Surface Tension Effect on Harmonics of Rayleigh-Taylor Instability

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Harmonic and intermodulation performance of optical-fiber Mach–Zehnder microphone

In this paper, closed-form mathematical expressions are obtained for the amplitudes of the harmonic and intermodulation products of the fiber optic Mach–Zehnder microphone excited by a multitone acoustical perturbation. The results show the strong dependence of the harmonic and intermodulation performance on the amplitude of the acoustical perturbation tones and the phase shift produced by the DC bias voltage applied to the reference fiber of the Mach–Zehnder interferometer. The results also show that depending on the phase shift produced by the DC bias voltage, either the third-order or the second-order intermodulation will be dominant. Compared to previously published results for other types of microphones, it appears that the phase shift produced by the DC bias voltage plays an important role in deciding the order of the dominant intermodulation product.     

Harmonic and intermodulation performance of hearing aids under large sound pressure levels

A mathematical model for the input-output functions of the hearing aids is presented. The model, basically a sine-series function, can easily yield closed-form expressions for the amplitudes of the harmonic and intermodulation components of the output when the input is formed of multitone large sound pressure levels. The special case of two-tone equal-amplitude incident pressure level is considered in detail. The results show that the third-order intermodulation component is always higher than the third-harmonic component. The results also show that the input-output functions exhibiting peak clipping exhibit the worst harmonic and intermodulation performance for large sound pressure levels. The simple wide-dynamic range compression (WDRC) input-output function exhibits the best harmonic and intermodulation distortion performance under large sound pressure levels. These results are consistent with the previously reported observations and reveal that there is a correlation between intelligibility of high-level speech and the harmonic and intermodulation performance of the hearing aid under large sound pressure levels.     

非线性兰姆波在厚度缓慢变化和衰减下的特性分析*

该文运用解析的方式推导了考虑声波衰减时兰姆波二次谐波的累积和传播规律,并用半解析方式将该理论推广到缓慢变厚度板的情况。由于色散特性,兰姆波二次谐波和基频波相速度不匹配,传播通常会产生拍频效应,使得二次谐波的振幅沿着传播距离周期性的归零。当考虑声波衰减或板的厚度缓慢变化的情况时,拍频效应将不再严格地被满足。二次谐波的振幅依然会沿着传播距离而振荡,但不会归零。该研究可以用于分析如何高效地激发和接收兰姆波的二次谐波,表征和评估不同厚度变化的结构中的微观结构损伤。     

Evaluation of left ventricular function with cardiac magnetic resonance imaging using Fourier fitting

The aims of this study were to investigate the applicability of Fourier fitting in the magnetic resonance (MR) evaluation of left ventricular (LV) function and to determine the optimal number of harmonics for fitting. Cine cardiac MR imaging was performed in 10 subjects, and an LV time–volume curve was generated. Fourier fitting was applied to the original curve using 1–10 harmonics, and the qualities of the time–volume curve and first-derivative curve were evaluated. LV functional parameters were calculated from curves generated with and without fitting. The quality of the original time–volume curve was good, and Fourier fitting had no substantial effect on functional parameters obtained directly from the time–volume curve such as ejection fraction. The first-derivative curve generated without fitting showed substantial artificial fluctuation. The application of Fourier fitting depressed the fluctuation and tended to decrease estimates of peak ejection rate and peak filling rate. Five or six harmonics appeared to be appropriate for obtaining a high-quality first-derivative curve. In conclusion, Fourier fitting was indicated to aid in reducing the artificial fluctuation of the first-derivative curve generated from cine cardiac MR imaging and to contribute to the evaluation of functional parameters derived from the first-derivative curve.     

表面张力对Rayleigh-Taylor不稳定性谐波的影响

Using the method of the parameter expansion up to the third order, explicitly investigates surface tension effect on harmonics at weakly nonlinear stage in Rayleigh-Taylor instability (RTI) for arbitrary Atwood numbers and compares the results with those of classical RTI within the framework of the third-order weakly nonlinear theory. It is found that surface tension strongly reduces the linear growth rate of time, resulting in mild growth of the amplitude of the fundamental mode, and changes amplitudes of the second and third harmonics, as is expressed as a tension factor coupling in amplitudes of the harmonics. On the one hand, surface tension can either decrease or increase the space amplitude; on the other hand, surface tension can also change their phases for some conditions which are explicitly determined.     

Generation of harmonics and chaos in the dynamics of anharmonic surfaces

Effective equations of motion of a surface atom placed in an anharmonic surface potential are derived for three kinds of substrates (i) continuous dispersionless, (ii) discrete with nearest neighbours harmonic interactions, and (iii) a substrate showing a strong spatial dispersion. The resulting equations of motion are differential equations in the case (i) and Volterra Integro-Differential Equations (VIDE) in the cases (ii) and (iii). Examples of non-linear surface response to phonons coming from the bulk are given for the dispersionless substrate.     

Output frequency properties of nonlinear systems

Nonlinear systems usually have complicated output frequencies. For the class of Volterra systems, some interesting properties of the output frequencies are studied in this paper. These properties show theoretically the periodicity of the output super-harmonic and inter-modulation frequencies and clearly demonstrate the mechanism of the interaction between different output harmonics incurred by different input nonlinearities in system output spectrum. These new results have significance in the analysis and design of nonlinear systems and nonlinear filters in order to achieve a specific output spectrum in a desired frequency band by taking advantage of nonlinearities. Examples and discussions are given to illustrate these new results.     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.