Thursday, April 27, 2006

Fractal Dust, LEDs and Cracks in the Cosmos

Dust aggregates formed in microgravity aboard the CODAG Shuttle experiment.
Micron sized SiO2 spheres rapdily aggregated in microgravity into low dimension fractal structures (Blum et al "Growth and Form of Planetary Seedlings: Results from a Microgravity Aggregation Experiment," Phys. Rev. Lett. 85, 2426 (2000). )

Physics News Update 775:"...At the APS meeting, Eric Adelberger, leader of the Washington group, summarized some of the other efforts underway in his lab such as the search for evidence of extra dimensions in the form of departures from Newtonian gravity (for instance, the inverse-square dependence) at a size scale of tens of microns. In fact, he said that something strange was happening at a measurement scale of about 70 microns; the most likely explanation of this, he conceded, was an experimental artifact."

Oo. Er.

So, a few years ago I did something whacky but fun.

Each year the Gravity Research Foundation runs an essay competition.
It is nice opportunity to indulge in some speculation that may not be mature enough for an actual fer reel letter, but is worth thinking about, a little bit.

So, back in 2001, I was thinking about fractal dust.
The Blum et al paper had just come out, and I had just come back from the Cosmic Genesis and Fundamenal Physics Workshop at Sonoma, so I was just freshly updated on the Large Extra Dimensions speculation...

Now, at the time there was a bubbling puzzle in planet formation, namely how Neptune and Uranus ever got started during the lifetime of the solar system, the timescaled inferred for aggregation were just too long, the gas and dust disk would be gone before planet formation got under way. (This is a non-problem now, best bet scenario is that Neptune formed much further in and was scattered out at early times, but it motivated the chain of thought).

So... thought I, that's funny.
IF micron dust grains are fractal, with low effective dimensions, then grain growth is rapid, and almost mass independent at low mass.
And, lo and behold, they are fractal, with effective dimension ~ 1.3.

Ok, neat. But, how could that be?
Well, one explanation is that when sub-micron grains aggregate, they see a strong non-Coulomb force at small radii, and coalescence is at high specifical angular momenta. This naturally leads to open, fractal structure growth, for a while, until impacts start compactifying the "dust bunnies". (see below)
Cool. Well, we can calculate that, and there are several candidates (van der Waals forces, heterogenous temporary free charge etc etc), but why not look at non-Newtonian gravity on small scales.

So, we plug'n'chug, and this works, for 2 Large Extra Dimensions, and a effective radius of curvature (this also works in Randall-Sundrum theory) is about 80 μ

So, I wrote it up, sent it to GRF, got an honourable mention, and IJMPD 10.6 781 publication.

Also got a writeup by Marcus Chown in New Scientist, and again with the even whackier follow up on Bose-Einstein condensates and Large Extra Dimensions

The interesting thing is not the planet formation, it is whether the fractal dust formation really is due to non-Newtonian gravity and hence "predicted" a n=2 Large Extra Dimension deviation at less than 100 μ.

So... maybe Adelberger is not seeing an experimental artifact.
We can hope, would make life a lot more interesting.

Oh, and I still think something like the BEC stuff would work, but maybe people can tell that I am not an actual experimental designer kinda person...

Experimental hints of Gravity in Large Extra Dimensions?
Recent conjectures suggest the universe may have large extra dimensions, through which gravity propagates. This implies gross departures from Newton's law of gravity at small length scales.
Here I consider some implications for particle dynamics on scales comparable to the compactification radius, $R_c \ltorder 1$ mm.
During planet formation, coalescence of micron sized dust grains to planetesimals is a rate critical step.
Blum et al (2000) found dust grain aggregates form low fractal dimension structures in microgravity, consistent with high angular momentum coalescence.
I consider the effects of non-Newtonian gravity on dust aggregation on scales less than $R_c$ and show they naturally coalesce into low dimensional structures with high specific angular momentum.
We infer $R_c \approx 80$ microns.


Anonymous Anonymous said...

Wouldn't the size distribution and fractal dimension of the aggregates depend on the material and the temperature as well? Surely TiO2 grains and FeS grains and SiO2 grains and Al2O3 grains and diamondoid grains aggregate differently? There are too many free variables. The 80 microns can't be an invariant?

But it was a delightfully wacky idea, well thought through.

-- Professor Jonathan Vos Post

4:13 PM  
Blogger Steinn said...

The $400 million question...
If the fractal dimension depends on E-M forces, like rms dipoles, then composition will matter a lot.
If it is something like Large Extra Dimensions, then it will be composition independent (hm... mething another whacky letter is in order).
It would be temperature dependent, only works at quite low temperatures - at high temperatures the collisions either shatter the grains or compactify them into packed 3-D structures.
Time for another Shuttle flight!

1:56 PM  

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