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git-svn-id: svn://svn.icms.temple.edu/lammps-ro/trunk@14239 f3b2605a-c512-4ea7-a41b-209d697bcdaa
116 lines
4.2 KiB
HTML
116 lines
4.2 KiB
HTML
<HTML>
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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>compute hexorder/atom command
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</H3>
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<P><B>Syntax:</B>
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</P>
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<PRE>compute ID group-ID hexorder/atom keyword values ...
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</PRE>
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<UL><LI>ID, group-ID are documented in <A HREF = "compute.html">compute</A> command
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<LI>hexorder/atom = style name of this compute command
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<LI>zero or more keyword/value pairs may be appended
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<LI>keyword = <I>degree</I>
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<PRE> <I>n</I> value = degree of order parameter
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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>compute 1 all hexorder/atom
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compute 1 all hexorder/atom n 4
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</PRE>
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<P><B>Description:</B>
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</P>
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<P>Define a computation that calculates <I>qn</I> the bond-orientational
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order parameter for each atom in a group. The hexatic (<I>n</I> = 6) order
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parameter was introduced by <A HREF = "#Nelson">Nelson and Halperin</A> as a way to detect
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hexagonal symmetry in two-dimensional systems. For each atom, <I>qn</I>
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is a complex number (stored as two real numbers) defined as follows:
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</P>
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<CENTER><IMG SRC = "Eqs/hexorder.jpg">
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</CENTER>
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<P>where the sum is over the <I>n</I> nearest neighbors
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of the central atom. The angle theta
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is formed by the bond vector rij and the <I>x</I> axis. theta is calculated
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only using the <I>x</I> and <I>y</I> components, whereas the distance from the
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central atom is calculated using all three
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<I>x</I>, <I>y</I>, and <I>z</I> components of the bond vector.
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Neighbor atoms not in the group
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are included in the order parameter of atoms in the group.
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</P>
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<P>The optional keyword <I>n</I> sets the degree of the order parameter.
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The default value is 6. For a perfect hexagonal lattice,
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<I>q</I>6 = exp(6 i phi) for all atoms, where the constant 0 < phi < pi/3
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depends only on the orientation of the lattice relative to the x axis.
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In an isotropic liquid, local neighborhoods may still exhibit
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weak hexagonal symmetry, but because the orientational correlation
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decays quickly with distance, the value of phi will be different for
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different atoms, and |<<I>q</I>6>| << 1.
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</P>
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<P>The value of <I>qn</I> will be zero for atoms not in the
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specified compute group. If the atom has less than <I>n</I> neighbors (within
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the potential cutoff), then <I>qn</I> is set to zero.
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</P>
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<P>The neighbor list needed to compute this quantity is constructed each
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time the calculation is performed (i.e. each time a snapshot of atoms
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is dumped). Thus it can be inefficient to compute/dump this quantity
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too frequently.
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</P>
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<P>IMPORTANT NOTE: If you have a bonded system, then the settings of
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<A HREF = "special_bonds.html">special_bonds</A> command can remove pairwise
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interactions between atoms in the same bond, angle, or dihedral. This
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is the default setting for the <A HREF = "special_bonds.html">special_bonds</A>
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command, and means those pairwise interactions do not appear in the
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neighbor list. Because this fix uses the neighbor list, it also means
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those pairs will not be included in the order parameter. One way
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to get around this, is to write a dump file, and use the
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<A HREF = "rerun.html">rerun</A> command to compute the order parameter for snapshots
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in the dump file. The rerun script can use a
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<A HREF = "special_bonds.html">special_bonds</A> command that includes all pairs in
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the neighbor list.
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</P>
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<P><B>Output info:</B>
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</P>
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<P>This compute calculates a per-atom array with 2 columns, giving the
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real and imaginary parts of <I>qn</I>, respectively.
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</P>
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<P>These values can be accessed by any command that uses
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per-atom values from a compute as input. See <A HREF = "Section_howto.html#howto_15">Section_howto
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15</A> for an overview of LAMMPS output
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options.
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</P>
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<P>The per-atom array contain pairs of numbers representing the
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real and imaginary parts of <I>qn</I>, a complex number subject to the
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constraint |<I>qn</I>| <= 1.
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</P>
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<P><B>Restrictions:</B> none
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</P>
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<P><B>Related commands:</B>
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</P>
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<P><A HREF = "compute_coord_atom.html">compute coord/atom</A>, <A HREF = "compute_centro_atom.html">compute centro/atom</A>
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</P>
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<P><B>Default:</B>
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</P>
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<P>The option default is <I>n</I> = 6.
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</P>
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<HR>
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<A NAME = "Nelson"></A>
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<P><B>(Nelson)</B> Nelson, Halperin, Phys Rev B, 19, 2457 (1979).
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</P>
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</HTML>
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