- Title
- Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics
- Creator
- Bailey, D. H.; Borwein, J. M.; Crandall, R. E.
- Relation
- Experimental Mathematics Vol. 18, Issue 1, p. 107-116
- Publisher Link
- http://dx.doi.org/10.1080/10586458.2009.10128885
- Publisher
- A. K. Peters
- Resource Type
- journal article
- Date
- 2009
- 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.
- Subject
- Winfree oscillators; high-precision arithmetic; Hurwitz zeta; Richardson extrapolation
- Identifier
- http://hdl.handle.net/1959.13/807948
- Identifier
- uon:7552
- Identifier
- ISSN:1058-6458
- Rights
- This is an electronic version of an article published in Experimental Mathematics Vol. 18, Issue 1, p. 107-116. Experimental Mathematics is available online at: http://www.tandfonline.com/openurl?genre=article&issn=1058-6458&volume=18&issue=1&spage=107
- Language
- eng
- Full Text
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