We examine a model of solid-solid phase transitions that includes thermo-elastic effects and an order parameter. The model is derived as a special case of the Gurtin-Fried model posed in one space dimension with a symmetric triple-well free energy in which the relative heights of the wells vary with temperature. We examine the temperature independent case, showing existence of a unique classical solution of a regularized system of partial differential equations using semigroup theory. This is followed by numerical study of a finite element algorithm for the temperature independent model. Finally, we present computational material concerning the temperature dependent model. / Ph. D.

The unit root revolution in time series modeling has created substantial interest in non- stationarity and its implications for empirical modeling. Beyond the original interest in trend vs. di¤erence non-stationarity, there has been renewed interest in testing and modeling structural breaks. The focus of my dissertation is on testing for departures from stationarity in a broader framework where unit root, mean trends and structural break non-stationarity constitute only a small subset of the possible forms of non-stationarity. In the fi¦rst chapter the most popular testing procedures for the assumption, in view of the fact that general forms of non-stationarity render each observation unique, I develop a testing procedure using a resampling scheme which is based on a Maximum Entropy replication algorithm. The proposed misspecification testing procedure relies on resampling techniques to enhance the informational content of the observed data in an attempt to capture heterogeneity 'locally' using rolling window estimators of the primary moments of the stochastic process. This provides an e¤ective way to enhance the sample information in order to assess the presence of departures from stationarity. Depending on the sample size, the method utilizes overlapping or non-overlapping window estimates. The e¤ectiveness of the testing procedure is assessed using extensive Monte Carlo simulations. The use of rolling non-overlapping windows improves the method by improving both the size and power of the test. In particular, the new test has empirical size very close to the nominal and very high power for a variety of departures from stationarity. The proposed procedure is then applied on seven macroeconomic series in the fourth chapter. Finally, the optimal choice of orthogonal polynomials, for hypothesis testing, is investigated in the last chapter. / Ph. D.

Some implementation characteristics of the Independent Modal-Space Control method are considered. It is shown that the control method is completely robust with respect to modeling errors and plant truncation effects. The globally optimal control of distributed systems requires distributed actuators. Instead of using distributed actuators, the distributed control is approximated with discrete actuators. Since the distributed control is closely approximated, the closed-loop poles are computed as a perturbation of the distributed control. The discrete actuators are located such that the control spillover is minimized. / M.S.

We live in the era of textit{Big Data} with significantly richer computational resources than the last two decades. The concurrence of computation resources and a large volume of data has boosted researchers' desire for developing feasible Markov Chain Monte Carlo (MCMC) algorithms for large parameter spaces. Dirichlet Process Mixture Models (DPMMs) have become a Bayesian mainstay for modeling heterogeneous structures, namely clusters, especially when the quantity of clusters is not known with the established MCMC methods. As opposed to many ad-hoc clustering methods, using Dirichlet Processes (DPs) in models provide a flexible and probabilistic approach for automatically estimating both cluster structure and quantity. While DPs are not fully parameterized, they depend on both a base measure and a concentration parameter that can heavily impact inferences. Determining the concentration parameter is critical and essential, since it adjusts the a-priori cluster expectation, but typical approaches for specifying this parameter are rather cavalier. In this work, we propose a new method for automatically and adaptively determining this parameter, which directly calibrates distances between clusters through an explicit link function within the DP. Furthermore, we extend our method to mixture models with Nested Dirichlet Processes (NDPs) that cluster the multilevel data and depend on the specification of a vector of concentration parameters. In this work, we detail how to incorporate our method in Markov chain Monte Carlo algorithms, and illustrate our findings through a series of comparative simulation studies and applications. / Ph. D.

Two methods, one for the identification and one for the control implementation of distributed-parameter systems are presented. The methods are designed to identify and control the actual distributed system, without resorting to discretization. They are implemented using discrete sensors and actuators. The identification process is carried out in two steps. First, the eigensolution of the distributed system is identified. The lowest frequencies and associated eigenfunctions are identified using an extension of a time-domain approach developed for discrete systems. The extension to distributed systems is carried out in this dissertation. To this end, the sensors output is interpolated to identify the eigenfunctions. Next, the parameters contained in the equations of motion are identified. The motion of distributed-parameter systems is described in terms of partial differential equations, so that these parameters are in general continuous functions of the spatial variables. For vibrating systems, these parameters ordinarily represent the mass, stiffness and damping distributions. These distributions are expanded in terms of finite series of known functions of the spatial variables multiplied by undetermined coefficients. Then, using the identified eigensolution and assuming that the general nature of the equation of motion is known, use is made of the least squares method, in conjunction with the eigenfunctions orthogonality to compute the undetermined coefficients, thus identifying the actual distributed system. The control system design is based on the concept of independent modal-space control. Implementation of the independent modal-space control method requires that the number of actuators be equal to the number of controlled modes. Because the actuators are discrete elements, control spillover into the uncontrolled modes is experienced. The effect of control spillover is to pump part of the energy imparted to the distributed system into the uncontrolled modes. It is shown that when the independent modal-space control method is used, the energy required to control the controlled modes does not depend on the actuators locations, so that the placement of the actuators does not represent a serious problem, as it can for coupled controls. A new concept in extracting modal coordinates from the system output, namely modal filters, is introduced. Modal filters extract the modal quantities from the sensors data by interpolating the output of the sensors to obtain continuous displacement patterns and by performing certain weighted integrations over the distributed domain. If the interpolation functions are chosen following the same guidelines as in the finite element method, the integrations can be carried out as offline computations, which facilitates the control implementation. It is shown that when modal filters are used, control of the actual distributed system is possible and no spatial discretization is necessary. In addition, observation spillover, a possible significant problem when observers are used, is eliminated. Two numerical examples are presented to illustrate the identification and control methods. The methods described in this dissertation are in terms of vibrating systems, with special emphasis on large flexible structures. However, these methods are applicable to any distributed-parameter system. / Ph. D.

This research proposes to simplify the energy consumption assessment for residential homes while building the foundation towards the development of prediction tools that can achieve a credible level of accuracy for confident decision making. The energy consumption assessment is based on simplified energy consumption models. The energy consumption analysis uses a reduced number of energy model equations utilizing a critical, limited set of parameters. The results of the analysis are used to develop the minimum set of consumption influence parameters with predicted effects for each energy consumption domain. During this research study, multiple modeling approaches and occupancy scenarios were utilized according to climate conditions in Blacksburg, Virginia. As a part of the analysis process, a parameter study was conducted to: develop a comprehensive set of energy consumption influence parameters, identify the inter-relationships among parameters, determine the impact of energy consumption influence parameters in energy consumption models, and classify energy consumption influence parameters under identified energy consumption domains. Based on the results of the parameter study, a minimum set of parameters and energy consumption influence matrices were developed. This research suggests the minimum set of parameters with predicted effects to be used during the development of the simplified baseline energy consumption model. / Ph. D.

In this thesis, confidence bounds on simple and more complex parameters are stated along with detailed computational procedures for finding these confidence bounds from the given data. Confidence bounds on the more familiar parameters, i.e., μ, ơ², μ₁ - μ₂, and ơ²₁/ơ²₂, are briefly presented for the sake of completeness. The confidence statements for the less familiar parameters and combinations of parameters are treated in more detail. In the cases of the non-centrality parameters of the non-central t², F and X² distributions, a variance-stabilizing transformation is used, a normal approximation is utilized, and confidence bounds are pub on the parameter. In the non-central t² and non-central F distributions iterative procedures are used to obtain confidence bounds on the non-centrality parameter, i.e., a first guess is made which is improved until the desired accuracy is obtained This procedure is unnecessary in the non-central X² distribution, since the expressions for the upper and lower limits can be reduced to closed form. Computational procedures and completely worked examples are included. / Master of Science

Identification is the process of determining values for the characteristic quantities, called parameters, of a system. Examples of such quantities are mass, inductance, resistance, spring coefficient, gain, et cetera. The decreasing cost of digital processors and the versatility of digital programming make digital methods an attractive means of accomplishing identification. It is important, however, that an identifier be able to track any change in a parameter if its output is to be used in any predictive capacity, such as in an adaptive controller. Most studies of digital identification have avoided the topic of time variations by using batch processing methods that implicitly assume constant parameters; this thesis does not. This thesis first investigates the parameter-tracking capabilities of a popular, real-time digital identification algorithm, the recursive weighted least squares method. This method is claimed to be able to track only slowly time-varying parameters. Based on the results of this study, a method of improving the accuracy of estimates of time-varying parameters is developed. This method, called conditioning, is a post-processor to the recursive weighted least squares algorithm. The results of tests of this method using three different plant simulations are presented, demonstrating the improved accuracy achieved by conditioning estimates of time-varying parameters. / M.S.

Parametric surface representations such as the B-spline and Bezier geometries are widely used among the aerospace, automobile, and shipbuilding industries. These surfaces have proven to be very advantageous for defining and combining primitive geometries to form complex models. However, the task of finding the intersection curve between two surfaces has remained a difficult one. Presently, most of the research done in this area has resulted in various subdivision techniques. These subdivision techniques are based on approximations of the surface using planar polygons. This thesis presents an analytical approach to the intersection problem. The approach taken is to approximate the B-spline surface using subsets such as the ruled surface. Once the B-spline surface has been simplified, elimination techniques which solve for the surface variables can be used to analytically determine the intersection curve between two B-spline surfaces. / Master of Science

Yes / Apigenin (4′,5,7-trihydroxyflavone, APG) has many potential therapeutic benefits; however, its poor aqueous solubility has limited its clinical applications. In this work, a large scale cocrystal screening has been conducted, aiming to discover potential APG cocrystals for enhancement of its solubility and dissolution rate. In order to reduce the number of the experimental screening tests, three computational prescreening tools, i.e., molecular complementarity (MC), hydrogen bond propensity (HBP), and hydrogen bond energy (HBE), were used to provide an initial selection of 47 coformer candidates, leading to the discovery of seven APG cocrystals. Among them, six APG cocrystal structures have been determined by successful growth of single crystals, i.e., apigenin-carbamazepine hydrate 1:1:1 cocrystal, apigenin-1,2-di(pyridin-4-yl)ethane hydrate 1:1:1 cocrystal, apigenin-valerolactam 1:2 cocrystal, apigenin-(dl) proline 1:2 cocrystal, apigenin-(d) proline/(l) proline 1:1 cocrystal. All of the APG cocrystals showed improved dissolution performances with the potential to be formulated into drug products.