Abstract:
Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences $S(f)\sim f^{-\alpha}$ and $S(k)\sim k^{-\gamma}$. The dependence of exponents $\alpha$ and $\gamma$ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration $(P(\tau)\sim\tau^{-\beta})$ and size $(P(s)\sim s^{-\nu})$ are constructed. It is found that exponent $\alpha$ in the time spectral dependence and exponent $\beta$ in the duration of fluctuations are connected via the relation $\alpha+\beta$ = 2. Exponents $\gamma$ and $\nu$ in the spatial spectral dependence and in the size distribution function are connected via an analogous relation ($\gamma+\nu$ = 2).
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