🌊 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only to discover later that Onsager himself had already made a start on that proof, scrawled in cryptic form in unpublished notebooks.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
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
Nature News & Comment
Mysteries of turbulence unravelled
Simulations follow how swirls in a fluid transfer and dissipate energy.
🎞 Why Stock Markets Crash?
http://www.aparat.com/v/h5HYd
https://www.youtube.com/watch?v=l-ohH1DGqRs
#complex_systems#stock_market#sornette#predict#crash
http://www.aparat.com/v/h5HYd
https://www.youtube.com/watch?v=l-ohH1DGqRs
#complex_systems#stock_market#sornette#predict#crash
آپارات - سرویس اشتراک ویدیو
Didier Sornette, Reflexivity-endogeneity pervades financial markets from high fr
Instabilities in financial markets
Simposio per il 202° anniversario del decreto di fondazione della Scuola Normale Superiore
19 ottobre 2012, Scuola Normale Superiore
Simposio per il 202° anniversario del decreto di fondazione della Scuola Normale Superiore
19 ottobre 2012, Scuola Normale Superiore
A predictor of financial crisis based on statistical methods
http://tasmania.ethz.ch/pubfco/fco.html
#crash#stock_market#sornette#financial_crisis_observatory
http://tasmania.ethz.ch/pubfco/fco.html
#crash#stock_market#sornette#financial_crisis_observatory
Forwarded from Deleted Account [SCAM]
Media is too big
VIEW IN TELEGRAM
What is Critical Slowing Down?
Forwarded from Deleted Account [SCAM]
This media is not supported in your browser
VIEW IN TELEGRAM
Mesmerizing drone and aerial video shows sharks swimming through massive schools of fish
Forwarded from Deleted Account [SCAM]
Visualizing Frustration: Through the Spinning Glass.webm
41.3 MB
Visualizing Frustration: Through the Spinning Glass
Deleted Account
Visualizing Frustration: Through the Spinning Glass.webm
🔹 Visualizing Frustration:
Through the Spinning-Glass
Randy Andrews Mentor: Ruben Andrist
August 15, 2014
📄 http://samoa.santafe.edu/media/cms_page_media/583/randypaper.pdf
Through the Spinning-Glass
Randy Andrews Mentor: Ruben Andrist
August 15, 2014
📄 http://samoa.santafe.edu/media/cms_page_media/583/randypaper.pdf
🔖 An exact method for computing the frustration index in signed networks using binary programming
Samin Aref, Andrew J. Mason, Mark C. Wilson
🔗 https://arxiv.org/pdf/1611.09030
📌 ABSTRACT
Computing the frustration index of a signed graph is a key to solving problems in different fields of research including social networks, physics, material science, and biology. In social networks the frustration index determines network distance from a state of structural balance. Although the definition of frustration index goes back to 1960, an exact algorithmic computation method has not yet been proposed. The main reason seems to be the complexity of computing the frustration index which is closely related to well-known NP-hard problems such as MAXCUT.
New quadratic and linear binary programming models are developed to compute the frustration index exactly. We introduce several speed-up techniques involving prioritised branching, local search heuristics, and valid inequalities inferred from graph structural properties. The computational improvements achieved by implementing the speed-up techniques allow us to calculate the exact values of the frustration index by running the optimisation models in Gurobi solver.
The speed-up techniques make our models capable of processing graphs with thousands of nodes and edges in seconds on inexpensive hardware. The solve time and solution quality comparison against the literature shows the superiority of our models in both random and real signed networks.
Samin Aref, Andrew J. Mason, Mark C. Wilson
🔗 https://arxiv.org/pdf/1611.09030
📌 ABSTRACT
Computing the frustration index of a signed graph is a key to solving problems in different fields of research including social networks, physics, material science, and biology. In social networks the frustration index determines network distance from a state of structural balance. Although the definition of frustration index goes back to 1960, an exact algorithmic computation method has not yet been proposed. The main reason seems to be the complexity of computing the frustration index which is closely related to well-known NP-hard problems such as MAXCUT.
New quadratic and linear binary programming models are developed to compute the frustration index exactly. We introduce several speed-up techniques involving prioritised branching, local search heuristics, and valid inequalities inferred from graph structural properties. The computational improvements achieved by implementing the speed-up techniques allow us to calculate the exact values of the frustration index by running the optimisation models in Gurobi solver.
The speed-up techniques make our models capable of processing graphs with thousands of nodes and edges in seconds on inexpensive hardware. The solve time and solution quality comparison against the literature shows the superiority of our models in both random and real signed networks.