K 79 Koverda, V. P. Statistics of fluctuations with a 1/f spectrum at phase transitions in a spatially distributed system / V. P. Koverda, V. N. Skokov // Physica A. - 2011. - Vol. 390, № 13. - С. 2468-2479 Рубрики: ФИЗИКА Кл.слова (ненормированные): 1/f-NOISE -- FIRST PASSAGE TIME -- AVALANCHES Аннотация: 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 |
K 79 Koverda, V. P. Statistics of avalanches in stochastic processes with a 1/fα spectrum / V. P. Koverda, V. N. Skokov // Physica A. - 2009. - Vol.388, №9. - С. 1804-1812 Рубрики: ФИЗИКА Кл.слова (ненормированные): 1/f-NOISE -- AVALANCHES -- FIRST PASSAGE TIME Аннотация: The results of numerical investigation of the Brownian motion in a two-dimensional potential field formed under the coupling of phase transitions at the conditions of the criticality induced by white noise are presented. The suggested system of stochastic equations at the white noise intensity that corresponds to the criticality of a noise-induced transition describes stationary random processes with power spectra S(f)∼f−α, where the exponent α varies in the range 0.8≤α≤1.8. The exponent α was found by the direct FFT method from numerical realizations of the Brownian motion processes. The exponent β of the distribution function P(τ)∼τ−β of the duration of low frequency extreme fluctuations was determined by numerical methods from the distributions of time of the first passage across a potential barrier with different realizations of white noise. The low frequency extreme fluctuations in many properties are similar to avalanches considered in models of self-organized criticality. The exponents α and β were determined directly from numerical realizations of random processes independently of each other. It is shown that the exponents α and β are related by the relation α+β=2. |
K 79 Koverda, V. P. Low-frequency fluctuations in stochastic processes with a 1/f α spectrum [Электронный ресурс] / V. P. Koverda, V. N. Skokov // Technical Physics. - 2009. - Vol.54, №6. - P770-774 Рубрики: ФИЗИКА Кл.слова (ненормированные): LOW-FREQUENCY FLUCTUATIONS -- STOCHASTIC PROCESSES -- 1/f(АЛЬФА)-СПЕКТР Аннотация: The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) 1/f α, where exponent α varies in the interval 0.8 ≤ α ≤ 1.8. Exponent β of distribution function P(τ) τ-β for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents α and β are connected through the relation α + β = 2 |
K 79 Koverda, V. P. Statistics of fluctuations with a 1/f spectrum at phase transitions in a spatially distributed system / V. P. Koverda, V. N. Skokov // Physica A. - 2011. - Vol. 390, № 13. - С. 2468-2479 Рубрики: ФИЗИКА Кл.слова (ненормированные): 1/f-NOISE -- FIRST PASSAGE TIME -- AVALANCHES Аннотация: 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 |
K 79 Koverda, V. P. Statistics of avalanches in stochastic processes with a 1/fα spectrum / V. P. Koverda, V. N. Skokov // Physica A. - 2009. - Vol.388, №9. - С. 1804-1812 Рубрики: ФИЗИКА Кл.слова (ненормированные): 1/f-NOISE -- AVALANCHES -- FIRST PASSAGE TIME Аннотация: The results of numerical investigation of the Brownian motion in a two-dimensional potential field formed under the coupling of phase transitions at the conditions of the criticality induced by white noise are presented. The suggested system of stochastic equations at the white noise intensity that corresponds to the criticality of a noise-induced transition describes stationary random processes with power spectra S(f)∼f−α, where the exponent α varies in the range 0.8≤α≤1.8. The exponent α was found by the direct FFT method from numerical realizations of the Brownian motion processes. The exponent β of the distribution function P(τ)∼τ−β of the duration of low frequency extreme fluctuations was determined by numerical methods from the distributions of time of the first passage across a potential barrier with different realizations of white noise. The low frequency extreme fluctuations in many properties are similar to avalanches considered in models of self-organized criticality. The exponents α and β were determined directly from numerical realizations of random processes independently of each other. It is shown that the exponents α and β are related by the relation α+β=2. |
K 79 Koverda, V. P. Low-frequency fluctuations in stochastic processes with a 1/f α spectrum [Электронный ресурс] / V. P. Koverda, V. N. Skokov // Technical Physics. - 2009. - Vol.54, №6. - P770-774 Рубрики: ФИЗИКА Кл.слова (ненормированные): LOW-FREQUENCY FLUCTUATIONS -- STOCHASTIC PROCESSES -- 1/f(АЛЬФА)-СПЕКТР Аннотация: The results of numerical analysis of the Brownian movement of a particle in the force field of the potential corresponding to interacting subcritical and supercritical phase transitions are considered. If the white noise intensity corresponds to the critical intensity of the noise-induced transition, the system of stochastic differential equations describes random steady-state processes with fluctuation power spectra inversely proportional to frequency f, S(f) 1/f α, where exponent α varies in the interval 0.8 ≤ α ≤ 1.8. Exponent β of distribution function P(τ) τ-β for the duration of low-frequency extremal fluctuations, which are analogous to avalanches considered in the models of self-organized criticality in many respects, varies between the same limits. It is shown that exponents α and β are connected through the relation α + β = 2 |