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The discovery of metamaterials has led to major advances in different fields of physics including optics, microwave engineering and acoustics. Specific to theoretical electromagnetism, the introduction of metamaterials have led to the development of negative-index materials (NIMs) with simultaneous negative permittivity and negative permeability with backward-wave propagation. In recent studies, exact analytical solutions for wave propagation from a step/graded-index interface between a right-handed material (RHM) and a left-handed material (LHM) have been obtained. This study attempts to provide numerical validation of the analytical solutions obtained by Dalarsson et al. by using the simulation tool CST. An square-SRR/strip-wire unit element was designed, with real part of relative permittivity equal to -1.96 and real part of relative permeability equal to -1.01. Such unit elements were orderly structured to produce a NIM structure. Furthermore, a positive-index material (PIM) structure was produced by reversing the sign of the material properties of the NIM. Both the results for the step- and graded-index interfaces have shown to possess backward-wave propagation for a normal incidence angle. The graded-index interface profiles have a more smooth and continuous wave propagation between the materials, which counteracts the effects of discontinuous material transitions present in step-index interface profiles. However, because the results of the present study were considerably affected by unwanted field effects, the analytical solutions are only qualitatively validated, and not validated in terms of their numerical accuracy. / Upptäckten av metamaterial har lett till stora framsteg inom olika fysikområden inklusive optik, mikrovågsteknik och akustik. Specifikt för teoretisk elektromagnetism, har introduktionen av metamaterial lett till utvecklingen av negativa indexmaterial (NIM) med samtidig negativ permittivitet och negativ permeabilitet med bakåtvågsutbredning. I nyligen genomförda studier, har exakta analytiska lösningar för vågutbredning över ett steg-/graderat- indexgränssnitt mellan ett högerhänt material (RHM) och ett vänsterhänt material (LHM) erhållits. Denna studie försöker tillhanda-hålla numerisk validering, med hjälp av simuleringsverktyget CST, av de analytiska lösningar som erhållits av Dalarsson et al. En square-SRR/strip-wire enhetselement designades, med realdelen av relativ permittivitet lika med -1,96 och realdelen av relativ permeabilitet lika med -1,01. Sådana enhetselement strukturerades för att producera en materialstruktur med negativt index. Dessutom producerades en materialstruktur med positivt index (PIM) genom att vända tecknet av materialegenskaperna hos det negativa indexmaterialet (NIM). Både resultaten för steggränssnittet och det graderade indexgränssnittet har visat sig ha bakåtvågutbredning för vinkelrätt infall. De graderade indexgränssnittsprofilerna har en mer jämn och kontinuerlig vågutbredning mellan materialen, vilket motverkar effekterna av diskontinuerliga materialövergångar som finns i stegindexgränssnittsprofiler. Men eftersom resultaten av den aktuella studien påverkades avsevärt av oönskade fälteffekter, har de analytiska lösningarna validerats endast kvalitativt och valideras inte i termer av deras numeriska noggrannhet.

In the upland hardwood forests of the southern Appalachians, management tools are needed based on the characteristics of the site to quantify the site quality where no accurate maps of site quality exist. Three studies were conducted to achieve this objective. The first study tested if independent measures of forest productivity, based on vegetation and environment, in a six-county study area in the Blue Ridge Mountains in North Carolina would correlate with measures of forest productivity obtained from U.S. Forest Service Forest Inventory Analysis (FIA) data. Specific hypotheses included: FIA measures of forest productivity are related to one another; FIA measures of forest productivity are related to FIA-measured landscape parameters; and FIA measures of forest productivity are related to independent measures of forest productivity based on landscape parameters and soil characteristics. Four predictive indices of forest productivity were used; three were generated in a geographic information system (GIS). FIA measures of forest productivity were not significantly correlated to FIA measured landscape parameters. FIA site productivity classes were significantly correlated to FIA measures of site index. Independent measures of forest productivity, particularly the Moisture Regime Index (MRI) and the Forest Site Quality Index (FSQI), were significantly correlated to FIA measures of site index. Topography can be used to delineate site quality, but the addition of soil depth can prove to be useful in the estimation. The second study was designed to develop methods, based on field and digital data, to identify colluvial soils in the central Ridge and Valley of southwestern Virginia. Two hypotheses were tested. First, on the linear side slopes of the study area, where site quality is low in stands with subxeric to xeric moisture regimes, vegetation and topography can indicate colluvial soils. A second hypothesis tested if the topographic signature of colluvial soils could be identified geospatially with a digital elevation model. Results indicated that the MRI and the Terrain Shape Index predicted the presence of colluvial deposits in the study area. The basal area of yellow-poplar was positively associated with colluvial soils. A GIS-based model found the slope difference of colluvial soils to be less steep than residual soils as the size of the neighborhood increased. The final study determined if measures of site quality in the Blue Ridge Mountains of North Carolina were related to the water budget. Specifically,the hypothesis that site index could be predicted by variables that represented the inputs, usage, and supply of water was tested. A second hypothesis questioned if site quality classes could be predicted by a combination of topography and the annual water budget. Regression models predicted site index to be a function of topography, available water supply, and the annual water budget, but the accuracy was low (R2=0.11 and 0.13). A classification approach yielded better results. Incorporating the annual water budget into the FSQI increased classification accuracy of predicted site index by 50%, and decreased the number of sites misclassified by one class by 8%. Where accurate maps of site quality do not exist, the MRI, the abundance of yellow-poplar, and the modified FSQI may be used to delineate site quality for site-specific management and, ultimately, greater return on investment for the landowner. / Ph. D.

Engineers of off-road equipment, on-road vehicles, pavement, and tires must assess the roughness of a terrain surface for the design of their products. The International Roughness Index (IRI), a standardized means of assessing longitudinal road roughness, quantifies roughness based on the average suspension travel for a particular vehicle at a prescribed speed. The Discrete Roughness Index (DRI) developed in this work address fundamental limitations of the IRI. Specifically, the DRI is calculated for each discretely measured location along a terrain surface and is applicable to vehicles traveling at varying speeds and using parameters other than the Golden Quarter-Car on which the IRI is based. The development of the DRI begins with a consistent discretization of the terrain surface, vehicle response, and the IRI. Next the Fractional Response Coefficient is developed, the properties of which are critical in the development of the DRI. The DRI is developed and its properties are discussed through theory and simulation of the ASTM E1926-08 profile. One important property of the average DRI is that it converges to the IRI as the distance between sampled points becomes smaller, for the particular case when the Golden Quarter-Car model is simulated at 80 kph. The DRI is not an alternative to the standard IRI, therefore, but a widely applicable roughness measure of which the standard IRI is a single specialized application. / Master of Science

Loblolly pine is an important managed tree species within the southeastern United States, and better understanding spatial patterns in its productivity has potential to contribute to both modeling and management of the species. Using recently-created pine management maps specific to Virginia and empirical relationships predicting pine LAI from the Landsat satellite, we conducted a statewide analysis of temporal patterns in stand-level southern pine leaf area index (LAI) following clear-cut and planting. Here, using 28 years of Landsat time-series data for 13,140 stands that were clear-cut between 2014-2017, we examined 1) when LAI peaked over the rotation, and 2) how LAI in each stand compared to a recommended fertilization threshold of 3.5 LAI. We found that, on average, winter LAI reached a maximum of 2.02., which can be approximately doubled to give a summer LAI of 4.04, and within stand peak occurred between years 13 and 15. We also found that around 45.8% of stands achieved an LAI value higher than 3.5: a fertilization threshold recommended for managed stands in Virginia. The dataset produced by our analysis will bolster information required for modeling loblolly pines as a plant functional type in regional land simulations, and the finding that most stands are below the recommended LAI fertilization threshold will fuel further management-motivated research. / Master of Science / Management of pines in the southeastern U.S. contributes to the region's economy and carbon sequestration potential. In this study, we used Virginia forest harvest maps to identify individual patches (stands) of pine forest which had each gone through a full harvest life cycle (rotation). With unique managed pine stands identified, we used satellite imagery to estimate growth of canopy leaf area over time within each stand, using a metric called leaf area index (LAI). We identified 13,140 separate stands, each with up to 28 years of available data. We took the first full-state census of areas of managed pines in Virginia, and their leaf area development. We acquired one LAI measurement from February of each year, for each stand in Virginia. Using February LAI for each of our stands, we found that an average stand in VA has a maximum winter LAI of 2.02 (meaning an approximate maximum summer LAI of 4.04), and that stands generally reached their peak LAI after around 14 years of growth. It is recommended, in VA, that a landowner fertilize their stand in the middle of a harvest rotation if summer peak LAI is under 3.5, at stand closure. We found that at ten years of stand age, 45.8% of stands were estimated to reach above this threshold. Since this study's dataset is the most comprehensive LAI dataset for managed pines in VA, it may be used to improve management outcomes as well as understand pine productivity for land surface modeling purposes.