Narrow Results

As one type of lip-driven wind instruments, although flutes have a very long history, the acoustics of flutes is still unclear. Here, using the admittance matching method, the resonance frequencies of different tones for a flute are calculated with the precise correction for geometrical sizes. The result shows that the given frequency spectra of the flute are almost the same as the designed values.

The Zwanzig's procedure (1960) for the description of the system of coupled harmonic oscillators is applied to the chain of interacting oscillations in order to find the adsorption power function, which is then determined by two terms: (i) the classical term proportional to the radio-frequency function squared and (ii) the additional term linear with respect to the radio-frequency magnetic field amplitude. From the physical point of view the first term is usually considered in oscillator effect. The second term found in the present paper via Zwanzig's procedure seems to be induced by fluctuations due to stochastic distributions of the oscillatory precession phases. It reflects well the chaos as described in a fractal approach of the first author (2012, paper joint with M. Nowak-Kȩpczyk and O. Suzuki).

The paper shows the use of Zwanzig's trajectories for spin wave description. The main idea consists in the application of Zwanzig's method to the description of the temporal derivative of magnetization in the direction of rf field in terms of Zwanzig's resolvents found for the magnetization components considered in the harmonic approximation. In particular, the spin waves resonance description can be tested. It reflects well the thermodynamical chaos as described in a fractal approach of the first author (2012, paper joint with Nowak-Kȩpczyk and Suzuki).

Ultrasonic receiving wave can reflect physical properties and damage degree of coal samples. Therefore, it is of great significance to deeply study the parameters of ultrasonic. In this paper, time-domain characteristics of receiving wave are analyzed systematically, which present good correlation with stress. The frequency spectrum of receiving wave is obtained using Fast Fourier Transform (FFT), and peak frequency and centroid frequency are calculated. During the entire loading process, peak frequency fluctuates around 110kHz, but corresponding centroid frequency decreases obviously at the end stage of loading. According to multifractal theory, the multifractal spectrum of wavelet packet energy characteristics is calculated. The results show that wavelet packet energy distribution has obvious multifractal characteristics, and multifractal parameter $\mathrm{\Delta }\alpha$ presents downward trend before coal samples buckling failure. Based on damage process of the coal samples, the reason of change in $\mathrm{\Delta }\alpha$ value is related to damage degree of coal samples. This research is of great significance for understanding the deformation and failure process of coal samples using ultrasonic technology.

During coal and rock loading, a significantly large number of electromagnetic signals are generated as a result of fracture appearance and crack expansion. The generation of electromagnetic signal is the comprehensive embodiment of the coal rock failure behavior. Therefore, the generated signals contain complex and rich messages that can reflect the damage process and degree of coal and rock. In this work, the multifractal theory is applied to analyze the nonlinear characteristics of the electromagnetic wave and its spectrum induced during coal rock, which present good correlation with failure process. The failure process of coal rock is non-uniform, non-continuous and nonlinear, during which, there is a good synchronization and correlation between the electromagnetic pulses and the stress drop, rather than the stress. Both waveform and its spectrum of electromagnetic signal have multifractal characteristics, the larger the fracture scale is, the more significant the multifractal characteristic of electromagnetic signal is, and the multifractal characteristic of electromagnetic signal from coal is higher than that from sandstone. The difference of fracture energy and size can be represented by the maximum of the multifractal dimension $D_{q\mathrm{\text{max}}}$ of the electromagnetic wave and its spectrum during coal rock failure. In the electromagnetic spectrum, small signals are always dominant, and the dominant frequency is only a few isolated points. What is more, with the increase of fracture size, the difference between the dominant frequency and the non-dominant frequency is gradually enhanced.

Standard functional forms of directional wave spectrum are presented and compared. Frequency spectra of the JONSWAP, Wallops, and TMA are presented as the functions of significant wave height and spectral peak period. In combination with these frequency spectra, directional spreading functions of cos^2s(θ/2), cos^2lθ, exp[κ cosθ], sech² βθ, the wrapped normal, and the Mitsuyasu types are compared for their functional shapes, angular standard deviations, and half-peak spreading angles. Empirical relations between the spreading parameters of these directional functions are presented.

The sound field of a harmonically radiating monopole moving along arbitrary trajectories in three-dimensional space is studied in the frequency range and represented as a convolution integral in Cartesian coordinates. The observation time of the motion of the source can be finite or infinite. This convolution integral is referred to as the “Cartesian Convolution Integral ” and is applied to point sources moving on special orbits described by circular and conical helices. For such helical orbits, an alternative approach in cylindrical or spherical coordinates leads to closed form expressions in the form of infinite series for the frequency spectra. The comparison of the results of the Cartesian Convolution Integral with those of the series expansion shows a very good agreement. Finally, the Cartesian Convolution Integral is used to calculate the spectral sound field of a source moving along an elliptical helix.