The n-point Steiner problem in the Euclidean plane is to find a least length path network connecting n points. In this thesis we will demonstrate how to find a least length path network T connecting n points on a closed 2-dimensional Riemannian surface of constant curvature by determining a region in the covering space that is guaranteed to contain T. We will then provide an algorithm for solving the n-point Steiner problem on such a surface.

In recent earthquakes, structures have not performed as well as expected resulting in a need for better means of retrofitting and improvements in seismic design. Fiber Reinforced Polymers (FRP), as a material with potential to increase strength and ductility of columns in conjunction with capacity design methodology, has promise for seismic design. By investigating the displacement, ductility, and flexural strength properties of FRP confined reinforced concrete circular cross sections, this study analyzes the seismic applications of FRP confinement. The study is performed by incorporating an FRP confined concrete stress-strain model into a developed Moment-Curvature and PM Interaction software. This software conducts a comparison between traditional steel and FRP confined sections while performing parameter studies on the 28-day unconfined concrete compressive strength, longitudinal reinforcing ratio, cross section diameter, FRP confinement jacket thickness-cross section diameter ratio, and FRP confinement system design variables. These studies validate FRP’s performance for seismic applications resulting in several design recommendations to increase displacement capacity, ductility, and flexural strength and, thus, seismic performance.

Pulse-shaped signals require a tool that can accurately analyse and identify the peak characteristics in the spectrum. One recently developed tool available to analyse non-stationary pulse-shaped waveforms with a suitable peak reconstruction is semiclassical signal analysis (SCSA). SCSA is a signal representation method that decomposes a real positive signal y(t) into a set of squared eigenfunctions through the discrete spectrum of the Schr¨odinger operator. In this study, we apply SCSA in two directions. First, we propose a new signal denoising method based on the signal curvature. We use this technique to show that denoising the pulse-shaped signal by regularizing its curvature can yield better peak-preserving performance than traditional filters, such as moving average filter or wavelet. Second, we apply SCSA to biomedical signal analysis. The localization abilities of L2 normalized squared eigenfunctions are used in blood pressure (BP) estimation. Based on existing properties, the systolic and diastolic phases are separated into photoplethysmograms (PPGs), which are then used as features for BP estimation. In addition, the Multiparameter Intelligent Monitoring in Intensive Care (MIMIC II) database is used to test the application with more than 8000 subjects. Another application uses SCSA features to characterize EEG and MEG signals, leading to more accurate epileptic spike detection and diagnosis in epileptic patients. Both applications are validated using real datasets, which guarantees statistical reliability and motivates future work of this model in clinical applications and equipment designs.

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A low-speed, axisymmetric turbulent boundary layer under a strong adverse pressure gradient is experimentally studied for its relevance to marine applications, urban air-transportation and turbulence ingestion noise. The combined effect of lateral curvature and streamwise pressure gradient are examined on the mean flow, turbulence structure, velocity correlations and wall pressure fluctuations. Additionally, the upstream influence of a rotor operating in this flow is examined to improve the understanding of the turbulence necessary to develop advanced noise prediction tools. Measurements were made in Virginia Tech Stability tunnel documenting the flow over a 0.432-m diameter body-of-revolution comprised of a forward nose-cone, a constant diameter mid-body and a 20 degree tail-cone, at a length based Reynolds number of 1.2 million. The principal finding of this work is the resemblance of the boundary layer to a free-shear layer where the turbulence far from the wall plays a dominant role, unlike in the canonical case of the flat-plate boundary layer. The mean flow along the tail developed inflection points in the outer regions and the associated velocity and turbulence stress profiles were self-similar with a recently proposed embedded shear layer scaling. As the mean flow decelerates downstream, the large-scale motions energize and grow along with the boundary layer thickness; However, the structure is roughly self-similar with the shear-layer scaling, emphasizing the role of the shear-layer in the large-scale structure. Additionally, the correlation structure is discussed to provide information towards the development of turbulence models and aeroacoustic predictions. The associated wall pressure fluctuations, measured with a longitudinal array of microphones, evolved significantly downstream with the dimensional wall pressure spectra weakening by over 20-dB per Hz. However, the spectra collapsed to within 2-dB with the wall-wake scaling, where the pressure-scale is the wall shear stress, and the time-scale is derived from the boundary layer thickness and edge velocity. The success of this scaling, even in the viscous roll-off regions, suggests the increasing importance of the outer region on the near-wall turbulence and wall-pressure. Investigation of the space-time structure revealed the presence of a quasi-periodic feature with the conditional signature of a roller-eddy. The structure appeared to scale with the wall-wake scaling, and was found to convect downstream at speeds matching those at the inflection points (and outer turbulence peak). It is hypothesized that the outer region turbulence in strong adverse pressure gradient flow strongly drive the near-wall turbulence and therefore both the wall pressure and shear stress. Subsequent measurements made with the rotor operating at the tail, using high-speed particle image velocimetry, provided the space-time structure of the inflow turbulence as a function of the rotor thrust. The impact of the rotor on the mean flow, turbulence and correlation structure in the vicinity of the rotor is discussed to supply information towards validating numerical simulations and developing turbulence models that account for the distortion due to the rotor. This work was sponsored by the Office of Naval Research, in particular Drs. Ki-Han Kim and John Muench under grants N00014-17-1-2698 and N00014-20-1-2650. / Doctor of Philosophy / Understanding turbulent flows adjacent to surfaces placed in fluid flows is necessary to develop efficient technologies to mitigate undesirable drag, vibrations and noise. Particularly, this is of an increased interest with the imminent abundance of urban short-haul air transportation. While several fundamental aspects of these flows have been clarified, certain specific areas still remain to be addressed, including the impact of curved surfaces, like those of submarine hulls and aircraft fuselage, and the impact of mean pressure gradients. This study seeks to fill some of these gaps by studying the flow over a body-of-revolution through wind tunnel experiments. The nature of the velocity and wall-pressure fluctuations are examined in detail. It was found that the boundary layer was significantly different from the canonical case of a flat-plate flow, with the mean velocity and turbulence structure developing the characteristics of a free-shear layer (flows unbounded by surfaces). Specifically, the velocity and turbulence intensity appeared self-similar with a recently proposed embedded shear layer scaling, which is based on the parameters at the inflection point in the mean velocity profile. The large-scale motions in the outer regions, despite energizing and growing as the flow decelerated downstream, appeared self-similar with the shear layer parameters, emphasizing the role of shear layer motions within in the boundary layer. This is important since the turbulence relatively further from the wall are now the important sources of pressure fluctuations and therefore drag, vibrations and noise. The associated wall-pressure fluctuation were studied with a focus on the wall-pressure spectrum and the space-time structure. A quasi-periodic feature was detected in the instantaneous fluctuations, which had a conditional structure reminiscent of a conditional roller, and appeared to convect downstream at speeds matching those at the inflection points in the velocity profile. Therefore it is hypothesized that the large-scale motions in the embedded shear layer play a dominant role on the near-wall turbulence and therefore on the wall pressure and shear-stress. This is different from the behavior of the wall-studied flow past a flat-plate. It is therefore important to factor this into technologies aiming to increase the efficiency and quieten the vehicles

Yes / Age at death estimation of human skeletal remains is one of the key issues in constructing a biological profile both in forensic and archaeological contexts. The traditional adult osteological methods evaluate macroscopically the morphological changes that occur with increasing age of specific skeletal indicators, such as the cranial sutures, the pubic bone, the auricular surface of the ilium and the sternal end of the ribs. Technologies such as CT and laser scanning are becoming more widely used in anthropology, and several new methods have been developed. This review focuses on how the osteological age-related changes have been evaluated in digital data. Firstly, the 3D virtual copies of the bones have been used to mimic the appearance of the dry bones and the application of the traditional methods. Secondly, the information directly extrapolated from CT scan has been used to qualitatively or quantitatively assess the changes of the trabecular bones, the thickness of the cortical bones, and to perform morphometric analyses. Lastly, the most innovative approach has been the mathematical quantification of the changes of the pelvic joints, calculating the complexity of the surface. The importance of new updated reference datasets, created thanks to the use of CT scanning in forensic settings, is also discussed. / CV was supported from the Danish Council for Independent Research (DFF – 4005-00102B – FTP)