Фізичне моделювання та діагностика попадання сторонніх предметів в обертову систему

The paper analyzes the vibroacoustic signals obtained by physical modeling of the rotating system, for example, an aircraft gas turbine engine, in the conditions of steady-state and non-steady-state modes. An air starter (supercharger) is used as a physical model of a rotating system, which is driven by a DC motor. The measuring system uses a dynamic microphone with an amplifier, a tachometer, a two-channel digital oscilloscope, a personal computer with technological and special software. The simulation of the ingress of foreign objects into the rotating system is performed by throwing paper balls during the rotation. The multilevel processing based on sequential application of methods of frequency-time analysis, multispectral analysis, and fractal analysis is proposed and substantiated for processing of measured vibroacoustic signals. The results of the frequency-time analysis showed that at the time of throwing the balls the intensity of the components at higher frequencies increases. For fragments of signal realization without throwing and with the throwing of balls the multispectral analysis is carried out and estimates of the bispectrum modulus are received in the form of contour images. At the third level of signal processing, the Minkowski dimension of the contour images of the bispectrum module estimates is determined. The Minkowski dimension is an integral quantitative indicator of the geometry of isolines and differs in value for the selected fragments of the vibroacoustic signal. So it can be used as a diagnostic sign of a foreign object entering the rotating system at the final level of processing. The obtained results can be used to improve the systems of condition monitoring of complex rotating systems, increase sensitivity, expand functionality and provide multi-class diagnostics in the event of damage and violation of normal operating modes

The Mean Minkowski Content of Homogeneous Random Fractals

Homogeneous random fractals form a probabilistic generalisation of self-similar sets with more dependencies than in random recursive constructions. Under the Uniform Strong Open Set Condition we show that the mean D-dimensional (average) Minkowski content is positive and finite, where the mean Minkowski dimension D is, in general, greater than its almost sure variant. Moreover, an integral representation extending that from the special deterministic case is derived.

Fractal Properties of CdTe Quantum Dots Dendrites-=SUP=-*-=/SUP=-

Here we present the analyses of fractal properties of CdTe dendrites. The spectral characteristics of dendrites obtained at different acids of the initial solution were investigated. We demonstrate the displacement of the local luminescence peak depended on the branches of the dendritic structure. The fractal dimension has been calculated by the box-counting method. We obtained the correlation between the local peak of luminescence and the Minkowski dimension.

Some Remarks on the Fractal Structure of Irrigation Balls

The paper is related to a conjecture by Pegon, Santambrogio and Xia concerning the dimension of the boundary of some sets which we are calling “irrigation balls”. We propose a notion of sub-balls and sub-spheres of prescribed radius and we prove that, generically, the only possible Minkowski dimension of sub-spheres is the one expected in the conjecture. At the same time, beside the scale transition properties and the dimension estimates on some significant sets, we propose a third approach to study the fractal regularity which relies on lower oscillation estimates on the landscape function, which turns out to behave as a Weierstrass-type function.

Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings

The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a p-adic fractal string L p , expressed in terms of the underlying complex dimensions. The general fractal tube formula obtained in this paper is illustrated by several examples, including the nonarchimedean Cantor and Euler strings. Moreover, we show that the Minkowski dimension of a p-adic fractal string coincides with the abscissa of convergence of the geometric zeta function associated with the string, as well as with the asymptotic growth rate of the corresponding geometric counting function. The proof of this new result can be applied to both real and p-adic fractal strings and hence, yields a unifying explanation of a key result in the theory of complex dimensions for fractal strings, even in the archimedean (or real) case.