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### region command

Syntax:

    region ID style args keyword arg ...

- ID = user-assigned name for the region
- style = delete or block or cone or cylinder or plane or prism or sphere or mesh/tet or union or intersect or wedge

        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)
        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)
        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)
            radius can be a variable (see below)
          lo,hi = bounds of cylinder in dim (distance units)
        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)
        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)
        sphere args = x y z radius
          x,y,z = center of sphere (distance units)
          radius = radius of sphere (distance units)
        mesh/tet args = file filename scale s move offx offy offz rotate phix phiy phiz
          file = obligatory keyword
          filename = name of ASCII VTK file containing the VTK tet-mesh data
          scale = obligatory keyword
          s = scaling factor for the mesh (dimensionless)
          move = obligatory keyword
          offx,offy,offz = offset for the mesh (distance units)
          rotate = obligatory keyword
          phix,phiy,phiz = angle of mesh rotation around x-, y-, and z-axis (in grad)
        wedge args = axis dim center c1 c2 radius r bounds lo hi angle0 alpha0 angle alpha
          axis = obligatory keyword
          dim = x or y or z ... wedge is aligned to this dimension
          center = obligatory keyword
          c1 = first center-coordinate
                 if dim == x then y-coord
                 if dim == y then z-coord
                 if dim == z then x-coord
          c2 = second center-coordinate
                 if dim == x then z-coord
                 if dim == y then x-coord
                 if dim == z then y-coord
          radius = obligatory keyword
          r = radius of cylinder
          bounds = obligatory keyword
          lo = dim-coord of lower flat face of cylinder of wedge
          hi = dim-coord of higher flat face of cylinder of wedge
          angle0 = obligatory keyword
          alpha0 = mathematically positive angle of the wedge's starting face
                     if axis == x then starting from y-axis
                     if axis == y then starting from z-axis
                     if axis == z then starting from x=axis
          angle = obligatory keyword
          alpha = mathematically positive angle between the wedge's starting and ending face in degrees
        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

        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
        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

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 1 wedge axis y  center 0 0  radius 10 bounds 0 10 angle0 -22.5 angle 45 units box side in

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 it's 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.

IMPORTANT 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.

IMPORTANT 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.

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's 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.

The radius value for style sphere and cylinder can be specified as an equal-style variable. 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.

See Section_howto 12 of the doc pages 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.

For style mesh/tet, a tetrahedral mesh can be read from an ASCII VTK file. You can apply offset, scaling and rotation to the imported mesh via dedicated keywords. If applying more then one of these operations, the offset is applied first and then the geometry is scaled. Then the geometry is rotated around the x-axis first, then around the y-axis, then around the z-axis.

IMPORTANT NOTE: Currently only ASCII VTK containing tetrahedra are supported. For periodic boundaries, the mesh is NOT mapped. Instead, a warning is generated if a vertex lies outside the simulation box.

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.

IMPORTANT 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 the 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 specfied 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 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 displacemet is 0.0, though that is not required.

Either of these varaibles 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 thru 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.

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.