Applied Mathematics Commons^™

Population Projection And Habitat Preference Modeling Of The Endangered James Spinymussel (Pleurobema Collina), Marisa Draper

Senior Honors Projects, 2010-2019

The James Spinymussel (Pleurobema collina) is an endangered mussel species at the top of Virginia’s conservation list. The James Spinymussel plays a critical role in the environment by filtering and cleaning stream water while providing shelter and food for macroinvertebrates; however, conservation efforts are complicated by the mussels’ burrowing behavior, camouflage, and complex life cycle. The goals of the research conducted were to estimate detection probabilities that could be used to predict species presence and facilitate field work, and to track individually marked mussels to test for habitat preferences. Using existing literature and mark-recapture field data, these goals were accomplished …

Spontaneous Calcium Release In Cardiac Myocytes: Store Overload And Electrical Dynamics, Amanda M. Alexander, Erin K. Denardo, Eric Frazier Iii, Michael Mccauley, Nicholas Rojina, Zana Coulibaly, Bradford E. Peercy, Leighton T. Izu

Spora: A Journal of Biomathematics

Heart disease is the leading cause of mortality in the United States. One cause of heart arrhythmia is calcium (Ca²⁺) mishandling in cardiac muscle cells. We adapt Izu's et al. mathematical reaction-diffusion model of calcium in cardiac muscle cells, or cardiomyocytes implemented by Gobbert, and analyzed in Coulibaly et al. to include calcium being released from the sarcoplasmic reticulum (SR), the effects of buffers in the SR, particularly calsequestrin, and the effects of Ca²⁺ influx due to voltage across the cell membrane. Based on simulations of the model implemented in parallel using MPI, our findings aligned with …

How Infectious Was #Deflategate?, Megan Eberle, Eric A. Eager, James Peirce

Spora: A Journal of Biomathematics

In mid-January 2015 the National Football League (NFL) started an investigation into whether the New England Patriots deliberately deflated the footballs used during their AFC Championship win. Like an infectious disease, the initial discussion regarding Deflategate grew rapidly on social media sites in the days after the release of the story, only to slowly dissipate as interest in the NFL waned following the completion of its season. We apply a simple epidemic model for the infectiousness of the Deflategate news story. We find that the infectiousness of Deflategate rivals that of many of the infectious diseases that we have seen …

The Dc Algorithm & The Constrained Fermat-Torricelli Problem, Nathan Peron Lawrence, George Blikas

Student Research Symposium

The theory of functions expressible as the Difference of Convex (DC) functions has led to the development of a rich field in applied mathematics known as DC Programming.We survey the work of Pham Dinh Tao and Le Thi Hoai An in order to understand the DC Algorithm (DCA) and its use in solving clustering problems. Further, we present several other methods that generalize the DCA for any norm. These powerful tools enable researchers to reformulate objective functions, not necessarily convex, into DC Programs.

The Fermat-Torricelli problem is visited in light of convex analysis and various norms. Pierre de Fermat proposed …

Uniform Stability In Nonlinear Infinite Delay Volterra Integro-Differential Equations Using Lyapunov Functionals, Youssef Raffoul, Habib Rai

Mathematics Faculty Publications

In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of nite delay Volterra Integro-dierential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-dierential equation

x′(t) = Px(t) + ^t∫ _−∞ C(t, s)g(x(s))ds.

Developing A Risk Analysis Model To Improve Study Abroad Awareness, Tyler Spain

Industrial Engineering Undergraduate Honors Theses

As international education opportunities increase in popularity among U.S. college students (McMurtrie, 2007), it is becoming more and more necessary for study abroad organizations to be aware of the risks students face as they travel abroad. While some international cities are riskier than others, it can be difficult to distinguish between cities which truly carry a high degree of risk for visiting students, and which cities are only perceived to be risky based on various personal misconceptions. The University of Arkansas Office of Study Abroad & International Exchange currently lacks a way to quantifiably analyze the risk of study abroad …

Data Driven Sample Generator Model With Application To Classification, Alvaro Emilio Ulloa Cerna

Mathematics & Statistics ETDs

Despite the rapidly growing interest, progress in the study of relations between physiological abnormalities and mental disorders is hampered by complexity of the human brain and high costs of data collection. The complexity can be captured by machine learning approaches, but they still may require significant amounts of data. In this thesis, we seek to mitigate the latter challenge by developing a data driven sample generator model for the generation of synthetic realistic training data. Our method greatly improves generalization in classification of schizophrenia patients and healthy controls from their structural magnetic resonance images. A feed forward neural network trained …

A Physiologically-Based Pharmacokinetic Model For The Antibiotic Levofloxacin, Paezha M. Mccartt

Undergraduate Honors Theses

Levofloxacin is in a class of antibiotics known as fluoroquinolones, which treat infections by killing the bacteria that cause them. A physiologically-based pharmacokinetic (PBPK) model was developed to investigate the uptake, distribution, and elimination of Levofloxacin after a single dose. PBPK modeling uses parameters such as body weight, blood flow rates, partition coefficients, organ volumes, and several other parameters in order to model the distribution of a particular drug throughout the body. Levofloxacin is only moderately bound in human blood plasma, and, thus, for the purposes of this paper, linear bonding is incorporated into the model because the free or …

Spontaneous Parametric Down Conversion Of Photons Through Β-Barium Borate, Luke Horowitz

Physics

An apparatus for detecting pairs of entangled 405nm photons that have undergone Spontaneous Parametric Down Conversion through β-Barium Borate is described. By using avalanche photo-diodes to detect the low-intensity converted beam and a coincidence module to register coincident photons, it is possible to create an apparatus than can be used to perform quantum information experiments under a budget appropriate for an undergraduate physics lab.

General Existence Results For Abstract Mckean-Vlasov Stochastic Equations With Variable Delay, Mark A. Mckibben

Mathematics Faculty Publications

Results concerning the global existence and uniqueness of mild solutions for a class of first-order abstract stochastic integro-differential equations with variable delay in a real separable Hilbert space in which we allow the nonlinearities at a given time t to depend not only on the state of the solution at time t, but also on the corresponding probability distribution at time t are established. The classical Lipschitz is replaced by a weaker so-called Caratheodory condition under which we still maintain uniqueness. The time-dependent case is discussed, as well as an extension of the theory to the case of a nonlocal …

Cfd Model For Ventilation In Broiler Holding Sheds, Christian Heymsfield

Biological and Agricultural Engineering Undergraduate Honors Theses

Broiler production in Arkansas was valued at over $3.6 billion in 2013 (University of Arkansas Extension of Agriculture). Consequently, improvement in any phase of the production process can have significant economic impact and animal welfare implications. From the time poultry leave the farm and until they are slaughtered, they can be exposed to harsh environmental conditions, both in winter and in summer. After road transportation, birds are left to wait in holding sheds once they arrive at the processing plant, for periods of approximately 30 minutes to two hours. This project was interested in this holding shed waiting time during …

The Maximal Thurston-Bennequin Number On Grid Number N Diagrams, Emily Goins Thomas

Graduate Theses and Dissertations

We will prove an upper bound for the Thurston-Bennequin number of Legendrian knots and links on a rectangular grid with arc index n.

TB(n)=CR(n)-[n/2]

In order to prove the bound, we will separate our work for when n is even and when n is odd. After we prove the upper bound, we will show that there are unique knots and links on each grid which achieve the upper bound. When n is even, torus links achieve the maximum, and when n is odd, torus knots achieve the maximum.

Acoustic Firearm Discharge Detection And Classification In An Enclosed Environment, Lorenzo Luzi, Eric Gonzalez, Paul Bruillard, Matthew Prowant, James Skorpik, Michael Hughes, Scott Child, Duane Kist, John E. Mccarthy

Mathematics Faculty Research

Two different signal processing algorithms are described for detection and classification of acoustic signals generated by firearm discharges in small enclosed spaces. The first is based on the logarithm of the signal energy. The second is a joint entropy. The current study indicates that a system using both signal energy and joint entropy would be able to both detect weapon discharges and classify weapon type, in small spaces, with high statistical certainty.

Spectral Numerical Calculation Of Non-Isothermal Flow Through A Rotating Curved Rectangular Duct With Moderate Curvature, Md. Zohurul Islam, Md. Saidul Islam, Rabindra Nath Mondal

Applications and Applied Mathematics: An International Journal (AAM)

The present paper investigates non-isothermal flow characteristics through a rotating curved rectangular duct, where co-existence of the rotational forces and fluid temperature gradients leads to the emergence of rotation-induced buoyancy effects. A spectral-based numerical scheme is employed as the principal tool for the simulation while Chebyshev polynomial and collocation method as the secondary tools. The outer wall of the duct is heated while the inner wall cooled, the top and bottom walls being thermally insulated. The emerging parameters controlling the flow characteristics are the rotation parameter, i.e., the Taylor number Tr ranging 0 to 2000, the Grashof number Gr = …

Effect Of Solid Volume Fraction On Forced Convective Flow Of Nanofluid Through Direct Absorption Solar Collector, Salma Parvin, Rehena Nasrin, M. A. Alim

Applications and Applied Mathematics: An International Journal (AAM)

The present work numerically investigates the heat transfer performance and entropy generation of forced convection through a direct absorption solar collector. The working fluid is Cu-water nanofluid. The simulations focus specifically on the effect of solid volume fraction of nanoparticle on the mean Nusselt number, total entropy generation, Bejan number and collector efficiency. Also Isotherms, heat function and entropy generation are presented for various solid volume fraction. The governing partial differential equations are solved using penalty finite element method with Galerkins weighted residual technique. The results show that the mean Nusselt number and mean entropy generation increases as the volume …

Viscous Dissipation And Heat Absorption Effect On Natural Convection Flow With Uniform Surface Temperature Along A Vertical Wavy Surface, Sujon Nath, Nazma Parveen

Applications and Applied Mathematics: An International Journal (AAM)

The effect of viscous dissipation and heat absorption on a steady two-dimensional natural convection laminar flow of viscous incompressible fluid with uniform surface temperature along a vertical wavy surface has been investigated. Using the appropriate variables; the basic equations are transformed to convenient form and then solved numerically employing very efficient method, namely Keller-Box method (KBM). Numerical results are presented by the shearing stress in terms of the local skin-friction coefficient; the rate of heat transfer in terms of local Nusselt number, streamline and isotherms, respectively for a wide range of the viscous dissipation parameter N and heat absorption parameter …

Prandtl Number Effect On Assisted Convective Heat Transfer Through A Solar Collector, Rehen Nasrin, Salma Parvin, M. A. Alim

Applications and Applied Mathematics: An International Journal (AAM)

Numerical study of the influence of Prandtl number on forced convective heat transfer through a riser pipe of a flat plate solar collector is done. The working fluid is Al2O3/water nanofluid. By Finite Element Method the governing partial differential equations are solved. The effect of the Prandtl number on the temperature and velocity field has been depicted. Comprehensive average Nusselt number, average bulk temperature, mean velocity, mid-height temperature inside the pipe, mean output temperature and collector efficiency are presented for the governing parameter mentioned above. Nu increases by 16% with the variation of Pr from 4.6 to 6.6 using nanofluid. …

Performance Analysis Of Solar Adsorption Cooling System - Effect Of Position Of Heat Storage Tank, Rifat A. Rouf, K. C. Amanul Alam, M. A. Hakim Khan, Bidyut B. Saha, Ibrahim I. El-Sharkawy

Applications and Applied Mathematics: An International Journal (AAM)

An insulated storage tank has been added with adsorption cooling system run by solar heat collected by CPC panel. It has been expected and seen that the storage tank has a vital contribution in the performance of the chiller. The storage tank is connected with a solar heat driven single stage two bed basic adsorption chillers activated with silica gel-water pair in two ways. The tank is connected in such a way that (i) the solar collectors supply hot water to the desorption bed, the outflow of the desorber is collected in the reserve tank. The reserve tank supplies water …

Solution Techniques And Error Analysis Of General Classes Of Partial Differential Equations, Wijayasinghe Arachchige Waruni Nisansala Wijayasinghe

Boise State University Theses and Dissertations

While constructive insight for a multitude of phenomena appearing in the physical and biological sciences, medicine, engineering and economics can be gained through the analysis of mathematical models posed in terms of systems of ordinary and partial differential equations, it has been observed that a better description of the behavior of the investigated phenomena can be achieved through the use of functional differential equations (FDEs) or partial functional differential equations (PFDEs). PFDEs or functional equations with ordinary derivatives are subclasses of FDEs. FDEs form a general class of differential equations applied in a variety of disciplines and are characterized by …

Schwarzschild Spacetime And Friedmann-Lemaitre-Robertson-Walker Cosmology, Zachary Cohen

Honors Scholar Theses

The advent of General Relativity via Einstein's field equations revolutionized our understanding of gravity in our solar system and universe. The idea of General Relativity posits that gravity is entirely due to the geometry of the universe -- that is, the mass distribution throughout the universe results in the ``curving" of spacetime, which gives us the physics we see on a large scale. In the framework of General Relativity, we find that the universe behaves differently than was predicted in the model of gravitation developed by Newton. We will derive the general relativistic model for a simple system near a …