The Fermi-Pasta-Ulam-Tsingou problem: A foray into the beautifully simple 42 points by Anon84 2 days ago | hide | past | favorite | 7 comments

 There's a strange pattern in figures 1 and 2 of the paper [1], showing the energy distribution between modes as a function of time. Rescale time so that the energy peaks of mode 1 happen at t=0 and t=1. Then the energy peaks of mode 2 happen at t=1/2, the energy peaks of mode 3 happen at t=1/3 and t=2/3, the energy peaks of mode 4 happen at t=1/4 and t=3/4, and so on. The peaks of mode N seem to happen at t=m/N where m/N is a fraction in lowest form.I have to believe Fermi would have noticed this pattern, but there seems to be little comment on it either in the paper, or in the linked article. Perhaps the reason for it is so obvious that he thought it not worth publishing. I just wish I knew what it was.This is an unrelated but nice quote:> "In the compound pendulum problem, one has a transfer of energy from one degree of freedom to another and back again, and not a continually increasing sharing of energy between the two. What is perhaps surprising in our problem is that this kind of behaviour still appears in systems with, say, 16 or more degrees of freedom."
 I'm confident that they did not know the reason, as if the dynamics were that well understood there would be no "problem" to be solved. I have no idea when/if it was later explained.Also worth noting that the graph isn't perfectly symmetric but this is presumably just due to accumulation of numerical errors.
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