No / Wounds arising from various conditions are painful, embarrassing and often requires treatment plans which are costly. A crucial task, during the treatment of wounds is the measurement of the size, area and volume of the wounds. This enables to provide appropriate objective means of measuring changes in the size or shape of wounds, in order to evaluate the efficiency of the available therapies in an appropriate fashion. Conventional techniques for measuring physical properties of a wound require making some form of physical contact with it. We present a method to model a wide variety of geometries of wound shapes. The shape modelling is based on formulating mathematical boundary-value problems relating to solutions of Partial Differential Equations (PDEs). In order to model a given geometric shape of the wound a series of boundary functions which correspond to the main features of the wound are selected. These boundary functions are then utilised to solve an elliptic PDE whose solution results in the geometry of the wound shape. Thus, here we show how low order elliptic PDEs, such as the Biharmonic equation subject to suitable boundary conditions can be used to model complex wound geometry. We also utilise the solution of the chosen PDE to automatically compute various physical properties of the wound such as the surface area, volume and mass. To demonstrate the methodology a series of examples are discussed demonstrating the capability of the method to produce good representative shapes of wounds.

This thesis investigates the performance of a phased array of antenna elements conforming to a paraboloidal surface. We hypothesize that such a conformal phased array would have performance comparable to that of a correspondingly sized planar array. The performance of a paraboloidal array of antenna elements was simulated using an array program, and the resulting gains, side-lobe levels, and half-power beamwidths compared to those of a similarly sized planar array. Furthermore, we propose a beam-forming feed network for this paraboloidal phased array, and discuss the influence that coupling between the elements could have on the array performance. Lastly, we propose that such an array be used in conjunction with a parabolic reflector antenna to form a versatile hybrid antenna with several potential applications. / Master of Science

This thesis investigates the design and the performance of low-power microsensors that communicate directly to a satellite or a constellation of satellites. Information is spread using pseudo noise (PN) or Barker codes. The sensors use a single circular microstrip patch element with a wide beamwidth or a miniature phased array antenna that continuously scans to access the satellite(s). The array beam is controlled with a beam-forming network (BFN), which contains 3 or 4-bit phase shifters, which can be made in micro-electro-mechanical systems (MEMS) or in monolithic microwave integrated circuits (MMIC). The antennas are designed using array simulation program called 'ARRAY' and the results are used in another simulation program called Advanced Design System (ADS) to simulate the whole sensor package that uses one of the antennas. The simulation results show that a sensor as small as 2.35 cm in diameter is able to send information with data rate of 1 kbps at bit error rate less than 10?? to low-earth orbit (LEO) satellites with a transmitted power of 27.5 microwatts (-15.6 dBm). / Master of Science

Yes / A novel design strategy for microstrip harmonic-suppression antennas is presented. The computational method is based on an integral equation solver using adaptive surface meshing driven by a genetic algorithm. Two examples are illustrated, all involving design of coaxially-fed air-dielectric patch antennas implanted with shorting and folded walls. The characteristics of the antennas in terms of the impedance responses and far ¯eld radiation patterns are discussed theoretically and experimentally. The performances of all of the GA-optimised antennas were shown to be excellent and the presented examples show the capability of the proposed method in antenna design using GA. / MSCRC

We study Hessenberg varieties in type A via their local defining equations, called patch ideals. We focus on two main classes of Hessenberg varieties: those associated to a regular nilpotent operator and to those associated to a semisimple operator. In the setting of regular semisimple Hessenberg varieties, which are known to be smooth and irreducible, we determine that their patch ideals are triangular complete intersections, as defined by Da Silva and Harada. For semisimple Hessenberg varieties, we give a partial positive answer to a conjecture of Insko and Precup that a given family of set-theoretic local defining ideals are radical. A regular nilpotent Hessenberg Schubert cell is the intersection of a Schubert cell with a regular nilpotent Hessenberg variety. Following the work of the author with Da Silva, Harada, and Rajchgot, we construct an embedding of the regular nilpotent Hessenberg Schubert cells into the coordinate chart of the regular nilpotent Hessenberg variety corresponding to the longest-word permutation in Bruhat order. This allows us to use work of Da Silva and Harada to conclude that regular nilpotent Hessenberg Schubert cells are also local triangular complete intersections. / Thesis / Master of Science (MSc) / Algebraic varieties provide a generalization of curves in the plane, such as parabolas and ellipses. One such family of these varieties are called Hessenberg varieties, and they are known to have connections to other areas of pure and applied mathematics, including to numerical linear algebra, combinatorics, and geometric representation theory. In this thesis, we view Hessenberg varieties as a collection of subvarieties, called coordinate charts, and study the computational geometry of each coordinate chart. Although this is a local approach, we recover global geometric data on Hessenberg varieties. We also provide a partial positive answer to an open question in the area.

Brown patch, caused by <i>Rhizoctonia solani</i> Kuhn, is an important disease on tall fescue (TF, <i>Festuca arundinacea</i> Schreb, synonym <i>Schedonorus phoenix</i> (Scop.) Holub). <i>Rhizoctonia zeae</i> Voorhees, a related pathogen, causes similar symptoms. Confusion over which <i>Rhizoctonia</i> species is causing symptoms and subjective visual evaluations of disease severity may contribute to variability in observed BP resistance of TF cultivars at multiple locations. The objectives of this study were to develop an objective digital image analysis (DIA) method for evaluating disease and to use DIA to screen tall fescue plant introductions (PIs) for resistance to <i>R. solani</i> and <i>R. zeae</i>. There was a strong correlation (r² = 0.97) between actual disease severity, measured by applying lesioned tissue of a known area to healthy leaves, and DIA calculated disease severity using scanned images of individual leaves (DIA-IL). The accuracy and precision of visual evaluations and DIA evaluations of entire plants (DIA-WP) were evaluated using DIA-IL as a standard of accuracy. Accuracy of DIA-WP was not significantly different from visual evaluation accuracy. Precision was significantly higher for DIA-WP. Evaluation of PIs and putatively BP resistant TF cultivars for resistance to <i>R. solani</i> and <i>R. zeae</i> using DIA-WP identified clones within each PI that ranked high for resistance to <i>R. solani</i> or <i>R. zeae</i>. No clones were identified with high resistance to both <i>R. solani</i> and <i>R. zeae</i>. Improved precision of DIA evaluation methods and inclusion of <i>R. zeae</i> in BP resistance breeding may decrease variability of TF cultivar performance across locations. / Master of Science

Accurate knowledge of the electron density structure of the Earth's upper atmosphere is crucial to forecasting the performance of transionospheric radio signals. For this research, we focus on storm-time structuring in the mid- to high latitude ionosphere where large gradients in electron density can cause severe degradation of communication and navigation signals. We begin in Chapter 2 with a review of the primary data sets and methods used to accomplish the collaborative, multi-instrument studies described in this dissertation. In Chapter 3, we compare observational techniques for tracking polar cap patches during a moderate geomagnetic storm interval. For the first time, we monitor the transportation of patches with high spatial and temporal resolution across the polar cap for 1--2~h using a combination of GPS TEC, all-sky airglow imagers (ASIs), and Super Dual Auroral Radar Network (SuperDARN) HF radar backscatter. Simultaneous measurements from these data sets allow for continuous tracking of patch location, horizontal extent, and velocity even under adverse observational conditions for one or more of the techniques. A focus is placed on the structuring of patches, particularly on the nightside ionosphere as they become wider in the dawn-dusk direction and develop narrow finger-like structures. In Chapter 4, we perform a superposed epoch analysis to characterize the average response of GPS TEC in the North American sector during more than 100 geomagnetic storms over a 13-year interval. For the first time a rigorous approach is used to fully separate storm-time, local time, longitudinal, and seasonal effects at midlatitudes where dense ground receiver coverage is available. The rapid onset of a positive phase is observed across much of the dayside and evening ionosphere followed by a longer-lasting negative phase across all latitudes and local times. Our results show clear seasonal variations in the storm-time TEC, such that summer events tend to be dominated by the negative storm response while winter events exhibit a stronger initial positive phase with minimal negative storm effects. A prominent magnetic declination effect is identified and examined in terms of thermospheric zonal winds pushing plasma upward/downward along magnetic field lines of opposite declination. Finally in Chapter 5 we summarize several co-authored studies which examined various storm-time phenomena utilizing GPS TEC mapping tools developed for this dissertation research, with topics including subauroral polarization stream (SAPS), storm enhanced density (SED), tongue of ionization (TOI), and polar cap patches. / Ph. D.

Das streng regulierte Gleichgewicht zwischen CO2-Aufnahme und Transpiration ist für Pflanzen essentiell und hängt von kontrollierten Turgoränderungen ab, die durch die Aktivität verschiedener Anionen- und Kationenkanäle verursacht werden. Diese Kanäle sind Teil von Signalkaskaden, die z. B. durch Phytohormone wie ABA (Abscisinsäure) und JA (Jasmonat) ausgelöst werden, die beide bei Trockenstress in den Schließzellen wirken. Darüber hinaus ist bekannt, dass JA an der Reaktion der Pflanze auf Pathogenbefall oder Verwundung beteiligt ist. GORK (guard cell outward rectifying K+ channel) ist der einzige bekannte, auswärts gleichrichtende K+-Kanal in Schließzellen und somit für den K+-Efflux beim Schließen der Stomata verantwortlich. Im Rahmen dieser Arbeit konnte nachgewiesen werden, dass GORK ein wesentlicher Bestandteil des JA-induzierten Stomatschlusses ist. Dies gilt für beide Auslöser, sowohl die Blattverwundung als auch die direkte Anwendung von JA. Patch-Clamp-Experimente an Protoplasten von Schließzellen untermauerten dieses Ergebnis, indem sie GORK-K+-Auswärtsströme als direktes Ziel von JA-Signalen entlarvten. Da bekannt ist, dass zytosolische Ca2+-Signale sowohl bei ABA- als auch bei JA-Signalen eine Rolle spielen, wurde die Interaktion von GORK mit Ca2+-abhängigen Kinasen untersucht. Eine antagonistische Regulation von GORK durch CIPK5-CBL1/9-Komplexe und ABI2 konnte durch DEVC (double electrode voltage clamp) sowie Protein-Protein-Interaktions-Experimente identifiziert und durch in-vitro Kinase-Assays untermauert werden. Patch-Clamp-Aufzeichnungen an Protoplasten von Schließzellen der cipk5-2 Funktions-Verlust-Mutante zeigten die Bedeutung von CIPK5 für den JA-induzierten Stomaschluss via Aktivierung von GORK. Die Interaktion verschiedener CDPKs (Ca2+-abhängige Proteinkinasen) mit GORK wurde ebenfalls untersucht. Neben der Ca2+-Signalübertragung ist auch die Produktion von ROS (reaktive Sauerstoffspezies) für die ABA- und MeJA-Signalübertragung von Bedeutung. In DEVC-Experimenten konnte ein reversibler Effekt von ROS auf die GORK-Kanalaktivität nachgewiesen werden, was ein Teil der Erklärung für diese ROS-Effekte bei ABA- und MeJA-Signalen sein könnte. / Maintaining the balance between CO2 uptake and transpiration is important for plants and depends on tightly controlled turgor changes caused by the activity of various anion and cation channels. These channels are part of signaling cascades triggered, for example, by phytohormones such as ABA (abscisic acid) and JA (jasmonate), both of which act during drought stress in guard cells. In addition, JA is known to be involved in the plant's response to pathogen attack or wounding. GORK (guard cell outward rectifying K+ channel) is the only known outward rectifying K+ channel in guard cells and therefore responsible for K+ efflux during stomatal closure. In the course of this work it could be demonstrated by stomatal aperture assays, that GORK is an essential part of JA-induced stomatal closure. This is true for both triggers, leaf wounding as well as direct MeJA (methyl jasmonate) application. Patch clamp experiments on guard cell protoplasts backed this finding by revealing GORK K+ outward currents as a target of JA signaling in guard cells. As cytosolic Ca2+ signals are known to be involved in both ABA as well as JA signaling, the interaction of GORK with Ca2+-dependent kinases was examined consequently. An antagonistic regulation of GORK by CIPK5-CBL1/9 complexes and ABI2 was identified by DEVC (double electrode voltage clamp) and protein-protein interaction experiments and backed up by in vitro kinase assays. Patch-clamp recordings on guard cell protoplasts of cipk5-2 kinase loss-of-function mutant revealed the importance of CIPK5 for JA-triggered stomatal closure via activation of GORK. The interaction of different CDPKs (Ca2+-dependent protein kinases) with GORK was also investigated. Besides Ca2+ signaling also ROS (reactive oxygen species) production is essential in ABA and MeJA signaling. In DEVC experiments a reversible effect of ROS on GORK channel activity could be demonstrated, which could be one piece in the explanation of those ROS effects in ABA and MeJA signaling.

The vertical load on a moving tire was estimated by using accelerometers attached to the inner liner of a tire. The acceleration signal was processed to obtain the contact patch length created by the tire on the road surface. Then an appropriate equation relating the patch length to the vertical load is used to calculate the load. In order to obtain the needed data, tests were performed on a flat-track test machine at the Goodyear Innovation Center in Akron, Ohio; tests were also conducted on the road using a trailer setup at the Intelligent Transportation Laboratory in Danville, Virginia. During the tests, a number of different loads were applied; the tire-wheel setup was run at different speeds with the tire inflated to two different pressures. Tests were also conducted with a camber applied to the wheel. An algorithm was developed to estimate load using the collected data. It was then shown how the estimated load could be used in a control algorithm that applies a suitable control input to maintain the yaw stability of a moving vehicle. A two degree of freedom bicycle model was used for developing the control strategy. A linear quadratic regulator (LQR) was designed for the purpose of controlling the yaw rate and maintaining vehicle stability. / Master of Science

Microstrip antennas are low in profile, light in weight, conformable in structure and are now developed for many applications. The main difficulty of the microstrip antenna is its narrow bandwidth. Several modern applications like satellite communications, remote sensing and multi-function radar systems will find it useful if there is dual band antenna operating from a single aperture. Some applications require covering both transmitting and receiving frequency bands which are spaced apart. Providing multiple antennas to handle multiple frequencies and polarizations becomes especially difficult if the available space is limited as with airborne platforms and submarine periscopes. Dual band operation can be realized from a single feed using slot loaded or stacked microstrip antenna or two separately fed antennas sharing a common aperture. The former design, when used in arrays, has certain limitations like complicated beam forming or diplexing network and difficulty to realize good radiation patterns at both the bands. The second technique provides more flexibility with separate feed system as beams in each frequency band can be controlled independently. Another desirable feature of a dual band antenna is easy adjustability of upper and lower frequency bands. This thesis presents investigation of a new dual band antenna, which is a hybrid of microstrip and waveguide radiating elements. The low band radiator is a Shorted Annular Ring (SAR) microstrip antenna and the high band radiator is an aperture antenna. The hybrid antenna is realized by forming a waveguide radiator in the shorted region of the SAR microstrip antenna. It is shown that the upper to lower frequency ratio can be controlled by the proper choice of various dimensions and dielectric material. Operation in both linear and circular polarization is possible in either band. Moreover, both broadside and conical beams can be generated in either band from this antenna element. Finite Element Method based software, HFSS and Method of Moments based software, FEKO were employed to perform parametric studies of the proposed dual band antenna. The antenna was not tested physically. Therefore, in most cases, both HFSS and FEKO were employed to corroborate the simulation results. / Master of Science