In frequency-domain photothermal radiometry (FD-PTR) a low-power intensity-modulated optical excitation generates thermal-wave field inside the sample and the subsequent infrared radiation from the sample is analyzed to detect material’s inhomogeneities. The non-contact nature of FD-PTR makes it very suitable for non-destructive evaluation of broad range of materials. Moreover, the methodology is based on intrinsic contrast of light absorption which can be used as a diagnostic tool for inspection of malignancy in biological tissues. Nevertheless, the bottom line is that the physics of heat diffusion allows for a highly damped and dispersive propagation of thermal-waves. As a result, the current FD-PTR modalities suffer from limited inspection depth and poor axial/depth resolution. The main objective of this thesis is to show that using alternative types of modulation schemes (such as linear frequency modulation and binary phase coding) and radar matched filter signal processing, one can obtain localized responses from inherently diffuse thermal wave fields. In this thesis, the photothermal responses of turbid, transparent, and opaque media to linear frequency modulated and binary phase coded excitations are analytically derived. Theoretical simulations suggest that matched-filtering in diffusion-wave field acts as constructive interferometry, localizing the energy of the long-duty excitation under a narrow peak and allowing one to construct depth resolved images. The developed technique is the diffusion equivalent of optical coherence tomography and is named thermal coherence tomography. It was found that the narrow-band binary phase coded matched filtering yields optimal depth resolution, while the broad-band linear frequency modulation can be used to quantify material properties through the multi-parameter fitting of the experimental data to the developed theory. Thermophotonic detection of early dental caries is discussed in detail as a potential diagnostic application of the proposed methodologies. The performance of the diagnostic system is verified through a controlled demineralization protocol as well as in teeth with natural caries.

In frequency-domain photothermal radiometry (FD-PTR) a low-power intensity-modulated optical excitation generates thermal-wave field inside the sample and the subsequent infrared radiation from the sample is analyzed to detect material’s inhomogeneities. The non-contact nature of FD-PTR makes it very suitable for non-destructive evaluation of broad range of materials. Moreover, the methodology is based on intrinsic contrast of light absorption which can be used as a diagnostic tool for inspection of malignancy in biological tissues. Nevertheless, the bottom line is that the physics of heat diffusion allows for a highly damped and dispersive propagation of thermal-waves. As a result, the current FD-PTR modalities suffer from limited inspection depth and poor axial/depth resolution. The main objective of this thesis is to show that using alternative types of modulation schemes (such as linear frequency modulation and binary phase coding) and radar matched filter signal processing, one can obtain localized responses from inherently diffuse thermal wave fields. In this thesis, the photothermal responses of turbid, transparent, and opaque media to linear frequency modulated and binary phase coded excitations are analytically derived. Theoretical simulations suggest that matched-filtering in diffusion-wave field acts as constructive interferometry, localizing the energy of the long-duty excitation under a narrow peak and allowing one to construct depth resolved images. The developed technique is the diffusion equivalent of optical coherence tomography and is named thermal coherence tomography. It was found that the narrow-band binary phase coded matched filtering yields optimal depth resolution, while the broad-band linear frequency modulation can be used to quantify material properties through the multi-parameter fitting of the experimental data to the developed theory. Thermophotonic detection of early dental caries is discussed in detail as a potential diagnostic application of the proposed methodologies. The performance of the diagnostic system is verified through a controlled demineralization protocol as well as in teeth with natural caries.

In this thesis, localization of the underwater sound sources using matched field processing technique is considered. Localization of the underwater sound sources is one of the most important problems encountered in underwater acoustics and signal processing. Many techniques were developed to localize sources in range, depth and bearing angle. However, most of these techniques do not consider or only slightly takes into account the environmental factors that dramatically effect the propagation of underwater sound. Matched field processing has been developed as a technique that fully considers the environmental factors. Matched field processing has proven to be successful in many applications such as localization of sources in range and depth, the determination of environmental parameters, and the evaluation of model accuracies. In this study, first a comparative analysis of narrowband matched field processors is given. Namely four main processors: Bartlett processor, Minimum Variance Distortionless Response (MVDR) processor, MVDR with neighboring location constraints and MVDR with environmental perturbation constraints are compared in terms of their probability of correct localization under certain environmental conditions. Secondly, a performance assesment for the most common broadband matched field processors is made. The correct localization performances for incoherent broadband matched field processor, Tolstoy/Michalopoulo&#039 / s coherent matched field processor and broadband matched field processor with environmental perturbation constraints is given for certain environmental conditions. Finally, a new weighting approach to combine data for broadband matched field processing is introduced. The fact that information from different frequencies may have different reliability depending on the environmental conditions is considered to develop a weighting scheme. It is shown that a performance gain compared to existing processors can be achieved by using the weighting scheme introduced in this study.

Shallow water acoustics is one of the most challenging areas of underwater acoustics; it deals with strong sea bottom and surface interactions, multipath propagation, and it often involves complex variability in the water column. The sea bottom is the dominant environmental influence in shallow water. An accurate solution to the Helmholtz equation in a shallow water waveguide requires accurate seabed acoustic parameters (including seabed sound speed and attenuation) to define the bottom boundary condition. Direct measurement of these bottom acoustic parameters is excessively time consuming, expensive, and spatially limited. Thus, inverted geo-acoustic parameters from acoustic field measurements are desirable. Because of the lack of convincing experimental data, the frequency dependence of attenuation in sandy bottoms at low frequencies is still an open question in the ocean acoustics community. In this thesis, geo-acoustic parameters are inverted by matching different characteristics of a measured sound field with those of a simulated sound field. The inverted seabed acoustic parameters are obtained from long range broadband acoustic measurements in the Yellow Sea '96 experiment and the Shallow Water '06 experiment using the data-derived mode shape, measured modal attenuation coefficients, measured modal arrival times, measured modal amplitude ratios, measured spatial coherence, and transmission loss data. These inverted results can be used to test the validity of many seabed geo-acoustic models (including Hamilton model and Biot-Stoll model) in sandy bottoms at low frequencies. Based on the experimental results in this thesis, the non-linear frequency dependence of seabed effective attenuation is justified.

This study focused on experimentally measuring the performance of a fully cooled, scaled up C3X turbine vane. Experimental measurements focused on investigating row-to-row interactions of coolant jets and the contributions of external film cooling and internal impingement cooling to overall cooling effectiveness. Overall effectiveness was experimentally measured using a thermally scaled, matched Biot number vane model featuring a realistic internal impingement scheme and had normalized surface temperatures that were representative of those found on engine components. A geometrically identical vane was also constructed out of low conductivity polystyrene foam to measure the normalized adiabatic wall temperature, or adiabatic effectiveness of the film cooling configuration. The vanes featured a full coverage film-cooling scheme with a five-row showerhead and 13 total rows of holes containing 149 total coolant holes. This study was the first study to make highly detailed measurements of overall effectiveness on a fully-cooled vane model and expands on previous studies of adiabatic and overall effectiveness on the showerhead and single rows of holes on a matched Biot vane by considering a fully cooled configuration to determine if the results from these previous studies also hold for a fully cooled configuration. Additionally, velocity and thermal fields were measured just upstream of two different suction side rows of holes in order to study the effect of introducing upstream coolant injection. The effects of mainstream turbulence and span-wise location were examined and at the downstream row of holes, the contributions of different rows of holes to the approach flow were compared. This study was the first to measure mean and fluctuating velocity data on the suction side of a turbine vane with upstream coolant injection. Understanding the effects of how upstream injection affects the performance of downstream rows of holes is critical to understanding the film cooling performance on a fully cooled turbine airfoil. / text

We are concerned with forward wave motion simulations in two-dimensional elastic, heterogeneous, semi-infinite media. We use Perfectly Matched Layers (PMLs) to truncate the semi-infinite extent of the physical domain to arrive at a finite computational domain. We use a recently developed hybrid formulation, where the Navier equations for the interior domain are coupled with a mixed formulation for an unsplit-field PML. Here, we implement the hybrid formulation using spectral elements, and report on its performance. The motivation stems from the following considerations: Of concern is the long-time instability that has been reported even in homogeneous and isotropic cases, when the standard complex-stretching function is used in the PML. The onset of the instability is always within the PML zone, and it manifests as error growth in time. It has been suggested that the instability arises when waves impinge at grazing angle on the PML-interior domain interface. Yet, the instability does not always appear. Furthermore, different values of the various PML parameters (mesh density, attenuation strength, order of attenuation function, etc) can either hinder or delay the onset of the instability. It is thus conjectured that the instability is associated with the spectral properties of the discrete operators. In this thesis, we report numerical results based on both Lagrange interpolants, and results based on spectral elements. Spectral elements are explored since they lead to diagonal mass matrices, have improved dispersion error, and, more importantly, have different spectral properties than Lagrangian-based finite elements. Spectral elements are thus used in an attempt to explore whether the reported instability issues could be alleviated. We design numerical experiments involving explosive sources situated at varying depths from the surface, capable of inducing grazing-angle waves. We use the energy decay as the primary metric for reporting the results of comparisons between various spectral element orders and classical Lagrange interpolants. We also report the results of parametric studies. Overall, it is shown that the spectral elements alone are not capable of removing the instability, though, on occasion, they can. Careful parameterization of the PML could also either remove it or alleviate it. The issue remains open. / text

Cognitive Radar (CR) is a paradigm shift from a traditional radar system in that previous knowledge and current measurements obtained from the radar channel are used to form a probabilistic understanding of its environment. Moreover, CR incorporates this probabilistic knowledge into its task priorities to form illumination and probing strategies thereby rendering it a closed-loop system. Depending on the hardware's capabilities and limitations, there are various degrees of freedom that a CR may utilize. Here we will concentrate on two: temporal, where it is manifested in adaptive waveform design; and spatial, where adaptive beamsteering is used for search-and-track functions. This work is divided into three parts. First, comprehensive theory of SNR and mutual information (MI) matched waveform design in signal-dependent interference is presented. Second, these waveforms are used in a closed-loop radar platform performing target discrimination and target class identification, where the extended targets are either deterministic or stochastic. The CR's probabilistic understanding is updated via the Bayesian framework. Lastly, we propose a multiplatform CR network for integrated search-and-track application. The two radar platforms cooperate in developing a four-dimensional probabilistic understanding of the channel. The two radars also cooperate in forming dynamic spatial illumination strategy, where beamsteering is matched to the channel uncertainty to perform the search function. Once a target is detected and a track is initiated, track information is integrated into the beamsteering strategy as part of CR's task prioritization.

We consider the motion of a Brownian particle trapped in an arbitrary bounded two or three-dimensional domain, whose boundary is reflecting except for a small absorbing window through which the particle can escape. We use the method of matched asymptotic expansions to calculate the mean first passage time, defined as the time taken for the Brownian particle to escape from the domain through the absorbing window. This is known as the narrow escape problem. Since the mean escape time diverges as the window shrinks, the calculation is a singular perturbation problem. We extend our results to include N absorbing windows of varying length in two dimensions and varying radius in three dimensions. We present findings in two dimensions for the unit disk, unit square and ellipse and in three dimensions for the unit sphere. The narrow escape problem has various applications in many fields including finance, biology, and statistical mechanics.

The increasing concentration of CO_(2) has been linked to global warming and changes in climate. Geologic sequestration of CO_(2) in deep saline aquifers is a proposed greenhouse gas mitigation technology with potential to significantly reduce atmospheric emissions of CO_(2). Feasibility assessments of proposed sequestration sites require realistic and computationally efficient models to simulate the subsurface pressure response and monitor the injection process, and quantify the risks of leakage if there is any. This study investigates the possibility of obtaining closed form expressions for spatial distribution of CO_(2) injected in brine aquifers and gas reservoirs. Four new semi-analytical solutions for CO_(2) injection in brine aquifers and gas reservoirs are derived in this dissertation. Both infinite and closed domains are considered in the study. The first solution is an analysis of CO_(2) injection into an initially brine-filled infinite aquifer, exploiting self–similarity and matched asymptotic expansion. The second is an expanding to the first solution to account for CO_(2) injection into closed domains. The third and fourth solutions are analyzing the CO_(2) injection in infinite and closed gas reservoirs. The third and fourth solutions are derived using Laplace transform. The brine aquifer solutions accounted for both Darcyian and non-Darcyian flow, while, the gas reservoir solutions considered the gas compressibility variations with pressure changes. Existing analytical solutions assume injection under constant rate at the wellbore. This assumption is problematic because injection under constant rate is hard to maintain, especially for gases. The modeled injection processes in all aforementioned solutions are carried out under constant pressure injection at the wellbore (i.e. Dirichlet boundary condition). One major difficulty in developing an analytical or semi-analytical solution involving injection of CO_(2) under constant pressure is that the flux of CO_(2) at the wellbore is not known. The way to get around this obstacle is to solve for the pressure wave first as a function of flux, and then solve for the flux numerically, which is subsequently plugged back into the pressure formula to get a closed form solution of the pressure. While there is no simple equation for wellbore flux, our numerical solutions show that the evolution of flux is very close to a logarithmic decay with time. This is true for a large range of the reservoir and CO_(2) properties. The solution is not a formation specific, and thus is more general in nature than formation-specific empirical relationships. Additionally, the solution then can be used as the basis for designing and interpreting pressure tests to monitor the progress of CO_(2) injection process. Finally, the infinite domain solution is suitable to aquifers/reservoirs with large spatial extent and low permeability, while the closed domain solution is applicable to small aquifers/reservoirs with high permeability.

Bending loss in silicon-on-insulator rib waveguides was calculated using conformal mapping of the curved waveguide to an equivalent straight waveguide. Finite-element analysis with perfectly matched layer boundaries was used to solve the vector wave equation. Transmission loss was experimentally measured as a function of bend radius for several SOI waveguides. Good agreement was found between simulated and measured losses, and this technique was confirmed as a good predictor for loss and for minimum bend radius for efficient design.