Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/807948
- Title
- Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics
- Author/Creator
-
Bailey, D. H.;
Borwein, J. M.;
Crandall, R. E.
- Institution
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- Description
- 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 [Quinn et al. 07] developed a certain N-oscillator scenario whose bifurcation phase offset small ⍉ is implicitly defined, with a conjectured asymptotic behavior sin ⍉ ~ 1−ᴄ₁/N, with experimental estimate ᴄ₁ = 0.605443657 . . .. We are able to derive the exact theoretical value of this "QRS constant" ᴄ₁ as a real zero of a particular Hurwitz zeta function. This discovery enables, for example, the rapid resolution of c1 to extreme precision. Results and conjectures are provided in regard to higher-order terms of the sin ⍉ asymptotic, and to yet more physics constants emerging from the original QRS work.
- Relation
- Experimental Mathematics Vol. 18, Issue 1, p. 107-116
- Relation
- http://akpeters.metapress.com/content/c04146u65516jr30/?p=1f3d0c8d7e254574a91f400fd06a2f8d&pi=8
- Date
- 2009
- Publisher
- A. K. Peters
- Keyword(s)
-
Winfree oscillators;
high-precision arithmetic;
Hurwitz zeta;
Richardson extrapolation
- Resource Type
- journal article
- Identifier
- http://hdl.handle.net/1959.13/807948
- Identifier
- ISSN:1058-6458
- Reviewed
- Full Text
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