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We study ground states in the nonlinear Schrödinger equation (NLS) with an isotropic harmonic potential, in energy-critical and energy-supercritical cases. In both cases, we prove existence of a family of ground states parametrized by their amplitude, together with the corresponding values of the spectral parameter. Moreover, we derive asymptotic behavior of the spectral parameter when the amplitude of ground states tends to infinity. We show that in the energy-supercritical case the family of ground states converges to a limiting singular solution and the spectral parameter converges to a nonzero limit, where the convergence is oscillatory for smaller dimensions, and monotone for larger dimensions. In the energy-critical case, we show that the spectral parameter converges to zero, with a specific leading-order term behavior depending on the spatial dimension. Furthermore, we study the Morse index of the ground states in the energy-supercritical case. We show that in the case of monotone behavior of the spectral parameter, that is for large values of the dimension, the Morse index of the ground state is finite and independent of its amplitude. Moreover, we show that it asymptotically equals to the Morse index of the limiting singular solution. This result suggests how to estimate the Morse index of the ground state numerically. / Dissertation / Doctor of Philosophy (PhD)

Construction of pavements requires the subgrades - which are the foundation of the structure, to be capable of supporting traffic loads that would be applied onto them. In the case that the subgrades are unable to support the structure, failure would occur. The subgrade being in-situ soil can be of poor quality if not properly constructed or improved if necessary. In Canada, the eastern region precisely Ontario and Quebec, is dominated by sensitive marine clays which when disturbed lose their strength drastically making them a geotechnical hazard. The soil's high sensitivity causes this behavior it poses. Therefore, to construct pavements in this type of soil, improvement techniques are required. One such is lime stabilization which improves the engineering properties of the soil. Research on the stabilization of sensitive marine clay in Canada has been conducted to a certain extent showing the effectiveness of the process in improving the soil's poor engineering properties. However, during the process of stabilization, the thermal (T), hydraulic (H), mechanical (M) and chemical (C) processes and interactions that occur influence the behavior of the stabilized clay. Environmental stresses such as moisture and temperature are also known to affect the coupled processes that occur. However, these coupled processes and their impact on the stabilized clay are not well known and understood. The goal of the research was to therefore, conduct various column experiments and monitoring to determine the evolution of the coupled THMC processes under normal curing and when daily thermal cycles were applied to the treated and untreated clay. Various columns were prepared in the laboratory to accommodate the compacted treated and untreated sensitive marine clay for monitoring over 28 days. In addition, columns from which samples for extensive geotechnical testing were collected, were prepared. The soils' strength and hydraulic conductivity were determined through testing while the suction, electrical conductivity and temperature evolution were determined by use of sensors placed within the columns. The developed mechanical properties of the soil were significantly improved by use of lime. This development of mechanical properties was further enhanced when the daily thermal cycles were applied to the soil due to increased curing temperature stimulated. In addition, to temperature and chemical reactions, it was observed that the hydraulic properties also contributed to the developed soil strength. The strongly coupled THMC processes were thus, observed during the treatment of the clay with lime. The results obtained will therefore, contribute to a better understanding of the coupled THMC processes that occur when sensitive marine clay is treated with lime. It will further contribute to cost effectively designing pavements in regions with sensitive marine clays or similar.

To measure the differences in ground reaction forces between running shoes, racing flats, and distance spikes, twenty intercollegiate distance runners ran across a force plate at 6.7m/s (for males) and 5.74m/s (for females) in each of the three types of shoes. In order to control for differences in foot strike, only subjects who had a heel strike were included in the data analysis (N=16). Repeated-measures ANOVA and Tukey's post-hoc test (p<0.05) revealed loading rate and impact peak to be significantly increased in the flats and spikes compared to running shoes. Stiffness in spikes was significantly higher than in running shoes. Stance time in spikes and flats was decreased. These results can be used to better inform competitive runners, coaches, and trainers of the risks and performance benefits when determining the frequency and duration of the use of competitive footwear in training.

Glacier models often fail to incorporate the geometry and/or physical properties of tributaries included in complex glaciers. Tributary glaciers have different source areas and flow conditions than the adjacent main valley glacier. Ice cores (~3m depth) and surface samples (<0.5m depth) were collected from Grenzgletscher (main valley glacier) and Zwillingsgletscher (tributary glacier) in the Gornergletscher system of the Swiss Alps. Stable water isotopes indicate seasonal variation, showing 1-2 annual layers. The mean d18O for Grenzgletscher is ~4.8‰ lower than for Zwillingsgletscher. This difference may be accounted for in part by elevation differences between the accumulation areas (~1.1‰ δ18O), increased avalanching in Grenzgletscher (~1.8 ‰ δ18O), and by varying climatic conditions at the time of precipitation (~0.9-1.4‰ variation in δ18O). Using a kinematic ice flow model, core ages were estimated using effective annual layer thickness (based on seasonal variations), annual accumulation rate and ice thickness. The Grenzgletscher core is ~4 years older than the Zwillingsgletscher core. Based on ages and flow distances, the tributary has a lower flow velocity (63-87 m/yr) compared to Grenzgletscher (61-134 m/yr). To understand thermal properties of the tributary, a 775 m GPR survey (200 MHz) was conducted along a flow line of Zwillingsgletscher. Topographic waves (ogives) observed on the surface are mimicked by the onset of reflectivity 10-20 m below the surface. Reflective regions are interpreted as warmer ice at the pressure melting point, overlain by colder ice. This thermal structure is likely related to acceleration through an ice fall. Since most tributary glaciers include ice falls, thermal properties of tributary glaciers may be different from those of the main valley glacier. The properties and geometry of tributary glaciers are significantly different from main valley glaciers and should therefore be incorporated into glacier models in the future.

Yoga adherents claim many benefits of the practice, including promotion of bone health and prevention of osteoporosis. However, few, if any, studies have investigated whether yoga enhances bone mineral density. Furthermore, none have identified force generation in yoga. The purpose of this study is to collect ground reaction force (GRF) data on a variety of common hatha yoga postures that would be practiced in fitness centers or private studios. Twelve female and eight male volunteers performed a sequence of 28 common hatha yoga postures while ground reaction force data were collected with an AMTI strain-gauge force plate. The sequence was repeated six times. Four variables were studied: the maximum vertical GRF, the mean vertical GRF, the maximum resultant GRF, and the mean resultant GRF. Univariate analysis was used to identify mean values and standard deviations for each of the four variables. Multivariate analysis revealed some variation due to gender but none due to age or weight. Means were similar across all poses and subjects, and standard deviations were small. This unique yoga sequence produced low impact forces in both upper and lower extremities. Further research is warranted to determine whether these forces are sufficient to promote osteogenesis or maintain current bone health in yoga practitioners.

The purpose of this study was to compare joint moments during the active peak vertical ground reaction force (PVGRF) when running in three conditions. Twenty-five subjects, sixteen male and nine female, were measured using 3-dimensional motion analysis while running barefoot, in Vibram FiveFingers® (VF®) minimalist running shoes and in traditional running shoes at a 7-minute-mile pace (3.84 m/s). Joint moment differences were calculated and compared using a mixed model analysis of variance. Results showed the VF® was effective at mimicking both the kinetic and kinematic attributes of barefoot running. The only significant difference found when comparing barefoot and VF® running was in the ankle angle (p < .005). All other variables in the lower extremity were the same for the two conditions. Though the subjects in our study had no previous experience with VF® (or barefoot) running they were able to closely mimic barefoot running upon initial running trials. Joint moments at the ankle were higher for barefoot and VF® running (p < .001) when compared with shod running. This may potentially lead to a greater risk of injury at the ankle joint when running barefoot or in VF®. The hip joint moments were only different when comparing the barefoot condition to the shod condition (p=.002), with the barefoot condition higher than shod running. The knee joint moment was smaller during the VF® and barefoot conditions when compared with shod running (p < .001) and may lead to a decrease in injury rates at the knee. Though a reduction in moments of the lower extremity may lead to a decrease of injury at the corresponding joint, it is important to consider the adaptations that take place as a result of varying stresses. According to Wolff's law, bone and surrounding tissue will adapt to the loads it is placed under. Taking this into consideration, it is important to remember that lower moments may lead to weaker bones and surrounding tissues and without compensation for these reduced loads, injury rates may remain the same over time.

This study involved a geographic information systems (GIS) approach to modeling ground water pollution potential in the Southern Edwards Aquifer Region in Texas. The DRASTIC ground water model was analyzed using two methods. First, the effects of adding land cover data to the drastic model were evaluated. In the second approach, the effects of the removal of DRASTIC variables were evaluated. Six, five, and four variable models were generated and analyzed.

Ground Penetrating Radar (GPR) research conducted in coastal environments is one area that is lacking in archaeology. Surveys conducted in this type of environment afford the opportunity to evaluate the practical use GPR under field conditions. Coastal environments are effective for this evaluation because they offer a host of conditions that GPR surveys do not normally encounter at one time. The relationship of the land to the coast, sub-surface conditions and reliable survey areas create a "perfect storm" to test how practical the use of GPR is in coastal environments. This research is a study of homestead cemeteries situated within the boundaries of Cape Canaveral Air Force Station (CCAFS), using GPR. The research has three main goals. The first is to utilize GPR to identify if there are any unknown burials at CCAFS. The second is to test the practical effectiveness of GPR in coastal environments where high water table, geology and saline conditions can limit the capability of the technique to resolve subsurface features. The third is to correlate data from the GPR survey with ethnographic information to enhance the protection and maintenance with what is already available for the cemeteries. Research methods include field-based geophysical data collection in addition to archival and ethnographic historic research. The field component, to which this research pertains, entailed an on-site GPR survey at the nine sites on Cape Canaveral Air Force Station. This was followed by analysis of the information from the survey using standard processing software. Subsequently, a thorough archival search was completed to link historic and ethnographic information with the archaeological data obtained on the cemeteries. The final result of this research was a report that provides a detailed description of the results of the GPR survey of the cemeteries at Cape Canaveral Air Force Station.

Geophysical techniques, such as ground-penetrating radar (GPR), have been successfully used by law enforcement agencies to locate graves and forensic evidence. However, more controlled research is needed to better understand the potential and limitations of this technology in the forensic context. The goal of this study was to determine the potential of GPR using both a 250 MHz and 500 MHz antennae to monitor eight controlled graves with six different burial scenarios using pig carcasses as human proxy cadavers. In addition, a conductivity meter was employed to determine the applicability of using this technology to locate unmarked graves. For the conductivity meter, the data was processed using an EM38 program in conjunction with the SURFER program to display a conductivity contour map of the grid. For the GPR imagery, reflection profile data was processed using the program REFLEXW while horizontal slices were processed using the GPR-SLICE program. Results indicate that the conductivity meter is not a viable option in the detection of clandestine graves when other geophysical tools are available. For the GPR, results indicate that while graves can still be detected after a two-year period, there is a marked decrease in the response, or resolution, of the burial scenarios. Furthermore, burials with grave goods interred along with the carcasses were far more likely to be detected than burials that were interred with no accompanying grave goods. When comparing the performance of the two antennae, the 250 MHz antenna provided increased resolution for large cadavers buried in deep graves.