<p> This thesis presents an optimal design method for MRI (Magnetic Resonance Imaging) teardrop gradient waveforms in two and three dimensions. Teardrop in two dimensions was introduced at ISMRM 2001 by Anand et al. to address the need for a high efficiency balanced k-space trajectory for real-time cardiac SSFP (Steady State Free Precession) imaging.</p> <p> We have modeled 2D and 3D teardrop gradient waveform design as nonlinear convex optimization problems with a variety of constraints including global constraints (e.g., moment nulling for motion insensitivity). Commercial optimization solvers can solve the models efficiently. The implementation of AMPL models and numerical testing results with the solver MOSEK are provided. This optimal design procedure produces physically realizable teardrop waveforms which enable real-time cardiac imaging with equipment otherwise incapable of doing it, and optimally achieves the maximum resolution and motion artifact reduction goals. The research may encompass other waveform design problems in MRI and has built a good foundation for further research in this area.</p> / Thesis / Master of Science (MSc)

Yes / In this communication, nine years of local radiosonde meteorological data, from 1997 to 2005, have been used to calculate the vertical refractivity gradient, ΔN, in the lowest atmospheric layer above the ground surface. The values obtained are used to estimate the parameter β0, which represents the probability of non-standard propagation. Hourly, monthly and yearly distributions of ΔN in the first 100 meters above the ground are given. Monthly and yearly variations of the mean of ΔN and β0 are provided and the β0 values are compared with the ITU maps.

Over the past fifty years, many states have recognized the benefits of making precast, prestressed multi-girder bridges continuous by connecting the girders with a continuity diaphragm. Although there is widespread agreement on the benefits of continuous construction, there has not been as much agreement on either the methods used for design of these systems or the details used for the continuity connections. To aid designers in choosing the most appropriate method, an analytical and experimental study was undertaken at Virginia Tech. Analyses were done to compare the differences in the predicted continuity moments for different design methods and assumptions over a range of commonly used systems of Precast Concrete Bulb Tee (PCBT) girders and cast-in-place slabs. The results of the analyses were used to develop three continuity connection details for testing during the experimental study. Three different continuity connections were tested using full depth PCBT 45 in. deep girders made continuous with a 6 ft wide slab. The bottom of the ends of the girders were made continuous with the continuity connection by extending prestressing strands for one test and extending 180 degree bent bars for the other test. Both connections adequately resisted service, cyclic, and ultimate loads. But, the test with the extended bars remained stiffer during cyclic loading and is recommended for use. A third test was performed on a system using only a slab cast across the top of the girders. Two primary cracks formed above the ends of the girders at the joint during service testing, after which no significant increase in damage took place. Results from the analytical study indicate that the predicted positive thermal restraint moments may be significant, similar in magnitude to the actual positive cracking moment capacities. Results from the experimental study indicate that restraint moments develop early due to thermal expansion of the deck during curing and subsequent differential shrinkage; however, the magnitudes of the early age restraint moments are much less than conventional analyses predict. / Ph. D.

An in depth study of the performance of thermally interdiffused concentration gradient polymer photovoltaic devices is carried out with particular attention to the effect of the thickness and the thermal treatments on the power conversion efficiency, short circuit current, open circuit voltage and other key electrical properties. Bilayer films of sequentially spin-cast donor and acceptor materials are exposed to various heat treatments in order to induce the interdiffusion. The depth profiles show concentration gradients in the donor and acceptor as a result of interdiffusion and these devices show an order of magnitude increase in the device performance compared to the bilayer devices. Dual spin-cast poly (3-octylthiophene-2,5-diyl) (P3OT)- [6,6] phenyl C61 butyric acid methyl ester (PCBM) and poly (3-hexylthiophene-2,5-diyl) (P3HT)-PCBM interdiffused devices are studied in detail by varying the thickness of the donor and acceptor layers as well as the annealing conditions for initial polymer layer and the time and temperature of the interdiffusion process. Auger spectroscopy and X-ray photoelectron spectroscopy along with ion beam milling are used to investigate the concentration gradient formed as a result of the interdiffusion. The sulfur signal present in the P3OT and P3HT backbone is detected to identify the concentration profiles in the P3OT-PCBM and P3HT-PCBM devices. The interdiffusion conditions and thickness of the active layers have been optimized to obtain the highest power conversion efficiency. The best device performance of the P3OT-PCBM interdiffused devices is achieved when the interdiffusion is carried out at 150°C for 20 minutes and the P3OT thickness is maintained at 70 nm and the PCBM thickness at 40-50 nm. The highest efficiency achieved for P3OT-PCBM interdiffused devices is 1.0% under AM1.5G solar simulated spectrum. In order to further increase the efficiency, P3OT is replaced by (P3HT) which has higher hole mobility. P3HT- PCBM based concentration gradient devices show improved device performance over P3OT-PCBM devices. Power conversion efficiency of the order of ~3.0% is obtained for P3HT-PCBM interdiffused devices when the interdiffusion is carried out at 150°C for 20 minutes. For both P3OT:PCBM and P3HT:PCBM devices, the optimum performance occurs when the concentration gradient extends across the entire film and is correlated with an increase in the short circuit current density and fill factor as well as a decrease in the series resistance. The results demonstrate that an interdiffused bilayer fabrication approach is a novel and efficient approach for fabrication of polymer solar cell devices. In addition, porphyrin derivative 5, 10, 15, 20-Tetraphenyl-21H, 23H-porphine zinc (ZnTPP) is studied as a new donor material for organic solar cells. ZnTPP: PCBM blend devices are investigated in detail by varying the weight ratio of the donor and acceptor materials in blend devices. The devices with ZnTPP: PCBM in 1:9 ratios showed the best device performance and the efficiency of the order of 0.2% is achieved under AM1.5G solar simulated conditions. Trimetallic Nitride Tempelated (TNT) endohedral fullerenes are also examined in this thesis as the novel acceptor materials. Bulk heterojunction or blend devices are fabricated with P3HT as the donor material and several TNT endohedral fullerenes as the acceptor material. Y3N@C₈₀PCBH based devices which are annealed both before and after the electrode deposition show improvement in the device performance compared to devices that are only annealed before the electrode deposition. The highest power conversion efficiency achieved for TNT endohedral fullerene devices is only 0.06%, suggesting that substantial additional work must be done to optimize the compatibility of the donor and acceptor as well as the device fabrication parameters. / Ph. D.

It is well known that for small Reynolds numbers, flow around a cylinder is laminar and stable. For larger Reynolds numbers, although the flow regime remains laminar, the formation of complex periodic structures appear downstream. The cyclic nature of this periodic flow is well characterized by the vortex shedding frequency and Strouhal number. However, complexities of these periodic structures downstream continue to be a topic of research. Periodic laminar 2D incompressible viscous flow around a cylinder is simulated using OpenFoam, an open source computational fluid dynamics program. To better understand these complex structures downstream, a customized computer graphical tool, VerFlow-V.01, was created to analyze and study OpenFoam simulation results. This study includes an investigation of calculating the details of drag and lift coefficients for the cylinder using mathematical models that integrate properties in subdomains, an approach not previously explored to the knowledge of the author. Numerical integration is accomplished using a finite difference approach for solving surface and contour integrals in subdomains of interest. Special attention is given to pressure and to the second invariant of the velocity gradient, as they have a clear mathematical relationship, which is consistent with results previously published. A customized visual data analysis tool, called VerFlow-V.01, allowed investigators to compare simulation data variables in a variety of useful ways, revealing details not previously understood. Main subroutines and a user's manual are included as appendices to encourage reproducibility and future development of the numerical, analytical and graphical models developed here. Together these models resulted in a new understanding of periodic laminar flow around a cylinder. A unique approach was developed to qualitatively understand the origins of drag and lift coefficients associated with properties mapped as images in subdomains of interest downstream. These results explain the development of convergent, eddy, and stream zones embedded in flow fields downstream. / Master of Science

The key to improving drying quality and reducing drying time and energy consumption lies in understanding and controlling moisture movement during drying. As wood dries, strains and stresses develop as a result of restraints imposed by moisture gradients and differential shrinkage in wood. So accurately measuring the moisture gradient in wood during drying will be helpful to improving drying quality. In this project, moisture gradients in red oak will be measured through four different techniques----<i><b>bandsaw slicing, Forstner bit layering, flaking and razor blade slicing</i></b>. The first two techniques are found in the literature. The last two are developed in this study. The results obtained with these four techniques were compared, and it was found that the newly developed techniques could get moisture gradients that were closer to the true value. The <i><b>thickness</i></b> of the slice was assumed to affect measuring the moisture gradient because of the environmental influences. So a thickness series was tested with the two new technique----flaking and razor blade slicing. The results showed that there was no slice or flake thickness effect on the moisture gradients.And an optimum slice and flake thickness was determined for the wood industries and research studies. Finally, the <i><b>directional</i></b> effect on transverse moisture movement during kiln drying was examined through measuring moisture gradients in the tangential and radial directions of wood. The results showed that moisture moved slightly faster in the radial direction than in the tangential direction during kiln drying and the moisture gradients in the tangential direction were slightly steeper than those in the radial direction. / Master of Science

Interleukin-1 (IL-1) is a multifunctional cytokine produced primarily by activated monocytes/macrophages and by a variety of other cell types. IL-1 plays an integral role in the immuno-inflammatory response of the body to a variety of stimuli including infection, trauma and other bodily injuries. Once IL-1 is released from the synthesizing cell, it acts as a hormone, initializing a variety of responses in different cells and tissues. These responses are believed to be crucial to survival and are termed acute-phase responses. NF-κB is a family of dimeric transcription factors that control the expression of hundreds of genes which regulate cellular stress responses, cell division, apoptosis, and inflammation. NF-κB dwells in the cytoplasm of the cell until activation in response to a wide range of extracellular stimuli including signaling molecules such as cytokines. NF-κB regulates transcription and gene expression through nucleocytoplasmic transport. Most previous studies on NF-κB activation have been performed using bulk assays to look at populations of cells. Determining cell variance at a single-cell level is crucial in understanding the full mechanisms of drug response. The goal of this study is to analyze the effects of variant concentrations of IL-1β on the activation of NF-κB in individual cells through use of a microfluidic gradient generator. The gradient generator was adopted from Jeon et al and used principles of diffusive mixing and splitting of flows in order create a solute concentration gradient. A soft lithography procedure was used. Briefly, the design was printed on a transparency using a high resolution printer. A master of the design is then created using an SU-8 photoresist and UV light to imprint the design on a silicon wafer. The master is then used to create a Polydimethylsiloxane (PDMS) mold of the design which can be irreversibly attached to a glass slide through oxidation in order to close off the microfluidic channels. FITC-conjugated β-Casein (a protein with similar molecular weight to IL-1β) was used in order to verify the gradient generated by the design. The concentration gradient was analyzed by measuring fluorescent intensity of images taken under a UV light microscope and found to agree with microfluidic simulations run on COMSOL. A procedure for culturing cells in a microfluidic device was then adapted from Jeon that is explained in detail in Chapter 3. Two main trends were revealed; firstly, as IL-1β concentration decreased, the percent of cells activated also decreased. Secondly, as IL-1β concentration decreased, the activation time of the responding cells increased. Cells were observed to act in a single-cell manner; in which multiple cells subjected to the same concentration would not all respond in the same fashion. No major activation threshold was observed but two minor thresholds were; the first at 0.02 ng/mL IL-1β where activation levels drop from 20% to around 5%. The second around 1 ng/mL, in which all greater concentrations show nearly complete activation of all cells exposed. Of the cells that activated, the activation times were recorded and analyzed as well. In general, a decrease in IL-1β concentration caused cells to take longer to activate. Concentrations greater than 5 ng/mL responded on average in 30 minutes with a significant amount of variation. Between 5 ng/mL and 0.1 ng/mL, activation time increased as IL-1β concentration decreased in a linear fashion when concentration was plotted on a base-10 log scale. Below 0.1 ng/mL, the trend disappears and an average activation time of around 95 minutes is observed that no longer depended on concentration. This is interesting because fewer and fewer cells are activating in this concentration range but activation time follows no trend and remains partially stochastic with times ranging from 80 to 105 minutes. The previous results were all observed with a continuous flow and stimulation of the cells. Experiments were also run by only exposing the cells to the IL-1β for 10 minutes and then replacing the flow with a buffer. These studies yielded interesting results; the fraction of activated cells reported the same trends and values as those that were continuously stimulated. The activation times, however, were delayed between 10 and 20 minutes but otherwise followed the same trend as the continuous stimulation. These results suggest that a brief exposure to an external stimulant is all it takes for the cascade of intercellular events to take place and cause NF-κB translocation. / Master of Science

Cette étude traite de la prise en compte du gradient de contrainte et du frottement pour calculer l’amorçage de fissures en fatigue. On s’intéresse notamment au dimensionnement d’une manille en Inconel 718 munie de bagues en Inconel 718montées avec interférence. Pour cela, on réalise des essais de fretting et de fatigue pour étudier les conditions d’amorçage de fissures en présence de gradient de contrainte et de frottement. Les résultats expérimentaux mettent en évidence l’effet du gradient des contraintes sur l’amorçage de fissures et justifient la prise en compte du gradient pour le dimensionnement en fatigue des structures. A travers ces essais balayant une gamme de gradient de contrainte étendue, on confirme que la présence d’un gradient de contrainte retarde l’amorçage de fissures. Les avantages et les inconvénients de plusieurs approches de fatigue multiaxiale intégrant le gradient de contrainte sont étudiés. De cette analyse, une proposition est faite permettant de décrire au mieux les résultats expérimentaux de fatigue et de fretting. Cette approche s’appuie sur l’utilisation d’une fonction de poids dépendant du gradient de la pression hydrostatique. Cette approche est similaire à des approches mises en oeuvre sur d’autres problématiques de fatigue ce qui permet de dégager quelques points de convergence pour traiter le problème du gradient de contrainte en fatigue. Un essai de fatigue sur une manille munie d’une bague montée avec interférence est réalisé. L’effet du gradient de contrainte sur l’amorçage de fissures dans ce système est trop faible pour que l’utilisation d’une approche intégrant l’effet de gradient soit pertinente. Cette observation est cohérente avec les résultats expérimentaux précédents obtenus dans cette étude. L’inconel 718 apparaît donc comme un matériau peu sensible à l’effet de gradient de contrainte. Une approche de fatigue multiaxiale de type Crossland permet une description raisonnable de la durée de vie du système. Une analyse numérique montre que la tenue en fatigue du système est peu sensible au coefficient de frottement alors que l’interférence a un impact beaucoup plus important. / This study focuses on the stress gradient effect and the friction to estimate the crack initiation condition in fatigue. The industrial application is a lug in Inconel 718 with shrink fitted rings also in Inconel 718.Fretting tests and fatigue tests are performed to measure crack initiation conditions with friction and stress gradient. The experimental results confirm the beneficial effect of the stress gradients on the fatigue crack initiation. These results justify the consideration of stress gradients to design structures against fatigue. Through these experiments which sweep over a large range of stress gradients, it is confirmed that stress gradient delays the crack initiation. The benefits and the drawbacks of several multiaxial fatigue approaches dealing with stress gradients are studied. Then, a proposal is done to describe accurately the experimental results of fatigue and of fretting. The proposal is based on a weight function and on the use of the gradient of hydrostatic pressure. This approach is very similar to some approaches already applied to other fatigue issues. This enables to highlight some similarities to deal with the effect of stress gradient in fatigue. Fatigue tests are finally performed on a lug with shrink fitted rings. The stress gradient effect on this application is too low to make relevant the use of a fatigue approach dealing with stress gradient. These experimental results are consistent with the previous results of fatigue and fretting. Therefore, the Inconel 718 appears as a low sensitive material to stress gradient. A multiaxial fatigue approach such the Crossland criterion enables to describe correctly the fatigue strength of this system. The numerical analysis shows that the fatigue strength of the system is not very sensitive to the coefficient of friction whereas the interference impacts significantly on the fatigue strength of the system.

Title: Gradient mapping of functions of several variables Author: Alena Skálová Department: Department of Mathematical Analysis Supervisor: doc. RNDr. Miroslav Zelený, Ph.D., Department of Mathematical Analysis Abstract: In the thesis we prove that the following statement holds true. For each d ≥ 2, for each open bounded set U ⊂ Rd and for each set F ⊂ Rd of the Borel class Fσ there exists an everywhere differentiable function u: Rd → R such that ∇u(x) ∈ U for all x ∈ Rd , ∇u(x) ∈ U for all x ∈ F, ∇u(x) ∈ ∂U for λd-almost all x ∈ Rd \ F.

Práce se zabývá vlivem disipativních proces· v mezních vrstvách, konkrétně vlivem viskozity tekutiny a dále vlivem difúze vodní páry ve vzduchu na vznik sil p·sobících na obtékaná tělesa. Z Croccovy věty plyne, že gradient entropie má sv·j podíl na vzniku cirkulace a d·sledkem toho i na vznik vztlakové síly. Práce zkoumá vznik vztlakové síly při obtékání rotujícího válce, v soft- waru FEniCS modeluje tuto situaci, porovnává s modelem nevazké nestlačitelné tekutiny a následně i s experimentem provedeným Ing. Zdeňkem Trávníčkem a Ing. Zuzanou Broučkovou. Taktéž zkoumá vznik vztlakové síly při vypařování na horní straně válce a srovnává s případem rotujícího válce. 1