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Plotting ellipsoids with R


New article: Generating polydisperse periodic RVEs containing ellipsoidal particles (part 1)

I'll post the rest on the series on this comment thread because my articles are not showing up on the imechanica RSS feed.

-- Biswajit

Part 4 of article on periodic RVE generation.

New article: Visualizing ellipsoids with VisIt and ParaView (a hack) :

-- Biswajit

Guess your concern here is mainly about visualization, but if you would allow me an idle musing on the side:

If the surface of a hollow ellipsoid (i.e. one which is not a sphere) emits a force-field (say, one that follows the inverse-square law), then, the net force per unit surface area at any point interior to the ellipsoid (other than the center) would be a function of the orientation of that surface. ... Due to symmetry, the net field at the center point would be zero at any orientation, be it a sphere or an ellipsoid. ... But coming back to the force per unit area, one that varies with the orientation of the surface is precisely what we want in order to reach the concept of stress, don't we?

... Just an idle musing, that's all... (Someone must have already written a journal paper that at least in part covers this idea.)




Yes, my concern is mostly with recording solutions to issues that I have run into.  I particularly like the one in the latest article.

Also, I have no idea what you are talking about in your comment; probably because I find it hard to understand things without pictures or equations as illustration.

-- Biswajit


I googled and found that:

(i) A lot of people from Laplace to Chandra have studied the problem of gravity (a force field having an inverse-square law) produced by an ellipsoid; e.g. see here [^] or here [PDF ^]. However, they seemed to have been focused on a dense ellipsoid, whereas what I was just idly musing about was a hollow one (i.e. an ellipsoidal shell). [Yes, my hunch turned out right; there are many papers on the broad topic as such.] The problem for the hollow sphere was solved by Newton himself [^]. But, apparently, not for a hollow ellipsoid.

(ii) As I just found out, someone else other than me had thought of the problem; see here [^].

(iii) Further, I was also wondering if for the hollow ellipsoid, gravity had a law of the form: F = r^{n}, where n is not equal to -2.

Anyway, forget about it. There are no [further and relevant] pictures. Sorry if I ended up distracting you.



Interesting that I was looking at Chandrasekhar's exact solutions for ellipsoid potentials just a few days ago.  Since you're interested in these problems, and are not completely against numerical solutions, you should try using the approach in to complete the quantities you are curious about.  The analytical solutions should provide a way of verifying your code.

-- Biswajit

Meow... [It means something like: "Friendly Respects," as emitted by a kitten when after you overpower/lift it [esp. after a playful game], it still insists on emitting some sound!]

OK. But weren't I clear that it all was just an [absolutely] idle musing to begin with? ... I mean, I googled only because you actually responded and all ... [But, yes, in one of the replies above, I did want to boast that my hunches were on target!]

No, I am NOT interested in this problem.

If I write anything more, I realize, it gets even worse, but, just out of curiosity: Looks like it's a particles-based approach. How would you classify it? as SPH? MD? simplification of both/similar/others? something more?

But then again, I am NOT interested.

SO, FORGET it [all]! [Meow!!]


PS: I have not harmed any puppies by mentioning kitten in the above comment. Honest! Swear to God!!  [I have been given to understand that puppies and kitten enter interpretations of political competitions esp. in the USA and India/Gujarat.]

PPS: Bye for now, strictly!

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