Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/807948
- Resolution of the Quinn-Rand-Strogatz constant of nonlinear physics
Bailey, D. H.;
Borwein, J. M.;
Crandall, R. E.
- The University of Newcastle. Faculty of Science & Information Technology, School of Mathematical and Physical Sciences
- 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.
- Experimental Mathematics Vol. 18, Issue 1, p. 107-116
- A. K. Peters
- Resource Type
- journal article
- Full Text