- Experiment. Math.
- Volume 18, Issue 1 (2009), 107-116.
Resolution of the Quinn–Rand–Strogatz Constant of Nonlinear Physics
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.
Experiment. Math. Volume 18, Issue 1 (2009), 107-116.
First available in Project Euclid: 27 May 2009
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Bailey, D. H.; Borwein, J. M.; Crandall, R. E. Resolution of the Quinn–Rand–Strogatz Constant of Nonlinear Physics. Experiment. Math. 18 (2009), no. 1, 107--116. http://projecteuclid.org/euclid.em/1243430534.