An entropy-based stability analysis of extreme fluctuations in a system featuring a 1/<Emphasis Type=Italic>f</Emphasis> spectrum

Extreme fluctuations are modeled by a point system of stochastic equations, in which power spectra inversely proportional to the frequency are produced under the effect of white noise. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which points to their stability in nature. By calculating the spectral entropy of random processes, it becomes possible to investigate their stability directly from power spectra without the need to calculate the amplitude distribution functions. The spectral entropy as a function of white noise amplitude has a minimum. The position of the spectral entropy minimum corresponds to the critical state of the system in which the spectra of fluctuating quantities are inversely proportional to the frequency.     

Arc current fluctuation power spectra in the system of a solid metal electrode and carbonate melt

Arc current fluctuations between a solid metal electrode and a liquid melt of alkaline carbonates at atmospheric pressure are measured. Arc current fluctuation power spectra are determined from the measurement data. It is shown that the fluctuation power is inversely proportional to the frequency (1/f-fluctuations). The fluctuations have a normal Gaussian distribution. The observed 1/f fluctuations exhibit scale invariance. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 11–15, January–February, 2007.     

Dust mode of carbon pellet ablation in the W7-AS stellarator

A new type of carbon pellet ablation in the high-density ion-heated plasma of the Wendelstein 7-AS stellarator is studied. In contrast to conventional ablation in the form of atoms or clusters, this type of ablation features the emission of small (micrometer) carbon particles from the surface of the pellet. The emission angles and velocities of such microparticles are determined. Their sizes are estimated with two methods. The experimental data are compared with theoretical predictions.     

Low-frequency fluctuations in stochastic processes with a 1/<Emphasis Type="Italic">f</Emphasis><Superscript>α</Superscript> spectrum

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.     

Magnetic anisotropy and magnetostriction in a Lu2Fe17 intermetallic single crystal

The magnetic anisotropy and magnetostriction of a Lu₂Fe₁₇ single crystal are investigated. The temperature dependence of the magnetic anisotropy constant K ₁ is measured in the range 4.2–300 K. The results obtained are compared with the data calculated using the Callen theoretical formula. It is found that the temperature dependence of K ₁ for the Lu₂Fe₁₇ single crystal deviates from the temperature curve predicted by the localized single-ion model. The inference is drawn that a certain contribution to the magnetic anisotropy of the Lu₂Fe₁₇ compound is made by the magnetic anisotropy of band electrons. The longitudinal, transverse, and volume magnetostrictions of the Lu₂Fe₁₇ single crystal are studied, and the magnetostriction constants are calculated. It is demonstrated that the exchange integral of Lu₂Fe₁₇, as for the Y₂Fe₁₇ compound, substantially depends on the atomic volume. This dependence is responsible for the considerable difference between the Curie temperatures of the Lu₂Fe₁₇ and Y₂Fe₁₇ compounds. It is revealed that the magnetostriction of the Lu₂Fe₁₇ single crystal in the temperature range of the magnetic phase transition is determined by the two-ion exchange and single-ion contributions.     

Chains and anti-chains in the lattice of epigroup varieties

Let ? _n be the variety of all epigroups of index ≤n. We prove that, for an arbitrary natural number n, the interval [? _n ,? _n+1] of the lattice of epigroup varieties contains a chain isomorphic to the chain of real numbers with the usual order and an anti-chain of the cardinality continuum.