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I sample a snapshot from a system with 50 particles including their position and instant velocities.

The snapshot is a list of 3 position and 3 velocities values per particle. i.e. 50 lines each of which is comprised of $(x,y,z,\dot{x},\dot{y},\dot{z})$ (AKA phase space coordinates).

My data set's layout is similar to the one used in Making a ListVectorPlot3D from data in an external file, hence it is, basically, a velocity field in 3D.

I want to calculate and plot the following properties of the dynamics: curl, div, stream of the fluid in 3D, vorticity.

How can I visualize those attributes of the velocity field in 3D? Something like this in 3D would be great:

enter image description here

I have only a 2D presentation:

In addition I think that calculating and to visualize the Covariance or correlation between the pairwise particles could be interesting too. 

data = Import["http://pastebin.com/raw/6Werdnpf"];
vecdata = Partition[#, 3] & /@ DeleteDuplicates[data];
Graphics3D[{ColorData[1][1], Arrowheads[Medium], Arrow[{First@#, Total@#}] & /@ vecdata}]
ListVectorPlot[Map[Most, vecdata, {2}]]

enter image description here

enter image description here

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    $\begingroup$ @C.E. frankly speaking, I am open to hear any suggestion. I want to plot the vortex lines in 3D, the vorticity, the div, or any other CFD property of the velocity field. Or any visualization of the 6D phase space or its subspaces. $\endgroup$
    – 0x90
    Commented Feb 5, 2017 at 7:44
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    $\begingroup$ ok, it's a legitimate question but if it doesn't receive any answers and you still want something then I would recommend to rewrite it as a question purely about Mathematica, along the lines of "I have this data. I want to make this type of plot. How do I do it in Mathematica?" $\endgroup$
    – C. E.
    Commented Feb 5, 2017 at 8:50
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    $\begingroup$ @C.E. no problem, thank you. I just don't want to limit people's creativity by giving such a reference plot. $\endgroup$
    – 0x90
    Commented Feb 5, 2017 at 9:00
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    $\begingroup$ Please STOP editing the title to bump up the question on the homepage. This question doesn't need 15 revisions... This question was cross-posted on Stack Overflow as a MATLAB question, which makes me agree with C. E. that this is a physics/I-need-this-done-somehow question masquerading as a Mathematica question. I would be inclined to close it as Off-topic: Out of Scope. $\endgroup$
    – rm -rf ♦
    Commented Feb 6, 2017 at 3:45
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    $\begingroup$ @R.M, It is purely a mathematica question in which I try to plot the vorticity of a vector field. Both this and the SO post are related though by the fact that I am trying to plot the same data set. $\endgroup$
    – 0x90
    Commented Feb 6, 2017 at 3:52

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