Computer Simulation of the Conventional Clock Model

The results of computer simulations of clocks, characterized by the power-law model of the spectral density of the normalized frequency fluctuations Sy(f) are described. The simulation generates slow fluctuations of the normalized frequency y, i.e., white (f0), flicker (f-1) and random walk (f-2) types. The two-smple Allan variance σ2y(τ) is used to test the spectral density of the generated time series. The uncertainty of the estimate as predicted by Lesage and Audoin is confirmed. Simulated clock time is obtained by integration of the sequence of normalized frequency samples у(tk, τ). The simulation of clock ensembles shows that after initial frequency equalization and synchronization, the clock times diverge, but remain normally distributed. The standard deviation of the observed clock time distribution turns out to be very close to t · σy(τ = t), confirming earlier assumptions published by Barnes et al. [2].