This thesis work consists of two research projects. The first project presented is on waveform design for car radars. These radars are used to detect other vehicles to avoid collision. In this project, we attempt to find the best waveform that distinguishes large objects from small ones. This helps the radar system reach more reliable decisions. We consider several models of the problem with varying complexity. For each model, we present optimization results calculated under various constraints regarding how the waveform is generated and how the reflected signal is processed. The results show that changing the radar waveform can result in better target classification. The second project is about digital-to-analog converter (DAC) linearization. Ideally, DACs have a linear input-output relation. In practice, however, this relation is nonlinear which may be harmful for many applications. A more linear input-output relation can be achieved by modifying the input to a DAC. This method, called predistortion, requires a good understanding of how DAC errors contribute to the nonlinearity. Assuming a simple DAC model, we investigate how different error functions lead to different types of nonlinearities through theoretical analyses and supporting computer simulations. We present our results in terms of frequency spectrum calculations. We show that the nonlinearity observed at the output strongly depends on how the error is modeled. These results are helpful in designing a predistorter for linearization.

The Cedar Mountain and Dakota Formations are significant gas producers in the southern Uinta Basin of Utah. To date, however, predicting the stratigraphic distribution and lateral extent of potential gas-bearing channel sandstone reservoirs in these fluvial units has proven difficult due to their complex architecture, and the limited spacing of wells in the region. A new strategy to correlate the Cedar Mountain and Dakota Formations has been developed using core, well-log, and 3D seismic data. The detailed stratigraphy and sedimentology of the interval were interpreted using descriptions of a near continuous core of the Dakota Formation from the study area. The gamma-ray and density-porosity log signatures of interpreted mud-dominated overbank, coal-bearing overbank, and channel sandstone intervals from the cored well were used to identify the same lithologies in nearby wells and correlate similar stratal packages across the study area. Data from three 3D seismic surveys covering approximately 140 mi2 (225 km2) of the study area were utilized to generate spectral decomposition, waveform classification, and percent less-than-threshold attributes of the Dakota-Cedar Mountain interval. These individual attributes were combined to create a composite attribute that was merged with interpreted lithological data from the well-log correlations. The overall process resulted in a high-resolution correlation of the Dakota-Cedar Mountain interval that permitted the identification and mapping of fluvial-channel reservoir fairways and channel belts throughout the study area. In the future, the strategy employed in this study may result in improved well-success rates in the southern Uinta Basin and assist in more detailed reconstructions of the Cedar Mountain and Dakota Formation depositional systems.

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This thesis focuses on the generation and applications of stable optical frequency combs. Optical frequency combs are defined as equally spaced optical frequencies with a fixed phase relation among themselves. The conventional source of optical frequency combs is the optical spectrum of the modelocked lasers. In this work, we investigated alternative methods for optical comb generation, such as dual sine wave phase modulation, which is more practical and cost effective compared to modelocked lasers stabilized to a reference. Incorporating these comblines, we have generated tunable RF tones using the serrodyne technique. The tuning range was ±1 MHz, limited by the electronic waveform generator, and the RF carrier frequency is limited by the bandwidth of the photodetector. Similarly, using parabolic phase modulation together with time division multiplexing, RF chirp extension has been realized. Another application of the optical frequency combs studied in this thesis is real time data mining in a bit stream. A novel optoelectronic logic gate has been developed for this application and used to detect an 8 bit long target pattern. Also another approach based on orthogonal Hadamard codes have been proposed and explained in detail. Also novel intracavity modulation schemes have been investigated and applied for various applications such as a) improving rational harmonic modelocking for repetition rate multiplication and pulse to pulse amplitude equalization, b) frequency skewed pulse generation for ranging and c) intracavity active phase modulation in amplitude modulated modelocked lasers for supermode noise spur suppression and integrated jitter reduction. The thesis concludes with comments on the future work and next steps to improve some of the results presented in this work.

Conducting research experiments on plutonium electrorefining is difficult due to the significant hazards and regulations associated with nuclear materials. Finding a surrogate for plutonium electrorefining studies would enable more fundamental research to be conducted. Potential surrogates were identified by determining the physical properties required to conduct electrorefining using a molten metal and molten salt in CaCl2 at 1123 K. More potential surrogates were identified by changing the matrix salt to be a LiCl-KCl-CaCl2 eutectic salt with electrorefining conducted at 673-773 K. Ce-CeCl3, In-InCl3, Zn-ZnCl2, Sn-SnCl2, and Bi-BiCl¬3 were investigated as potential plutonium electrorefining surrogates. Ce electrorefining in molten CaCl2 resulted in a difficult to separate colloid mixture of Ce, Ca and Cl. Electrorefining rates for In were too slow due to InCl3 volatilizing out of the molten salt. Zn was successfully electrorefined, but the metal obtained did not coalesce into one piece. Sn and Bi were successfully electrorefined and coalesced into solid product rings with high yields and coulombic efficiencies. While a surrogate could not be identified using the same conditions as plutonium electrorefining, two possible surrogates, Sn-SnCl2 and Bi-BiCl3,¬ were found that could imitate the physical configuration (i.e., molten salt on top of molten metal) of plutonium electrorefining at a reduced temperature using a eutectic LiCl-KCl-CaCl2 salt in place of CaCl2. Using this surrogate enables fundamental studies of aspects of plutonium electrorefining. One aspect of plutonium electrorefining research is to improve its efficiency and yield. Plutonium electrorefining is a time-intensive process which generates radioactive waste. Improvements in efficiency and yield can reduce process time and waste. One possible way of improving the efficiency of plutonium electrorefining is to study the impact of using an AC superimposed DC waveform. Four AC superimposed DC and two DC electrorefining runs were performed using bismuth as a plutonium surrogate. All six runs showed a high level of yield and coulombic efficiency. All six cathode rings were confirmed to be high-purity bismuth using scanning electron microscopy with energy dispersive x-ray analysis (SEM-EDS). While the results were inconclusive about the ability of AC superimposed DC waveforms to increase the efficiency of bismuth electrorefining, applying an AC superimposed DC waveform did not appear to decrease the efficiency or yield of the process. The change in waveform also did not result in impurities being present in the product cathode ring. Bismuth, in addition to being identified as a viable plutonium surrogate, has been investigated as a potential liquid electrode for molten salt electrorefining. Because of this, its electrochemical properties are of interest. However, bismuth's electrochemical behavior has received scant attention in eutectic LiCl-KCl melts and no studies were found in the ternary LiCl-KCl-CaCl2 melts. LiCl-KCl-CaCl2 melts offer some advantages over eutectic LiCl-KCl, such as lower melting point and higher oxide solubility. Cyclic voltammetry, square wave voltammetry, chronoamperometry, chronopotentiometry and open-circuit chronopotentiometry were used to measure electrochemical parameters, such as diffusivity and standard redox potential of bismuth electrodeposition in LiCl-KCl and LiCl-KCl-CaCl2 eutectics.

Nuclear physics experiments typically involve the collection and analysis of detector signals produced by the interaction of subatomic particles with matter to deduce various quantities. When heavy ions are involved, Si Detector signals are distorted by the formation of a plasma-like cloud from the interaction between the heavy ions and the detector material. The signal amplitude is reduced and delayed, two effects known as Pulse Height Defect (PHD) and Plasma Delay Time (PDT). A recent experiment was performed at the Institut Laue-Langevin(ILL) experimental nuclear reactor facility in Grenoble, using the LOHENGRIN mass spectrometer, to study these walk effects. The purpose of this project is to use a subset of the data to perform pulse shape analysis and develop a parametrization of the pulse waveform in order to better understand the PDT and PHD and how the pulses are affected. Initially, the PDT and PHD are estimated for masses 90, 100, 130 and 143 u using already established methods. The pulse waveforms are then investigated and a suitable parametrization of the pulse waveform is developed. The region around the pulse onset, which is important in extracting the timing characteristics of the pulse, is found to be described rather well by the Landau function. The Landau function parameters are further investigated and correlations with pulse shape characteristics are discussed. Finally, this novel parametrization is used as an alternative approach to estimate the PDT for the same masses as initially. Comparisons between the two methods indicate that the PDT is actually a combined effect of the physical plasma delay and the walk effects introduced by the underlying triggering routine that is used during offline analysis.

The standard approach to analyzing brain electrical activity is to examine the spectral density function (SDF) and identify frequency bands, defined apriori, that have the most substantial relative contributions to the overall variance of the signal. However, a limitation of this approach is that the precise frequency and bandwidth of oscillations are not uniform across cognitive demands. Thus, these bands should not be arbitrarily set in any analysis. To overcome this limitation, we propose three Bayesian Non-parametric models for time series decomposition which are data-driven approaches that identifies (i) the number of prominent spectral peaks, (ii) the frequency peak locations, and (iii) their corresponding bandwidths (or spread of power around the peaks). The standardized SDF is represented as a Dirichlet process mixture based on a kernel derived from second-order auto-regressive processes which completely characterize the location (peak) and scale (bandwidth) parameters. A Metropolis-Hastings within Gibbs algorithm is developed for sampling from the posterior distribution of the mixture parameters for each project. Simulation studies demonstrate the robustness and performance of the proposed methods. The methods developed were applied to analyze local field potential (LFP) activity from the hippocampus of laboratory rats across different conditions in a non-spatial sequence memory experiment to identify the most prominent frequency bands and examine the link between specific patterns of brain oscillatory activity and trial-specific cognitive demands. The second application study 61 EEG channels from two subjects performing a visual recognition task to discover frequency-specific oscillations present across brain zones. The third application extends the model to characterize the data coming from 10 alcoholics and 10 controls across three experimental conditions across 30 trials. The proposed models generate a framework to condense the oscillatory behavior of populations across different tasks isolating the target fundamental components allowing the practitioner different perspectives of analysis.

The main objective of this thesis is to develop novel misfit functions for full-waveform inversion such that (a) the estimation of the long-wavelength model will less likely stagnate in spurious local minima and (b) the inversion is immune to wavelet inaccuracy. First, I investigate the pros and cons of misfit functions based on optimal transport theory to indicate the traveltime discrepancy for seismic data. Even though the mathematically well-defined optimal transport theory is robust to highlight the traveltime difference between two probability distributions, it becomes restricted as applied to seismic data mainly because the seismic data are not probability distribution functions. We then develop a misfit function combining the local cross-correlation and dynamic time warping. This combination enables the proposed misfit automatically identify arrivals associated with a phase shift. Numerical and field data examples demonstrate its robustness for early arrivals and limitations for later arrivals.%, which means that a proper pre-processing step is still required. Next, we introduce differentiable dynamic time warping distance as the misfit function highlighting the traveltime discrepancy without non-trivial human intervention. Compared to the conventional warping distance, the differentiable version retains the property of representing the traveltime difference; moreover, it can eliminate abrupt changes in the adjoint source, which helps full-waveform inversion converge to geologically relevant estimates. Finally, we develop a misfit function entitled the deconvolutional double-difference measurement. The new misfit measures the first difference by deconvolution rather than cross-correlation. We also present the derivation of the adjoint source with the new misfit function. Numerical examples and mathematical proof demonstrate that this modification makes full-waveform inversion with the deconvolutional double-difference measurement immune to wavelet inaccuracy.

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