Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2001. / Vita. Includes bibliographical references (leaves 218-224). Available also in a digital version from Dissertation Abstracts.

Thesis (Ph. D.)--Lehigh University, 2003. / Includes vita. Includes bibliographical references (leaves 133-143).

Thesis (Ph. D.)--University of Missouri-Columbia, 2002. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.

Femtosecond laser microsurgery has emerged as a remarkable technique for precise ablation of biological systems with minimal damage to their surrounding tissues. The combination of this technique with nonlinear optical imaging provides a means of microscopic visualization to guide such surgery in situ. A clinical endoscope capable of image-guided femtosecond laser microsurgery will provide physicians a means for cellular-level microsurgery with the highest precision. This dissertation focuses the development of a miniaturized fiber-coupled probe for image-guided microsurgery, towards future realization as a clinical endoscope. The first part of the dissertation describes the development of an 18-mm diameter probe. This development includes delivery of femtosecond laser pulses with pulse energy in excess of 1 µJ through air-core photonic bandgap fiber, laser beam scanning by a microelectromechanical system scanning mirror, and development of a new image reconstruction methodology for extracting increased temporal information during Lissajous beam scanning. During testing, the 18-mm probe compares favorably with the state-of-the-art as a microscopic imaging tool and we present the first known demonstration of cellular femtosecond laser microsurgery through an optical fiber. The second part of the dissertation explores further refinement of the design into a streamlined package with 9.6 mm diameter and improved imaging resolution. Study of the optical performance through analytical and computer-aided optical design indicates that simple custom lenses can be designed that require only commercial-grade manufacturing tolerances while still producing a fully aberration-corrected microsurgical endoscope. With the 9.6-mm probe, we demonstrate nonlinear optical imaging, including tissue imaging of intrinsic signals from collagen, using average laser powers 2-3× lower than the current state-of-the-art. We also demonstrate the use of the 9.6-mm probe in conjunction with gold nanoparticles for enhanced imaging and microsurgery through plasmonics. Finally, in the third part of this dissertation, we detail bench-top development of a new clinical application for combined femtosecond laser microsurgery and nonlinear optical imaging: the treatment of scarred vocal folds. We show the utility of femtosecond laser microsurgery for creating sub-epithelial voids in vocal fold tissue that can be useful for enhancing localization of injectable biomaterial treatments. We demonstrate that a single compact fiber laser system can be utilized for both microsurgery and imaging. Furthermore, the proposed clinical technique is shown to be achievable with parameters (e.g., pulse energy, focused spot size) that were found to be attainable with fiber-coupled probes while still achieving ablation speeds practical for clinical use. / text

Mediational analysis quantifies proposed causal mechanisms through which treatments act on outcomes. In the presence of clustered data, conventional multiple regression mediational methods break down, requiring the use of hierarchical linear modeling techniques. As an additional consideration, nonlinear relationships in multilevel mediation models require unique specifications that are ignored if modeled linearly. Improper specification of nonlinear relationships can lead to a consistently overestimated mediated effect. This has direct implications for inferences regarding intervention causality and efficacy. The current investigation examined a specific nonlinear multilevel mediation model parameterization to account for nonlinear relationships in clustered data. A simulation study was conducted to compare linear and nonlinear model specifications in the presence of truly nonlinear data. MacKinnon et al.’s (2007a) empirical-M based PRODCLIN method for estimating the confidence interval surrounding the instantaneous indirect effect was used to compare confidence interval coverage rates surrounding both the linear and nonlinear models’ estimates. Overall, the nonlinear model’s estimates were less biased, more efficient, and produced higher coverage rates than the linear model specification. For conditions containing a true value of zero for the instantaneous indirect effect, bias, efficiency, and coverage rate values were similar for the linear and nonlinear estimators. For conditions with a non-zero value for the instantaneous indirect effect, both the linear and nonlinear models were substantially biased. However, the nonlinear model was always less biased and always produced higher coverage rates than the linear model. The nonlinear model was more efficient than the linear model for all but two design conditions. / text

This dissertation focuses on the development of visualization methods that enable us to examine longitudinal data in a unique way. We take inspiration from statistical and fluid mechanics to represent our data as a "flow" through time. Our visualizations represent vector fields (or flow plots), streamlines, and trajectories, and they are constructed in a similar manner to how one might analyze the aggregate motion of particles in a fluid. However, the subject of our research extends beyond ordinary fluid mechanics. We will use our visualizations to examine statewide standardized test scores in Texas from 2003 to 2011. The nature of the data makes it a perfect match for our methodology, since students' test scores tend to change over time in a semi-deterministic but nonlinear manner. Furthermore, our methods represent a departure from the standard ways of analyzing educational data. By visualizing the changes in students' test scores over a nine-year period, we discovered that our flow plots were changing with the eventual graduating class of 2012. The change in our visualizations was caused by an educational policy known as the Student Success Initiative, or SSI. The policy forced students to pass their standardized tests in 5th and 8th grade, or risk being held back a grade. To help with this process, students who initially failed were given extra instruction and additional opportunities to take the test. SSI was implemented in such a way that it would affect the class of 2012 and beyond, although we did not know of the program's existence until our plots had been developed. SSI had a successful impact on the educational career of Texas students; a far greater percentage of students were able to pass the 5th and 8th grade standardized tests after SSI was implemented. The striking feature of SSI, however, is that it also significantly improved test scores in 6th, 7th, 9th, and 10th grade. Despite its success at improving test scores over many years and grades, the program was eventually defunded. This was partially due to an inability to construct a lengthy longitudinal analysis of the program's influence. Our methodology would have conclusively shown the effectiveness of the SSI policy. Despite the defunding of the SSI, I am confident our methodology can be extended to illustrate changes in other data systems. These systems may or may not be related to education; our code and techniques are designed to be as universal as possible. We will explore several extensions to other data sets at the end of this dissertation. / text

This dissertation presents three inter-related studies. Chapter 2 presents a study of scaling of crack propagation in rubber sheets. Two different scaling laws for supersonic and subsonic cracks were discovered. Experiments and numerical simulations have been conducted to investigate subsonic and supersonic cracks. The experiments are performed at 85 °C to suppress strain-induced crystallites that complicate experiments at lower temperature. Calibration experiments were performed to obtain the parameters needed to compare with a theory including viscous dissipation. Both experiments and numerical simulations support supersonic cracks, and a transition from subsonic to supersonic is discovered in the plot of experimental crack speed curves versus extension ratio for different sized samples. Both experiments and simulations show two different scaling regimes: the speed of subsonic cracks scales with the elastic energy density while the speed of supersonic cracks scales with the extension ratio. Crack openings have qualitatively different shapes in the two scaling regimes. Chapter 3 describes a theory of oscillating cracks. Oscillating cracks are not seen very widely, but observed in rubber and gels. A theory has been proposed for the onset of oscillation in gels, but the oscillation of cracks in rubber has not been explained. This study provides a theory able to describe both rubber and gels and recover the experimental phase diagram for oscillating cracks in rubber. The main new idea is that the oscillations of cracks follow from basic features of fracture mechanics and are independent of details of the crack equation of motion. From the fact that oscillations exist, one can deduce some conditions on forms that equations of motion can take. A discrete model of hydraulic fracture is mentioned in Chapter 4. Hydraulic fracturing is a stimulation treatment wherein fluids are injected into reservoirs under high pressure to generate fractures in reservoirs. In this study, a lattice-based pseduo-3D model is developed to simulate hydraulic fracturing. This mode has been validated via a comparison with the KGD model. A series of pilot simulations was systematically tested for complex geometries under more realistic operation conditions, including flexible boundary conditions, randomness in elastic properties of shales and perforations. The simulation results confirm that perforation is likely to increase the complexity of fracture networks; the results also suggest that the interference between neighboring fractures is key to fracture network formation. / text

Several significant wave propagation problems in the fields of nonlinear optics and hydrodynamics are studied in this thesis. In optics, the physical model considered is the two-core optical fiber (TCF), which is an essential component of lightwave technology. In hydrodynamics, the motion of a wave packet on the free surface of water of finite depth allowing modulations from two mutually perpendicular and horizontal directions, governed by the famous Davey-Stewartson (DS) equations, is taken into account. The main contributions of this thesis are: In optics, the effects of the intermodal dispersion (IMD) and the birefringence induced effects, both of which always exist in the TCFs, have been ignored in the previous studies of the modulation instability (MI) of continuous waves (CWs) in the TCFs. In this thesis, a detailed analysis of these effects on the MI spectra has been done. It is found that IMD does not seriously affect the MI spectra of the symmetric/antisymmetric CW states, but can significantly modify the MI spectra of the asymmetric CW states. In exploring the birefringence induced effects, a particular class of asymmetric CW states, which admits analytical solutions and has no counterpart in the single-core fibers, is focused on. It is found that the MI spectra of a birefringent TCF in the normal dispersion regime can be distinctively different from those of a zero-birefringence TCF especially for the circular-birefringence TCF. All the findings of MI analysis can be well verified by the wave propagation dynamics. Another contribution of this thesis is that we find the dramatic pulse distortion and even pulse splitting phenomenon due to IMD in TCFs, which is unexpected in many situations, can be effectively suppressed and even avoided by Kerr nonlinearity, which has never been reported in the literatures in the studies of TCFs. In hydrodynamics, DS equations describe the evolution of weakly nonlinear, weakly dispersive wavepackets with slow spanwise dependences on a fluid of finite depth. Generally, DS equations are divided into two types e, i.e. DSI and DSII equations, depending on the specific fluid configurations (fluid depth, wavelength of the water wave, surface tension etc). Due to the importance of DS equations, many exact solutions have been derived by different nonlinear wave methods over the years in the literature. In this thesis, two new exact doubly periodic wave patterns of DS equations are derived by the use of properties of the theta functions, or equivalently, the Jacobi elliptic functions, and the corresponding solitary waves are also deduced in the long wave limits. The new feature of the two wave patterns found is that they can be applied to both DSI and DSII systems at the same time. / published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

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