Nonlinear signal processing, spectral, and fractal based stridor auscultation: A machine learning approach

The work reported in the paper analyses the adventitious stridor breath sound (ST) and the normal bronchial breath sound (BR) using spectral, fractal, and nonlinear signal processing methods. The sixty breath sound signals are subjected to power spectral density (PSD) and wavelet analyses to understand the temporal evolution of the frequency components. The energy envelope of the PSD plot of ST shows three peaks labelled as A (256 Hz), B (369 Hz), and C (540 Hz), of which A alone is present in BR at 265 Hz. The appearance of B and C in the PSD plot of ST is due to the obstructions in the trachea and upper airways caused by lesions. The phase portrait analysis of the time series data of ST and BR gives information about the randomness and the sample entropy of the dynamical system. The study reveals that the fractal dimension and sample entropy values are higher for BR, which may be due to the musical ordered behaviour of ST. The machine learning techniques based on the features extracted from the PSD data and phase portrait parameters offer good predictability, besides the classification of BR and ST, and thereby revealing its potential in pulmonary auscultation.

Dirac-like cone-based electromagnetic zero-index metamaterials

Metamaterials with a Dirac-like cone dispersion at the center of the Brillouin zone behave like an isotropic and impedance-matched zero refractive index material at the Dirac-point frequency. Such metamaterials can be realized in the form of either bulk metamaterials with efficient coupling to free-space light or on-chip metamaterials that are efficiently coupled to integrated photonic circuits. These materials enable the interactions of a spatially uniform electromagnetic mode with matter over a large area in arbitrary shapes. This unique optical property paves the way for many applications, including arbitrarily shaped high-transmission waveguides, nonlinear enhancement, and phase mismatch-free nonlinear signal generation, and collective emission of many emitters. This review summarizes the Dirac-like cone-based zero-index metamaterials’ fundamental physics, design, experimental realizations, and potential applications.

Modelling and Dynamic Analysis of an Unbalanced and Cracked Cardan Shaft for Vehicle Propeller Shaft Systems

The vibrational behaviour of misaligned rotating machinery is described and analysed in this paper. The model, constructed based on the equations of vehicle dynamics, considered the dynamic excitation of a single Hooke’s joint. The system adopted the breathing functions from a recent publication to approximate the actual breathing mechanism of a cracked driveshaft. The study aimed to understand the transmission of a nonlinear signal from the unbalanced and cracked driveshaft to an unbalanced driven shaft via a Hooke’s joint. The governing equation of the system was established based on the energy principle and the Lagrangian approach. The instantaneous frequency (IF) identification of the cracked driveshaft was extracted based on the synchrosqueezing wavelet technique. To correlate the results, the nonlinear synchrosqueezing wavelet transforms combined with the classical waves techniques were experimentally used in various scenarios for dynamic analysis of the Cardan shaft system. The variations in the dynamic response in the form of a rising trend of higher harmonics of rotational frequency and increased level of sub-harmonic peaks in both shafts were presented as significant crack indicators. The synchrosqueezing response showed breathing crack excitation played a crucial role in the mixed faults response and caused divergence of the vibration amplitudes in the rotor’s deflections. The simulation and test results demonstrated that the driveshaft damage features impacted the transfer motion to the driven shaft and the Hooke’s joint coupling was the principal source of instability in the system. The proposed model offers new perspectives on vibration monitoring and enhancement analysis to cover complex Cardan shaft systems.

Spectral Curves for the Derivative Nonlinear Schrödinger Equations

Currently, in nonlinear optics, models associated with various types of the nonlinear Schrödinger equation (scalar (NLS), vector (VNLS), derivative (DNLS)), as well as with higher and mixed equations from the corresponding hierarchies are usually studied. Typical tools for solving the problem of propagation of optical nonlinear waves are the forward and inverse nonlinear Fourier transforms. One of the methods for reconstructing a periodic nonlinear signal is based on the use of spectral data in the form of spectral curves. In this paper, we study the properties of the spectral curves for all the derivatives NLS equations simultaneously. For all the main DNLS equations (DNLSI, DNLSII, DNLSIII), we have obtained unified Lax pairs, unified hierarchies of evolutionary and stationary equations, as well as unified equations of spectral curves of multiphase solutions. It is shown that stationary and evolutionary equations have symmetries, the presence of which leads to the existence of holomorphic involutions on spectral curves. Because of this symmetry, spectral curves of genus g are covers over other curves of genus M and N=g−M, where M is a number of phase of solutions. We also showed that the number of the genus g of the spectral curve is related to the number of phases M of the solution of one of the two formulas: g=2M or g=2M+1. The third section provides examples of the simplest solutions.