Over the last few days, I’ve come across a lot of great posts at physics blogsphere.
… I can’t help but show these lovely exact solutions to the gravitational N-body problem. This one is beautiful in its simplicity: twenty-one point masses moving around in a figure-8.The N-body problem is one of the most famous, and easily stated, problems in mathematical physics: find exact solutions to point masses moving under their mutual Newtonian gravitational forces (i.e. the inverse-square law)…
Check it out – it has some beautiful animations to go along with it. 🙂
On another note, Three-Toed Sloth has a good post titled The Nobel Prize Winner as Neglected Genius on Onsager. It is triggered by an RMP article Reviews of Modern Physics 78 (2006): 87–135; free copy (courtesy : TTS ) which is a good but heavy read for those interested in this kind of stuff.
This is the abstract of the article.
Onsager and the theory of hydrodynamic turbulence
Gregory L. Eyink
Department of Applied Mathematics and Statistics, The Johns Hopkins University, Baltimore, Maryland 21218, USA
Katepalli R. Sreenivasan
International Center for Theoretical Physics, Trieste, Italy and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742, USA
(Published 17 January 2006)
Abstract: Lars Onsager, a giant of twentieth-century science and the 1968 Nobel Laureate in Chemistry, made deep contributions to several areas of physics and chemistry. Perhaps less well known is his ground-breaking work and lifelong interest in the subject of hydrodynamic turbulence. He wrote two papers on the subject in the 1940s, one of them just a short abstract. Unbeknownst to Onsager, one of his major results was derived a few years earlier by A. N. Kolmogorov, but Onsager’s work contains many gems and shows characteristic originality and deep understanding. His only full-length article on the subject in 1949 introduced two novel ideas — negative-temperature equilibria for two-dimensional ideal fluids and an energy-dissipation anomaly for singular Euler solutions — that stimulated much later work. However, a study of Onsager’s letters to his peers around that time, as well as his private papers of that period and the early 1970s, shows that he had much more to say about the problem than he published. Remarkably, his private notes of the 1940s contain the essential elements of at least four major results that appeared decades later in the literature: (1) a mean-field Poisson-Boltzmann equation and other thermodynamic relations for point vortices; (2) a relation similar to Kolmogorov’s 4/5 law connecting singularities and dissipation; (3) the modern physical picture of spatial intermittency of velocity increments, explaining anomalous scaling of the spectrum; and (4) a spectral turbulence closure quite similar to the modern eddy-damped quasinormal Markovian equations. This paper is a summary of Onsager’s published and unpublished contributions to hydrodynamic turbulence and an account of their place in the field as the subject has evolved through the years. A discussion is also given of the historical context of the work, especially of Onsager’s interactions with his contemporaries who were acknowledged experts in the subject at the time. Finally, a brief speculation is offered as to why Onsager may have chosen not to publish several of his significant results.