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ooblick magick
We all know that cornstarch + water (otherwise known as ooblick) is amazing stuff. However, these guys in texas at the center for nonlinear dynamics have taken it to a new level. If nothing else, you should check out the paper and definitely the movie. I wonder if this could be repeated just using a loudspeaker and function generator? Yet another reason to procrastinate on studying for finals!
[edit: you're too late! I guess the movie was "slashdotted," as it's no longer available from their web page. )-: edit2: nevermind, they fixed it.]
[edit3: here's an experiment with solitons that you can do on the surface of a pool: Falaco Solitons. Check out the paper gr-qc/0101098 in arXiv. "String theorists take note, for the
structure consists of a pair of topological 2-dimensional rotational defects in a surface of
discontinuity, globally connected and stabilized by a 1 dimensional topological defect or
string."]
On another note, I'm curious how much of antenna theory can be co-opted to make antennas for sound. A yagi for sound seems a bit unlikely, but parabolic reflectors certainly work, and it seems that there ought to be some magic with cavity resonators.
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I wonder how small a body of water you can have in which to demonstrate Falaco solitons. Hmm... conjecturing that the galaxies are Falaco solitons seems pretty wacky, since there is no fluid discontinuity such as the swimming pool surface.
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no! they're supposed to inspire! anyway, i added you because i felt similarly about you (posting cool stuff.. must be a part of it). (-: oh yeah, and because i'm moving to rochester, and, iirc, you're at RPI in Troy? nowhere near rochester, but another netherpart of new york state.
I don't understand this soliton stuff at all. how do the falaco solitons relate to the "solitary waves" we saw i.e. in the manchester channel? i have to do some reading. one of my goals for the next 1-2 years is to be able to understand my friend's masters thesis, "Pions versus Magnons: From QCD to Antiferromagnets and Quantum Hall Ferromagnets (http://www.arxiv.org/PS_cache/cond-mat/pdf/0310/0310353.pdf)" [pdf], on the arXiv as
cond-mat/0310353.hope i'm not just telling you a lot of stuff you've already read
See this (http://homepages.tversu.ru/~s000154/collision/main.html) for some maple animations of sine-Gordon solitons, and this (http://math.cofc.edu/faculty/kasman/SOLITONPICS/hmsol.html) for a physical system which those equations actually model.
The coolest thing I've learned about solitons so far is that, even though they are solutions to a nonlinear system, they obey a kind of superposition principle. That's how you can have a swimming pool with lots of Falaco solitons drifting around in it (although apparently always an even number). The graphs above illustrate some superimposed solutions, and some cases where solitons scatter against each other.
The Falaco solitons may have no mathematical relation to the solitons of John Scott Russel... I don't know. I'm pretty sure when you move from 1-d systems (like the 1-d sine gordon) to 2-d and 3-d systems, a lot of wacky things become possible. Such as our wacky friend, angular momentum.
What I would really like to understand is what the Falaco solitons have to do with topology. Kiehn stresses the phrase 'topological discontinuity' over and over again. I'm taking a topology class next semester but it's just introductory...
I think if I keep studying homology, cohomology, exterior algebras, manifolds, general topology, at some point everything will fall into place.