Coupled Crystal Oscillator System and Timing Device
At the National Observatory in Washington D.C., time is measured by averaging the times of an uncoupled ensemble. The measurements show a scaling law for phase-error reduction as, where is the number of crystals in the ensemble. Analytical and computational works show that certain patterns of collective behavior produced by a network of nonlinear oscillators leads to optimal phase-error that scales down as. In this talk we use symmetry-based methods to classify all possible patterns of oscillations, and their stability properties. Then we show why, among all possible patterns, a traveling wave, in which consecutive oscillators are out of phase by, yields the best phase-error reduction. Finally, we prove, analytically, that is the fundamental limit of of phase-error reduction that can be obtained with a network of nonlinear oscillators of any type, not just crystals.
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