Reduced Order Models (ROM) provide a low-dimensional alternative form of a system of differential equations. Such a form permits faster computation of solutions. In this paper, Poisson's Equation in two dimensions, the Heat Equation in one dimension, and a Nonlinear Reaction-Diffusion equation in one dimension are solved using the Galerkin formulation of the Finite Element Method (FEM) in conjunction with Newton's Method. Reduced Order Modeling (ROM) by Proper Orthogonal Decomposition (POD) is then used to accelerate the solution of successive linear systems required by Newton's Method. This is done to show the viability of the method on a simple problem. The Navier-Stokes (NS) Equations are introduced and solved by FEM. A ROM using both POD and clustering by Centroidal Voronoi Tesselation (CVT) are then used to solve the NS equations, and the results are compared with the FEM solution. The specific NS problem we consider has inhomogeneous Dirichlet boundary conditions and the treatment of the boundary conditions is explained. The resulting decrease in computation time required for solving the various equations are compared with ROM methods. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2012. / October 5, 2012. / Finite Element Methods, Navier-Stokes Equations, Nonlinear PDEs, Reduced Order Modeling / Includes bibliographical references. / Janet Peterson, Professor Directing Thesis; Tomasz Plewa, Committee Member; Sachin Shanbhag, Committee Member.

This dissertation presents and investigates ideas for improvement of the creation of quality centroidal voronoi tessellations on the sphere (SCVT) which are to be used for multiphysics, multidomain applications. As an introduction, we discuss grid generation on the sphere in a broad fashion. Next, we discuss the theory of CVTs in general, and specifically on the sphere. Subsequently we consider the iterative processes, such as Lloyd's algorithm, which are used to construct them. Following this, we describe a method for density functions via images so that we can shape generator density in an intuitive, yet arbitrary, manner, and then a method by which SCVTs can be easily adapted to conform to arbitrary sets of line segments, or shorelines. Then, we discuss sample meshes, used for various physical and nonphysical applications. Penultimately, we discuss two sample applications, as a proof of concept, where we adapt the Shallow Water Model from Model for Predictions Across Scales (MPAS) to use our grids for a more accurate border, and we also discuss elliptic interface problems both with and without hanging nodes. Finally, we share a few concluding remarks. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2011. / November 3, 2011. / Includes bibliographical references. / Max Gunzburger, Professor Co-Directing Dissertation; Janet Peterson, Professor Co-Directing Dissertation; Kyle Gallivan, University Representative; Gordon Erlebacher, Committee Member; Xiaoqiang Wang, Committee Member; Todd Ringler, Committee Member.

This thesis aims at theoretical and computational modeling of the continuum dislocation theory coupled with its internal elastic field. In this continuum description, the space-time evolution of the dislocation density is governed by a set of hyperbolic partial differential equations. These PDEs must be complemented by elastic equilibrium equations in order to obtain the velocity field that drives dislocation motion on slip planes. Simultaneously, the plastic eigenstrain tensor that serves as a known field in equilibrium equations should be updated by the motion of dislocations according to Orowan's law. Therefore, a stress- dislocation coupled process is involved when a crystal undergoes elastoplastic deformation. The solutions of equilibrium equation and dislocation density evolution equation are tested by a few examples in order to make sure appropriate computational schemes are selected for each. A coupled numerical scheme is proposed, where resolved shear stress and Orowan's law are two passages that connect these two sets of PDEs. The numerical implementation of this scheme is illustrated by an example that simulates the recovery process of a dislocated cubic crystal. The simulated result demonstrates the possibility to couple macroscopic(stress) and microscopic(dislocation density tensor) physical quantity to obtain crystal mechanical response. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2011. / November 7, 2011. / crystal plasticity, dislocation, dislocation density tensor, dislocation evolution equation / Includes bibliographical references. / Anter El-Azab, Professor Directing Thesis; Tomasz Plewa, Committee Member; Xiaoqiang Wang, Committee Member.

This dissertation compares and contrasts large-scale optimization algorithms in the use of variational and sequential data assimilation on two novel problems chosen to highlight the challenges in non-linear and non-smooth data assimilation. The first problem explores the impact of a highly non-linear observation operator and highlights the importance of background information on the data assimilation problem. The second problem tackles large-scale data assimilation with a non-smooth observation operator. Together, these two cases show both the importance of choosing an appropriate data assimilation method and, when a variational or variationally-inspired method is chosen, the importance of choosing the right optimization algorithm for the problem at hand. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2012. / November 21, 2011. / All-sky infrared satellite, Cloudy IR, Inverse problem, Limited Memory Bundle Method, Non-differentiable, Quasi-Newton / Includes bibliographical references. / Ionel Michael Navon, Professor Directing Thesis; Guosheng Liu, University Representative; Max Gunzburger, Committee Member; Gordon Erlebacher, Committee Member; Milijia Zupanski, Committee Member; Napsu Karmitsa, Committee Member.

The Internet email system as a popular online communication tool has been increasingly misused by ill-willed users to carry out malicious activities including spamming and phishing. Alarmingly, in recent years the nature of the email-based malicious activities has evolved from being purely annoying (with the notorious example of spamming) to being criminal (with the notorious example of phishing). Despite more than a decade of anti-spam and anti-phishing research and development efforts, both the sophistication and volume of spam and phishing messages on the Internet have continuously been on the rise over the years. A key difficulty in the control of email-based malicious activities is that malicious actors have great operational flexibility in performing email-based malicious activities, in terms of both the email delivery infrastructure and email content; moreover, existing anti-spam and anti-phishing measures allow for arms race between malicious actors and the anti-spam and anti-phishing community. In order to effectively control email-based malicious activities such as spamming and phishing, we argue that we must limit (and ideally, eliminate) the operational flexibility that malicious actors have enjoyed over the years. In this dissertation we develop and evaluate a sender-centric approach (SCA) to addressing the problem of email-based malicious activities so as to control spam and phishing emails on the Internet. SCA consists of three complementary components, which together greatly limit the operational flexibility of malicious actors in sending spam and phishing emails. The first two components of SCA focus on limiting the infrastructural flexibility of malicious actors in delivering emails, and the last component focuses on on limiting the flexibility of malicious actors in manipulating the content of emails. In the first component of SCA, we develop a machine-learning based system to prevent malicious actors from utilizing compromised machines to send spam and phishing emails. Given that the vast majority of spam and phishing emails are delivered via compromised machines on the Internet today, this system can greatly limit the infrastructural flexibility of malicious actors. Ideally, malicious actors should be forced to send spam and phishing messages from their own machines so that blacklists and reputation-based systems can be effectively used to block spam and phishing emails. The machine-learning based system we develop in this dissertation is a critical step towards this goal. In recent years, malicious actors also started to employ advanced techniques to hijack network prefixes in conducting email-based malicious activities, which makes the control and attribution of spam and phishing emails even harder. In the second component of SCA, we develop a practical approach to improve the security of the Internet inter-domain routing protocol BGP. Given that the key difficulties in adopting any mechanism to secure the Internet inter-domain routing are the overhead and incremental deployment property of the mechanism, our scheme is designed to have minimum overhead and it can be incrementally deployed by individual networks on the Internet to protect themselves (and their customer networks), so that individual networks have incentives to deploy the scheme. In addition to the infrastructural flexibility in delivering spam and phishing emails, malicious actors have enormous flexibility in manipulating the format and content of email messages. In particular, malicious actors can forge phishing messages as close to legitimate messages in terms of both format and content. Although malicious actors have immense power in manipulating the format and content of phishing emails, they cannot completely hide how a message is delivered to the recipients. Based on this observation, in the last component of SCA, we develop a system to identify phishing emails based on the sender- related information instead of the format or content of email messages. Together, the three complementary components of SCA will greatly limit the operational flexibility and capability that malicious actors have enjoyed over the years in delivering spam and phishing emails, and we believe that SCA will make a significant contribution towards addressing the spam and phishing problem on the Internet. / A Dissertation submitted to the Department of Computer Science in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2011. / November 4, 2011. / Flexibility, Phishing, Sender-centric, Spam / Includes bibliographical references. / Zhenhai Duan, Committee Member; Xufeng Niu, University Representative; Xin Yuan, Committee Member; Sudhir Aggarwal, Committee Member.

A significant component of forensic science is analyzing bones to assess the age at death of an individual. Forensic anthropologists often include the pubic symphysis in such studies. Subjective methods, such as the Suchey-Brooks method, are currently used to analyze the pubic symphysis. This thesis examines a more objective, quantitative method. The method analyzes 3D surface scans of the pubic symphysis and implements a thin plate spline algorithm which models the bending of a flat plane to approximately match the surface of the bone. The algorithm minimizes the bending energy required for this transformation. Results presented here show that there is a correlation between the minimum bending energy and the age at death of the individual. The method could be useful to medico-legal practitioners. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Fall Semester, 2012. / August 8, 2012. / Age estimation, Pubis Symphysis, Thin plate splines / Includes bibliographical references. / Dennis Slice, Professor Directing Thesis; John Burkardt, Committee Member; Ming Ye, Committee Member; Sachin Shanbhag, Committee Member.

In the present work, we investigate the internal fields generated by the dislocation structures that form during the deformation of copper single crystals. In particular, we perform computational modeling of the statistical and morphological characteristics of the dislocation structures obtained by dislocation dynamics simulation method and compare the results with X-ray microscopy measurements of the same data. This comparison is performed for both the dislocation structure and their internal elastic fields for the cases of homogeneous deformation and indentation of copper single crystals. A direct comparison between dislocation dynamics predictions and X-ray measurements plays a key role in demonstrating the fidelity of discrete dislocation dynamics as a predictive computational mechanics tool and in understanding the X-ray data. For the homogeneous deformation case, dislocation dynamics simulations were performed under periodic boundary conditions and the internal fields of dislocations were computed by solving an elastic boundary value problem of many-dislocation system using the finite element method. The distribution and pair correlation functions of all internal elastic fields and the dislocation density were computed. For the internal stress field, the availability of such statistical information paves the way to the development of a density-based mobility law of dislocations in continuum dislocation dynamics models, by correlating the internal-stress statistics with dislocation velocity statistics. The statistical analysis of the lattice rotation and the dislocation density fields in the deformed crystal made possible the direct comparison with X-ray measurements of the same data. Indeed, a comparison between the simulation and experimental measurements has been possible, which revealed important aspects of similarity and differences between the simulation results and the experimental data. In the case of indentation, which represents a highly inhomogeneous deformation, a contact boundary value problem was solved in conjunction with a discrete-dislocation dynamics simulation model; the discrete dislocation dynamics simulation was thus enabled to handle finite domains under mixed traction/displacement boundary conditions. The load-displacement curves for indentation experiments were analyzed with regard to cross slip, indentation speed and indenter shape. The lattice distortion fields obtained by indentation simulations were directly compared with their experimental counterparts. Other indentation simulations were also carried out, giving insight into different aspects of micro-scale indentation deformation. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester, 2012. / November 2, 2012. / Copper, Dislocation Dynamics, Indentation, Plasticity, Size effects / Includes bibliographical references. / Anter El-Azab, Professor Directing Thesis; Leon van Dommelen, University Representative; Gordon Erlebacher, Committee Member; Ming Ye, Committee Member; Xiaoqiang Wang, Committee Member.

Hydrodynamic instabilities are the driving force behind complex fluid processes that occur from everyday scenarios to the most extreme physical conditions of the universe. The Rayleigh-Taylor instability (RTI) develops when a heavy fluid is accelerated by a light fluid, resulting in sinking spikes, rising bubbles, and material mixing. Laser experiments have observed features of RTI that cannot be explained with pure hydrodynamic models. For this computational study we have implemented and verified extended physics mod- ules for anisotropic thermal conduction and self-generated magnetic fields in the FLASH- based Proteus code using the Braginskii plasma theory. We have used this code to simulate RTI in a basic plasma physics context. We obtain results up to 35 nanoseconds (ns) at various resolutions and discuss convergence and computational challenges. We find that magnetic fields as high as 1-10 megagauss (MG) are genereated near the fluid interface. Thermal conduction turns out to be essentially isotropic in these conditions, but plays the dominant role in the evolution of the system by smearing out small-scale structure and reducing the RT growth rate. This may account for the relatively feature- less RT spikes seen in experiments. We do not, however, observe mass extensions in our simulations. Without thermal conductivity, the magnetic field has the effect of generating what appears to be an additional RT mode which results in new structure at later times, when compared to pure hydro models. Additional physics modules and 3-D simulations are needed to complete our Braginskii model of RTI. / A Thesis submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Master of Science. / Summer Semester, 2012. / June 29, 2012. / astrophysics, computational, magnetic, physics, plasma, thermal / Includes bibliographical references. / Tomasz Plewa, Professor Directing Thesis; Michael Ionel Navon, Committee Member; Mark Sussman, Committee Member.

Motion segmentation is an essential pre-processing task in many computer vision problems. In this dissertation, the motion segmentation problem is studied and analyzed. At first, we establish a framework for the accurate evaluation of the motion field produced by different algorithms. Based on the framework, we introduce a feature tracking algorithm based on RankBoost which automatically prunes bad trajectories. The algorithm is observed to outperform many feature trackers using different measures. Second, we develop three different motion segmentation algorithms. The first algorithm is based on spectral clustering. The affinity matrix is built from the angular information between different trajectories. We also propose a metric to select the best dimension of the lower dimensional space onto which the trajectories are projected. The second algorithm is based on learning. Using training examples, it obtains a ranking function to evaluate and compare a number of motion segmentations generated by different algorithms and pick the best one. The third algorithm is based on energy minimization using the Swendsen-Wang cut algorithm and the simulated annealing. It has a time complexity of $O(N^2)$, comparing to at least $O(N^3)$ for the spectral clustering based algorithms; also it could take generic forms of energy functions. We evaluate all three algorithms as well as several other state-of-the several other state-of-the-art methods on a standard benchmark and show competitive performance. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Summer Semester, 2013. / June 13, 2013. / Computer Vision, Machine Learning, Motion Segmentation, Object Tracking / Includes bibliographical references. / Adrian Barbu, Professor Directing Thesis; Anke Meyer-Baese, Professor Co-Directing Thesis; Xiuwen Liu, University Representative; Dennis Slice, Committee Member; Xiaoqiang Wang, Committee Member.

Prediction markets are forums of trade where contracts on the future outcomes of events are bought and sold. These contracts reward buyers based on correct predictions and thus give incentive to make accurate predictions. Prediction markets have successfully predicted the outcomes of sporting events, elections, scientific hypothesese, foreign affairs, etc... and have repeatedly demonstrated themselves to be more accurate than individual experts or polling [2]. Since prediction markets are aggregation mechanisms, they have garnered interest in the machine learning community. Artificial prediction markets have been successfully used to solve classification problems [34, 33]. This dissertation explores the underlying optimization problem in the classification market, as presented in [34, 33], proves that it is related to maximum log likelihood, relates the classification market to existing machine learning methods and further extends the idea to regression and density estimation. In addition, the results of empirical experiments are presented on a variety of UCI [25], LIAAD [49] and synthetic data to demonstrate the probability accuracy, prediction accuracy as compared to Random Forest [9] and Implicit Online Learning [32], and the loss function. / A Dissertation submitted to the Department of Scientific Computing in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester, 2013. / March 29, 2013. / Aggregation, Artificial Prediction Markets, Classification, Density estimation, Machine Learning, Regression / Includes bibliographical references. / Adrian Barbu, Professor Directing Thesis; Anke Meyer-Baese, Professor Co-Directing Thesis; Debajyoti Sinha, University Representative; Ye Ming, Committee Member; Xiaoqiang Wang, Committee Member.