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Re: [lammps-users] Higher Dimensional Distribution Functions (Beyond RDF)
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Re: [lammps-users] Higher Dimensional Distribution Functions (Beyond RDF)


From: Axel Kohlmeyer <akohlmey@...24...>
Date: Fri, 11 May 2018 18:48:24 -0400



On Fri, May 11, 2018 at 1:17 PM, James Mansell <jmmansel@...4292...2...> wrote:
Hello LAMMPS users,

I would like to calculate the two-particle (pair) distribution function in small systems with external potentials having continuous "infinitely long" cylindrical symmetry.  [Forgive my abuse of terminology.]  Due to the external potential, RDF is no longer a sufficient descriptor.  I need four dimensions to describe this distribution.

​a 4d-distribution is tricky to visualize, you'd have to render multiple (nested?, transparent?) isosurfaces and possibly run a clipping plane through it. or do projections.
 

After searching the documentation and mailing list archives, I have not found any discussions of such a requirement, but I figure it is worth a shot to ask the following:

1. Does LAMMPS have any standard compute or other capability that might be helpful for doing this that I have overlooked?

​i don't think so.

2. Has anyone out there done something like this, or know of anyone who has done it, that could be helpful?

​nope.

3. Is this a somewhat reasonable thing to try to implement (in LAMMPS)?  I am considering writing a compute, which I have not done before.  I would rather know in advance if more experienced users think this is a bad idea (not that I would not try it anyway).

​it is not clear to me, what exactly you are after, thus i am hesitant to give specific advice. 

Incidentally, my systems are quite small and simple ( < 2,500 LJ particles, < 2,000 nm^-3), and by taking advantage of symmetries and other information, I believe a suitable "mesh" could be produced with fewer than 1E9 bins, perhaps significantly fewer.  So, it seems like the curse of dimensionality should be manageable IF I am careful.

I guess I could also consider a spatial decomposition other than discrete bins.  Or some other method entirely?

​if you are not under pressure to produce results, i would continue looking around in the published literature to review examples of what other people have done under similar circumstances. perhaps there is a more accessible approach.​

 
​axel.​



Any help is much appreciated.

Kind regards,

Matt
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--
Dr. Axel Kohlmeyer  akohlmey@...92......  http://goo.gl/1wk0
College of Science & Technology, Temple University, Philadelphia PA, USA
International Centre for Theoretical Physics, Trieste. Italy.