Complex Systems Studies
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🤔 "There is a fundamental error in separating the parts from the whole, the mistake of atomizing what should not be atomized. Unity and complementarity constitute reality."

Werner Heisenberg
🌀 #Turbulence occurs in a cascade: large eddies break down into smaller ones, which in turn split into even smaller ones, in a #fractal fashion.

Read more here:
🔗 http://www.nature.com/news/mysteries-of-turbulence-unravelled-1.22474
🌊 Lars Onsager: a cryptic genius

Theoretical physicist and chemist Lars Onsager (1903–76) was the type of scientist whom — so it was said — even geniuses such as Richard Feynman found intimidating to talk to. The Norwegian-born polymath “would announce his results by little, short, gnomic utterances”, says theoretical physicist Gregory Eyink. “And he was always right.”

In one of those terse revelations, Onsager announced in 1949 the surprising idea that turbulent fluids dissipate energy even in the absence of viscosity. That idea has now been proven mathematically.

In some cases, researchers have made sense of what Onsager said only in hindsight. In the 1990s, Eyink, who is now at Johns Hopkins University in Baltimore, Maryland, became the first person to take a major step towards validating Onsager’s argument on energy dissipation, only to discover later that Onsager himself had already made a start on that proof, scrawled in cryptic form in unpublished notebooks. Onsager had not bothered to publish this or much else on turbulence, in part because he was busy with other things — including work that led to him receiving the Nobel Prize in Chemistry in 1968 — but also because of the cold reception that others initially gave to his ideas4.

“I find his letter somewhat ‘screwy’”, Theodore von Kármán, considered the foremost US expert on turbulence in the 1940s, confessed to a colleague, regarding something Onsager had written to him. “Perhaps you could indicate to me in a few lines what the idea is, if any.” Linus Pauling, another chemistry Nobel prizewinner, responded to a letter from Onsager, saying: “Your work looks very interesting indeed to me, but it is too far over my head for me to appreciate it properly.”

Thanks to the efforts of Eyink and others, about 10% of Onsager’s notebooks and letters — which are kept at the University of Trondheim in Norway — have been digitized and are available for anyone to read online. Eyink says that he hopes other researchers will make the effort to study them, and that they will find insights not only in fluid dynamics, but also in many other fields in which Onsager worked, such as thermodynamics and condensed-matter physics.

Something similar happened in the past with the work of another oracle of the twentieth century, mathematician Srinivasa Ramanujan (1887–1920). Over the past decade, new results have been derived from enigmatic formulas that he had sketched in his notes but never published.

Read more here:
🔗 http://www.nature.com/news/mysteries-of-turbulence-unravelled-1.22474
A predictor of financial crisis based on statistical methods
http://tasmania.ethz.ch/pubfco/fco.html
#crash#stock_market#sornette#financial_crisis_observatory
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What is Critical Slowing Down?