Introduction: Wearable technologies play an important contemporary role in the measurement of physical activity (PA) and promotion of human health across the lifespan, including for young people (i.e., children, adolescents, and young adults). As new objective wearable technologies continue to develop, standardized approaches to documenting validation parameters (i.e., measures of accuracy, precision, and bias) are needed to ensure confidence and comparability in step-defined PA. Purpose: To produce validity parameters for step counting wearable technologies during treadmill walking in young people 6-20 years of age Methods: 120 participants completed 5-minute treadmill bouts from13.4 to 134.1 m·min-1. Participants wore eight technologies (two at the arm/wrist, four at the waist, one on the thigh, and one on the ankle) while steps were directly observed. Speed, wear location, and age -specific measures of accuracy (mean absolute percent error; MAPE), precision (correlation coefficient, standard deviation; SD, coefficient of variation; CoV), and bias (percent error; PE) were computed and cataloged. Results: Speed and wear location had a significant effect on accuracy and bias measures for wearable technologies (pConclusion: While the analyses indicate the significance of speed and wear location on wearable technology performance, the useful and comprehensive validity reference values cataloged herein will help optimize measurement of PA in youth. Future research should continue to rigorously validate new wearable technologies as they are developed, and also extend these standardized reference values developed in the laboratory to the free-living environment.

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.

With this research, we work towards the overall objective of customizing polymer molecules in terms of their molecular structure to optimize processing performance. The work includes analysis of the rheology in shear and shear-free flows for sparsely long-chain branched, LCB, polyethylene, PE, resins; determination of the consistency of the molecular based constitutive model, the pom-pom model; for these flows, and evaluation of the same PE resins in film-casting. As we progress towards molecular systems with defined molecular structural characteristics, we transition from a linear low density polyethylene, LLDPE, based series of PE resins to a high density polyethylene, HDPE, based series of PE resins, each with materials of varying degrees of sparse LCB. Evaluation of the shear step-strain rheology for the series of LLDPE-based PE resins allows for the assessment of any inadequacies associated with the step-strain experiments and the ability of the K-BKZ analog of the pom-pom constitutive model to predict step-strain rheological behavior. Finite rise time and wall slip are addressed to ensure the accuracy of the experimental step-strain measurements and eliminated as factors contributing to the stress relaxation moduli response. Analysis of the K-BKZ analog of the pom-pom constitutive model includes comparisons between experimental stress relaxation moduli and predictions from the model using pom-pom model parameters determined from extensional rheology. The results show inconsistencies in the model predictions, where the predictions fail to capture the short time behavior and accurately dampen at larger strains. Pom-pom model parameters are determined using the K-BKZ analog of the pom-pom constitutive model and fitting the stress relaxation moduli. These results are qualitatively consistent indicating that branching occurs on the longest backbone segments, but the values appear to be unrealistic with respect to the molecular theory. Analysis of film-width reduction or necking during film-casting for the series of LLDPE-based resins determines whether uniaxial extensional rheological characteristics, in particular strain-hardening, that are a result of LCB influence the film-necking properties. At the lowest drawdown ratio necking is observed to be reduced with increasing LCB, and thus strain-hardening characteristics. At the higher drawdown ratios it is observed that LCB no longer reduces necking and the curves merge to the results found for linear PE, except in the case of LDPE, which shows reduced necking at all drawdown ratios. Furthermore, comparisons of film necking are also made to separate the effects of molecular weight distribution, MWD, and LCB. The results indicate that both broadening the MWD and the addition of sparse LCB reduce the degree of necking observed. It is established that film necking is more significantly reduced by LCB than by broadening the MWD. Analysis of the uniaxial extensional and dynamic shear rheology with the pom-pom constitutive model reveals that a distribution of branches along shorter relaxation time modes is important in reducing necking at higher drawdown ratios. Factors such as shear viscosity effects, extrudate swell, and non-isothermal behavior were eliminated as contributing factors because of the similar shear viscosity curves, N1 curves, and activation energies among the sparsely LCB PE resins. The same experimental concepts have been extended to the series of HDPE-based resins, but the lack of adequate uniaxial extensional data prevents a thorough analysis with respect to uniaxial extensional characteristics. Regardless, in the context of step-strain rheology, the results were found to be similar with those of the LLDPE-based series of resins, where a distinctive shape at short times was observed for any of the PE resins possessing some level of LCB that was not apparent in the linear PE resins. Film-casting revealed similar results to those of the LLDPE-based materials as well, but a broader spectrum of drawdown ratios revealed greater insight into how the distribution of branching controls the film-casting response. At low drawdown ratios all materials exhibit the same necking behavior. At intermediate drawdown ratios separation occurs where the linear PE resins experiences the most drastic necking, the sparsely LCB PE resins show reduced necking, and the LDPE shows an even greater reduction in necking. Progression then to the higher drawdown ratios results in similar necking behavior for the linear and sparsely LCB PE resins and greatly reduced necking for the LDPE. These results support the idea that to reduce necking the backbone segments that dominate the film-casting behavior must contain some level of LCB. / Ph. D.

Eugene Clement created a design method for swept-back cambered step hulls with deadrise. The cambered step is designed to carry 90% of the planing vessels weight with the remaining 10% being support by a stern mounted hydrofoil. The method requires multiple design iterations in order to achieve an optimal design. Clement stated that the method was not suitable for cambered planing surfaces with high deadrise angles greater than 15 degrees. The goal of this thesis is to create a design procedure for swept-back cambered planing surfaces with high deadrise angles that does not require multiple iterations to obtain an optimal design. Computational fluid dynamics (CFD) program STAR CCM+ is used to generate a database for performance characteristics for a wide range of designs varying deadrise angle, load requirements, trim angle, and different camber values. The simulations are first validated with experimental data for two different cambered steps designed by Stefano Brizzolara and tested in the tow tank at the United States Naval Academy. A series of validation studies utilizing fixed and overset meshes led to a final simulation set up with an overset mesh that allowed for accurate prediction of drag, trim moment, wetted keel length, and the wake profile aft of the cambered planing surface. The database is fitted such that the final equations for optimal design values such as camber, trim angle, drag (shear and pressure), wetted keel length, wetted surface area, and trim moment are in terms of deadrise angle and lift. The optimized design equations are validated with CFD simulation. / Master of Science / Eugene Clement developed a new design method to improve the performance of ultra-fast planing crafts. A planing craft uses the force generated from the flow of water over the bottom to lift the vessel without the use of the static buoyancy force that classic boat designs rely on. Clement wanted to improve the performance of the planing vessel by reducing the total drag force caused by the flow of water on the bottom of the vessel. Clement's design method involves reducing the wetted surface area which reduces drag. Reducing the wetted surface area would normally cause the lifting force on the vessel to reduce, but with the addition of curvature in the smaller wetted surface area, the lifting force would remain the same. Clement's new design method requires multiple iterations to obtain an optimal design. The method limits the angle of the vessels bottom relative to horizontal to under 15 degree. The goal of this thesis is to create a new design method for planing vessels with bottoms that have an incline of 15 degrees or more relative to horizontal. The design method is created using Computational Fluid Dynamics (CFD) solver to model the planing surface moving through water. The CFD solver is validated with experimental test performed at the United States Naval Academy. The improved design method uses equations that can predict the forces and other design characteristics based on the desired vessel weight and seakeeping requirements.

Research has shown that older adults who have experienced a previous fall are 60-70% more likely to suffer future falls. A study was conducted to investigate if stress and anxiety associated with a fear of falling contributes to the increased incidents of falls among older adults. The investigation compared physiological parameters, with biomechanical parameters of walking for twenty-eight participants in two age groups: (18-35) and (65 or older). Both age groups were evaluated while walking over dry and slippery floor surfaces. Biomechanical parameters included: step length, required coefficient of friction (RCOF), slip distance, and heel contact velocity. Physiological parameters included: stress and anxiety. Overall, the results indicated that there were differences between older and younger adult's biomechanical parameters of walking, and their physiological stress and anxiety associated with an inadvertent slip. Younger adult's normal RCOF was higher and their normal step length was longer compared to older adults. Older adult's stress level after a slip was significantly higher than younger adults. However, younger and older adult's anxiety scores were not significantly different. Furthermore, younger and older adults modified their step length differently to avoid slipping, when walking over the slippery floor surface. It was concluded that some anxiety and stress may be beneficial in reducing the occurrence of inadvertent slips and falls due to an increased awareness of one's external environment. / Master of Science

This dissertation describes a new platform for the synthesis of thermally reversible polymers, based on Diels-Alder reactions of bis-cyclopentadienes (bis-CPDs) and bis-maleimides (bis-MIs), that meets two main objectives. First, the bis-CPD must resist characteristic self-coupling. Second, the CPD-MI adducts should undergo the retro-Diels-Alder (rDA) reaction (i.e., thermal depolymerization) in a temperature regime that is comparable or slightly higher than that of the freely reversible bis-furan/bis-MI polymers (rDA between 80 °C and 130 °C) but much lower than that of bis-CPD homopolymers (rDA above 160 °C). Structure-reactivity relationships gleaned from the literature and from related but as yet unpublished work in our own laboratories led to our main hypothesis that a CPD moiety bearing one sterically encumbering substituent such as isopropyl (𝑖Pr) or tert-butyl (𝑡Bu) and one electronwithdrawing substituent such as perfluoroaryl would have the desired reactivity and adduct stability in combination with an 𝑁-substituted maleimide. Synthetic considerations led to a bisCPD monomer design in which two alkylcyclopentadiene groups (alkyl = 𝑖Pr or 𝑡Bu) are connected by an octafluorobiphenylene linker. As an initial fundamental step (Chapter 3), 1-(nonafluorobiphenyl-4’-yl)-4-tertbutylcyclopentadiene (1) was synthesized to provide a monofunctional model for the proposed difunctional CPD monomer. Reactions of 1 and 𝑁-(4-fluorophenyl)maleimide (FMI) afforded up to five regio- and stereo-isomeric adducts (of fourteen possible). Variable-temperature reactivity studies combined with NMR spectroscopic analysis, X-ray crystallography, and computational modeling enabled product distributions to be understood according to a conventional kinetic-vs- iii thermodynamic framework. These studies also predicted the microstructure of polymers derived from the proposed bis-CPD monomer, which is structurally analogous to 1, and bis-MIs. Moreover, 1 does not undergo DA self-coupling under ordinary conditions (T < 180 °C). Thermolysis studies of the major adducts revealed that the rDA becomes observable on a laboratory timescale (hours) at about 140 °C, which is at the upper end of the temperature range reported for furan+MI adducts but well below that of CPD+CPD adducts. In contrast, adducts formed from either of the analogous monosubstituted cyclopentadienes (𝑡BuC₅H₅ and C₆F₅C₅H₅) do not undergo rDA below 180 °C. These results strongly support the proposed bis-CPD monomer design. In a second fundamental step (Chapter 4), the hypothesis that an electron-withdrawing CPD substituent would destabilize a CPD-MI adduct was further tested by reacting 𝑁-(4- fluorophenyl)maleimide with a series of triarylated cyclopentadienes (1,2,3-Ar₃C₅H₃ and 1,2,4- Ar₃C₅H₃, Ar = C₆F₅, C₆F₄CF₃, and Ar = C₅F₄N). The perfluorophenyl- and perfluorotolylsubstituted compounds were previously reported, but the perfluoropyridyl-substituted cyclopentadienes were prepared for this study using SNAr reactions of pentafluoropyridine and sodium cyclopentadienide. The least electron deficient cyclopentadiene in each series (Ar = C₆F₅) reacted the most quickly and with the highest ultimate equilibrium binding constant, confirming the electron-effects hypothesis as well as the underlying presumption that DA reactions of even relatively electron-poor CPDs with MI would behave according to normal-electron-demand principles. In the main section of this dissertation (Chapter 5) the proposed bis(cyclopentadiene)s reacted with a series of previously reported bis(maleimides) to form linear polymers having molecular weights (Mn) up to 40 kDa. Relationships among the length and flexibility of the bis-MI linker (C₆H₁₂, C₁₂H₂₄, C₆H₄OC₆H₄, and (C₂H₄O)₂), the identity of the CPD alkyl substitutent (CHMe₂, CMe₃ and CMe₂Ph) and the glass transition temperature (Tg) as measured by differential scanning calorimetry (DSC) were understood in terms of a general model of local segmental mobility and free volume. Solution thermolysis of a model polymer system (bis-MI linker = C₆H₁₂ (7), CPD alkyl substituent = 𝑡Bu) showed a rapid decrease in molecular weight at 160 °C as determined by size exclusion chromatography (SEC). Solution thermolysis in the presence of excess FMI (as a trap for free CPD moieties) revealed that the onset temperature for rDA on a laboratory time scale (hours) was as low as 120 °C. In the bulk, thermolysis above 250 °C under vacuum led to recovery of a small portion of the bis-CPD monomer, but bulk thermolysis at 200 °C did not reveal a change in molecular weight as determined by SEC. The current interpretation of these observations is that limited mobility in these glassy polymers prohibits retro-DA decoupling. These findings largely validate the main hypothesis of this dissertation. / Ph. D.

Step-growth polymerization facilitates the synthesis of a wide range of industrially applicable polymers, such as polyesters and polysulfones. The choice of backbone and end group structure within these polymers drastically impacts the final material properties and processability emphasizing the necessity for thorough understanding of structure-property relationships. Seemingly simple changes, such as exchanging a monomer for its regioisomer, affects the polymers fundamental packing structure triggering a domino effect ultimately influencing the morphological, thermal, mechanical and barrier properties. In conjunction, end groups provide a means by which tunable mechanical properties and application into unique processing methods can be achieved. Synthesizing polyesters with bibenzoate based monomers generates a large range of morphologies. Linear, 4,4' bibenzoate (4,4'BB), is widely considered a mesogenic monomer due to its ability to impart a liquid crystalline (LC) morphology on semi-aromatic polyesters with linear aliphatic spacers. In this body of work, semi-aromatic polyesters using one of 4,4'BB's regioisomers, either 3,4'BB or 3,3'BB, largely resulted in amorphous or semi-crystalline polymers depending on the selection of aliphatic diol. Incorporation of the meta isomer (3,4'BB) into traditionally LC polymers, such as poly(diethylene glycol 4,4'-bibenzoate) and poly(butylene 4,4'-bibenzoate), through copolymerization afforded two polymer series with tunable LC properties. The 3,4'BB exhibited selective disruption of crystalline domains over the LC phase generating a number of polymers with LC glass morphologies. The application of 3,4'BB to a fully-aromatic polyester enabled the synthesis of a novel melt-processable homopolyester with high thermal stability, poly(p-phenylene 3,4' bibenzoate). This structure afforded a nematic LC morphology which revealed beneficial shear-thinning properties similar to industrial standards. The unique LC morphology of this homopolyester inspired further characterization of the range of achievable properties using the basic structure, poly(phenylene bibenzoate), with all the possible regioisomers. This study afforded six polymers systematically varied in chain linearity from a completely meta to a completely para backbone configuration. A range of morphologies were achieved from high Tg amorphous polymers for the meta configurations to semi-crystalline or LC in the polymers with greater linearity. End group functionalization generates influence on polymer properties while limiting the impact on beneficial properties achieved through the backbone structure and packing. Post-polymerization reactions or the addition of a monofunctional endcapper to the polymerization both achieve end group control. In this dissertation, the addition of a monofunctional diester with a sulfonate moiety to a semi-aromatic LC polyester synthesis resulted in a telechelic ionomer. The non-covalent interaction of the ionic groups will hopefully improve the compression and transverse mechanical properties of the LCP. In contrast, post-polymerization functionalization incorporated acrylate groups onto the ends of a basic polysulfones. These reactive groups provided a handle for photo-curing which enabled the 3D printing of the polysulfones using vat photopolymerization. / Doctor of Philosophy / The research within this dissertation encompasses the design of new plastics for consumer and high-performance applications. Since the emergence of synthetic plastics in the 1920’s, these materials have become a necessity in our everyday life with a range of applications in food packaging, microelectronics, architecture, medical devices, automotive, and aerospace. Benefits over metals and glass primarily result from their light weight and wide range of mechanical properties which allow a range of material properties from soft and flexible plastic grocery bags to tough car parts. Different classes of plastics (polymers) are based primarily on the chemicals used to produce the materials, for example polyesters and polysulfones. The chemical structure of these core materials drastically impacts the final properties of the polymers, which in turn influences their application space. This work focused on how subtle changes to these starting chemical structures allows us to tune the final polymer properties. Within the class of polyesters, a focus was placed on materials known as liquid crystalline (LC) polyesters. A liquid crystalline polymer can achieve a physical state between a solid and a liquid which imparts many beneficial properties on the material processing. Liquid-crystal television displays utilized these properties to provide drastically thinner TV’s with higher resolution. Alternatively, LC polyesters find applications traditionally as high-performance fibers, insulators in microelectronics, and stainless-steel replacements in medical applications. Studying the role of chemical structure on the properties of LC polyester enabled the design of materials which improve upon the current technological standards. These changes enabled the design of LC polyesters with lower processing temperatures and the use of fewer starting materials which will inevitably save energy and money during their production. In the case of polysulfones, changing the chemical structure at the end of the polymer chain facilitated the application of novel processing methods, such as 3D printing. The ability to process using this method reduces the amount of material waste during production and provides an opportunity to design novel parts with intricate structures, inaccessible through traditional means.

The software environment for power electronics design is comprised of tools that address many interrelated disciplines including circuits design, physical layout, thermal management, structural mechanics, and electromagnetics. This usually results in a number of separate models that provide various views of a design, each of which is usually stored separately in proprietary formats. The problem is that the relationships between views (e.g., the circuit design that defines the functional connectivity between components, and the physical layout that provides physical paths to implement connections), are not explicitly captured. This makes it difficult to synchronize and maintain data consistency across all models as changes are made to the respective views. This thesis addresses this problem by describing power electronics modules using STEP AP210, the STandard for the Exchange of Product data, Application Protocol 210; which has been designated as ISO 10303-210. A multidisciplinary model was implemented for an integrated power electronics module (IPEM). It consists of two views of the IPEM: a functional network definition of the IPEM, and a physical implementation that satisfies the functional connectivity requirements. The relationships between these two views are explicitly recorded in the model. These relationships allow for the development of a method which verifies whether the connectivity data in both views are consistent. Finally, this thesis provides guidance for deploying STEP AP210 to unify multidisciplinary data resources during the design of integrated power electronics. / Master of Science

Objective Establish normative values for knee valgus angle during drop jump and step landings. Design Observational. Setting University biomechanics laboratory. Participants 100 physically active asymptomatic individuals (50 male, 50 female) aged 18–28 years old. Main outcome measures Knee valgus angle during drop jump and step landings. Results There were no differences between genders during the step landing task (p < 0.12) but there were differences during the drop jump landing task (p < 0.048). Both males and females showed no significant differences between sides for either of the tasks (p > 0.05) or between the valgus angle generated for either of the tasks (p > 0.05). Conclusion It would appear in order to be regarded as an average “normal” performance during a drop jump landing task knee valgus angle should be symmetrical and in the range of 7–13° for females and 3–8° for males. For a unilateral step landing task knee valgus angle should be symmetrical and in the range of 5–12° for females and 1–9° for males.

We present two approaches towards a characterization of the complete Pick property. We first discuss the lurking isometry method used in a paper by J.A. Ball, T.T. Trent, and V. Vinnikov. They show that a nondegenerate, positive kernel has the complete Pick property if $1/k$ has one positive square. We also look at the one-point extension approach developed by P. Quiggin which leads to a sufficient and necessary condition for a positive kernel to have the complete Pick property. We conclude by connecting the two characterizations of the complete Pick property. / Master of Science