yes / The envelope correlation for a two-element antenna array may be calculated using the antenna radiation fields, or more simply from the scattering parameters of the system. The use of scattering parameters provides a major simplification over the direct use of field data. In this paper we propose a modification of the scattering parameter method which also includes the antenna losses. This approach has the advantage of simplifying the antenna design process, especially when low envelope correlations are needed. It also offers a better prediction of the spatial envelope correlation, and a good framework for understanding the effects of the mutual coupling. The accuracy of this proposed method is illustrated by two examples.

Exact characterization and performance analysis of wireless networks should incorporate dependencies or correlations in space and time, i.e., study how the network performance varies spatially and temporally while having prior information about the performance at previous locations and time slots. This spatio-temporal correlation in wireless networks is usually characterized by studying metrics such as joint coverage probability at two spatial locations/time slots or spatio-temporal correlation coefficient. While developing models and analytical expressions for studying the two extreme cases of spatio-temoral correlation - i) uncorrelated scenario and ii) fully correlated scenario are easier, studying the intermediate case is non-trivial. In this thesis, we develop realistic and tractable analytical frameworks based on random spatial models (using tools from stochastic geometry) for modeling and analysis of correlation in cellular networks. With an ever increasing data demand, caching popular content in the storage of small cells (small cell caching) or the memory of user devices (device caching) is seen as a good alternative to offload demand from macro base stations and reduce backhaul loads. After providing generic results for traditional cellular networks, we study two applications exploiting spatio-temporal correlation in cache-enabled cellular networks. First, we determine the optimal cache content to be stored in the cache of a small cell network that maximizes the hit probability and minimizes the reception energy for the two extreme cases of correlation. Our results concretely demonstrate that the optimal cache contents are significantly different for the two correlation scenarios, thereby indicating the need of correlation-aware caching strategies. Second, we look at a distributed caching scenario in user devices and show that spatio-temporal correlation (user mobility) can be exploited to improve the network performance (in terms of coverage probability and local delay) significantly. / Master of Science

Full 360 degree 3D finite element models are the most complete representation of Oil Country Tubular Goods (OCTG) premium threaded connections. Full 3D models can represent helical threads and boundary conditions required to simulate make-up and service loading. A methodology is developed to create a 360 degree full 3D parametric finite element model with helical threads as an effective design and analysis tool. The approach is demonstrated with the creation of a metal-to-metal seal integral joint full 3D model with manufacturer supplied geometry. The premium connection is decomposed into smaller parts to generate parametric geometric features. A controlled parametric meshing scheme is developed to manage mesh density in contact regions to effectively represent the mechanics in regions of interest while minimizing total element count. The scripted parametric approach allows for efficient geometric and mesh updates. Several methods to reduce and manage model runtimes are presented. An elastic-plastic material model is created with material coupon tensile tests results. Digital Image Correlation (DIC) is used to measure full-field displacement and strain data on the surface of the box. Experimental set up and data processing procedures are discussed. Error metrics are developed to correlate the finite element model results with the DIC experimental data. The DIC make-up experimental results are used to reconcile the finite element model to develop a minimum error make-up model relative to the pin rotation. The friction coefficient is estimated and the make-up torque-turn behavior is verified. The calibrated 3D finite element model is validated with ISO_13769 load series B axial and internal pressure loading experimental DIC data. Metal-to-metal seal metrics of contact pressure and seal length are evaluated. / Master of Science

This thesis addresses development of a new force spectroscopy tool, correlation force spectroscopy (CFS), for the measurement of the mechanical properties of very small volumes of material (molecular to µm³) at kHz-MHz time-scales. CFS is based on atomic force microscopy (AFM) and the principles of CFS resemble those of dual-trap optical tweezers. CFS consists of two closely-spaced micro-cantilevers that undergo thermal fluctuations. Measurement of the correlation in thermal fluctuations of the two cantilevers can be used to determine the mechanical properties of the soft matter, e.g. a polymeric molecule, that connects the gap between the two cantilevers. Modeling of the correlations yields the effective stiffness and damping of the molecule. The resolution in stiffness is limited by the stiffness of the cantilever and the frequency by the natural frequency of the cantilevers, but, importantly, the damping resolution is not limited by the damping of the cantilever, which has enabled high-resolution measurements of the internal friction of a polymer. The concept of CFS was originally presented by Roukes' group in Caltech [Arlett et al., Lecture Notes in Physics, 2007]; I developed the first practical versions of CFS for experimentation, and have used it in two applications (1) microrheology of Newtonian fluids and (2) single molecule force spectroscopy. To understand the correlation in thermal fluctuations of two cantilevers I initially validated the theoretical approach for analyzing correlation in terms of deterministic model using the fluctuation-dissipation theorem [Paul and Cross, PRL, 2004]. I have shown that the main advantages of such correlation measurements are a large improvement in the ability to resolve stiffness and damping. Use of CFS as a rheometer was validated by comparison between experimental data and finite element modeling of the deterministic vibrations of the cantilevers using the known viscosity and density of fluids. Work in this thesis shows that the data can also be accurately fitted using a simple harmonic oscillator model, which can be used for rapid rheometric measurements, after calibration. The mechanical properties of biomolecules such as dextran and single stranded DNA (ssDNA) are also described. CFS measurements of single molecule properties of ssDNA reveal the internal friction of the molecule in solution. / Ph. D.

To reduce the variance of metamodel coefficients, simulation analysts often advocate the use of correlation induction strategies. Under certain conditions, these strategies have been shown to reduce the variance of metamodel coefficients without producing significant bias in the coefficient estimates. Although these procedures are very useful for estimating metamodels, the application of many statistical analysis techniques is inappropriate unless the analyst is assured that a pure error component is present in the response. Crenshaw and Tew have demonstrated the absence of pure error in experiments in which all random number streams are used to induce correlations. Mihram argues that a pure error component can be maintained by selecting the seeds for at least one random component randomly and non-repetitively for all design points and replications. In this thesis, random components for which seeds are randomly and non-repetitively selected are referred to as pure error generators. This thesis examines the selection of pure error generators in the context of univariate response, replicated simulation experiments. To assess the impact of pure error generator selection, we give the results of an extensive series of Monte-Carlo experiments in which the Schruben-Margolin strategy is applied for each possible pure error generator in each of two simulation models. To determine causes for the differences in pure error generator performance, four pure error generator selection methods are outlined, tested, and compared to the results of the Monte-Carlo experiments. The results strongly suggest the importance of careful pure error generator selection and indicate that the primary difference in their performance is related to their ability to maintain the prescribed correlation structures of the correlation induction strategy. / Master of Science

This thesis compared macrotexture measurements obtained using the volumetric method (Sand Patch) and three laser-based devices: MGPS system, ICC laser profiler, and Circular Texture Meter (CTMeter). The study used data from three sources: two controlled experiments conducted at the Virginia Smart Road, field data collected on eight newly constructed hot-mix-asphalt (HMA) roadway surfaces, and data collected on airport surfaces at the Wallops flight facility, Virginia. The data collected at the Virginia Smart Road, a controlled-access two-lane road that includes various HMA and concrete surfaces, was used for the main analysis. The other two sets of data were used for verification and validation of the model developed. The analysis of the data collected at the Virginia Smart Road showed that the CTMeter mean profile depth (MPD) has the highest correlation with the volumetric (Sand Patch) mean texture depth (MTD). Furthermore, texture convexity had a significant effect on the correlation between the measurements obtained with different devices. Two sets of models for converting the laser-based texture measurements to an estimated MTD (ETD) were developed. One set of equations considered all the data collected at the Virginia Smart Road, and the other excluded the measurements on the Open-Graded Friction Course (OGFC). The developed models were tested using measurements collected at eight roadway sections throughout Virginia and the Wallops flight facility. The model, excluding the OGFC section, was successfully applied to other sites. / Master of Science

The genus Chrysopelea encompasses the "flying" snakes. This taxon has the ability to glide via lateral aerial undulation and dorsoventral body flattening, a skill unique to this group, but in addition to other functions common to all colubrids. The skin must be extensible enough to allow this body shape alteration and undulation, and strong enough to withstand the forces seen during landing. For this reason, characterizing the mechanical properties of the skin may give insight to the functional capabilities of the skin during these gliding and landing behaviors. Dynamic and viscoelastic uniaxial tensile tests were combined with a modified particle image velocimetry technique to provide strength, extensibility, strain energy, and stiffness information about the skin with respect to orientation, region, and species, along with viscoelastic parameters. Results compared with two other species in this study and a broader range of species in prior studies indicate that while the skin of these unique snakes may not be specifically specialized to deal with larger forces, extensibility, or energy storage and release, the skin does have increased strength and energy storage associated with higher strain rates. The skin also has differing properties with respect to dorsoventral location, and regional differences in strength in the circumferential orientation. This may indicate that, although the properties of the skin may not be different, the rate at which the skin is strained in the different species may vary, thus altering the apparent properties of the skin during specific behaviors. / Master of Science

This thesis presents a comparison of correlation methods in risk analysis. A theoretical solution is given to the correlation problem along with a discussion of each method. Each method is compared to a developed test case and two other cost projects. Restrictions on correlation coefficients are also given followed by the advantages and disadvantages of each method. / Master of Science

Quantum mechanical methods are becoming increasingly useful and applicable tools to complement and support experiment. Nonetheless, some barriers to further applications of theoretical models still remain. A coupled cluster singles and doubles (CCSD) calculation, a reliable ab initio method, scales approximately on the order of 𝑂(𝑁⁶), where 𝑁 is a measure of the system size. This unfortunately limits the use of such high-accuracy methods to relatively small systems. Coupled cluster property calculations must be used in conjunction with reduced-scaling methods in order to broaden the range of applications to larger systems. In this work, we introduce some of the underlying theory behind such calculations and test the performance of several local correlation techniques for polarizabilities, optical rotations, and excited state properties. In general, when the computational cost is significantly reduced, the necessary accuracy is lost. Polarizabilities are less sensitive to the truncation schemes than optical rotations, and the excitation data is often only in agreement with the canonical result for the first few excited states. Additionally, we present a novel application of equation-of-motion coupled cluster singles and doubles to simulated circularly polarized luminescence spectra of eight chiral ketones. Both the absorption in the ground state and emission from the excited states were examined. Extensive geometry analyses were performed, revealing that optimized structures at the density functional theory were adequate for the calculation accurate coupled cluster excitation data. / Ph. D.

New methods for testing hypotheses in paired-comparison experiments are presented in this dissertation. The methods are developed on the basis of a very general mathematical model and they are, in general, quite easy to employ. Two tests of the null hypothesis that all treatments have equal stimuli, against its general alternative, are proposed. One test is for the case in which it is assumed prior to the experiment that no interaction will take place between repetitions and preference probabilities (the probabilities of the possible comparison preferences). The other test is for the case in which the above assumption cannot be made. The number of times a treatment is preferred is called its score. For the “no interaction" case, the test procedure is based on a test statistic that is a function D of the corrected sum of squares of the treatment scores. In the other case, the value of D is calculated for each group of homogeneous repetitions and then the values are summed to give the new test statistic. It is established that a X²-approximation may be used to determine the critical value of the test statistic for experiments outside the range of the tabled distributions. This test procedure is shown to be simpler than other approximate tests and, in general, at least as accurate with respect to errors of the first kind. It is shown that the two test methods discussed above may be extended to ranking experiments in balanced incomplete block designs with more than two treatments per block. To test the null hypothesis of no interaction between preference probabilities and repetitions, against its general alternative, a test method based on the theory of X² homogeneity tests is introduced. Means are presented for testing whether (1) a particular treatment is better than the average of the treatment stimuli; (2) two particular treatment stimuli are not equal; and (3) the treatment receiving the highest score is better than the average. The three test procedures are based essentially on the binomial distribution of the treatment scores under the null hypothesis. In each case, the test procedure is conservative. A procedure analogous to Tukey's test based on allowances is developed to test the null hypothesis of equal treatment stimuli and to separate the significantly different treatment scores when it rejects the null hypothesis. A method for judging contrasts of treatment scores similar to Scheffe's (1953) method for judging contrasts in the analysis of variance is proposed. The test method based on D, mentioned earlier, is used in place of the F-test employed in the Scheffe method. The use of paired-comparison experiments to test factorial effects is discussed and a test method based on orthogonal contrasts of the treatment scores is suggested. Because of correlations that arise, it is necessary to restrict this method to cases in which the only factors that are allowed to appear at more than two levels are those that will not interact with the other factors in the experiment. The test methods are illustrated through application on the data from two paired-comparison experiments. / Ph. D.