forked from lijiext/lammps
436 lines
22 KiB
HTML
436 lines
22 KiB
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<CENTER><A HREF = "http://lammps.sandia.gov">LAMMPS WWW Site</A> - <A HREF = "Manual.html">LAMMPS Documentation</A> - <A HREF = "Section_commands.html#comm">LAMMPS Commands</A>
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<HR>
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<H3>fix ave/spatial command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>fix ID group-ID ave/spatial Nevery Nrepeat Nfreq dim origin delta ... value1 value2 ... keyword args ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "fix.html">fix</A> command
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<LI>ave/spatial = style name of this fix command
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<LI>Nevery = use input values every this many timesteps
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<LI>Nrepeat = # of times to use input values for calculating averages
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<LI>Nfreq = calculate averages every this many timesteps
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<LI>dim, origin, delta can be repeated 1, 2, or 3 times for 1d, 2d, or 3d bins
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<PRE> dim = <I>x</I> or <I>y</I> or <I>z</I>
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origin = <I>lower</I> or <I>center</I> or <I>upper</I> or coordinate value (distance units)
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delta = thickness of spatial bins in dim (distance units)
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</PRE>
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<LI>one or more input values can be listed
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<LI>value = vx, vy, vz, fx, fy, fz, density/mass, density/number, c_ID, c_ID[I], f_ID, f_ID[I], v_name
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<PRE> vx,vy,vz,fx,fy,fz = atom attribute (velocity, force component)
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density/number, density/mass = number or mass density
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c_ID = per-atom vector calculated by a compute with ID
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c_ID[I] = Ith column of per-atom array calculated by a compute with ID
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f_ID = per-atom vector calculated by a fix with ID
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f_ID[I] = Ith column of per-atom array calculated by a fix with ID
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v_name = per-atom vector calculated by an atom-style variable with name
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</PRE>
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<LI>zero or more keyword/arg pairs may be appended
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<LI>keyword = <I>region</I> or <I>bound</I> or <I>discard</I> or <I>norm</I> or <I>ave</I> or <I>units</I> or <I>file</I> or <I>overwrite</I> or <I>title1</I> or <I>title2</I> or <I>title3</I>
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<PRE> <I>region</I> arg = region-ID
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<I>bound</I> args = x/y/z lo hi
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x/y/z = <I>x</I> or <I>y</I> or <I>z</I> to bound bins in this dimension
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lo = <I>lower</I> or coordinate value (distance units)
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hi = <I>upper</I> or coordinate value (distance units)
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<I>discard</I> arg = <I>mixed</I> or <I>no</I> or <I>yes</I>
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mixed = discard atoms outside bins only if bin bounds are explicitly set
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no = always keep out-of-bounds atoms
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yes = always discard out-of-bounds atoms
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<I>norm</I> arg = <I>all</I> or <I>sample</I>
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region-ID = ID of region atoms must be in to contribute to spatial averaging
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<I>ave</I> args = <I>one</I> or <I>running</I> or <I>window M</I>
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one = output new average value every Nfreq steps
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running = output cumulative average of all previous Nfreq steps
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window M = output average of M most recent Nfreq steps
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<I>units</I> arg = <I>box</I> or <I>lattice</I> or <I>reduced</I>
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<I>file</I> arg = filename
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filename = file to write results to
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<I>overwrite</I> arg = none = overwrite output file with only latest output
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<I>title1</I> arg = string
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string = text to print as 1st line of output file
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<I>title2</I> arg = string
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string = text to print as 2nd line of output file
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<I>title3</I> arg = string
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string = text to print as 3rd line of output file
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</PRE>
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</UL>
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<P><B>Examples:</B>
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</P>
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<PRE>fix 1 all ave/spatial 10000 1 10000 z lower 0.02 c_myCentro units reduced &
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title1 "My output values"
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fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
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fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass ave running
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fix 1 flow ave/spatial 100 5 1000 z lower 1.0 y 0.0 2.5 density/mass bound y 5.0 20.0 discard yes ave running
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</PRE>
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<P><B>IMPORTANT NOTE:</B>
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</P>
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<P> The fix ave/spatial command has been replaced by the more flexible
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<A HREF = "fix_ave_chunk.html">fix ave/chunk</A> and <A HREF = "compute_chunk_atom.html">compute
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chunk/atom</A> commands. The fix ave/spatial
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command will be removed from LAMMPS sometime in the summer of 2015.
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</P>
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<P>Any fix ave/spatial command can be replaced by the two new commands.
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You simply need to split the fix ave/spatial arguments across the two
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new commands. For example, this command:
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</P>
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<PRE>fix 1 flow ave/spatial 100 10 1000 y 0.0 1.0 vx vz norm sample file vel.profile
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</PRE>
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<P>could be replaced by:
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</P>
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<PRE>compute cc1 flow chunk/atom bin/1d y 0.0 1.0
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fix 1 flow ave/chunk 100 10 1000 cc1 vx vz norm sample file vel.profile
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Use one or more per-atom vectors as inputs every few timesteps, bin
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their values spatially into 1d, 2d, or 3d bins based on current atom
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coordinates, and average the bin values over longer timescales. The
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resulting bin averages can be used by other <A HREF = "Section_howto.html#howto_15">output
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commands</A> such as <A HREF = "thermo_style.html">thermo_style
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custom</A>, and can also be written to a file.
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</P>
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<P>The group specified with the command means only atoms within the group
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contribute to bin averages. If the <I>region</I> keyword is used, the atom
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must be in both the specified group and the specified geometric
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<A HREF = "region.html">region</A> in order to contribute to bin averages.
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</P>
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<P>Each listed value can be an atom attribute (position, velocity, force
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component), a mass or number density, or the result of a
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<A HREF = "compute.html">compute</A> or <A HREF = "fix.html">fix</A> or the evaluation of an
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atom-style <A HREF = "variable.html">variable</A>. In the latter cases, the
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compute, fix, or variable must produce a per-atom quantity, not a
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global quantity. If you wish to time-average global quantities from a
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compute, fix, or variable, then see the <A HREF = "fix_ave_time.html">fix
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ave/time</A> command.
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</P>
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<P><A HREF = "compute.html">Computes</A> that produce per-atom quantities are those
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which have the word <I>atom</I> in their style name. See the doc pages for
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individual <A HREF = "fix.html">fixes</A> to determine which ones produce per-atom
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quantities. <A HREF = "variable.html">Variables</A> of style <I>atom</I> are the only
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ones that can be used with this fix since all other styles of variable
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produce global quantities.
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</P>
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<P>The per-atom values of each input vector are binned and averaged
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independently of the per-atom values in other input vectors.
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</P>
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<P>The size and dimensionality of the bins (1d = layers or slabs, 2d =
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pencils, 3d = boxes) are determined by the <I>dim</I>, <I>origin</I>, and
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<I>delta</I> settings and how many times they are specified (1, 2, or 3).
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See details below.
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</P>
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<P>IMPORTANT NOTE: This fix works by creating an array of size Nbins by
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Nvalues on each processor. Nbins is the total number of bins; Nvalues
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is the number of input values specified. Each processor loops over
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its atoms, tallying its values to the appropriate bin. Then the
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entire array is summed across all processors. This means that using a
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large number of bins (easy to do for 2d or 3d bins) will incur an
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overhead in memory and computational cost (summing across processors),
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so be careful to use reasonable numbers of bins.
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</P>
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<HR>
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<P>The <I>Nevery</I>, <I>Nrepeat</I>, and <I>Nfreq</I> arguments specify on what
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timesteps the input values will be used to bin them and contribute to
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the average. The final averaged quantities are generated on timesteps
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that are a multiples of <I>Nfreq</I>. The average is over <I>Nrepeat</I>
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quantities, computed in the preceding portion of the simulation every
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<I>Nevery</I> timesteps. <I>Nfreq</I> must be a multiple of <I>Nevery</I> and
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<I>Nevery</I> must be non-zero even if <I>Nrepeat</I> is 1. Also, the timesteps
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contributing to the average value cannot overlap, i.e. Nfreq >
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(Nrepeat-1)*Nevery is required.
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</P>
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<P>For example, if Nevery=2, Nrepeat=6, and Nfreq=100, then values on
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timesteps 90,92,94,96,98,100 will be used to compute the final average
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on timestep 100. Similarly for timesteps 190,192,194,196,198,200 on
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timestep 200, etc. If Nrepeat=1 and Nfreq = 100, then no time
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averaging is done; values are simply generated on timesteps
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100,200,etc.
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</P>
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<HR>
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<P>Each per-atom property is also averaged over atoms in each bin. The
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way the averaging is one across the <I>Nrepeat</I> timesteps to produce
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output on the <I>Nfreq</I> timesteps, and across multiple <I>Nfreq</I> outputs,
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is determined by the <I>norm</I> and <I>av</I> keyword settings, as discussed
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below.
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</P>
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<P>Bins can be 1d layers or slabs, 2d pencils, or 3d boxes. This depends
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on how many times (1, 2, or 3) the <I>dim</I>, <I>origin</I>, and <I>delta</I>
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settings are specified in the fix ave/spatial command. For 2d or 3d
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bins, there is no restriction on specifying dim = x before dim = y, or
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dim = y before dim = z. Bins in a particular <I>dim</I> have a bin size in
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that dimension given by <I>delta</I>. Every Nfreq steps, when averaging is
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being performed and the per-atom property is calculated for the first
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time, the number of bins and the bin sizes and boundaries are
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computed. Thus if the simulation box changes size during a
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simulation, the number of bins and their boundaries may also change.
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In each dimension, bins are defined relative to a specified <I>origin</I>,
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which may be the lower/upper edge of the simulation box in that
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dimension, or its center point, or a specified coordinate value.
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Starting at the origin, sufficient bins are created in both directions
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to completely span the bin extent in that dimension. By default the
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bin extent is the entire simulation box.
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</P>
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<P>The <I>bound</I> keyword can be used one or more times to limit the extent
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of bin coverage in specified dimensions, i.e. to only bin a portion of
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the box. If the <I>lo</I> setting is <I>lower</I> or the <I>hi</I> setting is
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<I>upper</I>, the bin extent in that direction extends to the box boundary.
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If a numeric value is used for <I>lo</I> and/or <I>hi</I>, then the bin extent
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in the <I>lo</I> or <I>hi</I> direction extends only to that value, which is
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assumed to be inside (or at least near) the simulation box boundaries,
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though LAMMPS does not check for this.
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</P>
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<P>On each sampling timestep, each atom is mapped to the bin it currently
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belongs to, based on its current position. Note that the group-ID and
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region keyword can exclude specific atoms from this operation, as
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discussed above. Note that between reneighboring timesteps, atoms can
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move outside the current simulation box. If the box is periodic (in
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that dimension) the atom is remapping into the periodic box for
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purposes of binning. If the box in not periodic, the atom may have
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moved outside the bounds of any bin.
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</P>
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<P>The <I>discard</I> keyword determines what is done with any atom which is
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outside the bounds of any bin. If <I>discard</I> is set to <I>yes</I>, the atom
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will be ignored and not contribute to any bin averages. If <I>discard</I>
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is set to <I>no</I>, the atom will be counted as if it were in the first or
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last bin in that dimension. If (discard</I> is set to <I>mixed</I>, which is
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the default, it will only be counted in the first or last bin if bins
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extend to the box boundary in that dimension. This is the case if the
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<I>bound</I> keyword settings are <I>lower</I> and <I>upper</I>, which is the
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default. If the <I>bound</I> keyword settings are numeric values, then the
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atom will be ignored if it is outside the bounds of any bin. Note
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that in this case, it is possible that the first or last bin extends
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beyond the numeric <I>bounds</I> settings, depending on the specified
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<I>origin</I>. If this is the case, the atom is only ignored if it is
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outside the first or last bin, not if it is simply outside the numeric
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<I>bounds</I> setting.
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</P>
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<P>For orthogonal simulation boxes, the bins are also layers, pencils, or
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boxes aligned with the xyz coordinate axes. For triclinic
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(non-orthogonal) simulation boxes, the bins are so that they are
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parallel to the tilted faces of the simulation box. See <A HREF = "Section_howto.html#howto_12">this
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section</A> of the manual for a discussion of
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the geometry of triclinic boxes in LAMMPS. As described there, a
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tilted simulation box has edge vectors a,b,c. In that nomenclature,
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bins in the x dimension have faces with normals in the "b" cross "c"
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direction. Bins in y have faces normal to the "a" cross "c"
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direction. And bins in z have faces normal to the "a" cross "b"
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direction. Note that in order to define the size and position of
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these bins in an unambiguous fashion, the <I>units</I> option must be set
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to <I>reduced</I> when using a triclinic simulation box, as noted below.
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</P>
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<HR>
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<P>The atom attribute values (vx,vy,vz,fx,fy,fz) are self-explanatory.
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Note that other atom attributes (including atom postitions x,y,z) can
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be used as inputs to this fix by using the <A HREF = "compute_property_atom.html">compute
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property/atom</A> command and then specifying
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an input value from that compute.
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</P>
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<P>The <I>density/number</I> value means the number density is computed in
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each bin, i.e. a weighting of 1 for each atom. The <I>density/mass</I>
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value means the mass density is computed in each bind, i.e. each atom
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is weighted by its mass. The resulting density is normalized by the
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volume of the bin so that units of number/volume or density are
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output. See the <A HREF = "units.html">units</A> command doc page for the
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definition of density for each choice of units, e.g. gram/cm^3.
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</P>
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<P>If a value begins with "c_", a compute ID must follow which has been
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previously defined in the input script. If no bracketed integer is
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appended, the per-atom vector calculated by the compute is used. If a
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bracketed integer is appended, the Ith column of the per-atom array
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calculated by the compute is used. Users can also write code for
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their own compute styles and <A HREF = "Section_modify.html">add them to LAMMPS</A>.
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</P>
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<P>If a value begins with "f_", a fix ID must follow which has been
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previously defined in the input script. If no bracketed integer is
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appended, the per-atom vector calculated by the fix is used. If a
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bracketed integer is appended, the Ith column of the per-atom array
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calculated by the fix is used. Note that some fixes only produce
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their values on certain timesteps, which must be compatible with
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<I>Nevery</I>, else an error results. Users can also write code for their
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own fix styles and <A HREF = "Section_modify.html">add them to LAMMPS</A>.
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</P>
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<P>If a value begins with "v_", a variable name must follow which has
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been previously defined in the input script. Variables of style
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<I>atom</I> can reference thermodynamic keywords and various per-atom
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attributes, or invoke other computes, fixes, or variables when they
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are evaluated, so this is a very general means of generating per-atom
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quantities to spatially average.
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</P>
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<HR>
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<P>Additional optional keywords also affect the operation of this fix.
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The <I>region</I>, <I>bound</I>, and <I>discard</I> keywords were discussed above.
|
||
|
|
</P>
|
||
|
|
<P>The <I>norm</I> keyword affects how averaging is done for the output
|
||
|
|
produced every <I>Nfreq</I> timesteps. For an <I>all</I> setting, a bin
|
||
|
|
quantity is summed over all atoms in all <I>Nrepeat</I> samples, as is the
|
||
|
|
count of atoms in the bin. The printed value for the bin is
|
||
|
|
Total-quantity / Total-count. In other words it is an average over
|
||
|
|
the entire <I>Nfreq</I> timescale.
|
||
|
|
</P>
|
||
|
|
<P>For a <I>sample</I> setting, the bin 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 bin is the average of the <I>Nrepeat</I> "average sample values", In
|
||
|
|
other words it is an average of an average.
|
||
|
|
</P>
|
||
|
|
<P>The <I>ave</I> keyword determines how the bin values produced every <I>Nfreq</I>
|
||
|
|
steps are averaged with bin values produced on previous steps that
|
||
|
|
were multiples of <I>Nfreq</I>, before they are accessed by another output
|
||
|
|
command or written to a file.
|
||
|
|
</P>
|
||
|
|
<P>If the <I>ave</I> setting is <I>one</I>, then the bin values produced on
|
||
|
|
timesteps that are multiples of <I>Nfreq</I> are independent of each other;
|
||
|
|
they are output as-is without further averaging.
|
||
|
|
</P>
|
||
|
|
<P>If the <I>ave</I> setting is <I>running</I>, then the bin values produced on
|
||
|
|
timesteps that are multiples of <I>Nfreq</I> are summed and averaged in a
|
||
|
|
cumulative sense before being output. Each output bin value is thus
|
||
|
|
the average of the bin value produced on that timestep with all
|
||
|
|
preceding values for the same bin. This running average begins when
|
||
|
|
the fix is defined; it can only be restarted by deleting the fix via
|
||
|
|
the <A HREF = "unfix.html">unfix</A> command, or re-defining the fix by
|
||
|
|
re-specifying it.
|
||
|
|
</P>
|
||
|
|
<P>If the <I>ave</I> setting is <I>window</I>, then the bin values produced on
|
||
|
|
timesteps that are multiples of <I>Nfreq</I> are summed and averaged within
|
||
|
|
a moving "window" of time, so that the last M values for the same bin
|
||
|
|
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 bin
|
||
|
|
values on steps 8000,9000,10000. Outputs on early steps will average
|
||
|
|
over less than M values if they are not available.
|
||
|
|
</P>
|
||
|
|
<P>The <I>units</I> keyword determines the meaning of the distance units used
|
||
|
|
for the bin size <I>delta</I> and for <I>origin</I> and <I>bounds</I> values if they
|
||
|
|
are coordinate value. For orthogonal simulation boxes, any of the 3
|
||
|
|
options may be used. For non-orthogonal (triclinic) simulation boxes,
|
||
|
|
only the <I>reduced</I> option may be used.
|
||
|
|
</P>
|
||
|
|
<P>A <I>box</I> value selects standard distance units as defined by the
|
||
|
|
<A HREF = "units.html">units</A> command, e.g. Angstroms for units = real or metal.
|
||
|
|
A <I>lattice</I> value means the distance units are in lattice spacings.
|
||
|
|
The <A HREF = "lattice.html">lattice</A> command must have been previously used to
|
||
|
|
define the lattice spacing. A <I>reduced</I> value means normalized
|
||
|
|
unitless values between 0 and 1, which represent the lower and upper
|
||
|
|
faces of the simulation box respectively. Thus an <I>origin</I> value of
|
||
|
|
0.5 means the center of the box in any dimension. A <I>delta</I> value of
|
||
|
|
0.1 means 10 bins span the box in that dimension.
|
||
|
|
</P>
|
||
|
|
<P>Consider a non-orthogonal box, with bins that are 1d layers or slabs
|
||
|
|
in the x dimension. No matter how the box is tilted, an <I>origin</I> of
|
||
|
|
0.0 means start layers at the lower "b" cross "c" plane of the
|
||
|
|
simulation box and an <I>origin</I> of 1.0 means to start layers at the
|
||
|
|
upper "b" cross "c" face of the box. A <I>delta</I> 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.
|
||
|
|
</P>
|
||
|
|
<P>The <I>file</I> keyword allows a filename to be specified. Every <I>Nfreq</I>
|
||
|
|
timesteps, a section of bin info will be written to a text file in the
|
||
|
|
following format. A line with the timestep and number of bin is
|
||
|
|
written. Then one line per bin is written, containing the bin ID
|
||
|
|
(1-N), the coordinate of the center of the bin, the number of atoms
|
||
|
|
in the bin, and one or more calculated values. The number of values
|
||
|
|
in each line corresponds to the number of values specified in the fix
|
||
|
|
ave/spatial command. The number of atoms and the value(s) are average
|
||
|
|
quantities. If the value of the <I>units</I> keyword is <I>box</I> or
|
||
|
|
<I>lattice</I>, the "coord" is printed in box units. If the value of the
|
||
|
|
<I>units</I> keyword is <I>reduced</I>, the "coord" is printed in reduced units
|
||
|
|
(0-1).
|
||
|
|
</P>
|
||
|
|
<P>The <I>overwrite</I> keyword will continuously overwrite the output file
|
||
|
|
with the latest output, so that it only contains one timestep worth of
|
||
|
|
output. This option can only be used with the <I>ave running</I> setting.
|
||
|
|
</P>
|
||
|
|
<P>The <I>title1</I> and <I>title2</I> and <I>title3</I> keywords allow specification of
|
||
|
|
the strings that will be printed as the first 3 lines of the output
|
||
|
|
file, assuming the <I>file</I> keyword was used. LAMMPS uses default
|
||
|
|
values for each of these, so they do not need to be specified.
|
||
|
|
</P>
|
||
|
|
<P>By default, these header lines are as follows:
|
||
|
|
</P>
|
||
|
|
<PRE># Spatial-averaged data for fix ID and group name
|
||
|
|
# Timestep Number-of-bins
|
||
|
|
# Bin Coord1 Coord2 Coord3 Count value1 value2 ...
|
||
|
|
</PRE>
|
||
|
|
<P>In the first line, ID and name are replaced with the fix-ID and group
|
||
|
|
name. The second line describes the two values that are printed at
|
||
|
|
the first of each section of output. In the third line the values are
|
||
|
|
replaced with the appropriate fields from the fix ave/spatial command.
|
||
|
|
The Coord2 and Coord3 entries in the third line only appear for 2d and
|
||
|
|
3d bins respectively. For 1d bins, the word Coord1 is replaced by
|
||
|
|
just Coord.
|
||
|
|
</P>
|
||
|
|
<HR>
|
||
|
|
|
||
|
|
<P><B>Restart, fix_modify, output, run start/stop, minimize info:</B>
|
||
|
|
</P>
|
||
|
|
<P>No information about this fix is written to <A HREF = "restart.html">binary restart
|
||
|
|
files</A>. None of the <A HREF = "fix_modify.html">fix_modify</A> options
|
||
|
|
are relevant to this fix.
|
||
|
|
</P>
|
||
|
|
<P>This fix computes a global array of values which can be accessed by
|
||
|
|
various <A HREF = "Section_howto.html#howto_15">output commands</A>. The values can
|
||
|
|
only be accessed on timesteps that are multiples of <I>Nfreq</I> since that
|
||
|
|
is when averaging is performed. The global array has # of rows =
|
||
|
|
Nbins and # of columns = Ndim+1+Nvalues, where Ndim = 1,2,3 for
|
||
|
|
1d,2d,3d bins. The first 1 or 2 or 3 columns have the bin coordinates
|
||
|
|
(center of the bin) in the appropriate dimensions, the next column has
|
||
|
|
the count of atoms in that bin, and the remaining columns are the
|
||
|
|
Nvalue quantities. When the array is accessed with an I that exceeds
|
||
|
|
the current number of bins, than a 0.0 is returned by the fix instead
|
||
|
|
of an error, since the number of bins can vary as a simulation runs,
|
||
|
|
depending on the simulation box size. 2d or 3d bins are ordered so
|
||
|
|
that the last dimension(s) vary fastest. The array values calculated
|
||
|
|
by this fix are "intensive", since they are already normalized by the
|
||
|
|
count of atoms in each bin.
|
||
|
|
</P>
|
||
|
|
<P>No parameter of this fix can be used with the <I>start/stop</I> keywords of
|
||
|
|
the <A HREF = "run.html">run</A> command. This fix is not invoked during <A HREF = "minimize.html">energy
|
||
|
|
minimization</A>.
|
||
|
|
</P>
|
||
|
|
<P><B>Restrictions:</B>
|
||
|
|
</P>
|
||
|
|
<P>When the <I>ave</I> keyword is set to <I>running</I> or <I>window</I> then the number
|
||
|
|
of bins 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 <I>units</I> keyword is set to
|
||
|
|
<I>reduced</I>.
|
||
|
|
</P>
|
||
|
|
<P><B>Related commands:</B>
|
||
|
|
</P>
|
||
|
|
<P><A HREF = "compute.html">compute</A>, <A HREF = "fix_ave_atom.html">fix ave/atom</A>, <A HREF = "fix_ave_histo.html">fix
|
||
|
|
ave/histo</A>, <A HREF = "fix_ave_time.html">fix ave/time</A>,
|
||
|
|
<A HREF = "variable.html">variable</A>, <A HREF = "fix_ave_correlate.html">fix ave/correlate</A>,
|
||
|
|
<A HREF = "fix_ave_spatial_sphere.html">fix ave/spatial/sphere</A>
|
||
|
|
</P>
|
||
|
|
<P><B>Default:</B>
|
||
|
|
</P>
|
||
|
|
<P>The option defaults are bound = lower and upper in all dimensions,
|
||
|
|
discard = mixed, norm = all, ave = one, units = lattice, no file
|
||
|
|
output, and title 1,2,3 = strings as described above.
|
||
|
|
</P>
|
||
|
|
</HTML>
|