Department: Applied Mathematics ![[clear]](close-x.png "Remove this limiter")
53 matches in the database.
These are records: 1 - 30.
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1.
Adams, Joshua H.
A Homogenization Model of a Proton Exchange Membrane Photoelectrochemical Cell.
Degree: MS, Applied Mathematics, 2010, University of Akron
► This thesis models a proton exchange membrane photoelectrochemical cell (PEM PEC), which,…
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▼ This thesis models a proton exchange membrane photoelectrochemical cell (PEM PEC), which, with the aid of illumination, electrolyzes water and produces hydrogen and oxygen gas. The homogenized, one-dimensional model tracks proton concentration as well as electric potential across the width of the cell, which is comprised of three layers; a porous anode catalyst layer, at which the electrolysis reaction occurs, a proton exchange membrane layer, serving as a solid electrolyte, and and porous catalyst layer, at which the hydrogen gas is produced. Model parameters, including deviations from electroneutrality in the membrane and drift strength, are investigated, along with physical variations, including temperature, water content, and size adjustments. Additionally, electrical parameters, such as light intensity and applied current are varied. The largest improvement in cell performance occurs when the electrode lengths increase. The second being an increase in light intensity. The most detrimental effects on the cell are greater 'pore sizes' in the electrodes, followed by reducing both water contents and operating temperatures.
Advisors/Committee Members: Young, Gerald.
Subjects: Applied Mathematics
Keywords: Difference; PROTON; anode
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2.
Addo, Sandra E.
A Game-Theoretic Framework To Competitive Individual Targeting.
Degree: MS, Applied Mathematics, 2009, University of Akron
► Individual targeting is the process whereby a firm offers promotional incentives to…
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▼ Individual targeting is the process whereby a firm offers promotional incentives to individuals that the firm deems potential customers. With today's information-intensive marketing environments, most firms have considerable information about consumers in their databases, allowing them to determine those that are loyal to them and those that are potential customers. Firms are taking advantage of this new found ability to target individuals with promotions in order to increase both patronage and their customer loyalty base. We develop a game-theoretic model to investigate simultaneous price and quality competition where the firms are allowed to both manipulate the quality of their product and target individuals with promotional incentives. The firms play a two-stage game of price and quality competition and promotions in which regular prices are chosen in the first stage and then strategies for promotion are chosen in the second stage.We find that in an industry where a larger firm is promoting, customers who are highly sensitive to quality should be targeted to ensure increasing profit. The smaller firm should focus its sales and marketing activities on customers who are less price sensitive and should focus on building customer loyalty.
Advisors/Committee Members: Young, Gerald.
Subjects: Marketing; Mathematics
Keywords: Game Theory; Nash Equilibrium; Subgames; Customer loyalty; Perceived Price; Individual Targeting; Price-Quality Competition
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3.
Anderson, Curtis James.
Analysis of Controlled Over-Relaxation.
Degree: MS, Applied Mathematics, 2012, University of Akron
► To solve a large system of linear equations, iterative methods can often…
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▼ To solve a large system of linear equations, iterative methods can often be faster and more accurate than direct methods such as Gaussian elimination. A stationary iterative method can be derived from a splitting of the coefficient matrix as the difference of two matrices and generates a sequence of vectors that is expected to converge to the solution. Convergence depends on whether the spectral radius of the iteration matrix is within unity. Certain splittings generate different, well-known methods such as the Jacobi, Gauss-Seidel, and successive over-relaxation(SOR) iterative methods. Controlled over-relaxation(COR) is an extrapolated iterative method that is applicable to any splitting and its convergence depends on whether all the eigenvalues of the iteration matrix lie on one side of the vertical line x=1. This thesis presents several theorems on the convergence of COR. It is shown that for the optimal relaxation parameter COR converges at least as fast as the corresponding iterative method. Also, it is shown that for positive definite matrices, applying COR to the splitting of SOR will enlarge the interval on which the parameter for SOR may belong to. Bounds on the SOR parameter are derived. In addition to the study of well-known splittings, a theorem is presented that defines a class of splittings that is guaranteed convergent for COR. With a large sample of matrices the convergence of COR is compared to the corresponding Jacobi, Gauss-Seidel, and SOR methods. Additionally, matrix weighted extrapolated methods are considered and for a special case the optimal situation is studied.
Advisors/Committee Members: Hajjafar, Ali.
Subjects: Applied Mathematics
Keywords: SOR, COR, system of equations, iterative method, extrapolation
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4.
Arichi, Maiko.
Monitoring Ischemic Changes in Electrocardiograms using Dickinson-Steiglitz Discrete Hermite Functions.
Degree: MS, Applied Mathematics, 2005, University of Akron
► Ischemic heart disease is one of the main common causes of death…
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▼ Ischemic heart disease is one of the main common causes of death and an electrocardiogram (ECG) is used in the investigation of the heart disease. A method of real time detection of ischemic features from long term ECG signals based on Dickinson-Steiglitz discrete Hermite expansions is proposed. In this paper, the discrete Hermite functions were generated as eigenvectors of the extended tridiagonal matrix that commutes with the centered Fourier matrix. Each ECG complex was extracted from the long term ECG and expanded in terms of Hermite functions using a simple dot product. These coefficients were found to contain information about the shape of the corresponding ECG complex. The first 50 coefficients were used to reconstruct the ECG complex. These 50 coefficients were fed as input to train a committee Neural Network classifier to identify ST-segment and T-wave changes, which are one of the ischemic features in the ECG complex. The trained network was tested with long term ECG records from the MIT-BIH database. The performance was analyzed in terms of sensitivity and specificity. This results were compared with the ones that came from the same method used with a tridiagonal Hermite matrix (T matrix).
Advisors/Committee Members: Mugler, Dale.
Subjects: Mathematics
Keywords: ischemic monitoring, hermite function
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5.
Arichi, Maiko.
Direct Mathematical Method for Real-time Ischemic Detection from Electrocardiograms Using the Discrete Hermite Transform.
Degree: PhD, Applied Mathematics, 2011, University of Akron
► A real-time automated identification technique is developed for the detection of ischemic…
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▼ A real-time automated identification technique is developed for the detection of ischemic episodes in long term electrocardiographic (ECG) signals using mathematical expansions involving the Discrete Dilated Hermite Transform. The discrete Hermite functions are generated as eigenvectors of a symmetric tridiagonal matrix that commutes with the centered Fourier matrix. The Discrete Hermite Transform (DHmT) values are computed from a simple dot product between an individual ECG complex extracted from the European Society of Cardiology (ESC) ST-T database and the corresponding discrete Hermite function. These values are found to contain information about the ECG shape, highlighting changes between ST segment and T wave alterations which are the features of ischemic episodes. This information from the discrete Hermite transform, based on an orthonormal set of n-dimensional digital Hermite functions that serve as shape-identification functions, can be used to identify ischemic episodes from the ECG. The performance was analyzed in terms of sensitivity, specificity and positive predictive value.
Advisors/Committee Members: Mugler, Dale.
Subjects: Biomedical Engineering
Keywords: Signal Processing; Hermite Transform
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6.
Bagwell, Ross David.
Bifurcation and Stability of a Ring Problem Motivated by the Mechanics of Double-Walled Carbon Nanotubes.
Degree: MS, Applied Mathematics, 2012, University of Akron
► We derive governing equations for a planar ring subject to a radial…
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▼ We derive governing equations for a planar ring subject to a radial load and then specialize the equations to the classical ring problem where the ring is subject to a constant radial load and to the case where the ring is subject to a van der Waals force exerted by a second, rigid ring. In the classical problem, we study buckling for a circular solution as the uniform load is varied. In the two ring problem, we study buckling for a circular solution as the radius of the rigid ring is varied. We do this by using standard perturbation techniques in order to determine bifurcating solutions and then check the stability of the bifurcated solutions by comparing the energy of the trivial solution to the energy of the bifurcated solution. We assume that the system goes to whichever solution has the smaller energy, thus telling us if buckling occurs. For the two ring problem, when the rigid ring is outside the deformable ring and the radius of the rigid ring is increased, buckling occurs.
Advisors/Committee Members: Wilber, J. Patrick.
Subjects: Applied Mathematics
Keywords: double walled carbon nanotubes; bifurcation; stability analysis; classical ring
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7.
Baranyk, Bethany L.S.
A Model for Choosing a Four-Year University or a Two-Year Community College with the Presence of a Government Subsidy.
Degree: MS, Applied Mathematics, 2012, University of Akron
► Students today face the decision of choosing either a four-year university or…
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▼ Students today face the decision of choosing either a four-year university or a two-year community college when pursuing higher education. This choice as well as the government's choice of subsidizing the four-year university or the two-year community college is analyzed using game theory. The two players of the game are the individual and the government. The individual, who intends on receiving a four-year degree, can choose to either directly attend a four-year university or first attend a two-year community college before enrolling in a four-year institution. The government can choose to subsidize the four-year university and the two-year community college either at the same level or different levels. The goal of both the individual and the government is to optimize their lifetime earnings. We find that looking at the immediate future, the individual should directly attend a four-year institution regardless of ability. However, looking at the distant future, we find the choice does depend on the individual's own merit, and based upon ability the individual should choose to attend community college first before enrolling in a university unless the subsidy for the four-year university is greater than the subsidy for the two-year community college. We also find that at retirement age, the lifetime earnings of the individual are not significantly affected by the presence or absence of a government subsidy.
Advisors/Committee Members: Forcey, Stefan.
Subjects: Applied Mathematics; Higher Education
Keywords: game theory, higher education, community college, university, subsidy
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8.
Brackman, Matthew D.
Modeling and Simulation of Damage Evolution in Crevice Corrosion.
Degree: MS, Applied Mathematics, 2012, University of Akron
► While much progress has been made in transport models of crevice corrosion,…
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▼ While much progress has been made in transport models of crevice corrosion, damage evolution of the metal surface during this process has received less attention. This work focuses on mathematical modeling and simulation of the damage evolution to provide quantitative descriptions of the time varying shape of the corroded surface. The base model uses the potentiodynamic polarization data for nickel (Ni) in sulfuric acid and assumes well-mixed solution chemistry inside and outside the crevice, consistent with a pure potential drop model and experimental/modeling work in the literature. Asymptotic analysis is used to simplify the governing equations and develop an evolution equation for the Ni surface. Metal surface shapes, potential profiles and other characteristic features of the corrosion are predicted. Predicted results agree well with the published laboratory investigations. Since the model calculates the true crevice gap in real time, it provides new insights into the movement of the peak current density, potential drop down the crevice length and the critical length to gap ratio necessary to propogate potential drop controlled crevice corrosion.
Advisors/Committee Members: Young, Gerald.
Subjects: Materials Science; Mathematics
Keywords: modeling; simulation; crevice corrosion; damage evolution; mathematics; math modeling
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9.
Brubaker, Lauren P.
Completely Residual Based Code Verification.
Degree: MS, Applied Mathematics, 2006, University of Akron
► Mathematical models of physical processes often include partial differential equations (PDEs). Oftentimes…
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▼ Mathematical models of physical processes often include partial differential equations (PDEs). Oftentimes solving PDEs analytically is not feasible and a numerical method is implemented to obtain an approximate solution. Too often the assumption is made that the solution should be trusted when codes are prone to implementation errors. Code verification is a field of mathematics that shows the algorithm has been implemented without mistakes and has correctly solved the problem. Currently no one method of code verification is universally accepted. The Method of Manufactured Exact Solutions (MMES) is the most commonly used, but it has a considerable disadvantage of altering the code after verification. We have developed a new method, Completely Residual Based Code Verification (CRBCV), which does not require any modification. By using several solution methods, we have shown that CRBCV is dependable when verifying the heat equation with linear and nonlinear source terms and a frontal polymerization model.
Advisors/Committee Members: Gross, Laura K.
Subjects: Mathematics
Keywords: Code verification; Partial Differential Equations; Numerical Methods; Method of Manufactured Exact Solutions; Frontal Polymerization; Heat Equation; Residual
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10.
Buckman, Kevin D.
A Mathematical Model of Biofilm Growth and Decay with Applications of Antimicrobial.
Degree: MS, Applied Mathematics, 2012, University of Akron
► A biofilm is a structured community of microorganisms held together by a…
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▼ A biofilm is a structured community of microorganisms held together by a matrix of polysaccharides, nucleic acids, and proteins. Bacteria in biofilms show a higher resistance to antimicrobials than planktonic bacteria. In this paper, a mathematical model is developed that describes the growth of a biofilm by nutrient and the decay of a biofilm through applications of antimicrobial. The model includes reaction-diffusion equations used to describe the movement of nutrients and antimicrobial, the soluble components of the biofilm. The transport of living bacteria, inert bacteria, persister bacteria, and the matrix, also known as extracellular polymeric substance, is represented by advection equations. The system of partial differential equations is solved numerically using FiPy, a finite volume method package for the Python programming language. For treatment of the biofilm, the model describes the delivery of antimicrobial in two forms: as an aqueous solution that diffuses through the biofilm-fluid interface and as nanospheres that are embedded within the biofilm and release antimicrobial as they degrade. We examine the efficiency of treatment of a biofilm for various treatment scenarios that include different types of nanospheres and different placements of nanospheres.
Advisors/Committee Members: Wilber, J. Patrick.
Subjects: Biology; Computer Science; Environmental Science; Mathematics
Keywords: biofilm; antimicrobial; mathematical modeling of biofilm; continuum model; finite volume method; Python; FiPy
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11.
Busuladzic, Ines.
TWO-DIMENSIONAL HEAT TRANSFER AND THERMAL STRESS ANALYSIS IN THE FLOAT GLASS PROCESS.
Degree: MS, Applied Mathematics, 2007, University of Akron
► We consider the glass manufacturing process where the glass floats on a…
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▼ We consider the glass manufacturing process where the glass floats on a tin layer through a furnace and the temperature of the glass changes from 1100 degrees C at the entrance to 600 degrees C at the exit from the furnace. Two float glass systems, a pure-layer and a multi-layer system, are considered. For each system asymptotic analysis is performed on the governing equations and corresponding boundary conditions. The small parameter is the ratio of the glass height to its length. The asymptotic analysis results in a simpler heat transfer model that is subsequently solved numerically. Further, analysis of thermal stresses in the glass ribbon is performed under plane strain assumption, so that the strain (but not stress) transversal to the axis of the ribbon vanish. No-stress boundary conditions are imposed on the remaining parts of the boundary of the ribbon. The asymptotic analysis is performed on thermal stresses up to and including third order terms in order to obtain a solution valid up to first order in the small parameter. Once the thermal stresses are determined, we optimize the temperature of the air to minimize the longitudinal thermal stresses while the temperature of the glass is fixed at 1100 degrees C at the entrance and 600 degrees C and at the exit from the furnace.
Advisors/Committee Members: Golovaty, Dmitry.
Keywords: heat transfer, thermal stresses, float glass, temperature, asymptotic expansion, optimization
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12.
Diep, My Tieu.
Uniqueness of Entropy Solutions to Hyperbolic-Parabolic Conservation Laws.
Degree: MS, Applied Mathematics, 2011, University of Akron
► We consider an initial value problem for the hyperbolic-parabolic equation: u_t +…
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▼ We consider an initial value problem for the hyperbolic-parabolic equation: u_t + [F(t, x, u)]_x = e u_xx in QT := R x (0, T), u(·, 0)= u_0 in R. Here the flux function has the form F(t, x, u) = K(x)f(u), where f(u) and K(x) are scalar functions. Our purpose is to prove the uniqueness result for entropy solutions of the problem which is of interest in fluid and statistical mechanics. It is known that if K(x)in W_{loc}^{1,1}(R) and f(u) is locally Lipschitz, then the equation has a unique entropy solution. In this thesis we are able to show the uniqueness for entropy solutions of the equation under a much weaker condition: K(x) has locally bounded variation and f(u) is continuous. Our result is useful because in some applications the flux function f(u) is only continuous. We in fact establish a L1-contraction principle for entropy solutions from which one can deduce the uniqueness as a particular consequence.
Advisors/Committee Members: Nguyen, Truyen.
Subjects: Applied Mathematics
Keywords: entropy solution, uniqueness, conservation law, hyperbolic-parabolic.
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13.
Fang, Fang.
A Study of the Longterm Dynamics of a Discretization of a Light Viscoelastic Rod Carrying a Heavy Block.
Degree: MS, Applied Mathematics, 2011, University of Akron
► A heavy rigid body attached to a relatively light deformable body is…
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▼ A heavy rigid body attached to a relatively light deformable body is a common structure in many mechanical systems. The longterm dynamics of this structure characterize the true features of the structure response to external excitation. Therefore, the study of the longterm dynamics can provide fundamental guidance for engineering design and production. In this thesis, we study a system that describes the longitudinal motion of a light viscoelastic rod carrying a heavy particle. We discretize this problem by replacing the rod with K light particles connected by massless springs. The discretized problem is governed by a system of coupled nonlinear ordinary differential equations. We let ε denote the ratio of the mass of one of the light particles to the mass of the end particle. This introduces a small parameter into the problem. We use a singular perturbation approach developed by O’Malley and Hoppensteadt to analyze this problem. We focus on the K = 1 case; and the longterm dynamics of this case is reduced to the longterm dynamics of the order 1 outer problem based on the matching condition and the approximate solutions. The longterm dynamics of the order 1 outer problem depends on whether the restoring force f of the springs in the discretized system is monotone or non-monotone. For monotone restoring forces, we show that there exists an invariant manifold M that attracts all solutions to a system equivalent to the order 1 outer problem. The dynamics on M is governed by a classical second-order ordinary differential equation. We also illustrate that the longterm dynamics on M determines the longterm dynamics of the order 1 outer problem. For non-monotone restoring forces, the invariant manifold M still exists. We show by considering a specific example that M fails to attract all solutions.
Advisors/Committee Members: Wilber, J. Patrick.
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14.
Gouin, Marlena.
Acid Mine Drainage Remediation Utilizing Iron-Oxidizing Bacteria.
Degree: MS, Applied Mathematics, 2011, University of Akron
► Acid mine drainage is pollution that occurs when water trapped in abandoned…
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▼ Acid mine drainage is pollution that occurs when water trapped in abandoned coal mines leaks out and pollutes the local water systems. One of the most abundant metals found in acid mine drainage is iron. Iron often precipitates out of the system naturally in the form of iron(III) hydroxide, leading to a decrease in fluid pH. Iron oxidizing bacteria can promote this reaction process, assisting in the removal of Fe(II) ions from the acid mine drainage. The increase in acidity can be detrimental to surrounding wildlife. The purpose of this paper is to develop a model that includes the hyrodynamics and reactive transport of ions in the system. The model predictions will be compared to local field data and those found in the literature. In addition the model analyzes the precipitation of the iron(III) hydroxide crust as a function of space and time. Several parameters are varied to observe predictions made by the model with different physical circumstances. Forcing low concentrations of oxygen in the system produces slower the rate of iron(III) hydroxide crust growth. Increasing the angle of inclination while holding the flow rate fixed causes a very small decrease in iron(III) hydroxide crust growth. Decreasing the flow rate of the system while maintaining a fixed angle of inclination to simulate a thinning of the liquid layer produces a slower iron(III) hydroxide crust growth rate. When the angle of inclination is varied with fixed fluid film thickness, as the angle of inclination increases, iron(III) hydroxide crust growth decreases. When the the forward rate for surface reactions and the reverse rate for bulk reactions are increased, both decreased the rate of iron(III) hydroxide crust production. When the reverse rate for surface reactions and the forward rate for bulk reactions are increased, they increase iron(III) hydroxide crust growth rate. An increase in iron oxidizing bacteria can increase the oxidation of Fe(II). Therefore, an increase in the abundance of iron oxidizing bacteria can increase the rate of iron(III) hydroxide crust growth.
Advisors/Committee Members: Young, Gerald.
Subjects: Mathematics
Keywords: acid mine drainage; bacteria; iron
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15.
Groshong, Kimberly Ann.
Modeling the Effect of Calcium Concentration and Volumetric Flow Rate Changes on the Growth of Rimstone Dam Formations Due to Calcium Carbonate Precipitation.
Degree: MS, Applied Mathematics, 2008, University of Akron
► Rimstone dams, formed in cave environments and composed primarily of calcium carbonate,…
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▼ Rimstone dams, formed in cave environments and composed primarily of calcium carbonate, are constructed through both chemical and mechanical processes. As calcium rich water flows over a sloped limestone cave floor, calcium carbonate precipitates from the solution. Standard fluid mechanics equations govern the hydrodynamics. Chemical kinetics describe movement through the boundaries and explain the bulk and surface reactions that influence precipitation. The free boundaries, gas-fluid and solid-fluid interfaces, couple the hydrodynamic and reactive transport equations. The chemical kinetics of bulk and surface reactions that result in precipitation are determined. This research focuses on the effect of changing the volumetric flow rate and altering the concentrations of calcium on the growth of the mineral-fluid boundary by developing and solving, through thin-film fluid flow approximations, appropriate hydrodynamic and reactive transport equations. Three general volumetric flow conditions are explored in this paper. The effect of slow, moderate, and fast flow rates under conditions of constant flow; exponentially decreasing flow, modeling drought conditions; and seasonal flow fluctuations about a base rate are investigated. The greatest growth was observed during seasonal fluctuations with a moderate volumetric flow rate. Greatest deposition, near the initial position, was with high concentrations of calcium flowing with a fast flow rate. Further downstream, the largest growth required small concentrations of calcium, which maintained a high pH condition in the system. From the developed equation for the mineral boundary, growth was affected by pH conditions driven from bulk reactions and influenced by degassing of carbon dioxide and surface reactions from the alterations in calcium concentration, ultimately driving the system pH.
Advisors/Committee Members: Young, Gerald.
Subjects: Geochemistry; Geology; Geophysics; Mathematics
Keywords: Rimstone Dams; calcium precipitation; cave formations; asymptotic expansion; volumetric flow rate; coupled differential equations
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16.
Gyrya, Vitaliy.
Variational Problems on Domains with Inclusions Homogenization Through Gamma-Convergence.
Degree: MS, Applied Mathematics, 2005, University of Akron
► Consider a composite material consisting of a periodic (with a period d)…
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▼ Consider a composite material consisting of a periodic (with a period d) collection of alternating flat plates (laminates) with two different values of thermal conductivity. Suppose that thermal conductivity is equal to 1 in the first set of plates and it is equal to c in the second set of plates. We focus on finding the effective conductivity of the laminated composite when the parameter c is large and the parameter d is small. This problem can be solved by determining the partial differential equation governing the homogenized temperature distribution. Rather than go this route, we choose to formulate the problem in a variational form. Then the conductivity of a composite for the given values c and d can be determined by minimizing an appropriate energy functional. We use the theory of Γ-convergence to find the asymptotic limits of both minimizers and their respective minimum energy values as (c-1,d) approaches (0,0). We show that these limits are independent of the direction in which (c-1,d) approaches (0,0) in the parameter space. Further, we show that the minimum energy values do not exceed the minimum value of the limiting energy functional.
Advisors/Committee Members: Golovaty, Dmitry.
Subjects: Mathematics
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17.
Hamrick, Paul M.
SIMULATION OF THE CONCENTRATION FIELD DURING PHYSICAL VAPOR DEPOSITION ONTO A NANOFIBER SUBSTRATE.
Degree: MS, Applied Mathematics, 2006, University of Akron
► Plasma enhanced physical vapor deposition (PEPVD) is one method to coat nanofibers…
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▼ Plasma enhanced physical vapor deposition (PEPVD) is one method to coat nanofibers and nanostructures with thin film materials. Experimental efforts in coating electrospun polymer nanofibers suggest a complicated relationship between coating morphology and operating conditions. This motivates a theoretical model for coating growth. The model presented here assumes a coating growth that is uniform along the axial dimension of the nanofiber but non-uniform in the radial direction. The concentration of vaporized aluminum surrounding the coating growth is non-uniform due to the geometry of the coating growth, therefore modeling the morphology of the growth requires that the surrounding concentration field be determined. The concentration field would then be supplied to an evolution equation. The mode of mass transport is diffusion, therefore the mathematical model consists of Laplace's equation over a polar domain. The domain is an annulus with an irregular inner boundary. A finite difference method is employed to solve the system. The irregular inner boundary geometry, as well as a complicated inner boundary condition, requires that interpolation schemes and ghost points be used at points on and near the boundary. The resulting matrix system is solved with a block SOR iterative method.
Advisors/Committee Members: Kreider, Kevin L.
Subjects: Mathematics
Keywords: nanowire; nanotube; deposition; Plasma Enhanced Physical Vapor Deposition; concentration field; diffusion; irregular boundary; finite difference; interpolation; ghost point; block SOR
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18.
Hoffman, Matt J.
Use of a Diffusive Approximation of Radiative Transfer for Modeling Thermophotovoltaic Systems.
Degree: MS, Applied Mathematics, 2010, University of Akron
► Thermophotovoltaic (TPV) energy conversion is the conversion of heat energy to electrical…
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▼ Thermophotovoltaic (TPV) energy conversion is the conversion of heat energy to electrical energy via light. When a TPV material is heated, it emits ultraviolet light. This light is then collected by TPV diode cells and converted into electrical energy. In order to be used commercially, TPV energy conversion must become more efficient. A majority of the current research focuses on increasing the efficiency of the TPV diode cells. This thesis focuses on how to design the emitter, so the optimal amount of light reaches the TPV diode cells. This system is modeled inside an exhaust tube, which could be a smokestack of a factory or an exhaust pipe of a car. This model uses the diffusion approximation of the radiative transfer equation and homogenization. It shows how to optimize the geometry of the emitter and homogenize it with another material to maximize emission, while using the least amount of TPV material. This model is presented in axisymmetric coordinates. Different light sources include a ring source, a pancake source, a cylinder source, and a solid sphere source. It is shown that a light source composed of a mixture of a TPV material and a more optically transparent material could be more efficient than using a source of pure TPV material. This mixture is always more efficient if it is arranged in alternating layers on a small scale in the radial direction.
Advisors/Committee Members: Young, Dr. Gerald.
Subjects: Chemical engineering; Mathematics
Keywords: TPV; diffusion approximation; radiative transfer equation; homogenization
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19.
Jittavanich, Kotchanun.
Modeling, Simulations, and Parametric Studies of the Dip Coating Process with the Effect of Solvent Evaporation Rate and Bulk Reaction Rate.
Degree: MS, Applied Mathematics, 2008, University of Akron
► In this paper we study the dip coating problem. We present a…
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▼ In this paper we study the dip coating problem. We present a thin film model based on the lubrication approximation that includes an evaporation effect of the solvent and the bulk reaction effect of erbium oxide to determine the thickness of the coatings. We solve the problem numerically with the modified two-step Lax-Wendroff scheme [1]. While the two main mechanisms influencing the final film thickness are the solvent evaporation rate and the erbium oxide reaction, we also study how the dynamic viscosity, the angle of the inclined substrate, the characteristic depth of the solution thickness, the initial profile of the solution thickness, and the length of substrate affect the coating thickness. The developed model can be used in many coating industries to predict the coating thickness and approximate drying time
Advisors/Committee Members: Young, Gerald.
Keywords: effect; thickness of the coatings
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20.
Johnston, Joshua D.
Analytically and Numerically Modeling Reservoir-Extended Porous Slider and Journal Bearings Incorporating Cavitation Effects.
Degree: PhD, Applied Mathematics, 2011, University of Akron
► The technology of porous bearings is well-known in industry. In classical cases,…
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▼ The technology of porous bearings is well-known in industry. In classical cases, the porous medium acts as an external reservoir making their use ideal for applications where an external lubricant supply is undesirable or impractical or when fluid has to be delivered on a continual basis. The work considered here looks to extend the benefits of typical porous bearings to allow for the bearing to be sealed, containing, from the onset of operation, all necessary lubricant. The goal of this work is to demonstrate a bearing that circulates the fluid between a fluid film and an eccentric reservoir, using a porous medium as an intermediary; a system that is capable of supporting a realistic load, while simultaneously pumping the fluid back and forth between the lubricating region and the reservoir. The method used to investigate such a bearing is a mixture of analytical and numerical techniques. For the analysis, a non-dimensionalization scheme is used to analyze both the momentum and thermal governing equations at their differing orders of magnitude. Upon doing so, the governing momentum equations are reduced considerably which allows for a straight-forward numerical solution procedure. The governing thermal equations are solved using an asymptotic expansion approach, keeping the first and second order terms and equations. This is done so to more accurately model the effects the circulating fluid has on the thermal performance of the bearing. The phenomenon of cavitation is also discussed, utilizing a method that integrates cavitation into the governing equations and numerical solution procedure. Unlike other cavitation models that decouple cavitation from the governing momentum equations, this model accounts for mass flow continuity which leads to more realistic results. Practical design considerations, including how to determine the effective permeability and the effective heat transfer coefficient at the exterior wall of the bearing, are discussed. These parameters, used extensively in the analytical and numerical modeling of the bearing, are essentially functions of other physical parameters. Once these relationships are established, their values can be utilized by someone looking to design a bearing considered in this work with a set of performance criteria in mind. The combination of analytical work and numerical computations produces a comprehensive look at this new type of bearing. A long slider bearing and both long and short journal bearings are discussed in a parametric fashion, whereby the effects of varying the operational and geometric parameters are investigated by examining the accompanying pressure and temperature fields. The model presented here demonstrates the feasibility of a bearing that is capable of supporting a load while eliminating the need for an external lubricant supply and the necessary infrastructure that is required to actively feed a bearing with lubricant. It is shown that the temperatures stay within operating limits utilizing a realistic heat transfer coefficient and a realistic thermal conductivity for the lubricant while generating pressures inside the film that can support a load and simultaneously pump fluid between the film and reservoir regions.
Advisors/Committee Members: Young, Gerald.
Subjects: Mathematics; Mechanical Engineering
Keywords: bearing; cavitation; numerical analysis; partial differential equations; slider; journal; porous medium; heat transfer
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21.
Joyner, James Thomas.
ASYMPTOTIC ANALYSIS OF FRONTAL POLYMERIZATION IN A MEDIUM WITH PERIODIC MONOMER DISTRIBUTION.
Degree: MS, Applied Mathematics, 2006, University of Akron
► Frontal polymerization (FP) is a process in which a monomer-initiator mixture is…
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▼ Frontal polymerization (FP) is a process in which a monomer-initiator mixture is converted into polymer through a self-sustaining reaction front. We study FP in a two-dimensional rectangular domain where the front propagates parallel to the axis of periodic, small reagent variations. The problems setup is motivated by the experimental use of polymerization to produce gradient materials. Further, it allows us to investigate the fundamental question of validity of Snell's law for reaction waves in a non-uniform medium. First we present a derivation of the one-step kinetics model. Then, we seek an asymptotic, steady-state traveling-wave solution using the assumption of high activation energy. As a part of our analysis, we show that the Snell's law does not hold for the ranges of parameters for which our asymptotic analysis is valid. We propose a modification to our asymptotic procedure that may reveal applicability of Snell's law in FP.
Advisors/Committee Members: Golovaty, Dmitry.
Keywords: MONOMER; POLYMERIZATION; monomer concentration; FRONTAL POLYMERIZATION
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22.
Justice, Brad L.
Modelling of Calcium Carbonate Precipitation in Natural Karst Environments Under Hydrodynamic and Chemical Kinetic Control.
Degree: MS, Applied Mathematics, 2006, University of Akron
► Rimstone dams are barriers composed mainly of calcium carbonate deposited from solution…
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▼ Rimstone dams are barriers composed mainly of calcium carbonate deposited from solution in ground and surface waters. These structures form a subclass of travertine formations which include flowstone and stalactites, and often appear in close proximity to these features. The initial formation of rimstone dams requires some degree of cave slope, a semi-continuous flow of water, and the preexistence of irregularities in the cave floor. These dams develop at heights from a few millimeters to several meters within free-surface streams, and create a self-propagating dam and pool structure which grows upward. The genesis and evolution of rimstone dams is theorized to be the result of hydrodynamic and chemical-kinetic control. The purpose of this paper is to develop a model, the scope of which encompasses both hydrodynamics and the reactive transport, which is qualitatively consistent with observed and experimentally derived results, and method for analyzing the mechanism governing the formation of these unique rimstone features.
Advisors/Committee Members: Young, Gerald.
Subjects: Geophysics
Keywords: c5; CALCIUM CARBONATE; Rimstone; Rimstone dams; c3
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23.
Kilker, Nathan.
The Cauchy-Born Rule Applied to a Discrete Model of a Nonwoven Fiber Mesh.
Degree: MS, Applied Mathematics, 2012, University of Akron
► Valvular heart disease is a serious condition afflicting millions of Americans, contributing…
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▼ Valvular heart disease is a serious condition afflicting millions of Americans, contributing to thousands of deaths yearly. Heart valve replacement surgeries are temporary solutions that are costly and carry inherent risks. Recent tissue engineering research has suggested the use of an endothelial seeded, nonwoven polymer fiber scaffold mesh to replace damaged valve tissue. The polymer mesh (scaffold) must be strong enough to continue regular heart function until it is resorbed and replaced by the recipient's heart tissue. Of primary concern in the design of the scaffold are the mechanical properties of the scaffold, particularly stress-strain relations. A two dimensional, discrete model of the mesh is developed to simulate the mechanical behavior of the mesh under tensile loading. Continuum approximation of the discrete energy functional is derived using the Cauchy-Born rule and the partial differential equations of linear elasticity are obtained for small deformations of the mesh using variational techniques.
Advisors/Committee Members: Golovaty, Dmitry.
Subjects: Engineering; Mathematics
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24.
Kozy, James E. III.
A Game-Theoretic Analysis of Home Court Advantage and Optimal Offensive Strategy in Basketball.
Degree: MS, Applied Mathematics, 2011, University of Akron
► This paper intends to construct a game-theoretic model with which to analyze…
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▼ This paper intends to construct a game-theoretic model with which to analyze the impact of home court advantage on a visiting team's offensive strategy, specifically the balance between two and three-point shots attempted. We develop the Home Court Advantage Model to assist in our analysis. The model determines the optimal offensive strategy when one takes into account parameters that reflect the changes in offensive output by a basketball team when playing on the road. In this case this is manifested in lower shooting percentages, particularly on two-point shot attempts. The model also accounts for statistical data suggesting that three-point shot percentages are not affected as dramatically by home court advantage as are two-point shot percentages. We draw several conclusions, including that as a team's two-point shot percentage decreases, the team should actually shoot more two-point shots to optimize their overall offensive efficiency. We conclude our model with a study of the home court advantage of the 2008-2009 Cleveland Cavaliers, applying the model specifically to post-season play.
Advisors/Committee Members: Young, Gerald.
Subjects: Mathematics
Keywords: Game Theory; Nash Equilbrium; Basketball
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25.
Leta, James V.
An Elastica Model that Describes the Buckling of Cross-sections of Nanotubes.
Degree: MS, Applied Mathematics, 2011, University of Akron
► Multi-walled carbon nanotubes (MWNT) are well-known for their superior mechanical properties. Their…
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▼ Multi-walled carbon nanotubes (MWNT) are well-known for their superior mechanical properties. Their size, tensile strength, and flexibility make them an attractive choice for a variety of practical applications. Thus numerous studies have been conducted in an effort to better understand the response of MWNT to applied loading. In this paper, we develop a nonlinear continuum model that describes equilibrium configurations of double-walled carbon nanotubes (DWNT). The DWNT is assumed to deform in such a way that enables us to reduce our analysis to a single cross-section perpendicular to the axis of the DWNT. We model the cross-section of a DWNT as 2 circular concentric rings that interact through a van der Waals body force. Utilizing our continuum assumption and the Lennard-Jones 12-6 potential function, we derive an expression for the body force. We apply Euler's elastica theory to derive a two-point boundary value problem that consist of a system of 4 nonlinear ordinary differential equations with periodic boundary conditions. Using standard techniques of bifurcation theory, we establish a trivial branch of circular solutions and give a complete description of the critical radii at which buckled solutions bifurcate from the trivial branch.
Advisors/Committee Members: Wilber, J. Patrick.
Subjects: Applied Mathematics; Mechanics; Nanoscience
Keywords: nanomechanics; nonlinear elasticty; continuum mechanics; elastica; buckling; bifurcation theory
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26.
Lora, Marissa Rose.
Modeling Alcohol Abuse Patterns in Hispanic-American Populations Using an SIR Model.
Degree: MS, Applied Mathematics, 2011, University of Akron
► SIR (Susceptible-Infected-Recovered) models may be used to examine the dynamics of socially…
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▼ SIR (Susceptible-Infected-Recovered) models may be used to examine the dynamics of socially based phenomena, such as alcohol abuse, by assuming such issues are a product of social contact and interaction. Recent studies have shown that there is an increase in the prevalence of abusive drinking behavior in the Hispanic-Immigrant population due to the increase in interaction with the U.S. population. By altering the governing differential equations of the SIR model, it is possible to model the increase in alcohol abuse in the Hispanic population. The Sanchez et al. model is analyzed by seeking steady state solutions and performing a linear stability analysis. We find that the base state is stable if the rate at which individuals enter the drinking sub-population is less than the rate at which individuals leave the drinking sub-population. For the bifurcating solution, the upper branch is stable and the lower branch is unstable. If the population lies on the upper branch, then there exists a finite population of abusive drinkers in the population. Finally, the effect of the standard population on the Hispanic population is examined through various examples. The standard population may have a great impact on the Hispanic population if the rate at which Hispanics come into contact with individuals from the standard population is large enough.
Advisors/Committee Members: Clemons, Curtis.
Subjects: Mathematics
Keywords: acculturation; SIR; epidemiology; alcohol abuse; Hispanic
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27.
Macavei, Diana.
A Game Theoretic Approach to the Problem of Determining the Optimal Number of Years of Education.
Degree: MS, Applied Mathematics, 2011, University of Akron
► Higher education leads to higher productivity and thus to higher income. The…
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▼ Higher education leads to higher productivity and thus to higher income. The issue of the cost of higher education versus the economic return is addressed in this paper using a game theoretic approach. The game has two players: the worker and the government. Each has two choices: the worker can choose to get higher education or not and the government can choose to subsidize some portion of the schooling or not. Both players have the same goal which is to maximize their income. We find that if the taxation rate imposed by the government exceeds the ratio of the increment of net loss of income due to subsidy to the increment of net gain of income due to that subsidy, then the government should subsidize some portion of the education. We also confirm that the individual should continue education if the extra income in a lifetime is greater than the cost of schooling.
Advisors/Committee Members: Young, Gerald.
Subjects: Mathematics
Keywords: game theory; government subsidy for education; optimal number of years of education
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28.
Martinez, Adam P.
A Geometric Tiling Algorithm for Approximating Minimal Covering Sets.
Degree: MS, Applied Mathematics, 2011, University of Akron
► The cover generation problem is relevant to the problem of creating large-scale…
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▼ The cover generation problem is relevant to the problem of creating large-scale wire- less sensor networks. Wireless sensor networks have short-ranged sensor nodes that may not be capable of transmitting to base station. Quickly and efficiently placing relay nodes allows the sensors to save on battery power and transmit information back to the base station via the relay nodes. Placing a minimal cover of relays is at least an NP-hard problem. We present a geometric tiling algorithm to construct an approximation to a minimal covering set in O(n) time. The algorithm fills the target region with a triangular grid of relays and then culls unnecessary points from the grid. A brief analysis of the algorithm is presented and a comparison to another cover-generation algorithm is performed.
Advisors/Committee Members: Norfolk, Timothy.
Keywords: wireless sensor; network; geometric tiling
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29.
McCallum, Katie Arlene.
Probabilistic Analysis of Pipeline Reliability Using a Markov Process.
Degree: MS, Applied Mathematics, 2012, University of Akron
► This paper develops a basic foundation for a tool that can be…
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▼ This paper develops a basic foundation for a tool that can be used to predict the probability of a leak occurring in an oil pipeline due to pitting corrosion. The methodology is directly applicable to other steel equipment and infrastructure. Using a simple Markov chain process, we formulate equations for probability distributions of a pit being in a defined set of corroded states. Each state represents a specific pit depth. By adjusting transition rates between states we represent the corrosivity and mitigation conditions to which the oil pipeline is subjected. The transition rate models used here are flexible and capable of accommodating a wide range of corrosivity and mitigation scenarios. We discuss hypothetical cases, such as increasing CO2 content in oil causing gradual corrosion versus an episodic event causing rapid changes in the corrosivity conditions, demonstrating the ability to make adjustments to the model in order to simulate varying operational conditions.
Advisors/Committee Members: Young, Gerald.
Subjects: Mathematics
Keywords: Markov; corrosion; oil pipeline; leakage probability
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30.
Miller, Ian Timothy.
Probabilistic finite element modeling of aerospace engine components incorporating time-dependent inelastic properties for ceramic matrix composite (CMC) materials.
Degree: MS, Applied Mathematics, 2006, University of Akron
► The research included in this abstract pertains to probabilistic finite-element creep analysis…
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▼ The research included in this abstract pertains to probabilistic finite-element creep analysis of a composite combustor liner. A composite combustor liner is an aerospace engine component that is subjected to very high temperatures, ranging between 1500 - 2100 degrees Fahrenheit. A creep analysis of this component is essential for rational design as creep (a slow time-dependent information under constant load) is prevalent at high temperatures. In a probabilistic analysis, many, if not all, of the state variables are represented by random variables with appropriate probability distributions incorporating relevant parameters. This formalism is much more realistic, as it more accurately describes the variability in properties and loadings that are inherent in the composition of aerospace materials and loadings encountered by aerospace components.
Advisors/Committee Members: Hajjafar, Ali.
Keywords: Creep Analysis; Reliability Analysis; Aerospace Engine Components; Ceramic Matrix Composite Materials; Finite Element Analysis
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