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In my experience (PhD student working on laser plasma interaction experiments) these PIC codes are pretty closely guarded by their creators. There are a few out there, for example OSIRIS, VORPAL, and TurboWave in addition to VLPL. Of these I think only VORPAL is commercially available (through Tech-X) and the others you would need to contact the groups ...
I've been looking at this Java archive General Relativity (GR) Package written by Wolfgang Christian, Mario Belloni, and Anne Cox It includes a lot of simple programs about Newtonian mechanics, special relativity and general relativity, including the aforementioned GROrbits. It doesn't permit custom metrics - you are limited to Schwarzschild ...
For particle/light motion in 2D space, my nomination would be GROrbits It's free and requires a JVM to run, there is also a web start version for the brave ;) Sorry but I've never found anything aimed at visualizing metrics or curvature (apart from plotting programs of course).
To integrate the expression over the area you need to write the area of the surface element (the ring of charge that is a distance $r$ away). If we write the position of a point on that surface in spherical coordinates (rather than (x',y',z')) then a little element of surface becomes $$dA = R \sin\theta d\theta R d\phi$$ which they stated explicitly in the ...
By the sounds of it you have made a mistake with the units. In fact, you should not be using SI units at all in your simulation; astronomical values in SI units vary by such huge orders of magnitude that they are often a source of floating point errors that can destroy trajectories. You should instead use the astronomical system of units. Specifically, ...
Two programs that can do the job are: XCrySDen (free) and Material Studio (commercial). I think the MS visualizer is free. For XCrySDen and the other software you might need to convert from one format to another. For instance from .cif to .struct or .xyz, you can find scripts online to help you do the format conversion and then use the software to visualize ...
+1 for python, scipy, numpy. The other advantage is that it does scripting so if you have to do this for many experiments, you'll be able to do the whole directory, rather than just one at a time.
Here is some documentation for Matlab's fft: https://www.google.nl/url?sa=t&source=web&rct=j&ei=d50VVcCiFumz7gbl54G4Aw&url=http://www.mathworks.com/help/matlab/ref/fft.html&ved=0CBwQFjAA&usg=AFQjCNEW3G7KD5j1-T99VPbdeCb80SHHLg Octave is supposed to be very similar.
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