Applied Mathematics Commons^™

Theoretical Open-Loop Model Of Respiratory Mechanics In The Extremely Preterm Infant, Laura Ellwein Fix, Joseph Khoury, Russell R. Moores Jr., Lauren Linkous, Matthew Brandes, Henry J. Rozycki

Mathematics and Applied Mathematics Publications

Non-invasive ventilation is increasingly used for respiratory support in preterm infants, and is associated with a lower risk of chronic lung disease. However, this mode is often not successful in the extremely preterm infant in part due to their markedly increased chest wall compliance that does not provide enough structure against which the forces of inhalation can generate sufficient pressure. To address the continued challenge of studying treatments in this fragile population, we developed a nonlinear lumped-parameter respiratory system mechanics model of the extremely preterm infant that incorporates nonlinear lung and chest wall compliances and lung volume parameters tuned to …

Resistance Temperature Detectors In A Cryostat Refrigeration System, Kirsten Marie Manahan, Alice Callen

STAR Program Research Presentations

The Large Synoptic Survey Telescope (LSST) is a ground-based telescope that will survey the Southern sky every few nights. Located in the telescope will be a 3.2 gigapixel digital camera. To ensure proper instrumentation of the camera, there must be a monitored stable temperature. As part of my research, I assembled resistance temperature detectors and tested them to verify their reliability in measuring temperature in the camera’s cryostat refrigeration cooling system. Resistance temperature detectors function by the principle of thermal resistivity, in which their electrical resistances vary as temperature varies. Through testing, I was able to determine whether these particular …

Examples Of The Birkhoff Theorem And Its Generalizations, Charles G. Torre

Tutorials on... in 1 hour or less

In this worksheet I demonstrate three versions of Birkhoff's theorem, which is a characterization of spherically symmetric solutions of the Einstein equations. The three versions considered here correspond to taking the "Einstein equations" to be: (1) the vacuum Einstein equations; (2) the Einstein equations with a cosmological constant (3) the Einstein-Maxwell equations. I will restrict my attention to 4-dimensional spacetimes.

How To Make Tetrads, Charles G. Torre

How to... in 10 minutes or less

This is a worksheet which demonstrates tools for creating orthonormal and null tetrads for a given spacetime.

Applied Mathematical Programming, Man-Keun Kim, Bruce A. Mccarl, Thomas H. Spreen

Textbooks

This book is intended to both serve as a reference guide and a text for a course on Applied Mathematical Programming for upper undergraduate and Master level students in Economics, Applied Economics, Agricultural and Resource Economics, and Management; primarily based on McCarl and Spreen (2013). The material presented in McCarl and Spreen (2013) concentrates upon conceptual issues, problem formulation, computerized problem solution, and results interpretation; it is designed for the advanced readers who are familiar with mathematical economics including linear and matrix algebra and also with advanced modeling skills. Upper level undergraduate and/or Master students may not be beneficial from …

Sequential Probing With A Random Start, Joshua Miller

HMC Senior Theses

Processing user requests quickly requires not only fast servers, but also demands methods to quickly locate idle servers to process those requests. Methods of finding idle servers are analogous to open addressing in hash tables, but with the key difference that servers may return to an idle state after having been busy rather than staying busy. Probing sequences for open addressing are well-studied, but algorithms for locating idle servers are less understood. We investigate sequential probing with a random start as a method for finding idle servers, especially in cases of heavy traffic. We present a procedure for finding the …

Recurrent Neural Networks And Their Applications To Rna Secondary Structure Inference, Devin Willmott

Theses and Dissertations--Mathematics

Recurrent neural networks (RNNs) are state of the art sequential machine learning tools, but have difficulty learning sequences with long-range dependencies due to the exponential growth or decay of gradients backpropagated through the RNN. Some methods overcome this problem by modifying the standard RNN architecure to force the recurrent weight matrix W to remain orthogonal throughout training. The first half of this thesis presents a novel orthogonal RNN architecture that enforces orthogonality of W by parametrizing with a skew-symmetric matrix via the Cayley transform. We present rules for backpropagation through the Cayley transform, show how to deal with the Cayley …

Symmetric Criticality In General Relativity, Charles G. Torre

Research Vignettes

In this worksheet I explore the local Lagrangian version of the Principle of Symmetric Criticality (PSC) due to Anderson, Fels, and Torre], which asserts the commutativity of the processes (i) of symmetry reduction (for finding group-invariant fields) and (ii) forming Euler-Lagrange equations. There are two obstructions to PSC, which I will call the Lie algebra obstruction and the isotropy obstruction. In this worksheet I will illustrate these obstructions in the General Theory of Relativity.

Modeling The Disappearance Of The Neanderthals Using Concepts Of Population Dynamics And Ecology, Michael F. Roberts, Stephen E. Bricher

Faculty Publications

Current hypotheses regarding the disappearance of Neanderthals (NEA) in Europe fall into two main categories: climate change, and competition. Here we review current research and existing mathematical models that deal with this question, and we propose an approach that incorporates and permits the investigation of the current hypotheses. We have developed a set of differential equations that model population dynamics of anatomically modern humans (AMH) and NEA, their ecological relations to prey species, and their mutual interactions. The model allows investigators to explore each of the two main categories or combinations of both, as well as various forms of competition …

Random Walks On Simple Two-Dimensional Manifolds, Tom Eichlersmith

Departmental Honors Projects

A C++ implementation of random walks is constructed with examples for the plane, sphere, and torus included. This package is available publicly, and can be expanded to different situations on the included surfaces as well as other surfaces. The random walks are studied by measuring how long they take to reach a pre-defined escape region on the surface. These escape regions and their interaction with the surface are what affect the behavior of the random walks the most.

Modeling Public Opinion, Arden Baxter

Honors Program Theses

The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.

Existing And Regularity Of Minimizers For Nonlocal Energy Functionals, Mikil D. Foss, Petronela Radu, Cory Wright

Department of Mathematics: Faculty Publications

In this paper, we consider minimizers for nonlocal energy functionals generalizing elastic energies that are connected with the theory of peridynamics [19] or nonlocal diffusion models [1]. We derive nonlocal versions of the Euler-Lagrange equations under two sets of growth assumptions for the integrand. Existence of minimizers is shown for integrands with joint convexity (in the function and nonlocal gradient components). By using the convolution structure, we show regularity of solutions for certain Euler-Lagrange equations. No growth assumptions are needed for the existence and regularity of minimizers results, in contrast with the classical theory.

Computing Eigenmodes Of Elliptic Operators On Manifolds Using Radial Basis Functions, Vladimir Delengov

CGU Theses & Dissertations

In this work, a numerical approach based on meshless methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data points. We derive expressions for such matrices for the Laplace-Beltrami operator via so-called Reilly’s formulas and use them to solve the respective eigenvalue problem. Numerical studies of proposed methods are performed in order to demonstrate convergence on simple examples of one-dimensional curves and two-dimensional surfaces.

Sdes, Jumps And Estimates, Jose L. Menaldi

Mathematics Faculty Research Publications

Long Title: Stochastic Ordinary Differential Equations with Jumps: Theory and Estimates. Chapters: Stochastic Integrals - Initial Approach to SDEs - Estimates of SDEs - Other Formulations of SDEs - SDEs with Reflection - PDE Connections.

The Study Of Non-Newtonian Nanofluid With Hall And Ion Slip Effects On Peristaltically Induced Motion In A Non-Uniform Channel, Sara I. Abdelsalam, M. M. Bhatti

Basic Science Engineering

In this study, we considered the unsteady peristaltic motion of a non-Newtonian nanofluid under the influence of a magnetic field and Hall currents. The simultaneous effects of ion slip and chemical reaction were also taken into consideration. The flow problem was suggested on the basis of the continuity, thermal energy, linear momentum, and nanoparticle concentration, which were further reduced with the help of Ohm's law. Mathematical modelling was executed using the lubrication approach. The resulting highly nonlinear partial differential equations were solved semi-analytically using the homotopy perturbation technique. The impacts of all the pertinent parameters were investigated mathematically and graphically. …

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

Monotonicity Of Set-Valued Mappings And Full Stability Of General Parametrical Variational Systems, Dat Pham

Wayne State University Dissertations

The dissertation introduces and studies the notions of Lipschitzian and Holderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly variable sufficient conditions for, such full stability properties under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli.

Iterative Matrix Factorization Method For Social Media Data Location Prediction, Natchanon Suaysom

HMC Senior Theses

Since some of the location of where the users posted their tweets collected by social media company have varied accuracy, and some are missing. We want to use those tweets with highest accuracy to help fill in the data of those tweets with incomplete information. To test our algorithm, we used the sets of social media data from a city, we separated them into training sets, where we know all the information, and the testing sets, where we intentionally pretend to not know the location. One prediction method that was used in (Dukler, Han and Wang, 2016) requires appending one-hot …

Borrowing Capacity, Financial Instability, And Contagion: Case Study Of The U.S. Subprime Mortgage Crisis, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We use the case of the 2007 United States subprime mortgage crisis to investigate the impact of borrowing capacity limitations on financial instability and contagion. We divide an economy into agents that interact via flow of funds and express the financial instability level of each agent as a function of time derivatives of its wealth, cash inflows, and borrowing capacity. We show that among these factors, the borrowing capacity, which is determined by other economic constraints, has the largest impact on financial instability. It is suggested that borrowing capacity limitations could even cause contagion through feedback loop formed by flow …

Investigation Of Volatile Organic Compounds (Vocs) Detected At Vapor Intrusion Sites, Mohammadyousef Roghani

Theses and Dissertations--Civil Engineering

This dissertation investigates unexplained vapor intrusion field data sets that have been observed at hazardous waste sites, including: 1) non-linear soil gas concentration trends between the VOC source (i.e. contaminated groundwater plume) and the ground surface; and, 2) alternative pathways that serve as entry points for vapors to infiltrate into buildings and serve to increase VOC exposure risks as compared to the classic vapor intrusion model, which primarily considered foundation cracks as the route for vapor entry. The overall hypothesis of this research is that theoretical knowledge of fate and transport processes can be systematically applied to vapor intrusion field …

Climate Modeling, Outgoing Longwave Radiation, And Tropical Cyclone Forecasting, Thomas Rechtman

Honors Undergraduate Theses

Climate modeling and tropical cyclone forecasting are two significant is- sues that are continuously being improved upon for more accurate weather forecasting and preparedness. In this thesis, we have studied three climate models and formulated a new model with a view to determine the outgoing longwave radiation (OLR) budget at the top of the atmosphere (TOA) as ob- served by the National Oceanic and Atmospheric Administration’s (NOAA) satellite based Advanced Very High Resolution Radiometer (AVHRR). In 2006, Karnauskas proposed the African meridional OLR as an Atlantic hur- ricane predictor, the relation was further proven in 2016 by Karnauskas and Li …

Mathematical Models Of Mosquito Populations, Hanna Reed

Honors Undergraduate Theses

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting …

Computational Methods In Civil Engineering, Nir Krakauer

Open Educational Resources

No abstract provided.

Optimal Supply Delivery Under Military Specific Constraints, Talena Fletcher

College of Graduate Studies: Theses & Dissertations

Through-out military history, the need to safely and effectively allocate resources to various military operations was a task of extreme importance. Satisfying the needs of multiple consumers by optimally pairing with appropriate suppliers falls into the category of vehicle routing problems (VRP), which has been intensively studied over the years. In general, finding the optimal solution to VRP is known to be NP-hard. The proposed solutions rely on mathematical programming and the size of the problems that can be optimally solved is typically limited. In military settings, balancing the needs of multiple consumers with the current operational environment has always …

Blow Up Solution Of Bose-Einstein Condensates With Anisotropic Trapping Potential And Rotation, Christopher Leonard

College of Graduate Studies: Theses & Dissertations

In this paper we will analyze a nonlinear Schrodinger equation with quadratic anisotropic trapping potential used to describe a Bose-Einstein condensate. We will find sufficient condition for the global existence of the solution and for the blow up result using physical properties associated to the equation such as the mass, energy, and angular momentum along with some other identities related to the equation. We will finish the thesis with showing some graphical representations describing the solution of the equation.

Investigation Of Toppling Ball Flight In American Football With A Mechanical Field-Goal Kicker, Chase M Pfeifer, Timothy J. Gay, Jeff A. Hawks, Shane Farritor, Judith M. Burnfield

Department of Mechanical and Materials Engineering: Faculty Publications

A mechanical field-goal kicking machine was used to investigate toppling ball flight in American football place-kicking, eliminating a number of uncontrollable impact variables present with a human kicker. Ball flight trajectories were recorded using a triangulation-based projectile tracking system to account for the football’s 3-dimensional position during flight as well as initial launch conditions. The football flights were described using kinematic equations relating to projectile motion including stagnant air drag and were compared to measured trajectories as well as projectile motion equations that exclude stagnant air drag. Measured football flight range deviations from the non-drag equations of projectile motion corresponded …

Material Thermal Property Estimation Of Fibrous Insulation: Heat Transfer Modeling And The Continuous Genetic Algorithm, Elora Frye

Theses and Dissertations

Material thermal properties are highly sought after to better understand the performance of a material under particular conditions. As new materials are created, their physical properties will determine their performance for various applications. These properties have been estimated using many techniques including experimental testing, numerical modeling, and a combination of both. Existing methods can be time consuming, thus, a time-efficient and precise method to estimate these thermal properties was desired. A one-dimensional finite difference numerical model was developed to replicate the heat transfer through an experimental apparatus. A combination of this numerical model and the Continuous Genetic Algorithm optimization technique …

Developing A Cyberterrorism Policy: Incorporating Individual Values, Osama Bassam J. Rabie

Theses and Dissertations

Preventing cyberterrorism is becoming a necessity for individuals, organizations, and governments. However, current policies focus on technical and managerial aspects without asking for experts and non-experts values and preferences for preventing cyberterrorism. This study employs value focused thinking and public value forum to bare strategic measures and alternatives for complex policy decisions for preventing cyberterrorism. The strategic measures and alternatives are per socio-technical process.

Data-Driven Predictive Framework For Modeling Complex Multi-Physics Engineering Applications, Arturo Schiaffino Bustamante

Open Access Theses & Dissertations

Computational models are often encountered in multiple engineering application, such as structural design, material science, heat transfer and fluid dynamics. These simulations offer the engineers the capability of understanding complex physical situations before putting them to practice, either through experimentation or prototyping. The current advances in computational sciences, hardware architecture, software development and big data technology, have allowed the construction of sturdy predicting frameworks for analyzing a wide array of natural phenomena across different disciplines, either through the implementation of statistical methods, such as big data, and uncertainty quantification, or through high performance computing of a numerical model. The objective …

Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy

Articles

The orientation and activity of antibodies immobilized on solid surfaces are of direct relevance to many immunosensing applications. We therefore investigate a mathematical model which estimates the fraction of antibodies which are available for reaction in a randomly adsorbed sample. Numerical simulations are presented which highlight the separate effects of antibody orientation, accessibility and loss of binding ability on the amount of captured antigen. The assay response can then be expressed as a function of total antibody density and used for optimizing the surface coverage strategy under various conditions.