Dissertations

Permanent URI for this collectionhttps://www.lib.ncsu.edu/resolver/1840.20/24

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Now showing 1 - 20 of 222

A Comparison of Physiologically-Based Pharmacokinetic (PBPK) Models of Methyl-Tertiary Butyl Ether (MTBE).
(2017-12-07) Smith, Nikki Shavon; Hien Tran, Co-Chair; Marina Evans, Co-Chair; Leonard Stefanski, Graduate School Representative; Jesus Rodriguez, Member; Xiao-Biao Lin, Member
A Data-Driven Framework for Modeling the Neurogenesis-to-Gliogenesis Switch.
(2020-05-28) Mennicke, Christine Victoria; Mansoor Haider, Chair; Troy Ghashghaei, Member; Alen Alexanderian, Member; Ralph Smith, Member
A High Order Compact Scheme for Interior/Exterior 3D Wave Equation by the Method of Difference Potentials.
(2022-10-13) Smith, Fouche Frantz; Semyon Tsynkov, Chair; Ralph Smith, Member; Alina Chertock, Member; Zhilin Li, Member; Eli Turkel, External; Ramon Malheiros, Graduate School Representative
A Hybrid-Finite-Volume-Finite-Difference Scheme and Augmented Method for Chemotaxis System.
(2022-04-28) Hu, Hengrui; Alina Chertock, Chair; Mansoor Haider, Member; Semyon Tsynkov, Member; Zhilin Li, Member; Hien Tran, Graduate School Representative
A Machine Learning Approach to Predict Loan Default.
(2019-07-29) Owen, Hailey Markay; Hien Tran, Chair; Alen Alexanderian, Member; Kevin Flores, Member; Marcia Gumpertz, Graduate School Representative; Negash Medhin, Member
A Model-Driven Approach to Experimental Validation of Predator-Prey Dynamics in a System of Terrestrial Arthropods.
(2018-03-20) Laubmeier, Amanda Nicole; Harvey Banks, Chair; Lorena Bociu, Member; Kevin Flores, Member; Hien Tran, Member; Bradley Taylor, Graduate School Representative
A Nonlinear Conservation Law Modeling Carbon Sequestration.
(2016-11-28) Brown, Elisabeth Mary Margaret; Michael Shearer, Chair; Alina Chertock, Member; Ralph Smith, Member; Mansoor Haider, Member; Brian Blackley, Graduate School Representative
A Robin Robin Domain Decomposition Method for a Stokes-Darcy System with a Locally Modified Mesh.
(2016-07-25) Wang, Zhaohui; Zhilin Li, Chair; Xiao Lin, Member; Kazufumi Ito, Member; Donald Martin, Graduate School Representative; Hua Zhou, Member
Accurate Gradient Computation for Elliptic Interface Problems with Discontinuous and Variable Coefficients
(2015-04-23) Chen, Guanyu; Zhilin Li, Chair; Alina Chertock, Member; Xiao Lin, Member; Yichao Wu, Graduate School Representative; Ernest Stitzinger, Member
Active Incipient Fault Detection With Multiple Simultaneous Faults.
(2010-10-20) Fair, Martene; Stephen Campbell, Committee Chair; Ernest Stitzinger, Committee Member; Negash Medhin, Committee Member; Robert White, Committee Member
Active Subspace Techniques, Bayesian Inference and Uncertainty Propagation for Nuclear Neutronics and Chemistry Models.
(2019-07-25) Coleman, Kayla Danielle; Ralph Smith, Chair; Stephen Campbell, Member; Pierre Gremaud, Member; Brian Reich, Member
Adaptive Control of Hysteretic Smart Material Systems
(2009-11-05) Fan, Xiang; Ralph Smith, Committee Chair
Smart materials exhibit nonlinearities and hysteresis when driven at field levels necessary to meet stringent performance criteria in high performance applications. This requires models and control designs that effectively compensate for the nonlinear, hysteretic field-coupled material behavior. In this dissertation, we investigate model identification using the homogenized energy model and adaptive control of hysteresis in smart hysteretic system, while the approaches are applicable to control of a wide class of ferroelectric, ferromagnetic and ferroelastic materials, we illustrate the ideas through the example of controlling a ferroelectric actuator. We pursue the problem of hysteresis control through two complimentary approaches: linear adaptive control using an inverse compensator and nonlinear adaptive control. Inverse control is a fundamental approach to accommodate hysteresis effect by constructing a right inverse of the hysteresis. Due to the open-loop nature of inverse control, the performance of the inverse compensation is susceptible to model uncertainties and to error introduced by inexact inverse algorithms. The objective of adaptive control is to design a controller that can adjust its behavior to tolerate uncertainties or time-varying parameters. We employ the homogenized energy model to quantify the hysteresis. On the basis of the hysteresis model, we propose an adaptive control framework by combining inverse compensation with adaptive control techniques, and investigate the parameter identification methods for the hysteresis model. We prove the asymptotic tracking property of the proposed adaptive inverse control algorithm, discuss the issue of parameters convergence and illustrate the performance of the proposed control method through simulations. Adaptive nonlinear control is a more challenging task and has received increasing attention in recent years. The challenge addressed here is how to fuse hysteresis models with available adaptive control techniques to have the basic requirement of stability of the system. In this dissertation, an adaptive variable structure control approach, serving as an illustration, is fused with the homogenized energy model without constructing a hysteresis inverse. The global stability of the system and tracking a desire trajectory to a certain precision are achieved under certain conditions. Simulations are performed on an unstable nonlinear system. The purpose of exploring new avenues to fuse the model of hysteresis nonlinearities with the available adaptive controller designs without constructing a hysteresis inverse is achieved and illustrated with the promising simulation results. This provides a step toward the development of a general nonlinear adaptive control framework for hysteretic systems.
An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix
(2007-03-09) Chanchana, Prakash; Carl D. Meyer, Committee Chair; Ernie L. Stitzinger, Committee Member; Zhilin Li, Committee Member; Min Kang, Committee Member
We present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz's formula with a special inverse iteration algorithm discussed in [10, Linear Algebra Appl., 15 (1976), pp 235-242]. Numerical experiments demonstrate that our algorithm is able to compute the Perron root accurately and faster than other well known algorithms; in particular, when the size of the matrix is large. The proof of convergence of our algorithm is also presented.
Analysis and Validation of Three-dimensional Models for Corneal Topography from Optical Coherence Tomography Point Cloud Data.
(2020-08-07) Mendlow, Micaela Rose; Mansoor Haider, Chair; Ralph Smith, Member; David Crouse, Graduate School Representative; Hien Tran, Member; Eric Buckland, External; Alen Alexanderian, Member
Analysis of Fluid Flow Models with Biological Applications.
(2018-11-02) Noorman, Marcella Jo; Harvey Banks, Co-Chair; Lorena Bociu, Co-Chair; Eric Chi, Graduate School Representative; Stephen Campbell, Member; Hien Tran, Member
Analysis of Numerical Methods for Fault Detection and Model Identification in Linear Systems with Delays
(2003-09-19) Drake, Kimberly J; Steve Campbell, Committee Chair
Recently an approach for multi-model identification and failure detection in the presence of bounded energy noise over finite time intervals has been introduced. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test. This approach has several advantages; but, as presented, observation over the full time interval was required before a decision could be made. We develop an algorithm which modifies this approach to permit early decision making with the hyperplane test. In addition, we extend this approach to handle problems that include delays. The original method requires the formulation and solution of an optimal control problem. We approach these problems in three ways. The first is through the Method of Steps, reformulating the system without delays so that we might apply existing theory with modifications. Also, we approximate the delayed systems using splines and central differences, eliminating the delay so that existing theory will apply. Approximations allow for more complicated models than the Method of Steps; however, the Method of Steps is a true solution, rather than an approximate one. Thus, solutions using the Method of Steps serve as a basis of comparison and verification of the approximate methods.
Analysis of Thermal Conductivity in Composite Adhesives
(2001-08-08) Bihari, Kathleen L.; H. T. Banks, Chair; K. Ito, Member; H. T. Tran, Member; J.-P. Fouque, Member
Thermally conductive composite adhesives are desirable in many industrial applications, including computers, microelectronics, machinery and appliances. These composite adhesives are formed when a filler particle of high conductivity is added to a base adhesive. Typically, adhesives are poor thermal conductors. Experimentally only small improvements in the thermal properties of the composite adhesives over the base adhesives have been observed. A thorough understanding of heat transfer through a composite adhesive would aid in the design of a thermally conductive composite adhesive that has the desired thermal properties.In this work, we study design methodologies for thermally conductive composite adhesives. We present a three dimensional model for heat transfer through a composite adhesive based on its composition and on the experimental method for measuring its thermal properties. For proof of concept, we reduce our model to a two dimensional model. We present numerical solutions to our two dimensional model based on a composite silicone and investigate the effect of the particle geometry on the heat flow through this composite. We also present homogenization theory as a tool for computing the "effective thermal conductivity" of a composite material.We prove existence, uniqueness and continuous dependence theorems for our two dimensional model. We formulate a parameter estimation problem for the two dimensional model and present numerical results. We first estimate the thermal conductivity parameters as constants, and then use a probability based approach to estimate the parameters as realizations of random variables. A theoretical framework for the probability based approach is outlined.Based on the results of the parameter estimation problem, we are led to formally derive sensitivity equations for our system. We investigate the sensitivity of our composite silicone with respect to the thermal conductivity of both the base silicone polymer and the filler particles. Numerical results of this investigation are also presented.
An Analytical and Numerical Study of a Class of Nonlinear Evolutionary PDEs.
(2013-08-20) Pendleton, Terrance Lamar; Alina Chertock, Chair; Roby Sawyers, Graduate School Representative; Michael Shearer, Member; Pierre Gremaud, Member; Mark Hoefer, Member
An Analytical and Numerical Study of Granular Flows in Hoppers
(2000-11-09) Matthews, John V. III; Pierre A. Gremaud, Chair; C. T. Kelley, Member; M. Shearer, Member; D. G. Schaeffer, Member
This work investigates the characteristics of a steady state flow of granular material,under the influence of gravity, in two and three dimensional hoppers of simple geometry.Simulations of such flows are of particular interest to various industries, such as the foodand mining industries, where the handling of large quantities of granular materials in hop-persand silos is routine. While understanding and simulation of time-dependent phenomenaare the ultimate goals in this field, those phenomena are still poorly understood and thustheir study is beyond the scope of this research. It has been observed that steady flowscan provide reasonable approximations, and the corresponding steady state model has con-sequentlybeen the focus of a great deal of research. Historically, these steady state modelshave been approached using only smooth radial fields, and even today most practical hop-perdesign uses these fields as their basis. Our work represents the first time that qualitynumerical methods have been brought to bear on the model equations in their original form,without assuming smoothness of the resulting fields. Two different, yet related, models forstress/velocity consisting of systems of hyperbolic conservation laws and algebraic relationsare considered and discussed. The radial stress and velocity fields, and the stability of thosefields, are studied briefly with both analytical and numerical results presented. More im-portantly,a Runge-Kutta Discontinuous Galerkin method is implemented and applied tovarious boundary value problems involving perturbed stress and velocity fields arising fromdiscontinuous changes in parameters such as hopper wall angle or hopper wall friction.
An Application of a Reduced Order Computational Methodology for Eddy Current Based Nondestructive Evaluation Techniques
(2001-06-11) Joyner, Michele Lynn; H.T. Banks, Chair; H.T. Tran, Member; Pierre A. Gremaud, Member; Kazufumi Ito, Member
In the field of nondestructive evaluation, new and improved techniques are constantly being sought to facilitate the detection of hidden corrosion and flaws in structures such as airplanes and pipelines. In this dissertation, we explore the feasibility of detecting such damages by application of an eddy current based technique and reduced order modeling. We begin by developing a model for a specific eddy current method in which we make some simplifying assumptions reducing the three-dimensional problem to a two-dimensional problem. (We do this for proof-of-concept.) Theoretical results are then presented which establish the existence and uniqueness of solutions as well as continuous dependence of the solution on the parameters which represent the damage. We further discuss theoretical issues concerning the least squares parameter estimation problem used in identifying the geometry of the damage. To solve the identification problem, an optimization algorithm is employed which requires solving the forward problem numerous times. To implement these methods in a practical setting, the forward algorithm must be solved with extremely fast and accurate solution methods. Therefore in constructing these computational methods, we employ reduced order Proper Orthogonal Decomposition (POD) techniques which allows one to create a set of basis elements spanning a data set consisting of either numerical simulations or experimental data. We investigate two different approaches in forming the POD approximation, a POD/Galerkin technique and a POD/Interpolation technique. We examine the error in the approximation using one approach versus the other as well as present results of the parameter estimation problem for both techniques. Finally, results of the parameter estimation problem are given using both simulated data with relative noise added as well as experimental data obtained using a giant magnetoresistive (GMR) sensor. The experimental results are based on successfully using actual experimental data to form the POD basis elements (instead of numerical simulations) thus illustrating the effectiveness of this method on a wide range of applications. In both instances the methods are found to be efficient and robust. Furthermore, the methods were fast; our findings suggest a significant reduction in computational time.

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Browsing Dissertations by Discipline "Applied Mathematics"