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This doctoral dissertation has mainly concentrated on modeling studies of shorter period acoustic-gravity waves propagating in the upper atmosphere. Several cases have been investigated in the literature, which are focusing on the propagation characteristics of high-frequency gravity wave packets. The dissertation consists of five main divisions of which each has its own significance to be addressed, and these five chapters are also bridged in order with each other to present a theme about gravity wave ducting dynamics, energetics, and airglows. The first chapter is served as an introduction of the general topic about atmospheric acoustic-gravity waves. Some of the historical backgrounds are provided as an interesting refreshment and also as a motivation reasoning this scientific research for decades. A new 2-D, time-dependent, and nonlinear model is introduced in the second chapter (the AGE-TIP model, acronymically named atmospheric gravity waves for the Earth plus tides and planetary waves). The model is developed during this entire doctoral study and has carried out almost all research results in this dissertation. The third chapter is a model application for shorter period gravity waves ducted in a thermally stratified atmosphere. In spite of mean winds the thermal ducting occurs because ducted waves are fairly common occurrences in airglow observations. One-dimensional Fourier analysis is applied to identify the ducted wave modes that reside within multiple thermal ducts. Besides, the vertical energy flux and the wave kinetic energy density are derived as wave diagnostic variables to better understand the time-resolved vertical transport of wave energy in the presence of multiple thermal ductings. The fourth chapter is also a model application for shorter period gravity waves, but it instead addresses the propagation of high-frequency gravity waves in the presence of mean background wind shears. The wind structure acts as a significant directional filter to the wave spectra and hence causes noticeable azimuthal variations at higher altitudes. In addition to the spectral analysis applied previously the wave action has been used to interpret the energy coupling between the waves and the mean flow among some atmospheric regions, where the waves are suspected to extract energy from the mean flow at some altitudes and release it to other altitudes. The fifth chapter is a concrete and substantial step connecting theoretical studies and realistic observations through nonlinearly coupling wave dynamic model with airglow chemical reactions. Simulated O (1S) (557.7 nm) airglow images are provided so that they can be compared with observational airglow images. These simulated airglow brightness variations response accordingly with minor species density fluctuations, which are due to propagating and ducting nonlinear gravity waves within related airglow layers. The thermal and wind structures plus the seasonal and geographical variabilities could significantly influence the observed airglow images. By control modeling studies the simulations can be used to collate with concurrent observed data, so that the incoherencies among them could be very useful to discover unknown physical processes behind the observed wave scenes.

Laser-induced breakdown spectroscopy (LIBS) is an advanced data analysis technique for spectral analysis based on the direct measurement of the spectrum of optical emission from a laser-induced plasma. Assignment of different atomic and ionic lines, which are signatures of a particular element, is the basis of a qualitative identification of the species present in plasma. The relative intensities of these atomic and ionic lines can be used for the quantitative determination of the corresponding elements present in different samples. Calibration curve based on absolute intensity is the statistical method of determining concentrations of elements in different samples. Since we need an exact knowledge of the sample composition to build the proper calibration curve, this method has some limitations in the case of samples of unknown composition. The current research is to investigate the usefulness of ANN for the determination of the element concentrations from spectral data. From the study it is shown that neural networks predict elemental concentrations that are at least as good as the results obtained from traditional analysis. Also by automating the analysis process, we have achieved a vast saving in the time required for the data analysis.

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Borehole induced structures seen in image logs from the Coso Geothermal Field, CA record variation in the azimuth of principal stress. Image logs of these structures from five boreholes were analyzed to quantify the stress heterogeneity for three geologically distinct locations: two boreholes within the Coso Geothermal Field (one in an actively produced volume), two on the margin of the Coso Geothermal Field and outside the production area, and a control borehole several tens of kilometers south of the Coso Geothermal Field. Average directions of Shmin and its standard deviation are similar along the eastern portion of the geothermal field at ~107 ± 28°; this is distinct from the western portion which has an azimuth of 081 ± 18° and also distinct from outside the geothermal field where the average azimuth is 092 ± 47°. These relationships suggest a correlation of stress orientation and heterogeneity with slip on the Coso Wash fault, suggesting that ~20 years of production has not affected the Shmin.orientation. The slope of power spectrum quantifies the length-scale dependence of stress rotations for the volume of the brittle crust penetrated by each borehole. Spectral analysis was applied to the depth variation of stress direction and it demonstrates that: (1) the data set contains distinct wavelengths of stress rotation, (2) that the relative power of these wavelengths in the total scaling of stress directions demonstrates a fractal distribution and (3) in a manner consistent with earthquakes causing the stress rotations. While the vertically averaged Shmin orientation for the three eastern boreholes varied by as little as 1°, the spectral slopes varied by 0.4 log (deg2 *m)(m) from the inside to the margin unproduced areas of the Coso Geothermal Field. The two boreholes inside the field had spectral slopes within one standard deviation, even though Shmin orientations were not parallel. These results suggest that at the kilometer length scale, the source of stress heterogeneity is dominated by proximity to recent fault slip, whereas the centimeter to meter stress heterogeneity is dominated by earthquake activity. / Geology

With the proliferation of renewable energy and its integration into the modern power grid, we face some new issues. Aside from the increased switching rate, which results in faster dynamic behavior, realistic models for these Inverter-Based Resources (IBRs) are not widely available. This complicates researching the behavior of this quickly changing system, and without proper models, simulations may not be totally reliable. To address this, it is recommended that measurement data be used, which includes the entire grid and all of its unique characteristics. Signal processing techniques have been employed exclusively to construct spectrograms, which are time-frequency representations of a signal's spectral information. These spectrograms show ridges that represent the system's changing modes. It can be extremely beneficial to track these modes and generate labeled data representing the evolution of modes as the system evolves. This labeled data can aid in the development of correlation and causation hypotheses linking specific abnormal behaviors to proximity to instability. This can also assist analyze these IBRs and identify flaws in their modeling. This thesis describes a step-by-step process for creating spectrograms, reducing them for better visualization, and then estimating mode evolution with a ridge-tracking algorithm based on penalized jump criteria. The results show that the tracker works effectively with both synthetic and real PMU data. / Master of Science / By 2050, the number of electric cars on the road will increase almost tenfold, and renewable energy will make up almost 50% of the global power mix. While this is great news for the environment, it also poses new challenges to the power sector in ensuring the reliable delivery of clean energy. To address this, we need to collect real-time information about the system. A spectrogram is a visual representation of the power grid's dynamic behavior, providing essential information about frequency and power. Despite its extensive use in biomedical data, this tool is not used much in the power system industry. Spectrograms can be used as a forensic tool or preventive measure to detect system instability. Our project aims to track the system's dynamic behavior using ambient data, which is shown to be rich in information. The proposed algorithm suggests a detailed step-by-step methodology to use this tool for system identification and monitoring. The work's novelty lies in the tracking algorithm developed to identify and track the spectral components in a time-frequency representation.

Previous studies have shown that spectral analysis based on force data can elucidate fundamental physical phenomena during chemical mechanical planarization (CMP). While it has not been literally described elsewhere, such analysis was partly motivated by modern violinmakers and physicists studying Old Italian violins, who were trying to discover spectral relations to sound quality. In this paper, we draw parallels between violins and CMP as far as functionality and spectral characteristics are concerned. Inspired by the de facto standard of violin testing via hammer strikes on the base edge of a violin's bridge, we introduce for the first time, a mobility plot for the polisher by striking the wafer carrier head of a CMP polisher with a hammer. Results show three independent peaks that can indeed be attributed to the polisher's natural resonance. Extending our study to an actual CMP process, similar to hammered and bowed violin tests, at lower frequencies the hammered and polished mobility peaks are somewhat aligned. At higher frequencies, peak alignment becomes less obvious and the peaks become more isolated and defined in the case of the polished wafer spectrum. Lastly, we introduce another parameter from violin testing known as directivity, , which in our case, we define as the ratio of shear force variance to normal force variance acquired during CMP. Results shows that under identical polishing conditions, increases with the polishing removal rate.

This thesis consists of two parts. In the first part, we study a class of special functions Aik (y), k = 2, 4, 6, ··· generalising the classical Airy function Ai(y) to higher orders and in the second part, we apply expressions and properties of Ai4(y) to spectral problem of a specific operator. The first part is however motivated by latter part. We establish regularity properties of Aik (y) and particularly show that Aik (y) is smooth, bounded, and extends to the complex plane as an entire function, and obtain pointwise bounds on Aik (y) for all k. Some analytic properties of Aik (y) are also derived allowing one to express Aik (y) as a finite sum of certain generalised hypergeometric functions. We further obtain full asymptotic expansions of Aik (y) and their first derivative Ai'(y) both for y > 0 and for y < 0. Using these expansions, we derive expressions for the negative real zeroes of Aik (y) and Ai'(y). Using expressions and properties of Ai4(y), we extensively study spectral properties of a non-local operator H whose physical interpretation is the massless relativistic quartic anharmonic oscillator in one dimension. Various spectral results for H are derived including estimates of eigenvalues, spectral gaps and trace formula, and a Weyl-type asymptotic relation. We study asymptotic behaviour, analyticity, and uniform boundedness properties of the eigenfunctions Ψn(x) of H. The Fourier transforms of these eigenfunctions are expressed in two terms, one involving Ai4(y) and another term derived from Ai4(y) denoted by Āi4(y). By investigating the small effect generated by Āi4(y) this work shows that eigenvalues λn of H are exponentially close, with increasing n Ε N, to the negative real zeroes of Ai4(y) and those of its first derivative Ai'4(y) arranged in alternating and increasing order of magnitude. The eigenfunctions Ψ(x) are also shown to be exponentially well-approximated by the inverse Fourier transform of Ai4(|y| - λn) in its normalised form.