A new method of numerical integration is presented here, the variable-step Stormer-Cowell method. The method uses error control to regulate the step size, so larger step sizes can be taken when possible, and is double-integration, so only one evaluation per step is necessary when integrating second-order differential equations. The method is not variable-order, because variable-order algorithms require a second evaluation. The variable-step Stormer-Cowell method is designed for space surveillance applications,which require numerical integration methods to track orbiting objects accurately. Because of the large number of objects being processed, methods that can integrate the equations of motion as fast as possible while maintaining accuracy requirements are desired. The force model used for earth-orbiting objects is quite complex and computationally expensive, so methods that minimize the force model evaluations are needed. The new method is compared to the fixed-step Gauss-Jackson method, as well as a method of analytic step regulation (s-integration), and the variable-step variable-order Shampine-Gordon integrator. Speed and accuracy tests of these methods indicate that the new method is comparable in speed and accuracy to s-integration in most cases, though the variable-step Stormer-Cowell method has an advantage over s-integration when drag is a significant factor. The new method is faster than the Shampine-Gordon integrator, because the Shampine-Gordon integrator uses two evaluations per step, and is biased toward keeping the step size constant. Tests indicate that both the new variable-step Stormer-Cowell method and s-integration have an advantage over the fixed-step Gauss-Jackson method for orbits with eccentricities greater than 0.15. / Ph. D.

The Mekong River Basin (MRB) is one of the largest transboundary basins in the world shared between six south Asian countries. The Mekong river supports a population of more than sixty million people through irrigation and fisheries for their survival and hosts approximately 88,000 MW of unharnessed hydropower potential. The construction of the dams for the supply of energy has a wide-ranging effect on the downstream regions of reservoirs, causing unprecedented and devastating damage to the environment and livelihood of people. The dissertation examines the optimal operation of the dams for the equitable distribution of water between irrigation, domestic, and hydropower sectors with minimal effect on the downstream ecosystem by estimating the cascading effects of dams in the MRB. The hydrological characteristic of the MRB was simulated using the high resolution (1 km) Variable Infiltration Capacity (VIC) hydrological model with the Lohmann et al. (1996, 1998) routing scheme and general circulation models projection for the future till 2099. Remote sensing products were used for the derivation of the reservoir behaviors, while the net irrigation water requirement (NIWR) was simulated by the irrigation scheme embedded in the improved VIC model. The VIC-MODFLOW (VIC-MF) coupled model was used for the investigation of the interaction between the surface and groundwater movement. The hydropower potential of the dams was estimated using the modified Hanasaki et al. (2006) approach by explicitly considering the irrigation water demand from the expanding and intensifying agricultural activities. A system dynamic model for the MRB was developed for the sustainable optimization of water allocation to meet the needs from the irrigation, domestic, hydropower generation, and ecological sectors. Economic analysis was performed to evaluate the existing and future conditions over the resource surplus regions with consideration of social impacts. Streamflows in the MRB varied substantially with the peak monthly streamflow from 10 m3/sec to 40,000 m3/sec. The inflows to dams in both main river and tributaries are projected to increase from 1.2% to 25% under RCP 4.5 and a decrease of 28.5% - 74.7% under RCP 8.5 during 2020-2099 as compared to the historic mean. The NIWR for the MRB was calculated as 65,000 million m3 for the observed period (1981-2019) with a decrease of 0.25% for the future period. The groundwater interaction is expected to enhance the surface streamflow resulting in additional inflow to dams. The multipurpose reservoirs were able to generate the desired annual energy ranging from 15 GWh to 400 GWh along with satisfying more than 80% of the irrigation water demand. Similarly, the irrigation reservoirs also satisfied more than 80% of the water demand for irrigation and hydropower reservoirs to generate the required energy between 2 GWh and 18990 GWh. Climate change will enhance the hydropower potential with an average increase of 7.3% and 5.3% in the future under RCP 4.5 and RCP 8.5, respectively. The increase in the irrigated area (5% and 10%) reduces the energy generation of the multipurpose dams by 1.5%, however, the addition of a crop cycle lowers the energy generation by more than 10%. The system dynamics model showed the multipurpose dams produced annual energy of 316 GWh and satisfied more than 60% of the irrigation, municipal, and industrial sectors water demand during 2006-2019. Similarly, irrigation dams supplying more than 60% of the irrigation water demand, and 50% of the municipal and industrial sectors demand. Climate change has a positive influence on the performance of the dams. The assessment of the shadow price shows that the dam operation in Thailand, Laos PDR, and China will be sufficient to meet the water demands of the energy, irrigation, municipal, and industrial sectors, while the energy sector of Cambodia and Vietnam may experience adverse impacts. / Doctor of Philosophy / The Mekong River Basin (MRB) is one of the largest transboundary basins in the world shared between six south Asian countries. The Mekong river supports more than sixty million people through irrigation and fisheries for their survival and hosts unharnessed hydropower potential. The construction of the dams has a wide-ranging effect on the downstream regions of reservoirs, causing damage to the environment and livelihood of people. The dissertation studies the optimal operation of the dams in the MRB for the equitable distribution of water between irrigation, domestic, and hydropower sectors with minimal effect on the ecosystem. The streamflow of the MRB was simulated using the hydrological model with a routing scheme and future projection till 2099. Remote sensing products were used for the derivation of the reservoir behaviors. The water requirement for the irrigation and the groundwater-surface interaction was simulated by the irrigation scheme embedded in the hydrological model and groundwater coupled model. The hydropower potential of the dams was estimated by explicitly considering the irrigation water demand from the expanding and intensifying agricultural activities. A dynamic model for the MRB was developed for the sustainable optimization of water allocation to meet the needs from the irrigation, domestic, hydropower generation, and ecological sectors. Economic analysis was performed to evaluate the existing and future conditions over the resource surplus regions with consideration of social impacts. Streamflows in the MRB varied substantially between the dams based on the location at the mainstem or tributaries. The inflows to dams in both main river and tributaries in the future is expected to increase under low-carbon emission and decrease under high-carbon emission conditions. The irrigation water for the MRB was calculated as 65,000 million m3 for the period 1981-2019 and expected to decrease in the future. The groundwater interaction is expected to increase the surface streamflow resulting in additional inflow to dams. The multipurpose reservoirs were able to generate the desired annual energy ranging along with satisfying more than 80% of the irrigation water demand. Similarly, the irrigation reservoirs also satisfied more than 80% of the water demand for irrigation and hydropower reservoirs to generate the required energy. Climate change will favor the hydropower energy potential in the future. The increase in the irrigated area and the addition of a crop cycle reduces the energy generation of the multipurpose dams. The system dynamics model showed the multipurpose dams produced 97% of the demand energy and satisfied more than 60% of the irrigation, municipal, and industrial sectors water demand during 2006-2019. Similarly, irrigation dams supplying more than 60% of the irrigation water demand, and 50% of the municipal and industrial sectors demand. Climate change has a positive influence on the performance of the dams. The assessment of the shadow price shows that the dam operation in Thailand, Laos PDR, and China will be sufficient to meet the water demands of the energy, irrigation, municipal, and industrial sectors, while the energy sector of Cambodia and Vietnam may experience adverse impacts.

An infinitely variable transmission (IVT) is a transmission that can smoothly and continuously vary the speed ratio between an input and output from zero to some other positive or negative ratio; they are a subset of continuously variable transmissions (CVTs), which themselves do not have the ability to produce a zero gear ratio. In this thesis, the operation, analysis, and development of a novel, highly configurable, Cam-based Infinitely Variable Transmission of the ratcheting drive type is presented. There are several categories of CVTs in existence today, including traction, belt, and ratcheting types. Drives of these types, their attributes, and associated design challenges are discussed to frame the development of the Cam-based IVT. The operation of this transmission is kinematically similar to a planetary gearset, and therefore, its operation is described with that in mind including a description of the six major components of the transmission, those being the cam, followers, carriers, planet gears, sun gears, and one way clutches. The kinematic equation describing its motion is derived based on the similarities it shares with a planetary gearset. Additionally, the equations for the cam design are developed here as the operation of the CVT is highly dependent on the shape of the cam. There are six simple inversions of this device and each inversion has special characteristics and limitations, for example, the available gear range. A method was developed to select the most suitable inversion, gearing, and follower velocity for a given application. The contact stress between the rollers and cam is the limiting stress within the transmission. A parametric study is used to quantify the relationship between this stress and the transmission parameters. Based off those results, two optimization strategies and their results are discussed. The first is an iterative brute force type numerical search and the second is a genetic algorithm. The optimization results are shown to be similar and successfully reduced the contact stress by 40%. To further improve the transmission performance, several mechanisms were developed for this unique transmission. These include a compact and lightweight differential mechanism based on a cord and pulley system to reduce the contact force on the rollers. In addition, a unique external/inverted cam topology was developed to improve the contact geometry between the rollers and said cam. A prototype was built based on both the optimization strategies and these mechanisms and is described within. Finally, a Prony brake dynamometer with cradled motor was constructed to test the transmission; the results of those tests show the Cam-based IVT to be 93% efficient at low input torque levels. / Master of Science

Tensegrity structures consist of isolated compression members (rigid bars) suspended by a continuous network of tension members (cables). Tensegrity structures can be used as variable geometry truss (VGT) mechanisms by actuating links to change their length. This paper will present a new method of position finding for tensegrity structures that can be used for actuation as VGT mechanisms. Tensegrity structures are difficult to understand and mathematically model. This difficulty is primarily because tensegrity structures only exist in specific stable tensegrity positions. Previous work has focused on analysis based on statics, dynamics, and virtual work approaches. This work considers tensegrity structures from a kinematic viewpoint. The kinematic approach leads to a better understanding of the conditions under which tensegrity structures exist in the stable positions. The primary understanding that comes from this kinematic analysis is that stable positions for tensegrity structures exist only on the boundaries of nonassembly of the structure. This understanding also allows the tensegrity positions to be easily found. This paper presents a method of position finding based on kinematic constraints and applies that method to several example tensegrity structures. / Master of Science

This dissertation focuses on three research projects: 1) construction of simultaneous prediction intervals/bounds for at least k out of m future observations; 2) semi-parametric degradation model for accelerated destructive degradation test (ADDT) data; and 3) spatial variable selection and application to Lyme disease data in Virginia. Followed by the general introduction in Chapter 1, the rest of the dissertation consists of three main chapters. Chapter 2 presents the construction of two-sided simultaneous prediction intervals (SPIs) or one-sided simultaneous prediction bounds (SPBs) to contain at least k out of m future observations, based on complete or right censored data from (log)-location-scale family of distributions. SPI/SPB calculated by the proposed procedure has exact coverage probability for complete and Type II censored data. In Type I censoring case, it has asymptotically correct coverage probability and reasonably good results for small samples. The proposed procedures can be extended to multiply-censored data or randomly censored data. Chapter 3 focuses on the analysis of ADDT data. We use a general degradation path model with correlated covariance structure to describe ADDT data. Monotone B-splines are used to modeling the underlying degradation process. A likelihood based iterative procedure for parameter estimation is developed. The confidence intervals of parameters are calculated using the nonparametric bootstrap procedure. Both simulated data and real datasets are used to compare the semi-parametric model with the existing parametric models. Chapter 4 studies the Lyme disease emergence in Virginia. The objective is to find important environmental and demographical covariates that are associated with Lyme disease emergence. To address the high-dimentional integral problem in the loglikelihood function, we consider the penalized quasi loglikelihood and the approximated loglikelihood based on Laplace approximation. We impose the adaptive elastic net penalty to obtain sparse estimation of parameters and thus to achieve variable selection of important variables. The proposed methods are investigated in simulation studies. We also apply the proposed methods to Lyme disease data in Virginia. Finally, Chapter 5 contains general conclusions and discussions for future work. / Ph. D.

Demand for energy-saving variable speed drives in low-cost, high-volume appliances has increased due to energy and environmental concerns and hence the need to comply with new regulations. Switched reluctance motor (SRMs) have been considered by many as attractive alternatives for brush commutated motors or permanent magnet brushless dc motors (PMBDCMs) in such cost-sensitive applications. The SRMs' unique features such as simple and fault-tolerant structure and unidirectional flow of their phase currents endow them with the possibility of various configurations on both machine and converter topologies for different applications. In the present study, three different variable-speed motor drive systems are proposed, studied, and implemented for their deployment in low-cost, high-volume applications with the power rating of 1.5kW or less. Two different two-phase SRMs and three different power converters are employed to realize three different low-cost drive systems. The first drive system is realized using a novel converter requiring only a single-controllable switch and an asymmetric two-phase 8/4 SRM capable of self-starting and four-quadrant operation. The second drive system is realized using another novel converter requiring two controllable switches, that way to achieve better control and utilization of the asymmetric 8/4 motor. The target applications for both drive systems are low power, low performance drives such as fans, hand tools, small appliances, etc. The third system is realized using a high-speed two-phase 4/2 SRM and a split ac source converter, which is designed for high-speed applications such as vacuum cleaners, ultracentrifuges, etc. The control and design aspects for each drive system are studied. Selection of optimal firing angles and optimal number of winding turns are also investigated. All of the drive systems are first demonstrated on the position sensor-based speed-control scheme. To make the drive system even more cost-competitive, operation without the position sensor using the novel parameter insensitive sensorless control scheme is proposed and implemented. Concept, analysis, simulation, and experimental verification of the proposed sensorless scheme are discussed in detail. / Ph. D.

Spectral reflectance-based, remote sensing technology has been used to adjust in-season nitrogen (N) fertilizer rates for wheat to account for spatial variability in grain yield potential at a sub-meter resolution. The objective of this study was to examine the relationships among spectral reflectance indices, corn tissue N content, chlorophyll measurements, plant size and spacing measurements, and grain yield to develop a similar strategy for variable-rate N management in corn. Irrigated and non-irrigated studies were conducted during the 2002 and 2003 growing seasons in eastern Virginia. Plots were treated with various rates of preplant, starter, and sidedress N fertilizer to establish a wide range of grain yield potential. Spectral measurements, tissue N, chlorophyll measurements, and plant physical measurements were collected at growth stages V6, V8, and V10. At maturity, grain yield was determined and correlated with in-season data and optimum N rate to calibrate in-season, variable-rate N fertilization strategies. Results from these studies indicate that spectral reflectance is well correlated with plant N uptake and chlorophyll meter readings and can also be correlated with final grain yield. These relationships may be used to develop a model to predict in-season, variable N application rates for corn production at a sub-meter resolution. / Master of Science

As data collection techniques improve, oftentimes the number of covariates exceeds the number of observations. When this happens, regression models become oversaturated and, thus, inestimable. Many classical and Bayesian techniques have been designed to combat this difficulty, with various means of combating the oversaturation. However, these techniques can be tricky to implement well, difficult to interpret, and unstable. What is proposed is a technique that takes advantage of the natural clustering of variables that can often be found in biological and ecological datasets known as the omics datasests. Generally speaking, omics datasets attempt to classify host species structure or function by characterizing a group of biological molecules, such as genes (Genomics), the proteins (Proteomics), and metabolites (Metabolomics). By clustering the covariates and regressing on a single value for each cluster, the model becomes both estimable and stable. In addition, the technique can account for the variability within each cluster, allow for the inclusion of expert judgment, and provide a probability of inclusion for each cluster. / Ph. D.

In this thesis we propose a novel modification to Bayesian decision tree methods. We provide a historical survey of the statistics and computer science research in decision trees. Our approach facilitates covariate selection explicitly in the model, something not present in previous research. We define a transformation that allows us to use priors from linear models to facilitate covariate selection in decision trees. Using this transform, we modify many common approaches to variable selection in the linear model and bring these methods to bear on the problem of explicit covariate selection in decision tree models. We also provide theoretical guidelines, including a theorem, which gives necessary and sufficient conditions for consistency of decision trees in infinite dimensional spaces. Our examples and case studies use both simulated and real data cases with moderate to large numbers of covariates. The examples support the claim that our approach is to be preferred in large dimensional datasets. Moreover, our approach shown here has, as a special case, the model known as Bayesian CART. / Ph. D.

Nitrate (NO⁻3) export can vary widely among forested watersheds with similar nitrogen loading, geology, and vegetation, which suggests the importance of understanding differing internal retention mechanisms. Transport should be studied at the hillslope scale because the hillslope is the smallest unit with spatial and temporal resolution to reflect many relevant NO⁻3 retention and transport (flow-generation) processes, and headwater forested watersheds are largely comprised of sections of hillslopes. I conducted two experiments to elucidate subsurface flow dynamics and NO⁻3 transport and retention mechanisms on a constructed experimental hillslope model. In the first experiment, I tested whether decadal pedogenetic changes in soil properties in the experimental hillslope used by Hewlett and Hibbert (1963) would lead to changes in recession flow. I repeated (twice) their seminal experiment, whose results led to the development of the Variable Source Area paradigm, by also saturating, covering, and allowing the experimental hillslope to drain until it no longer yielded water. In the historical experiment there was fast drainage for 1.5 d, followed by slow drainage for ~140 d, which led the authors to conclude that recession flow in unsaturated soil could sustain baseflow throughout droughts. This long, slow drainage period was not reproduced in my experiments. Shapes of the drainage curves in my experiments were similar to the historical curve, but slow drainage was truncated, ending after 17 and 12 d, due likely to a leak in the boundary conditions, rather than to pedogenetic changes since the historical experiment. Leakage to bedrock, analogous to the leak in the hillslope model, is a commonly observed phenomenon and this study highlights how that can reduce drainage duration and the contribution of moisture from soils to support baseflow. In the second experiment, I tested whether movement of NO⁻3, which is considered a mobile ion, would be delayed relative to movement of water through a hillslope. I added concentrated pulses of ¹⁵NO⁻3 and a conservative tracer (²H₂O) on the same experimental hillslope, which was devegetated and irrigated at hydrologic steady state. Retention of the ¹⁵NO⁻3 tracer was high in the soil surface (0–10 cm) layer directly where the tracer was added. The portion of the ¹⁵NO⁻3 tracer that passed through this surface layer was further retained/removed in deeper soil. The reduction in the peaks in δ¹⁵N breakthrough was an order of magnitude larger than in δ₂H breakthrough at the outlet 5 m downslope of the tracer addition. The peaks in δ¹⁵N were also delayed relative to the peaks in δ₂H by 1, 6, 9 and 18.5 d for slope distances of 0, 2, 4, and 5 m, respectively, from tracer addition to the outlet. The excess mass of ¹⁵NO⁻3 recovered at the outlet was less than 3% of the original tracer mass injected. Nitrification and denitrification were estimated to be roughly 1:1 and were large fluxes relative to lateral transport into and out of the riparian zone. This tracer experiment shows that bedrock leakage, coupled with multiple retention/removal mechanisms can significantly delay export of added NO⁻3 with implications of additional NO⁻3 sink strength at the watershed scale. / Ph. D. / Nitrate (NO₃⁻) export can vary widely among forested watersheds with similar nitrogen loading, geology, and vegetation, which suggests the importance of understanding differing internal process mechanisms. I conducted two experiments to illustrate how water and NO₃⁻ moved on a constructed hillslope model. In the first experiment, I quantified differences in soil properties in the hillslope model used by Hewlett and Hibbert (1963). Then I repeated (twice) the seminal drainage experiment described in Hewlett and Hibbert (1963). The same hillslope (21.8°; 40%) was wetted up, covered, and allowed to drain until water stopped exiting at the outlet. In the historical experiment there was fast drainage for 1.5 d, followed by slow drainage for ~140 d, which led the authors to hypothesize that slow drainage in surface soil could continually contribute water to streams even during droughts. This long, slow drainage period was not reproduced in my experiments. Drainage was similar at the beginning of drainage between my experiments and the historical experiment, but in my experiment the slow drainage ended earlier (after 17 and 12 d) due likely to a leak in the constructed hillslope model, rather than to significant changes that occurred in the soil itself since the original experiment. This leak in the hillslope model is similar to leakage to bedrock, which is commonly observed in natural hillslopes. In the second experiment, I tested whether NO₃⁻ and water would move through a hillslope at the same rate. I added concentrated pulses of NO₃⁻ (as ¹⁵NO₃⁻ and water (as ²H₂O) on the same devegetated experimental hillslope. Retention of the ¹⁵NO₃⁻ tracer was high in the surface (0–10 cm) where the tracer was added, with little change in the immediately surrounding soil, despite high rates of water input immediately after tracer addition and throughout the experiment. The portion of the ¹⁵NO₃⁻ tracer that passed through the surface layer was further processed by microbes in deeper soil as it traveled downslope. This body of work shows that bedrock leakage, coupled with multiple retention mechanisms throughout the soil profile, can significantly delay export of added NO₃⁻ at the watershed scale.