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Acoustic Figures

Acoustic Figures. A. D. Jackson 7 May 2007. Ernst Florenz Friedrich Chladni (1756-1827). Some of Chaldni’s original acoustic figures. Hans Christian Ørsted (1777-1851). Kongens Nytorv, 4-5 September 1807. These dust piles fascinated Faraday. Sophie Germain (1776 – 1831).

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Acoustic Figures

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  1. Acoustic Figures A. D. Jackson 7 May 2007

  2. Ernst Florenz Friedrich Chladni(1756-1827)

  3. Some of Chaldni’s original acoustic figures

  4. Hans Christian Ørsted (1777-1851)

  5. Kongens Nytorv, 4-5 September 1807

  6. These dust piles fascinated Faraday

  7. Sophie Germain (1776 – 1831)

  8. • Germain primes, [p,q] if p is prime and q=(2p+1) is also prime. • Substantial contributions to Fermat’s last theorem. • A correct description of acoustic resonances in thin plates. She received Napoleon’s prize on her 3rd attempt. One kilo of pure gold!

  9. Ørsted’s dust piles inspired the discovery of electromagnetic induction. Michael Faraday (1791-1867)

  10. Charles Wheatstone (1802 - 1875)

  11. Heusler, Müller, Altland, Braun, Haake, “Periodic-Orbit Theory of Level Correlations” arXiv:nlin/0610053 “We present a semiclassical explanation of the so-called Bohigas-Giannoni-Schmidt conjecture which asserts universality of spectral fluctuations in chaotic dynamics. We work with a generating function whose semiclassical limit is determined by quadruplets of sets of periodic orbits. The asymptotic expansions of both the non-oscillatory and the oscillatory part of the universal spectral correlator are obtained. Borel summation of the series reproduces the exact correlator of random-matrix theory.” … a less general but simpler picture might be useful.

  12. a=1 a=1.2 a=100

  13. Nearest-neighbor distributions for the cardioid family: spectrum of N (always RMT) spectrum of H (Poisson to RMT)

  14. “Random” billiards: Poisson distributed Gaussian distributed (RMT for all t > 0) Nearest-neighbor distributions for random billiards: (Note that spectrum of N is always given by RMT.) Since spectral correlations of N are always RMT, the change in the statistics of H can only be due to the support of this spectrum. (There is nothing else!)

  15. …It’s time for some acoustic coffee!

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