Open Access
2009 Resolution of the Quinn–Rand–Strogatz Constant of Nonlinear Physics
D. H. Bailey, J. M. Borwein, R. E. Crandall
Experiment. Math. 18(1): 107-116 (2009).


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 $c_1 = 0.605443657\dotsc$. 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.


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D. H. Bailey. J. M. Borwein. R. E. Crandall. "Resolution of the Quinn–Rand–Strogatz Constant of Nonlinear Physics." Experiment. Math. 18 (1) 107 - 116, 2009.


Published: 2009
First available in Project Euclid: 27 May 2009

zbMATH: 1200.11098
MathSciNet: MR2548991

Primary: 11Y60
Secondary: 11M06

Keywords: high-precision arithmetic , Hurwitz zeta , Richardson extrapolation , Winfree oscillators

Rights: Copyright © 2009 A K Peters, Ltd.

Vol.18 • No. 1 • 2009
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