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Title
Hadamard-Babich ansatz and fast Huygens sweeping method for point-source elastic wave equations in an inhomogeneous medium at high frequencies
Creator
Song, Jian
Date
2022
Collection
Electronic Theses & Dissertations
Description
Asymtotic methods are efficient for solving wave equations in the high frequency regime. In the thesis, we first develop a new asymptotic ansatz for point source elastic wave equations in an inhomogeneous medium. Then, we propose a fast Huygens sweeping method to construct a globally valid Green's functions in the presence of caustics. Finally, an Eulerian partial-differential-equation method is proposed to compute complex-valued eikonals in attenuating media.In Chapter 3, we develop the...
Show moreAsymtotic methods are efficient for solving wave equations in the high frequency regime. In the thesis, we first develop a new asymptotic ansatz for point source elastic wave equations in an inhomogeneous medium. Then, we propose a fast Huygens sweeping method to construct a globally valid Green's functions in the presence of caustics. Finally, an Eulerian partial-differential-equation method is proposed to compute complex-valued eikonals in attenuating media.In Chapter 3, we develop the Hadamard-Babich (H-B) ansatz for frequency-domain point source elastic wave equations in an inhomogeneous medium in the high-frequency regime. First, we develop a novel asymptotic series, dubbed Hadamard’s ansatz, to form the fundamental solution of the Cauchy problem for the time-domain point-source (TDPS) elastic wave equations in the region close to the source. Then, the governing equations for the unknown asymptotics of the ansatz are derived including the traveltime functions and dyadic coefficients. A matching condition is proposed to initialize the data of unknowns at the source. To treat singularity of dyadic coefficients at the source, smoother dyadic coefficients are then introduced. Directly taking the Fourier transform of Hadamard’s ansatz in time, we obtain the H-B ansatz for the frequency-domain point-source (FDPS) elastic wave equations. To verify the feasibility of the new ansatz, we truncate the ansatz to keep only the first two terms to compute the resulting asymptotic solutions. Numerical examples demonstrate the accuracy of our method.In Chapter 4, we propose a new truncated Hadamard-Babich ansatz based globally valid asymptotic method, dubbed the fast Huygens sweeping method, for computing Green's functions of FDPS elastic wave equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the fast Huygens sweeping method is that the Huygens-Kirchhoff secondary-source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics can be treated automatically and implicitly. The precomputed asymptotic ingredients can be used to construct Green's functions of elastic wave equations for many different point sources and for arbitrary frequencies. The second novelty is that a butterfly algorithm is adapted to accelerate matrix-vector products induced by the discretization of the Huygens-Kirchhoff integral. The computational cost of the butterfly algorithm is O(NlogN) which is in nearly optimal complexity in terms of the total number of mesh points N. The prefactor of the complexity depends only on the specified accuracy and is independent of the frequency parameter. Numerical examples are presented to demonstrate the performance and accuracy of the new method. In Chapter 5, we propose a Eulerian partial-differential-equation method to solve complex-valued eikonals in attenuating media. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Therefore, a unified framework to eulerianize several popular approximate real-space ray-tracing methods for complex-valued eikonals is proposed so that the real and imaginary parts of the eikonal function satisfy the classical real-space eikonal equation and a novel real-space advection equation, respectively, and we dub the resulting method the Eulerian partial-differential-equation method. We further develop highly efficient high-order methods to solve these two equations by using the factorization idea and the Lax-Friedrichs weighted essentially non-oscillatory (WENO) schemes. Numerical examples demonstrate that the proposed method yields highly accurate complex-valued eikonals, analogous to those from ray-tracing methods.
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Title
The integration of computational methods and nonlinear multiphoton multimodal microscopy imaging for the analysis of unstained human and animal tissues
Creator
Murashova, Gabrielle Alyse
Date
2019
Collection
Electronic Theses & Dissertations
Description
Nonlinear multiphoton multimodal microscopy (NMMM) used in biological imaging is a technique that explores the combinatorial use of different multiphoton signals, or modalities, to achieve contrast in stained and unstained biological tissues. NMMM is a nonlinear laser-matter interaction (LMI), which utilizes multiple photons at once (multiphoton processes, MP). The statistical probability of multiple photons arriving at a focal point at the same time is dependent on the two-photon absorption ...
Show moreNonlinear multiphoton multimodal microscopy (NMMM) used in biological imaging is a technique that explores the combinatorial use of different multiphoton signals, or modalities, to achieve contrast in stained and unstained biological tissues. NMMM is a nonlinear laser-matter interaction (LMI), which utilizes multiple photons at once (multiphoton processes, MP). The statistical probability of multiple photons arriving at a focal point at the same time is dependent on the two-photon absorption (TPA) cross-section of the molecule being studied and is incredibly difficult to satisfy using typical incoherent light, say from a light bulb. Therefore, the stimulated emission of coherent photons by pulsed lasers are used for NMMM applications in biomedical imaging and diagnostics.In this dissertation, I hypothesized that due to the near-IR wavelength of the Ytterbium(Yb)-fiber laser (1070 nm), the four MP-two-photon excited fluorescence (2PEF), second harmonic generation (SHG), three-photon excited fluorescence (3PEF) and third harmonic generation (THG), generated by focusing this ultrafast laser, will provide contrast to unstained tissues sufficient for augmenting current histological staining methods used in disease diagnostics. Additionally, I hypothesized that these NMMM images (NMMMIs) can benefit from computational methods to accurately separate their overlapping endogenous MP signals, as well as train a neural network for image classification to detect neoplastic, inflammatory, and healthy regions in the human oral mucosa. Chapter II of this dissertation explores the use of NMMM to study the effects of storage on donated red blood cells (RBCs) using non-invasive 2PEF and THG without breaching the blood storage bag. Unlike the lack of RBC fluorescence previously reported, we show that with two-photon (2P) excitation from an 800 nm source, and three-photon (3P) excitation from a 1060 nm source, there was sufficient fluorescent signal from hemoglobin as well as other endogenous fluorophores. Chapter III employs NMMM to establish the endogenous MP signals present in healthy excised and unstained mouse and Cynomolgus monkey retinas using 2PEF, 3PEF, SHG, and THG. We show the first epi-direction detected cross-section and depth-resolved images of unstained isolated retinas obtained using NMMM with an ultrafast fiber laser centered at 1070 nm and a 303038 fs pulse. Two spectrally and temporally distinct regions were shown; one from the nerve fiber layer (NFL) to the inner receptor layer (IRL), and one from the retinal pigmented epithelium (RPE) and choroid. Chapter IV focuses on the use of minimal NMMM signals from a 1070 nm Yb-fiber laser to match and augment H&E-like contrast in human oral squamous cell carcinoma (OSCC) biopsies. In addition to performing depth-resolved (DR) imaging directly from the paraffin block and matching H&E-like contrast, we showed how the combination of characteristic inflammatory 2PEF signals undetectable in H&E stained tissues and SHG signals from stromal collagen can be used to analytical distinguish healthy, mild and severe inflammatory, and neoplastic regions and determine neoplastic margins in a three-dimensional (3D) manner. Chapter V focuses on the use of computational methods to solve an inverse problem of the overlapping endogenous fluorescent and harmonic signals within mouse retinas. The least-squares fitting algorithm was most effective at accurately assigning photons from the NMMMIs to their source. This work, unlike commercial software, permits using custom signal source reference spectra from endogenous molecules, not from fluorescent tags and stains. Finally, Chapter VI explores the use of the OSCC images to train a neural network image classifier to achieve the overall goal of classifying the NMMMIs into three categories-healthy, inflammatory, and neoplastic. This work determined that even with a small dataset (< 215 images), the features present in NMMMIs in combination with tiling, transfer learning can train an image classifier to classify healthy, inflammatory, and neoplastic OSCC regions with 70% accuracy.My research successfully shows the potential of using NMMM in tandem with computational methods to augment current diagnostic protocols used by the health care system with the potential to improve patient outcomes as well as decrease pathology departmental costs. These results should facilitate the continued study and development of NMMM so that in the future, NMMM can be used for clinical applications.
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Title
Multi-Modality Nondestructive Evaluation Techniques for Inspection of Plastic and Composite Pipeline Networks
Creator
Alzuhiri, Mohand
Date
2022
Collection
Electronic Theses & Dissertations
Description
The extensive adoption of plastic pipelines is a growing phenomenon in different fields of the industry, with applications that extend from municipal water and sewer systems to the water lines in nuclear reactors. The large-scale adoption is motivated by the unique features of plastics like corrosion and chemical resistance, low cost, and design flexibility. While the dielectric nature of plastic pipelines provides unique design capabilities, it also introduces new challenges for the...
Show moreThe extensive adoption of plastic pipelines is a growing phenomenon in different fields of the industry, with applications that extend from municipal water and sewer systems to the water lines in nuclear reactors. The large-scale adoption is motivated by the unique features of plastics like corrosion and chemical resistance, low cost, and design flexibility. While the dielectric nature of plastic pipelines provides unique design capabilities, it also introduces new challenges for the operators when it comes to inspecting and ensuring the integrity of these pipelines’ networks. In this study, a multi-modal approach is adopted to address the threats affecting the safety of small diameter plastic pipelines and explore possible inspection solutions for emerging materials like composites. Structured light endoscopes with RGB-D inspection capability were developed for the inspection of surface defects in small diameter pipelines with novelties a) Design and miniaturization of RGB-D structured light sensor with electronic stabilization, b) Development of an algorithm to automatically calibrate the sensor when placed in a cylindrical environment, c) Design of a single shot phase measurement SL sensor that employs the sensor movement to improve the 3D reconstruction, and d) Design a stereoscopic SL sensor for 360-degree inspection. EM-based inspection was adopted to inspect subsurface defects and classify materials around the inspected pipelines. An investigative study was performed to test the probability of detecting cold fusion in butt fusion joints by using emerging NDE techniques, and a coplanar capacitive sensor was designed for the detection of legacy crossbores in gas pipelines. Finally, a thermoacoustic imaging system was developed in this study with potential applications for the inspection of composites and medical imaging. The novelties of this work can be summarized as follows: a) Development of a simulation model to study the thermoacoustic waves generation and the effect of multiple experimental parameters on the performance of thermoacoustic imaging systems, b) Improving the signal to noise ratio of pulsed TAI imaging systems by adoption non-coherent pulse compression. In summary, this study presents a multi-modal approach for the inspection of pipeline networks by adopting optical RGB-D imaging sensors for surface inspection, EM-based sensors for subsurface inspection and classification of objects outside the pipe, and finally, a hybrid imaging method with potential applications in medical imaging and inspection of composites.
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