Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Applied sciences (7)
- Pure sciences (6)
- Biological sciences (2)
- Flexible wings (2)
- Heat transfer (2)
-
- Skin (2)
- Spectral Element Method (2)
- Thermal deformation (2)
- Thin films (2)
- Ultrashort-pulsed lasers (2)
- A Comparison of Corporations (1)
- Affymetrix microarray images (1)
- Akaike Information Criterion (ATC) (1)
- Algorithms (1)
- Applied math (1)
- Applied mathematics (1)
- Axiom of Choice (1)
- BMB (1)
- Bagging Classifier (1)
- Ballet (1)
- Bicluster Analysis (1)
- Blood vessels (1)
- Born approximation (1)
- Brain Connectivity (1)
- Cantilever beams (1)
- Centrality (1)
- Chemistry (1)
- Classification (1)
- Coefficient of Determination (R2) (1)
- Compact finite difference (1)
- Publication Year
- Publication Type
Articles 1 - 30 of 35
Full-Text Articles in Physical Sciences and Mathematics
Glucose Regulation Using An Intelligent Pid Controller, Parker Willmon
Glucose Regulation Using An Intelligent Pid Controller, Parker Willmon
Mathematics Senior Capstone Papers
Type 1 diabetes is a condition characterized by a lack of insulin production. This lack of insulin causes glucose concentration in the blood to increase after meals. In order to maintain blood glucose levels, diabetics must inject insulin using needles or an insulin pump. Additionally, the lack of insulin can cause glucose levels to decrease overnight. This project uses a proportional integral derivative (PID) controller to modify the rate of insulin and glucagon infusion when glucose levels are increasing or decreasing, respectively. A system of 13 differential equations were used to anticipate changes in glucose concentration as insulin and glucagon …
Predicting And Comparing The Stock Value Of Chick-Fil-A, Mark Yates
Predicting And Comparing The Stock Value Of Chick-Fil-A, Mark Yates
Mathematics Senior Capstone Papers
This project focuses on estimating the stock value of Chick-fil-A as if it were a publicly traded company using a comparable analysis method or CAM. We begin by obtaining financial information from Chick-fil-A as well as the amount of locations there are chain-wide. Next we find two publicly traded fast food companies, one that is larger, and one that is smaller than Chick-fil-A and obtain the same information from them. The idea is that Chick-fil-A will lie between theses two companies and we can use the CAM to estimate their stock value. The CAM gives us a multiple of the …
The Axiom Of Choice And Related Topics, Bryan Mccormick
The Axiom Of Choice And Related Topics, Bryan Mccormick
Mathematics Senior Capstone Papers
In this paper I will be discussing the Axiom of Choice and its equivalent statements. The Axiom of Choice is an axiom of Zermelo-Fraenkel set theory that states that given a collection of non-empty sets, there exists a choice function which selects one element from each set to form a new set. The equivalents of the Axiom of Choice that I will be discussing include Zorn’s Lemma, which states that a partially ordered set with every chain being bounded above contains a maximal element, and the Well-Ordering Theorem, which states that every set has a well ordering. In addition to …
Shallow Water Equations And Floor Topography Affect On Sea Surface, Chase Jones
Shallow Water Equations And Floor Topography Affect On Sea Surface, Chase Jones
Mathematics Senior Capstone Papers
For this research project, we have been doing research on the shallow water equations: a set of hyperbolic partial differential equations. These equations exist as a set of three primary equations [2]. However, there is another version of the shallow water equations called the Saint Venant’s equations. These equations are similar to the standard shallow water equations, but these equations have been reduced to one-dimension. The primary goal of our research has been to investigate the behavior and mathematical construction of the Saint Venant’s equations and model these equations using COMSOL. Regardless of the equation type, standard or Saint Venant’s, …
A Tutorial Of The Immersed Interface Method, Sheng Xu
A Tutorial Of The Immersed Interface Method, Sheng Xu
Science Seminars
The immersed interface method is a computational methodology to solve differential equations with non-smooth solutions across interfaces. In this talk, Dr. Xu will use a simple example to demonstrate the main ingredients and features of this method. He will then present the application of the method to the simulation of fluid flows and make the connection of the application with the simple example.
This talk is a tutorial of the method for undergraduate students.
Come at 3:30pm for refreshments, speaker at 4:00pm
A Framework Of Multi-Dimensional And Multi-Scale Modeling With Applications, Zilong Li
A Framework Of Multi-Dimensional And Multi-Scale Modeling With Applications, Zilong Li
Doctoral Dissertations
In this dissertation, a framework for multi-dimensional and multi-scale modeling is proposed. The essential idea is based on oriented space curves, which can be represented as a 3D slender object or 1D step parameters. SMILES and Masks provide functionalities that extend slender objects into branched and other objects. We treat the conversion between 1D, 2D, 3D, and 4D representations as data unification. A mathematical analysis of different methods applied to helices (a special type of space curves) is also provided. Computational implementation utilizes Model-ViewController design principles to integrate data unification with graphical visualizations to create a dashboard. Applications of multi-dimensional …
Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa
Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa
Doctoral Dissertations
Ultrasonography is considered a relatively safe option for the diagnosis of benign and malignant cancer lesions due to the low-energy sound waves used. However, the visual interpretation of the ultrasound images is time-consuming and usually has high false alerts due to speckle noise. Improved methods of collection image-based data have been proposed to reduce noise in the images; however, this has proved not to solve the problem due to the complex nature of images and the exponential growth of biomedical datasets. Secondly, the target class in real-world biomedical datasets, that is the focus of interest of a biopsy, is usually …
Predicting Win Rates In Competitive Overwatchtm, Andrea Sibley
Predicting Win Rates In Competitive Overwatchtm, Andrea Sibley
Mathematics Senior Capstone Papers
OverwatchTM is a video game published by Blizzard Entertainment R where two teams comprised of six people each compete against one another to accomplish a specific goal. The goal of each game is dependent on which map is being played. The maps are divided into four categories: Assault, Escort, Control, and Hybrid. A data set comprised of 3000 games of competitive OverwatchTM is used to determine how likely a team is to win their match. The factors used to determine the likelihood of winning are the map type and the skill ranking for each team. The data set is pre-processed …
The Mathematical Modeling Of Ballet, Kendall Gibson
The Mathematical Modeling Of Ballet, Kendall Gibson
Mathematics Senior Capstone Papers
This project aims to analyze the connections between ballet and mathematics. Specifically, this project focuses on analyzing the three-dimensional surfaces created as a dancer performs ballet choreography. The primary goal is to use a Vicon motion capture system in conjunction with MATLAB to model the three-dimensional lines and surfaces created by a dancer’s legs as she performs specific ballet movements. The movements used for this experiment were a pique turn and a rond de jambe. The data was collected using sensors to create objects in Vicon to record the position of the ankle, knee, and hip of the working leg …
Spatiotemporal Subspace Feature Tracking By Mining Discriminatory Characteristics, Richard D. Appiah
Spatiotemporal Subspace Feature Tracking By Mining Discriminatory Characteristics, Richard D. Appiah
Doctoral Dissertations
Recent advancements in data collection technologies have made it possible to collect heterogeneous data at complex levels of abstraction, and at an alarming pace and volume. Data mining, and most recently data science seek to discover hidden patterns and insights from these data by employing a variety of knowledge discovery techniques. At the core of these techniques is the selection and use of features, variables or properties upon which the data were acquired to facilitate effective data modeling. Selecting relevant features in data modeling is critical to ensure an overall model accuracy and optimal predictive performance of future effects. The …
Generalized Partial Directed Coherence And Centrality Measures In Brain Networks For Epileptogenic Focus Localization, Joshua Aaron Adkinson
Generalized Partial Directed Coherence And Centrality Measures In Brain Networks For Epileptogenic Focus Localization, Joshua Aaron Adkinson
Doctoral Dissertations
Accurate epileptogenic focus localization is required prior to surgical resection of brain tissue for treatment of patients with intractable temporal lobe epilepsy, a clinical need that is partially fulfilled to date through a subjective, and at times inconclusive, evaluation of the recorded electroencephalogram (EEG). Using brain connectivity analysis, patterns of causal interactions between brain regions were derived from multichannel EEG of 127 seizures in nine patients with focal, temporal lobe epilepsy (TLE). The statistically significant directed interactions in the reconstructed brain networks were estimated from three second intracranial multi-electrode EEG segments using the Generalized Partial Directed Coherence (GPDC) and validated …
Thermal Analysis In A Triple-Layered Skin Structure With Embedded Vasculature, Tumor, And Gold Nanoshells, Casey O. Orndorff
Thermal Analysis In A Triple-Layered Skin Structure With Embedded Vasculature, Tumor, And Gold Nanoshells, Casey O. Orndorff
Doctoral Dissertations
In hyperthermia skin cancer treatment, the objective is to control laser heating of the tumor (target temperatures of 42-46 °C) so that the temperatures of the normal tissue surrounding the tumor remains low enough not to damage the normal tissue. However, obtaining accurate temperature distributions in living tissue related to hyperthermia skin cancer treatment without using an intruding sensor is a challenge. The objective of this dissertation research is to develop a mathematical model that can accurately predict the temperature distribution in the tumor region and surrounding normal tissue induced by laser irradiation. The model is based on a modified …
Computational Micro-Flow With Spectral Element Method And High Reynolds Number Flow With Discontinuous Galerkin Finite Element Method, Haibo Zhang
Doctoral Dissertations
In this dissertation, two numerical methods with high order accuracy, Spectral Element Method (SEM) and Discontinuous Galerkin Finite Element Method (DG-FEM), are chosen to solve problems in Computational Fluid Dynamics (CFD). The merits of these two methods will be discussed and utilized in different kinds of CFD problems. The simulations of the micro-flow systems with complex geometries and physical applications will be presented by SEM. Moreover, the numerical solutions for the Hyperbolic Flow will be obtained by DG-FEM. By solving problems with these two methods, the differences between them will be discussed as well.
Compressible Navier-Stokes equations with Electro-osmosis body …
Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine
Sensitivity Of Mixed Models To Computational Algorithms Of Time Series Data, Gunaime Nevine
Doctoral Dissertations
Statistical analysis is influenced by implementation of the algorithms used to execute the computations associated with various statistical techniques. Over many years; very important criteria for model comparison has been studied and examined, and two algorithms on a single dataset have been performed numerous times. The goal of this research is not comparing two or more models on one dataset, but comparing models with numerical algorithms that have been used to solve them on the same dataset.
In this research, different models have been broadly applied in modeling and their contrasting which are affected by the numerical algorithms in different …
Analysis Of A Mathematical Model For The Heave Motion Of A Micro Aerial Vehicle With Flexible Wings Having Non-Local Damping Effects, Jonathan B. Walters
Analysis Of A Mathematical Model For The Heave Motion Of A Micro Aerial Vehicle With Flexible Wings Having Non-Local Damping Effects, Jonathan B. Walters
Doctoral Dissertations
In this work we analyze a one dimensional model for a flexible wing micro aerial vehicle which can undergo heaving motion. The vehicle is modeled with a non-local type of internal damping known as spatial hysteresis as well as viscous external damping. We present a rigorous theoretical analysis of the model proving that the linearly approximated system is well-posed and the first order feedback system operators generate exponentially stable C0–semigroups.
Furthermore, we present numerical simulations of control designs used on the linearly approximated model to control the associated nonlinear model in two different strategies. The first strategy used to …
Numerical Solutions For Problems With Complex Physics In Complex Geometry, Yifan Wang
Numerical Solutions For Problems With Complex Physics In Complex Geometry, Yifan Wang
Doctoral Dissertations
In this dissertation, two high order accurate numerical methods, Spectral Element Method (SEM) and Discontinuous Galerkin method (DG), are discussed and investigated. The advantages of both methods and their applicable areas are studied. Particular problems in complex geometry with complex physics are investigated and their high order accurate numerical solutions obtained by using either SEM or DG are presented. Furthermore, the Smoothed Particle Hydrodynamics (SPH) (a mesh-free weighted interpolation method) is implemented on graphics processing unit (GPU). Some numerical simulations of the complex flow with a free surface are presented and discussed to show the advantages of SPH method in …
Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey
Modeling And Control Of Nanoparticle Bloodstream Concentration For Cancer Therapies, Scarlett S. Bracey
Doctoral Dissertations
Currently, the most commonly used treatments for cancerous tumors (chemotherapy, radiation, etc.) have almost no method of monitoring the administration of the treatment for adverse effects in real time. Without any real time feedback or control, treatment becomes a "guess and check" method with no way of predicting the effects of the drugs based on the actual bioavailability to the patient's body. One particular drug may be effective for one patient, yet provide no benefit to another. Doctors and scientists do not routinely attempt to quantifiably explain this discrepancy. In this work, mathematical modeling and analysis techniques are joined together …
Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii
Generalized Finite-Difference Time-Domain Schemes For Solving Nonlinear Schrödinger Equations, Frederick Ira Moxley Iii
Doctoral Dissertations
The nonlinear Schrödinger equation (NLSE) is one of the most widely applicable equations in physical science, and characterizes nonlinear dispersive waves, optics, water waves, and the dynamics of molecules. The NLSE satisfies many mathematical conservation laws. Moreover, due to the nonlinearity, the NLSE often requires a numerical solution, which also satisfies the conservation laws. Some of the more popular numerical methods for solving the NLSE include the finite difference, finite element, and spectral methods such as the pseudospectral, split-step with Fourier transform, and integrating factor coupled with a Fourier transform. With regard to the finite difference and finite element methods, …
Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings
Exploration Of Aqueous Interfaces And Their Effect On Ion Behavior, Oneka T. Cummings
Doctoral Dissertations
An in-depth understanding of a wide range of physical, chemical, atmospheric and biological processes can only be achieved after the structure and dynamics of interfaces and the interfacial behavior of aqueous species, such as ions, are thoroughly studied and understood. This dissertation describes computational studies conducted to gain a more comprehensive understanding of such interfaces and the behavior of ions in the bulk and interfacial regions of the (1) air/water interface, and (2) alkane/water interfaces.
At the air/water interface the effect of counterion (sodium cations) charge and the influence of ion pairing on anion (chloride) propensity for the air/water interface …
A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi
A Mathematical Model And Numerical Method For Thermoelectric Dna Sequencing, Liwei Shi
Doctoral Dissertations
DNA sequencing is the process of determining the precise order of nucleotide bases, adenine, guanine, cytosine, and thymine within a DNA molecule. It includes any method or technology that is used to determine the order of the four bases in a strand of DNA. The advent of rapid DNA sequencing methods has greatly accelerated biological and medical research and discovery. Thermoelectric DNA sequencing is a novel method to sequence DNA by measuring the heat that is released when DNA polymerase inserts a deoxyribonucleoside triphosphate into a growing DNA strand. The thermoelectric device for this project is composed of four parts: …
New Microarray Image Segmentation Using Segmentation Based Contours Method, Yuan Cheng
New Microarray Image Segmentation Using Segmentation Based Contours Method, Yuan Cheng
Doctoral Dissertations
The goal of the research developed in this dissertation is to develop a more accurate segmentation method for Affymetrix microarray images. The Affymetrix microarray biotechnologies have become increasingly important in the biomedical research field. Affymetrix microarray images are widely used in disease diagnostics and disease control. They are capable of monitoring the expression levels of thousands of genes simultaneously. Hence, scientists can get a deep understanding on genomic regulation, interaction and expression by using such tools.
We also introduce a novel Affymetrix microarray image simulation model and how the Affymetrix microarray image is simulated by using this model. This simulation …
The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown
The Search For An Optimal Means Of Determining The Minmax Control Parameter Using Sensitivity Analysis, John Teye Brown
Doctoral Dissertations
The use of computational methods for design and simulation of control systems allows for a cost-effective trial and error approach. In this work, we are concerned with the robust, real-time control of physical systems whose state space is infinite-dimensional. Such systems are known as Distributed Parameter Systems (DPS). A body whose state is heterogeneous is a distributed parameter. In particular, this work focuses on DPS systems that are governed by linear Partial Differential Equations, such as the heat equation. We specifically focus on the MinMax controller, which is regarded as being a very robust controller. The mathematical formulation of the …
Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao
Mathematical Modeling Of Pipeline Features For Robotic Inspection, Yang Gao
Doctoral Dissertations
Underground pipeline systems play an indispensable role in transporting liquids in both developed and developing countries. The associated social and economic cost to repair a pipe upon abrupt failure is often unacceptable. Regular inspection is a preventative action that aims to monitor pipe conditions, catch abnormalities and reduce the chance of undesirable surprises. Robots with CCTV video cameras have been used for decades to inspect pipelines, yielding only qualitative information. It is becoming necessary and preferable for municipalities, project managers and engineers to also quantify the 3-D geometry of underground pipe networks. Existing robots equipped specialized hardware and software algorithms …
Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon
Near-Optimal Scheduling And Decision-Making Models For Reactive And Proactive Fault Tolerance Mechanisms, Nichamon Naksinehaboon
Doctoral Dissertations
As High Performance Computing (HPC) systems increase in size to fulfill computational power demand, the chance of failure occurrences dramatically increases, resulting in potentially large amounts of lost computing time. Fault Tolerance (FT) mechanisms aim to mitigate the impact of failure occurrences to the running applications. However, the overhead of FT mechanisms increases proportionally to the HPC systems' size. Therefore, challenges arise in handling the expensive overhead of FT mechanisms while minimizing the large amount of lost computing time due to failure occurrences.
In this dissertation, a near-optimal scheduling model is built to determine when to invoke a hybrid checkpoint …
Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn
Modeling And Control For Heave Dynamics Of A Flexible Wing Micro Aerial Vehicle Distributed Parameter System, Lisa M. Kuhn
Doctoral Dissertations
In recent years, much research has been motivated by the idea of biologically-inspired flight. It is a conjecture of the United States Air Force that incorporating characteristics of biological flight into air vehicles will significantly improve the maneuverability and performance of modern aircraft. Although there are studies which involve the aerodynamics, structural dynamics, modeling, and control of flexible wing micro aerial vehicles (MAVs), issues of control and vehicular modeling as a whole are largely unexplored. Modeling with such dynamics lends itself to systems of partial differential equations (PDEs) with nonlinearities, and limited control theory is available for such systems.
In …
A Numerical Method For Studying Thermal Deformation In 3d Double-Layered Thin Films With Imperfect Interfacial Thermal Contact Exposed To Ultrashort-Pulsed Lasers, Runzhou Liu
Doctoral Dissertations
Micro heat transfer induced by Ultrashort-pulsed lasers is an important research topic in mechanical engineering and material science. In order to apply ultrashort-pulsed lasers successfully, studying the thermal deformation in double-layered thin films with imperfect thermal interfacial contact induced by ultrashort-pulsed lasers is important for preventing thermal damage. For the ultrashort-pulsed laser, the thermal damage is different from that caused by the long-pulsed lasers, and ultrafast cracks occur after heating.
This dissertation presents a new finite difference method for investigating the thermal deformation in a 3D gold-chromium thin film with imperfect interfacial thermal contact exposed to ultrashort-pulsed lasers. The method …
Improving The Accuracy Of The Generalized Fdtd-Q Scheme For Solving The Linear Time-Dependent Schrödinger Equation, James John Elliot Iii
Improving The Accuracy Of The Generalized Fdtd-Q Scheme For Solving The Linear Time-Dependent Schrödinger Equation, James John Elliot Iii
Doctoral Dissertations
This dissertation improves the accuracy of the Generalized Finite Difference Time Domain (FDTD) scheme by determining a differential operator that is capable of achieving reasonable accuracy when used to obtain even-order derivatives up to order fourteen. The Generalized FDTD scheme is an explicit, scheme used to solve the time-dependent Schrödinger equation, and being an explicit scheme, it must utilize a carefully devised ratio of the temporal step to the spatial step to maintain numerical stability. This ratio is called the mesh ratio, and the Generalized FDTD scheme allows this ratio to be significantly relaxed. As the mesh ratio increases, the …
Results In Lattices, Ortholattices, And Graphs, Jianning Su
Results In Lattices, Ortholattices, And Graphs, Jianning Su
Doctoral Dissertations
This dissertation contains two parts: lattice theory and graph theory. In the lattice theory part, we have two main subjects. First, the class of all distributive lattices is one of the most familiar classes of lattices. We introduce "π-versions" of five familiar equivalent conditions for distributivity by applying the various conditions to 3-element antichains only. We prove that they are inequivalent concepts, and characterize them via exclusion systems. A lattice L satisfies D0π, if a ✶ (b ✶ c) ≤ (a ✶ b) ✶ c for all 3-element antichains { a, b, c}. We consider …
A Numerical Method For Solving The Elliptic And Elasticity Interface Problems, Liqun Wang
A Numerical Method For Solving The Elliptic And Elasticity Interface Problems, Liqun Wang
Doctoral Dissertations
Interface problems arise when dealing with physical problems composed of different materials or of the same material at different states. Because of the irregularity along interfaces, many common numerical methods do not work, or work poorly, for interface problems. Matrix-coefficient elliptic and elasticity equations with oscillatory solutions and sharp-edged interfaces are especially complicated and challenging for most existing methods. An accurate and efficient method is desired.
In 1999, the boundary condition capturing method was proposed to deal with Poisson equations with interfaces whose variable coefficients and solutions may be discontinuous. In 2003, a weak formulation was derived. Built on previous …
Shape Reconstruction And Classification Using The Response Matrix, Wei Wang
Shape Reconstruction And Classification Using The Response Matrix, Wei Wang
Doctoral Dissertations
This dissertation presents a novel method for the inverse scattering problem for extended target. The acoustic or electromagnetic wave is scattered by the target and received by all the transducers around the target. The scattered field on all the transducers forms the response matrix which contains the information of the geometry of the target. The objective of the inverse scattering problem is to reconstruct the shape of the scatter using the Response Matrix.
There are two types of numerical methods for solving the inverse problem: the direct imaging method and the iterative method. Two direct imaging methods, MUSIC method and …