Statistics of fluctuations with a [formula omitted] spectrum at phase transitions in a spatially distributed system

Abstract

A study has been made on the statistics of fluctuations in a spatially distributed system, which describes the interaction of nonequilibrium phase transitions. It is shown that at a certain intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations have power laws S(f)∼f−α and S(k)∼k−γ. The dependence of the exponents α and γ on the value of the diffusion coefficient determining the spatial interaction of fluctuations have been found. Extreme low-frequency fluctuations has been revealed and distribution functions of their duration P(τ)∼τ−β and size P(s)∼s−ν have been determined. It has been found that the exponent α of the frequency dependence of time spectra and the exponent β of the distribution function of the fluctuation duration are related by the relation α+β=2. The exponent of the spatial spectrum γ and the exponent of the size distribution function ν are related by a similar relation: γ+ν=2.The results of experimental studies on fluctuations in a typical nonequilibrium phase transition such as transient modes of water boiling on a wire heater are presented. It was demonstrated that the critical exponents, which describe the power dependence of power spectra of fluctuations and the amplitude distribution of extreme surges, are related by the relation α+β=2 both in experiments and in the theoretical model of interacting heterogeneous phase transitions.