Resolution of the Quinn–Rand–Strogatz Constant of Nonlinear Physics

D. H. Bailey, J. M. Borwein, R. E. Crandall
2009 Experimental Mathematics  
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 [14] developed a certain N -oscillator scenario whose bifurcation phase offset φ is implicitly defined, with a conjectured asymptotic behavior: sin φ ∼ 1 − c 1 /N , with experimental estimate c 1 = 0.605443657 . . .. We are able to derive the exact theoretical value of this "QRS constant" c 1 as a
more » ... stant" 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 φ asymptotic, and to yet more physics constants emerging from the original QRS work.
doi:10.1080/10586458.2009.10128885 fatcat:unxmwm2jyjcpbdgr24q5iym3ta