Similarity of relaxation in supercooled liquids and interacting arrays of oscillators

Dielectric relaxation and dynamic light scattering of small molecule glass-forming liquids invariably show that the fractional exponent beta(alpha) of the Kohlrausch-Williams-Watts correlation function, exp[-(t/tau(alpha))(beta(alpha))], used to fit the alpha-relaxation data is temperature dependent, increasing towards the value of unity as temperature is raised and the relaxation time tau decreased. Comparing different glass formers, another property is the existence of a correlation between the value of (1-beta(alpha)) at the glass temperature, T(g), and the T(g)-scaled temperature dependence of tau(alpha). We analyze a system of interacting arrays of globally coupled nonlinear oscillators. Each array has its oscillators coupled among themselves with a coupling strength K. The coupling between arrays is characterized by the interarray coupling strength K'. The decay of the phase coherence r for each array is slowed down by the interarray coupling and its time dependence is well approximated at sufficiently long times by exp[-(t/tau)(beta)]. For a fixed K', on increasing K the results exhibit a decrease of tau and a concomitant increase of beta, similar to the properties of dielectric relaxation and dynamic light scattering of glass-forming liquids on increasing temperature. For each K' we define K(g) to be the value of K at which tau is equal to an arbitrarily chosen long time. We find that beta(K(g)) is correlated with the K(g)-scaled K dependence of tau. The results obtained in this manner at various fixed values of K' reproduce the relaxation properties and temperature dependencies of strong, intermediate, and fragile glass-forming liquids.