This thesis consists of results relating to the theoretical and computational advances in modeling the Normal-Normal hierarchical model. / Statistics

We present a fast direct algorithm for the solution of linear systems arising from elliptic equations. We extend the work of Xia et al. (2009) on combining the multifrontal method with hierarchical matrices. We offer a more geometric interpretation of that approach, extend it in two dimensions to the unstructured mesh case, and detail an adaptive decomposition procedure for selectively refined meshes. Linear time complexity is shown for a quasi-uniform grid and demonstrated via numerical results for the adaptive algorithm. We also provide an extension to three dimensions with proven linear complexity but a more practical variant with slightly worse scaling is also described. / text

To obtain a suitable mathematical model of the input-output behavior of highly nonlinear, multi-scale, nonparametric phenomena, we introduce an adaptive radial basis function approximation approach. We use this approach to estimate the discrepancy between traditional model areas and the multiscale physics of systems involving distributed sensing and technology. Radial Basis Function Networks offers the possible approach to nonparametric multi-scale modeling for dynamical systems like the adaptive wing with the Synthetic Jet Actuator (SJA). We use the Regularized Orthogonal Least Square method (Mark, 1996) and the RAN-EKF (Resource Allocating Network-Extended Kalman Filter) as a reference approach. The first part of the algorithm determines the location of centers one by one until the error goal is met and regularization is achieved. The second process includes an algorithm for the adaptation of all the parameters in the Radial Basis Function Network, centers, variances (shapes) and weights. To demonstrate the effectiveness of these algorithms, SJA wind tunnel data are modeled using this approach. Good performance is obtained compared with conventional neural networks like the multi layer neural network and least square algorithm. Following this work, we establish Model Reference Adaptive Control (MRAC) formulations using an off-line Radial Basis Function Networks (RBFN). We introduce the adaptive control law using a RBFN. A theory that combines RBFN and adaptive control is demonstrated through the simple numerical simulation of the SJA wing. It is expected that these studies will provide a basis for achieving an intelligent control structure for future active wing aircraft.

To aid in resolving some of the ambiguity in the literature about the impact of different forms of WOM on brand performance, this dissertation investigates how WOM influences three consumer responses to WOM: purchase, WOM retransmission, and additional information search. The author investigates these questions by analyzing a database comprising more than three years of detailed WOM data from a unique, nationally representative panel merged with other secondary sources that provide various measures of brand strength (the American Consumer Satisfaction Index and Harris Interactive’s Equitrend). Using a series of hierarchical regression models, the results from this study reveal numerous insights into the contextual factors that moderate the impact of a WOM episode. For example, negative WOM about a brand has a larger absolute effect on consumer purchase intentions than positive WOM, but positive WOM has a larger positive effect on WOM retransmission than the positive effect of negative WOM. Offline WOM tends to exacerbate the effect of positive and negative brand sentiment on purchase intentions. WOM between stronger social ties tends to have greater impact on brand-related responses than WOM between weak ties, except in the case of motivating additional information search. The results also indicate that strong brands (those with higher levels of brand equity) tend to reap greater benefits from WOM. For example, negative, mixed, or neutral WOM has greater influence on purchase, and WOM from weak social ties about strong brands motivates higher levels of information search than when WOM from weak ties is about weaker brands.

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abstract: Deterministic solutions are available to estimate the resilient modulus of unbound materials, which are difficult to interpret because they do not incorporate the variability associated with the inherent soil heterogeneity and that associated with environmental conditions. This thesis presents the stochastic evaluation of the Enhanced Integrated Climatic Model (EICM), which is a model used in the Mechanistic-Empirical Pavement Design Guide to estimate the soil long-term equilibrium resilient modulus. The stochastic evaluation is accomplished by taking the deterministic equations in the EICM and applying stochastic procedures to obtain a mean and variance associated with the final design parameter, the resilient modulus at equilibrium condition. In addition to the stochastic evaluation, different statistical analyses were applied to determine that the uses of hierarchical levels are valid in the unbound pavement material design and the climatic region has an impact on the final design resilient moduli at equilibrium. After determining that the climatic regions and the hierarchical levels are valid, reliability was applied to the resilient moduli at equilibrium. Finally, the American Association of State Highway and Transportation Officials (AASHTO) design concept based on the Structural Number (SN) was applied in order to illustrate the true implications the hierarchical levels of design and the variability associated with environmental effects and soil properties have in the design of pavement structures. The stochastic solutions developed as part of this thesis work together with the SN design concept were applied to five soils with different resilient moduli at optimum compaction condition in order to evaluate the variability associated with the resilient moduli at equilibrium condition. These soils were evaluated in five different climatic regions ranging from arid to extremely wet conditions. The analysis showed that by using the most accurate input parameters obtained from laboratory testing (hierarchical Level 1) instead of Level 3 analysis could potentially save the State Department of Transportation up to 10.12 inches of asphalt in arid and semi-arid regions. / Dissertation/Thesis / M.S. Civil and Environmental Engineering 2011

With an increasing demand for alternative clean energy solutions, much effort is being invested in the progression of nanoscale semiconductor materials in hopes of better harnessing solar energy. ZnO and TiO2 remain the most prominent photocatalytically active materials. This thesis reports on a comparison between nanoscale core-shell and hierarchical Zn-Ti-O/ZnO heterostructures. After a seed layer thickness optimization, hydrothermally grown ZnO nanorods were coated with mixed concentrations of Ti and Zn within an oxygen rich sputtering environment at two distinct temperature zones. Core-shell structures resulted from low temperature (23°C) depositions while hierarchical branch structures grew at high temperature (800°C). Excluding deposition temperature and the strategic variation of Zn and Ti gun power, every fabrication process remained identical between the two resultant heterostructure groups. Amongst the variety of samples produced, one from each heterostructure group proved notably similar in structural dimension, composition, and crystallization, yet demonstrated distinct differences in photoluminescence and dye degradation via UV-visible light spectroscopy. While photoluminescence results indicated core-shell heterostructure more photocatalytically promising, hierarchical heterostructure prevailed as the more powerful photocatalyst. Increased surface area due to hierarchical branching in conjunction with enhanced light exposure was believed responsible for the improved photocatalytic effectiveness.

Elements from differential association and importation theory were incorporated into a contextual model to explain drug abuse inside prison. Data came from self-administered questionnaires given to more than 1,000 inmates in 30 different correctional institutions throughout Kentucky, Tennessee, and Ohio. Hierarchical linear modeling was used to examine the impact of correctional context on individual behavior. Results indicated that drug abuse inside prison varies across different correctional institutions. The effect of prior street-drug use on drug abuse in prison also varied across contexts. Moreover, an aggregate measure of crowding explained both drug abuse in prison as well as the effect of prior street-drug use on substance abuse in prison.

While designed and adopted at the federal level, the Clean Air Act (CAA) and Clean Water Act (CWA) rely on states for implementation. The result of this implementation framework is a disparity in environmental conditions across the nation. The objective of this research is to examine how the implementation stage of the policy process affects program outcomes. The findings indicate that the primary means of shaping program outcomes are the decision-making criterion and subsequent behavior of implementing officials, where their value based actions dictate service delivery. These decisions are, in turn, shaped by the context of the work, where organizations and the socio-political environment influence the basis for decision-making. These findings connect broader organizational and socio-political factors with program outcomes through an indirect relationship, rather than assume a direct relationship as previous authors have done. The findings explain a significant portion of the variance in both air and water program outcomes across the nation. This research indicates the importance of front-line operators in the implementation process, an issue that has been left-out of other work. These conclusions can be used to enhance performance management by practitioners, through a greater understanding of how organizations and individuals affect program outcomes. Finally, the theoretical framework and methodological techniques suggest that previous implementation research has failed to properly specify statistical models, which enhances the literature on the subject.

Though the past two decades have seen a dramatic increase in research toward self-cleaning repellent surfaces, multiple challenges exist in the creation of biorepellent surfaces for everyday use. Environmental concerns persist with many of the chemicals utilized in this field and the need for scalable, low-cost alternatives remains. Spread of pathogens including bacteria and viruses in healthcare and public settings also presents a need for stable surfaces. In the work presented here, we report on the current status of antimicrobial nanomaterials and coatings toward virus repellency, followed by an investigation into the application of polysiloxane nanostructures in creation of flexible hierarchical surfaces. Using n-propyltrichlorosilane (n-PTCS) coated on activated polyolefin (PO) we were able to demonstrate superhydrophobicity, reporting water contact angles above 153° paired with <1° sliding angles on hierarchical surfaces. A transfer assay, that closely mimics contact with high-touch surfaces, using Escherichia coli K-12 transfected with green fluorescent protein (GFP) reported a 1.6-log (97.5%) reduction in fluorescence on surfaces compared to planar PO controls, paired with a 1.2-log (93%) reduction in CFU/mL in comparison to control groups. Additionally, surfaces demonstrated a contact angle of 140.8° with citrated whole blood. Droplets of blood incubated on our surfaces for 15 min showed a 93% reduction in visible staining, while submersion in citrated whole blood for 20 minutes revealed an 87% reduction in blood adhered to the surfaces. The applications for these biorepellent surfaces have widespread potential, including the demonstrated need for prevention of surface contamination to minimize spread of hospital acquired infections (HAIs) within the healthcare system. / Thesis / Master of Applied Science (MASc) / The goal of creating a surface capable of repelling biological samples continues to present challenges due to surface stability, scalability, and cost of manufacturing techniques. Beyond this, many of the existing solutions use fluorine-based chemicals that present a risk to the environment due to the difficulty in breaking down these molecules. This thesis aims to understand the current state of repellent surfaces used for biological applications, including prevention of surface contamination by bacteria and viruses, then investigates the use of more environmentally friendly methods to produce repellent surfaces. Using a silicone-based coating combined with heat induced shrinking of shape memory polymers (SMPs), we have created a flexible surface with multiscale roughness that demonstrates repellency to bacteria and whole blood.