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Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics

Bailey, David H. and Borwein, Jonathan M. and Crandall, Richard E. (2009) Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics. Experimental Mathematics, 18 . pp. 107-116.

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    Abstract

    Herein we develop connections between zeta functions and some recent ``mysterious" constants of nonlinear physics. In an important analysis of coupled Winfree oscillators, Quinn, Rand, and Strogatz developed a certain $N$-oscillator scenario whose bifurcation phase offset $\phi$ is implicitly defined, with a conjectured asymptotic behavior: $\sin \phi \sim 1 - c_1/N$, with experimental estimate $c_1 = 0.605443657\ldots$. We are able to derive the exact theoretical value of this ``QRS constant'' $c_1$ as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of $c_1$ to extreme precision. Results and conjectures are provided in regard to higher-order terms of the $\sin \phi$ asymptotic, and to yet more physics constants emerging from the original QRS work.

    Item Type: Article
    Additional Information: pubdom FALSE
    Subjects: 65-xx Numerical analysis
    41-xx Approximations and expansions
    Faculty: UNSPECIFIED
    Depositing User: lingyun ye
    Date Deposited: 05 Jun 2007
    Last Modified: 05 Jan 2015 16:16
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/345

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