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posted by takyon on Thursday August 06 2015, @07:15PM   Printer-friendly
from the dusty dept.

In a breakthrough study, an international team of scientists, including Professor Nikolai Brilliantov from the University of Leicester, has solved an age-old scientific riddle by discovering that planetary rings, such as those orbiting Saturn, have a universally similar particle distribution.

The study, which is published in the academic journal Proceedings of the National Academy of Sciences (PNAS), also suggests that Saturn's rings are essentially in a steady state that does not depend on their history.

[...] Professor Brilliantov from the University of Leicester's Department of Mathematics explained: "Saturn's rings are relatively well studied and it is known that they consist of ice particles ranging in size from centimetres to about ten metres. With a high probability these particles are remains of some catastrophic event in a far past, and it is not surprising that there exists debris of all sizes, varying from very small to very large ones.

"What is surprising is that the relative abundance of particles of different sizes follows, with a high accuracy, a beautiful mathematical law 'of inverse cubes'. That is, the abundance of 2 metre-size particles is 8 times smaller than the abundance of 1 metre-size particles, the abundance of 3 metre-size particles is 27 times smaller and so on. This holds true up to the size of about 10 metres, then follows an abrupt drop in the abundance of particles. The reason for this drastic drop, as well as the nature of the amazing inverse cubes law, has remained a riddle until now. We have finally resolved the riddle of particle size distribution. In particular, our study shows that the observed distribution is not peculiar for Saturn's rings, but has a universal character. In other words, it is generic for all planetary rings which have particles to have a similar nature."

[...] Professor Brilliantov added: "The rather general mathematical model elaborated in the study with the focus on Saturn's rings may be successfully applied to other systems, where particles merge, colliding with slow velocities and break into small pieces colliding with large impact speeds. Such systems exist in nature and industry and will exhibit a beautiful law of inverse cubes and drop in large particle abundance in their particle size distribution."

"Size distribution of particles in Saturn's rings from aggregation and fragmentation" at PNAS and Arxiv.


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  • (Score: 3, Interesting) by wonkey_monkey on Thursday August 06 2015, @08:20PM

    by wonkey_monkey (279) on Thursday August 06 2015, @08:20PM (#219252) Homepage

    The reason for this drastic drop ... has remained a riddle until now. We have finally resolved the riddle of particle size distribution. In particular, our study shows that the observed distribution is not peculiar for Saturn's rings, but has a universal character. In other words, it is generic for all planetary rings which have particles to have a similar nature.

    So what is the reason for the drop? The article seems to focus on the fact that this kind of distribution will be found elsewhere, but doesn't explain anything about why the distribution has the properties it does.

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  • (Score: 2) by Translation Error on Thursday August 06 2015, @09:10PM

    by Translation Error (718) on Thursday August 06 2015, @09:10PM (#219271)
    Oh, that's not the riddle they solved. The riddle they solved is 'Why are Saturn's rings so special?' and the answer is 'They're not'.

    Yeah, I'm not very impressed either.
  • (Score: 3, Informative) by c0lo on Thursday August 06 2015, @09:58PM

    by c0lo (156) Subscriber Badge on Thursday August 06 2015, @09:58PM (#219285) Journal

    doesn't explain anything about why the distribution has the properties it does.

    Because of the Bolzmann distribution he set at the foundation of their demo (for the kinetic energies) and the collision cross section which varies with n2/3 with the number of "individual particles" in a larger boulder (collision cross-section varies with r2, the radius of a spherical cow in vacuum varies with n1/3 with the number of particles in the cow).

    The result is that, after accounting for agglutination, destruction and chipping rates, the distribution of spherical cows made from n particles varies with a exp(-λ*n) n-3/2 .

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    • (Score: 2) by edIII on Thursday August 06 2015, @10:41PM

      by edIII (791) on Thursday August 06 2015, @10:41PM (#219301)

      *raises hand*

      Question: If the cow is spherical because of the vacuum, wouldn't it explode instead?

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  • (Score: 2, Informative) by Anonymous Coward on Thursday August 06 2015, @10:02PM

    by Anonymous Coward on Thursday August 06 2015, @10:02PM (#219288)

    Some excerpts from the paper conclusion:

    We have developed a kinetic model for the particle size distribution in a dense planetary ring and showed that the steady-state distribution emerges from the dynamic balance between aggregation and fragmentation processes. The model quantitatively explains properties of the particle size distribution of Saturn’s rings inferred from observations. It naturally leads to a power-law size distribution with an exponential cutoff (Eq. 19). Interestingly, the exponent q=2.5+3μ is universal, for a specific class of models we have investigated in detail.

    . . .

    Our results essentially depend on three basic assumptions: (i) Ring particles are aggregates composed from primary grains that are kept together by adhesive (or gravitational) forces; (ii) the aggregate sizes change due to binary collisions, which are aggregative, bouncing, or disruptive (including collisions with erosion); and (iii) the collision rates and type of impacts are determined by sizes and velocities of colliding particles. We stress that the power-law distribution with a cutoff is a direct mathematical consequence of the above assumptions only; that is, there is no need to suppose a power-law distribution and search for an additional mechanism for a cutoff as in previous semiquantitative approaches (9).