoms command. Or the surface of the region can be used as a boundary wall via the fix wall/region command.

Commands which use regions typically test whether an atom’s position is contained in the region or not. For this purpose, coordinates exactly on the region boundary are considered to be interior to the region. This means, for example, for a spherical region, an atom on the sphere surface would be part of the region if the sphere were defined with the side in keyword, but would not be part of the region if it were defined using the side out keyword. See more details on the side keyword below.

Normally, regions in LAMMPS are “static”, meaning their geometric extent does not change with time. If the move or rotate keyword is used, as described below, the region becomes “dynamic”, meaning its location or orientation changes with time. This may be useful, for example, when thermostatting a region, via the compute temp/region command, or when the fix wall/region command uses a region surface as a bounding wall on particle motion, i.e. a rotating container.

The delete style removes the named region. Since there is little overhead to defining extra regions, there is normally no need to do this, unless you are defining and discarding large numbers of regions in your input script.

The lo/hi values for block or cone or cylinder or prism styles can be specified as EDGE or INF. EDGE means they extend all the way to the global simulation box boundary. Note that this is the current box boundary; if the box changes size during a simulation, the region does not. INF means a large negative or positive number (1.0e20), so it should encompass the simulation box even if it changes size. If a region is defined before the simulation box has been created (via create_box or read_data or read_restart commands), then an EDGE or INF parameter cannot be used. For a prism region, a non-zero tilt factor in any pair of dimensions cannot be used if both the lo/hi values in either of those dimensions are INF. E.g. if the xy tilt is non-zero, then xlo and xhi cannot both be INF, nor can ylo and yhi.

Note

Regions in LAMMPS do not get wrapped across periodic boundaries, as specified by the boundary command. For example, a spherical region that is defined so that it overlaps a periodic boundary is not treated as 2 half-spheres, one on either side of the simulation box.

Note

Regions in LAMMPS are always 3d geometric objects, regardless of whether the dimension of a simulation is 2d or 3d. Thus when using regions in a 2d simulation, you should be careful to define the region so that its intersection with the 2d x-y plane of the simulation has the 2d geometric extent you want.

For style cone, an axis-aligned cone is defined which is like a cylinder except that two different radii (one at each end) can be defined. Either of the radii (but not both) can be 0.0.

For style cone and cylinder, the c1,c2 params are coordinates in the 2 other dimensions besides the cylinder axis dimension. For dim = x, c1/c2 = y/z; for dim = y, c1/c2 = x/z; for dim = z, c1/c2 = x/y. Thus the third example above specifies a cylinder with its axis in the y-direction located at x = 2.0 and z = 3.0, with a radius of 5.0, and extending in the y-direction from -5.0 to the upper box boundary.

Added in version 4May2022.

For style ellipsoid, an axis-aligned ellipsoid is defined. The ellipsoid has its center at (x,y,z) and is defined by 3 axis-aligned vectors given by A = (a,0,0); B = (0,b,0); C = (0,0,c). Note that although the ellipsoid is specified as axis-aligned it can be rotated via the optional rotate keyword.

For style plane, a plane is defined which contain the point (px,py,pz) and has a normal vector (nx,ny,nz). The normal vector does not have to be of unit length. The “inside” of the plane is the half-space in the direction of the normal vector; see the discussion of the side option below.

For style prism, a parallelepiped is defined (it is too hard to spell parallelepiped in an input script!). The parallelepiped has its “origin” at (xlo,ylo,zlo) and is defined by 3 edge vectors starting from the origin given by A = (xhi-xlo,0,0); B = (xy,yhi-ylo,0); C = (xz,yz,zhi-zlo). Xy,xz,yz can be 0.0 or positive or negative values and are called “tilt factors” because they are the amount of displacement applied to faces of an originally orthogonal box to transform it into the parallelepiped.

A prism region that will be used with the create_box command to define a triclinic simulation box must have tilt factors (xy,xz,yz) that do not skew the box more than half the distance of corresponding the parallel box length. For example, if xlo = 2 and xhi = 12, then the x box length is 10 and the xy tilt factor must be between -5 and 5. Similarly, both xz and yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2. Note that this is not a limitation, since if the maximum tilt factor is 5 (as in this example), then configurations with tilt = …, -15, -5, 5, 15, 25, … are all geometrically equivalent.

For style sphere, a sphere is defined with its center at (x,y,z) and with radius as its radius.

The radius value for styles sphere and cylinder, and the parameters a,b,c for style ellipsoid, can each be specified as an equal-style variable. Likewise, for style sphere and ellipsoid the x-, y-, and z- coordinates of the center of the sphere/ellipsoid can be specified as an equal-style variable. And for style cylinder the two center positions c1 and c2 for the location of the cylinder axes can be specified as a equal-style variable. For styles block, cone, prism, and plane all properties can be defined via equal-style variables. For style plane, the components of the direction vector normal to plane should be either all constants or all defined by equal-style variables.

If the value is a variable, it should be specified as v_name, where name is the variable name. In this case, the variable will be evaluated each timestep, and its value used to determine the radius of the region.

Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent radius or have a time dependent position of the sphere or cylinder region.

Note

Whenever a region property, such as a coordinate or an upper/lower bound, is defined via an equal-style variable, the variable should not cause any of the region boundaries to move too far within a single timestep. Otherwise, bad dynamics will occur. “Too far” means a small fraction of the approximate distance of closest approach between two particles, which for the case of Lennard-Jones particles is the distance of the energy minimum while for granular particles it is their diameter. An example is a rapidly varying direction vector in region plane since a small change in the normal to plane will shift the region surface far away from the region point by a large displacement. Similarly, bad dynamics can also occur for fast changing variables employed in the move/rotate options.

See the Howto tricilinc page for a geometric description of triclinic boxes, as defined by LAMMPS, and how to transform these parameters to and from other commonly used triclinic representations.

The union style creates a region consisting of the volume of all the listed regions combined. The intersect style creates a region consisting of the volume that is common to all the listed regions.

Note

The union and intersect regions operate by invoking methods from their list of sub-regions. Thus you cannot delete the sub-regions after defining a union or intersection region.

The side keyword determines whether the region is considered to be inside or outside of the specified geometry. Using this keyword in conjunction with union and intersect regions, complex geometries can be built up. For example, if the interior of two spheres were each defined as regions, and a union style with side = out was constructed listing the region-IDs of the 2 spheres, the resulting region would be all the volume in the simulation box that was outside both of the spheres.

The units keyword determines the meaning of the distance units used to define the region for any argument above listed as having distance units. It also affects the scaling of the velocity vector specified with the vel keyword, the amplitude vector specified with the wiggle keyword, and the rotation point specified with the rotate keyword, since they each involve a distance metric.

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 spacings which are used as follows:

- For style block, the lattice spacing in dimension x is applied to xlo and xhi, similarly the spacings in dimensions y,z are applied to ylo/yhi and zlo/zhi.

- For style cone, the lattice spacing in argument dim is applied to lo and hi. The spacings in the two radial dimensions are applied to c1 and c2. The two cone radii are scaled by the lattice spacing in the dimension corresponding to c1.

- For style cylinder, the lattice spacing in argument dim is applied to lo and hi. The spacings in the two radial dimensions are applied to c1 and c2. The cylinder radius is scaled by the lattice spacing in the dimension corresponding to c1.

- For style ellipsoid, the lattice spacing in dimensions x,y,z are applied to the ellipsoid center x,y,z. The spacing in dimensions x,y,z are applied to the ellipsoid radii a,b,c respectively.

- For style plane, the lattice spacing in dimension x is applied to px and nx, similarly the spacings in dimensions y,z are applied to py/ny and pz/nz.

- For style prism, the lattice spacing in dimension x is applied to xlo and xhi, similarly for ylo/yhi and zlo/zhi. The lattice spacing in dimension x is applied to xy and xz, and the spacing in dimension y to yz.

- For style sphere, the lattice spacing in dimensions x,y,z are applied to the sphere center x,y,z. The spacing in dimension x is applied to the sphere radius.

If the move or rotate keywords are used, the region is “dynamic”, meaning its location or orientation changes with time. These keywords cannot be used with a union or intersect style region. Instead, the keywords should be used to make the individual sub-regions of the union or intersect region dynamic. Normally, each sub-region should be “dynamic” in the same manner (e.g. rotate around the same point), though this is not a requirement.

The move keyword allows one or more equal-style variables to be used to specify the x,y,z displacement of the region, typically as a function of time. A variable is specified as v_name, where name is the variable name. Any of the three variables can be specified as NULL, in which case no displacement is calculated in that dimension.

Note that equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a region displacement that change as a function of time or spans consecutive runs in a continuous fashion. For the latter, see the start and stop keywords of the run command and the elaplong keyword of thermo_style custom for details.

For example, these commands would displace a region from its initial position, in the positive x direction, effectively at a constant velocity:

    variable dx equal ramp(0,10)
    region 2 sphere 10.0 10.0 0.0 5 move v_dx NULL NULL

Note that the initial displacement is 0.0, though that is not required.

Either of these variables would “wiggle” the region back and forth in the y direction:

    variable dy equal swiggle(0,5,100)
    variable dysame equal 5*sin(2*PI*elaplong*dt/100)
    region 2 sphere 10.0 10.0 0.0 5 move NULL v_dy NULL

The rotate keyword rotates the region around a rotation axis R = (Rx,Ry,Rz) that goes through a point P = (Px,Py,Pz). The rotation angle is calculated, presumably as a function of time, by a variable specified as v_theta, where theta is the variable name. The variable should generate its result in radians. The direction of rotation for the region around the rotation axis is consistent with the right-hand rule: if your right-hand thumb points along R, then your fingers wrap around the axis in the direction of rotation.

The move and rotate keywords can be used together. In this case, the displacement specified by the move keyword is applied to the P point of the rotate keyword which is equivalent to applying the rotation first and then the translation.

The open keyword can be used (multiple times) to indicate that one or more faces of the region are ignored for purposes of particle/wall interactions. This keyword is only relevant for regions used by the fix wall/region and fix wall/gran/region commands. It can be used to create “open” containers where only some of the region faces are walls. For example, a funnel can be created with a cone style region that has an open face at the smaller radius for particles to flow out, or at the larger radius for pouring particles into the cone, or both.

Note that using the open keyword partly overrides the side keyword, since both exterior and interior surfaces of an open region are tested for particle contacts. The exception to this is a union or intersect region which includes an open sub-region. In that case the side keyword is still used to define the union/intersect region volume, and the open settings are only applied to the individual sub-regions that use them.

The indices specified as part of the open keyword have the following meanings:

For style block, indices 1-6 correspond to the xlo, xhi, ylo, yhi, zlo, zhi surfaces of the block. I.e. 1 is the yz plane at x = xlo, 2 is the yz-plane at x = xhi, 3 is the xz plane at y = ylo, 4 is the xz plane at y = yhi, 5 is the xy plane at z = zlo, 6 is the xy plane at z = zhi). In the second-to-last example above, the region is a box open at both xy planes.

For style prism, values 1-6 have the same mapping as for style block. I.e. in an untilted prism, open indices correspond to the xlo, xhi, ylo, yhi, zlo, zhi surfaces.

For style cylinder, index 1 corresponds to the flat end cap at the low coordinate along the cylinder axis, index 2 corresponds to the high-coordinate flat end cap along the cylinder axis, and index 3 is the curved cylinder surface. For example, a cylinder region with open 1 open 2 keywords will be open at both ends (e.g. a section of pipe), regardless of the cylinder orientation.

For style cone, the mapping is the same as for style cylinder. Index 1 is the low-coordinate flat end cap, index 2 is the high-coordinate flat end cap, and index 3 is the curved cone surface. In the last example above, a cone region is defined along the z-axis that is open at the zlo value (e.g. for use as a funnel).

For all other styles, the open keyword is ignored. As indicated above, this includes the intersect and union regions, though their sub-regions can be defined with the open keyword.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

Note

Currently, only block and sphere style regions are supported by KOKKOS. The code using the region (such as a fix or compute) must also be supported by KOKKOS or no acceleration will occur.

## Restrictions

A prism cannot be of 0.0 thickness in any dimension; use a small z thickness for 2d simulations. For 2d simulations, the xz and yz parameters must be 0.0.

## Related commands

lattice, create_atoms, delete_atoms, group

## Default

The option defaults are side = in, units = lattice, and no move or rotation.