</P>

<PRE>variable x equal "xlo + 0.25*lx" 

</PRE>

<P>Similarly, these variable definitions will move the indenter at a

constant velocity:

<P>Similarly, either of these variable definitions will move the indenter

from an initial position at 2.5 at a constant velocity of 5:

</P>

<PRE>variable x0 equal 2.5

variable vx equal 5.0

variable x equal "v_x0 + step*dt*v_vx" 

<PRE>variable x equal "2.5 + 5*elaplong*dt"

variable x equal vdisplace(2.5,5) 

</PRE>

<P>If a spherical indenter's radius is specified as v_r, then these

variable definitions will grow the size of the indenter at a specfied

variable x equal "xlo + 0.25*lx" :pre

Similarly, these variable definitions will move the indenter at a

constant velocity:

Similarly, either of these variable definitions will move the indenter

from an initial position at 2.5 at a constant velocity of 5:

variable x0 equal 2.5

variable vx equal 5.0

variable x equal "v_x0 + step*dt*v_vx" :pre

variable x equal "2.5 + 5*elaplong*dt"

variable x equal vdisplace(2.5,5) :pre

If a spherical indenter's radius is specified as v_r, then these

variable definitions will grow the size of the indenter at a specfied

</H3>

<P><B>Syntax:</B>

</P>

<PRE>region ID style args keyword value ... 

<PRE>region ID style args keyword arg ... 

</PRE>

<UL><LI>ID = user-assigned name for the region 

    N = # of regions to follow, must be 2 or greater

    reg-ID1,reg-ID2, ... = IDs of regions to intersect 

</PRE>

<LI>zero or more keyword/value pairs may be appended 

<LI>zero or more keyword/arg pairs may be appended 

<LI>keyword = <I>side</I> or <I>units</I> or <I>vel</I> or <I>wiggle</I> or <I>rotate</I> 

<LI>keyword = <I>side</I> or <I>units</I> or <I>move</I> or <I>rotate</I> 

<PRE>  <I>side</I> value = <I>in</I> or <I>out</I>

    <I>in</I> = the region is inside the specified geometry

  <I>units</I> value = <I>lattice</I> or <I>box</I>

    <I>lattice</I> = the geometry is defined in lattice units

    <I>box</I> = the geometry is defined in simulation box units

  <I>vel</I> args = Vx Vy Vz

    Vx,Vy,Vz = components of velocity vector (velocity units)

  <I>wiggle</I> args = Ax Ay Az period

    Ax,Ay,Az = components of amplitude vector (distance units)

    period = period of oscillation (time units)

  <I>rotate</I> args = Px Py Pz Rx Ry Rz period

    Px,Py,Pz = origin point of axis of rotation (distance units)

  <I>move</I> 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

 <I>rotate</I> 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 

    period = period of rotation (time units) 

</PRE>

</UL>

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 wiggle 1 1 0 10 

region 2 sphere 0.0 0.0 0.0 5 side out move v_left v_up NULL 

</PRE>

<P><B>Description:</B>

</P>

wall/region</A> command.

</P>

<P>Normally, regions in LAMMPS are "static", meaning their geometric

extent does not change with time.  If the <I>vel</I> or <I>wiggle</I> or

<I>rotate</I> 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.

extent does not change with time.  If the <I>move</I> or <I>rotate</I> 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.

</P>

<P>The <I>delete</I> style removes the named region.  Since there is little

overhead to defining extra regions, there is normally no need to do

regardless of whether the <A HREF = "dimension.html">dimension</A> 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 is the 2d geometric object you want.

x-y plane of the simulation has the 2d geometric extent you want.

</P>

<P>For style <I>cone</I>, an axis-aligned cone is defined which is like a

<I>cylinder</I> except that two different radii (one at each end) can be

</UL>

<HR>

<P>If the <I>vel</I> or <I>wiggle</I> or <I>rotate</I> keywords are used, the region

is "dynamic", meaning its location or orientation changes with time.

No more than one of these keywords can be used at a time.  These

keywords cannot be used with a <I>union</I> or <I>intersect</I> style region.

Instead, the keywords should be used to define the individual

sub-regions of the <I>union</I> or <I>intersect</I> region.  Normally, each

sub-region should be "dynamic" in the same manner (e.g. rotate around

the same point), though this is not a requirement.

</P>

<P>The <I>vel</I> style moves the region at a constant velocity, so that its

position <I>X</I> = (x,y,z) as a function of time is given in vector

notation as

</P>

<PRE>X(t) = X0 + V * delta 

<P>If the <I>move</I> or <I>rotate</I> keywords are used, the region is "dynamic",

meaning its location or orientation changes with time.  These keywords

cannot be used with a <I>union</I> or <I>intersect</I> style region.  Instead,

the keywords should be used to make the individual sub-regions of the

<I>union</I> or <I>intersect</I> 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.

</P>

<P>The <I>move</I> keyword allows one or more <A HREF = "variable.html">equal-style

variables</A> 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.

</P>

<P>Note that equal-style variables can specify formulas with various

mathematical functions, and include <A HREF = "thermo_style.html">thermo_style</A>

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 <I>start</I> and <I>stop</I> keywords of the

<A HREF = "run.html">run</A> command and the <I>elaplong</I> keyword of <A HREF = "thermo_style.html">thermo_style

custom</A> for details.

</P>

<P>For example, these commands would displace a region from its initial

position, in the positive x direction, effectively at a constant

velocity:

</P>

<PRE>variable dx equal ramp(0,10)

region 2 sphere 10.0 10.0 0.0 5 move v_dx NULL NULL 

</PRE>

<P>where <I>X0</I> = (x0,y0,z0) is its position at the time the region is

specified, <I>V</I> is the specified velocity vector with components

(Vx,Vy,Vz), and <I>delta</I> is the time elapsed since the region was

specified. 

<P>Note that the initial displacemet is 0.0, though that is not required.

</P>

<P>The <I>wiggle</I> style moves the region in an oscillatory fashion, so that

its position <I>X</I> = (x,y,z) as a function of time is given in vector

notation as

<P>Either of these varaibles would "wiggle" the region back and forth in

the y direction:

</P>

<PRE>X(t) = X0 + A sin(omega*delta) 

<PRE>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 

</PRE>

<P>where <I>X0</I> = (x0,y0,z0) is its position at the time the region is

specified, <I>A</I> is the specified amplitude vector with components

(Ax,Ay,Az), <I>omega</I> is 2 PI / <I>period</I>, and <I>delta</I> is the time

elapsed since the region was specified.

</P>

<P>The <I>rotate</I> style rotates the region around a rotation axis <I>R</I> =

(Rx,Ry,Rz) that goes thru a point <I>P</I> = (Px,Py,Pz).  The <I>period</I> of

the rotation is also specified.  The direction of rotation for the

region around the rotation axis is consistent with the right-hand

<P>The <I>rotate</I> keyword rotates the region around a rotation axis <I>R</I> =

(Rx,Ry,Rz) that goes thru a point <I>P</I> = (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 <I>R</I>, then your fingers

wrap around the axis in the direction of rotation.

</P>

<P>The <I>move</I> and <I>rotate</I> keywords can be used together.  In this case,

the displacement specified by the <I>move</I> keyword is applied to the <I>P</I>

point of the <I>rotate</I> keyword.

</P>

<P><B>Restrictions:</B>

</P>

<P>A prism cannot be of 0.0 thickness in any dimension; use a small z

</P>

<P><B>Default:</B>

</P>

<P>The option defaults are side = in, units = lattice, and no

velocity, wiggling, or rotation.

<P>The option defaults are side = in, units = lattice, and no moving or

rotation.

</P>

</HTML>

[Syntax:]

region ID style args keyword value ... :pre

region ID style args keyword arg ... :pre

ID = user-assigned name for the region :ulb,l

style = {delete} or {block} or {cone} or {cylinder} or {plane} or {prism} or {sphere} or {union} or {intersect} :l

  {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 :pre

zero or more keyword/value pairs may be appended :l

keyword = {side} or {units} or {vel} or {wiggle} or {rotate} :l

zero or more keyword/arg pairs may be appended :l

keyword = {side} or {units} or {move} or {rotate} :l

  {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

  {vel} args = Vx Vy Vz

    Vx,Vy,Vz = components of velocity vector (velocity units)

  {wiggle} args = Ax Ay Az period

    Ax,Ay,Az = components of amplitude vector (distance units)

    period = period of oscillation (time units)

  {rotate} args = Px Py Pz Rx Ry Rz period

    Px,Py,Pz = origin point of axis of rotation (distance units)

    Rx,Ry,Rz = axis of rotation vector

    period = period of rotation (time units) :pre

  {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 :pre

:ule

[Examples:]

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 wiggle 1 1 0 10 :pre

region 2 sphere 0.0 0.0 0.0 5 side out move v_left v_up NULL :pre

[Description:]

wall/region"_fix_wall_region.html command.

Normally, regions in LAMMPS are "static", meaning their geometric

extent does not change with time.  If the {vel} or {wiggle} 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.

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

regardless of whether the "dimension"_dimension.html 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 is the 2d geometric object you want.

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

:line

If the {vel} or {wiggle} or {rotate} keywords are used, the region

is "dynamic", meaning its location or orientation changes with time.

No more than one of these keywords can be used at a time.  These

keywords cannot be used with a {union} or {intersect} style region.

Instead, the keywords should be used to define the individual

sub-regions of the {union} or {intersect} region.  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 {vel} style moves the region at a constant velocity, so that its

position {X} = (x,y,z) as a function of time is given in vector

notation as

X(t) = X0 + V * delta :pre

where {X0} = (x0,y0,z0) is its position at the time the region is

specified, {V} is the specified velocity vector with components

(Vx,Vy,Vz), and {delta} is the time elapsed since the region was

specified. 

The {wiggle} style moves the region in an oscillatory fashion, so that

its position {X} = (x,y,z) as a function of time is given in vector

notation as

X(t) = X0 + A sin(omega*delta) :pre

where {X0} = (x0,y0,z0) is its position at the time the region is

specified, {A} is the specified amplitude vector with components

(Ax,Ay,Az), {omega} is 2 PI / {period}, and {delta} is the time

elapsed since the region was specified.

The {rotate} style rotates the region around a rotation axis {R} =

(Rx,Ry,Rz) that goes thru a point {P} = (Px,Py,Pz).  The {period} of

the rotation is also specified.  The direction of rotation for the

region around the rotation axis is consistent with the right-hand

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"_variable.html 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"_thermo_style.html

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"_run.html command and the {elaplong} keyword of "thermo_style

custom"_thermo_style.html 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 :pre

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 :pre

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

[Default:]

The option defaults are side = in, units = lattice, and no

velocity, wiggling, or rotation.

The option defaults are side = in, units = lattice, and no moving or

rotation.

</P>

<P>The run begins on startstep.  Startstep can span multiple runs, using

the <I>start</I> keyword of the <A HREF = "run.html">run</A> command.  See the

<A HREF = "run.html">run</A> command for details of how to do this.

<A HREF = "run.html">run</A> command for details of how to do this.  Note that the

<A HREF = "thermo_style.html">thermo_style</A> keyword elaplong =

timestep-startstep.

</P>

<P>The swiggle(x,y,z) and cwiggle(x,y,z) functions each take 3 arguments:

x = coord0, y = amplitude, z = period.  They use the elapsed time to

</P>

<P>The run begins on startstep.  Startstep can span multiple runs, using

the <I>start</I> keyword of the <A HREF = "run.html">run</A> command.  See the

<A HREF = "run.html">run</A> command for details of how to do this.

<A HREF = "run.html">run</A> command for details of how to do this.  Note that the

<A HREF = "thermo_style.html">thermo_style</A> keyword elaplong =

timestep-startstep.

</P>

<HR>