This question is important for understanding the effects of ionizing radiation, but it’s also just *cool*.

The growth of snowflakes depends heavily on the temperature and humidity of the air, and as they fall or get blown back up through different air conditions, they grow in different ways at different times, leading to complex and individual patterns.

I’m not an expert on how this works, but I’ve posted a couple of articles about them on Google+, which I’ll append below. You definitely want to check out Kenneth Libbrecht’s website for more information!

You may also enjoy my blog article about ice, even though that’s not about snowflakes.

Snowflakes are amazingly diverse! The first scientific classification of them goes back to Ukichiro Nakaya. Trained as a nuclear physicist, in 1932. Nakaya was appointed to a professorship in Hokkaido, in the north of Japan. There were no facilities to do nuclear research, so Nakaya turned his attention to snowflakes! Besides studying natural snow, he created artificial snowflakes, and figured out which kinds form in which conditions. In 1954 he summarized his work in a book, *Snow Crystals: Natural and Artificial*. This is his classification.

For more on the history of snowflakes, and amazing photos of them, see Kenneth Libbrecht’s page:

• Kenneth Libbrecht, Early snow crystal observations.

Triangular snowflakes! They’re one of the minor mysteries of science. They’re uncommon, but pretty easy to find if you look. How do they form? Apparently not just by chance! This paper claims that if you start with a snowflake that’s a slightly irregular hexagon, as it falls through the air it will tend to become triangular in shape:

• K. G. Libbrecht and H. M. Arnold, Aerodynamic stability and the growth of triangular snow crystals, http://arxiv.org/abs/0911.4267.

A perfectly hexagonal snowflake falls horizontally through still air. But suppose one of its six edges grows out a bit more than the rest, by some random fluctuation. Then this edge becomes shorter – yes, think about it, or look at the picture in the paper! This makes the snowflake unbalanced: the opposite edge tilts down. It and its two neighboring edges then start to grow faster, because they have the first chance to meet the incoming moist air. This makes the snowflake become a bit triangular – like the one in the upper left picture here.

But more research is called for! The authors write:

“Unfortunately, producing a more complete, quantitative aerodynamic model will be difficult. Researchers have only recently developed viable numerical techniques for modeling the diffusion-limited growth of faceted crystals, even for relatively simple physical cases. Adding aerodynamic instabilities and their resulting growth changes in full 3D will likely be a considerable challenge. Nevertheless, even our simple qualitative model makes a number of testable predictions.”

]]>http://www.demilked.com/macro-snowflakes-diy-camera-alexey-kljatov/

]]>Jeff Miller, the author of the authoritative

Earliest Known Uses of Some of the Words of Mathematics

http://jeff560.tripod.com

writes in the entry

EIGENVALUE, EIGENFUNCTION, EIGENVECTOR and related terms

http://jeff560.tripod.com/e.html

”The eigen terms are associated with David Hilbert (1862-1943), though he may have been following such constructions as Eigentöne in acoustics (cf. H. L. F. Helmholtz Lehre von den tonempfindungen). Eigenfunktion and Eigenwert appear in the first of Hilbert’s communications on integral equations “Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen”, Nachrichten von d. Königl. Ges. d. Wissensch. zu Göttingen (Math.-physik. Kl.) (1904) p. 49.-91. (The communications from 1904-1910 were collected as Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen 1912). In Whittaker & Watson’s Course of Modern Analysis “Eigenfunktion” is translated as “autofunction.” Eigenvektor appears in the exposition of the finite-dimensional case in Courant & Hilbert Methoden der Mathematischen Physik (1924).”

]]>Nobody is going to support themselves doing scientific research if they only earn 100 euros for solving a problem of that difficulty! You can make money more quickly scrubbing floors.

I bet most *published* scientific research is at least partially supported by government grants. (A lot of privately supported research doesn’t get published.)

I mean there nowadays seem to exist new methods for more or less cost-effective scientific reasoning, like on this page you can make 100 euros by solving these:

Problem 2.3 (Martin-Löf random sequences and convergence)

100 Euro are offered for the construction of a universal semimeasure with posterior convergence individually for all Martin-Löf random sequences. Universal may be defined in either of the following ways:

(a) dominating all enumerable semimeasures Eq.(2.27),

(b) being Solomonoff’s M for some universal Turing machine U Eq.(2.21),

(c) being Levin’s mixture ξU for some U with general weights Eq.(2.26).

and there are of course also corporations etc. which may be interested in funding research which is dedicated to finding new solutions for their evergrowing quests….

]]>This paper is free online! We live in a semi-barbaric age where science is probing the finest details of matter, space and time—but many of the discoveries, paid for by taxes levied on the hard-working poor, are snatched, hidden, and sold by profiteers. Luckily, a revolution is afoot…

Interesting question in this context is how much of science research is still being paid for by taxes.

]]>Hi John. I believe you linked to this website in an earlier post. As background the pages on ‘water ionisation and pH’ and ‘water models’ may be of interest.

]]>I am thinking that an amplification of the emission can be obtained using stimulated emission (like in the laser): if the ultrasound produce sonoluminescence (light emission with sound, instead of electromagnetic pumping energy), then two reflective mirror can produce stimulated emission, the emitter population can be deduced from the energy of the laser emission (and the frequency of the laser); so that if the length of the cavity can be changed (to obtain different frequencies), then some population number can be obtained. A comparison with the concentration of the cations, and higher level structure, can give the emitters type.

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