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This paper describes the investigation of bending strength and elastic wave signal characteristics of Si₃N₄ monolithic and Si₃N₄/SiC composite ceramics with crack healing ability. The elastic wave signals, generated during the compression load by a Vickers indenter on the brittle materials, were recorded in real time, and the AE signals were analyzed by the time-frequency analysis method. The three-point bending test was performed on the Si₃N₄ monolithic and Si₃N₄/SiC composite ceramic specimens with/without crack-healed. Consequently the bending strength of the crack-healed specimens at 1300°C was completely recovered up to that of the smooth specimens. And the frequency properties of crack-healed specimens tended to be similar to the distribution of the dominant smooth specimens frequency. This study suggests that the results of the signal information for the anisotropic ceramics show a feasible technique to guarantee structural integrity of a ceramic component.

On the basis of the lattice Boltzmann method for the Navier–Stokes equation, we have done a numerical experiment of a forced turbulence in real space and time. Our new findings are summarized into two points. Firstly, in the analysis of the mean-field behavior of the velocity field using the exit-time statistics, we have verified Kolmogorov's scaling and Taylor's hypothesis at the same time. Secondly, in the analysis of the intermittent velocity fluctuations using a non-equilibrium probability distribution function and the wavelet denoising, we have clarified that the coherent vortices sustain the power-law velocity correlation in the non-equilibrium state.

Blood component non-invasive measurement based on near-infrared (NIR) spectroscopy has become a favorite topic in the field of biomedicine. However, the various noises from instrument measurement and the varying background from absorption of other components (except target analyte) in blood are the main causes, which influenced the prediction accuracy of multivariable calibration. Thinking of backgrounds and noises are always found in high-scale approximation and low-scale detail coefficients. It is possible to identify them by wavelet transform (WT), which has multi-resolution trait and can break spectral signals into different frequency components retaining the same resolution as the original signal. Meanwhile, associating with a criterion of uninformative variable elimination (UVE), it is better to eliminate backgrounds and noises simultaneously and visually. Basic principle and application technology of this pretreatment method, wavelet transform with UVE criterion, were presented in this paper. Three experimental near-infrared spectra data sets, including aqueous solution with four components data sets, plasma data sets, body oral glucose tolerance test (OGTT) data sets, which, including glucose (the target analyte in this study), have all been used in this paper as examples to explain this pretreatment method. The effect of selected wavelength bands in the pretreatment process were discussed, and then the adaptability of different pretreatment method for the uncertainty complex NIR spectra model in blood component non-invasive measurements were also analyzed. This research indicates that the pretreatment methods of wavelet transform with UVE criterion can be used to eliminate varying backgrounds and noises for experimental NIR spectra data directly. Under the spectra area of 1100 to 1700 nm, utilizing this pretreatment method is helpful for us to get a more simple and higher precision multivariable calibration for blood glucose non-invasive measurement. Furthermore, by comparing with some other pretreatment methods, the results imply that the method applied in this study has more adaptability for the complex NIR spectra model. This study gives us another path for improving the blood component non-invasive measurement technique based on NIR spectroscopy.

Studies reveal that the most prominent cause of bearing failure is a crack on any of its mating surfaces. When the crack is initiated, the bearing can still be used for some duration, but this is majorly depending upon the loading conditions. This work primarily focuses on the effects of different levels of static loading on the crack propagation after crack initiation. To analyze the effect of static loading, an axial groove defect was seeded on the outer race of a taper roller bearing randomly and bearing run continuously under five different static loading conditions. Initially, the bearing was made to run under loading conditions to initiate the crack naturally but the crack was not initiated even after 800 h of running. Therefore, crack was initiated artificially for the purpose of studying crack propagation. It was observed from the experimentation that in the case of maximum static load of 20 kg, the crack propagates rapidly in terms of area after 109 h of continuous running, whereas in the case of no load, it started propagating quickly after 267.5 h of running. Statistical analysis was also carried out for the recorded signals at different intervals of times, and it was observed that the Shannon entropy value was showing a sudden rise with the edge breakage (visually verified) while the crack was propagating. However, in the statistical analysis, none of the parameters showed a correlation with crack propagation. To develop the correlation of crack propagation, Shannon entropy of high, medium and low frequency bands of continuous wavelet-based (CWT) was carried out using different wavelets. Shannon entropy for high frequency band of CWT using Daubechies 10 as mother wavelet has responded well to the crack propagation as the value showed a sudden rise and an overall increase for edge breakage and crack propagation, respectively. A high frequency band of CWT using Daubechies 10 was found suitable for detecting edge breakage and crack growth at the same time because of its capability to respond to transient characteristics for a large duration of time.

In this paper, a generalized wavelet collocation operational matrix method based on Haar wavelets is proposed to solve fractional relaxation–oscillation equation arising in fluid mechanics. Contrary to wavelet operational methods accessible in the literature, we derive an explicit form for the Haar wavelet operational matrices of fractional order integration without using the block pulse functions. The properties of the Haar wavelet expansions together with operational matrix of integration are utilized to convert the problems into systems of algebraic equations with unknown coefficients. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

The irreversibility, temperature, and entropy are identified for an atomic system of solid material. Thermodynamics second law is automatically satisfied in the time evolution of molecular dynamics (MD). The irreversibility caused by an atom spontaneously moves from a non-stable equilibrium position to a stable equilibrium position. The process is dynamic in nature associated with the conversion of potential energy to kinetic energy and the dissipation of kinetic energy to the entire system. The forward process is less sensitive to small variation of boundary condition than reverse process, causing the time symmetry to break. Different methods to define temperature in molecular system are revisited with paradox examples. It is seen that the temperature can only be rigorously defined on an atom knowing its time history of velocity vector. The velocity vector of an atom is the summation of the mechanical part and the thermal part, the mechanical velocity is related to the global motion (translation, rotation, acceleration, vibration, etc.), the thermal velocity is related to temperature and is assumed to follow the identical random Gaussian distribution for all of its $x$, $y$ and $z$ component. The $z$-velocity (same for $x$ or $y$) versus time obtained from MD simulation is treated as a signal (mechanical motion) corrupted with random Gaussian distribution noise (thermal motion). The noise is separated from signal with wavelet filter and used as the randomness measurement. The temperature is thus defined as the variance of the thermal velocity multiply the atom mass and divided by Boltzmann constant. The new definition is equivalent to the Nose–Hover thermostat for a stationary system. For system with macroscopic acceleration, rotation, vibration, etc., the new definition can predict the same temperature as the stationary system, while Nose–Hover thermostat predicts a much higher temperature. It is seen that the new definition of temperature is not influenced by the global motion, i.e., translation, rotation, acceleration, vibration, etc., of the system. The Gibbs entropy is calculated for each atom by knowing normal distribution as the probability density function. The relationship between entropy and temperature is established for solid material.