Digital Commons Network^™

An Examination Of Physical Literacy: Learning Through A Technology Integrated, Flipped Classroom Approach., Euan M. S. Frew

Theses and Dissertations

Technology integrated, flipped classroom design offers opportunities to engage students on various levels and through meaningful ways. Introducing this learning environment to students at an early age is likely to change their motivation for learning towards physical literacy and influence their lifelong participation in physical activity. The purpose of this action research was to evaluate the implementation of a new technology integrated, Flipped Classroom in a physical education class, to increase eighth -grade students’ physical literacy at an international middle school. The following research questions guided this study: (a) How and to what extent does a technology integrated, flipped classroom, …

Tool Migration: A Framework To Study The Cross-Disciplinary Use Of Mathematical Constructs In Science, Chia-Hua Lin

Theses and Dissertations

This dissertation is concerned with the scientific practice in which a mathematical construct that was originally developed to study a particular subject matter subsequently used in other disciplines or sub-disciplines for a different subject matter, a phenomenon that I call ‘tool migration.’ I argue that tool migration can be ‘epistemically risky.’ Specifically, uprooting a research tool from one disciplinary context and re-situating it for use in another can change how the tool is applied; whatever has made the tool useful and reliable in the first place may not have stayed the same in the new context. Using the migrations of …

Hill Functions For Stochastic Gene Regulatory Networks From Master Equations With Split Nodes And Time-Scale Separation, Ovidiu Lipan, Cameron Ferwerda

Physics Faculty Publications

The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo …

Mathematical Motivation Beliefs: A Study On The Influences Of The Mathematical Motivation Beliefs Of Students In A Predominantly African American Environment In Mississippi, Kendrick Laterrell Savage

Theses and Dissertations

The purpose of this study is to examine the influences certain factors have on the mathematical motivation beliefs of students in a predominantly African American setting. Mathematical motivation beliefs, for the purpose of this study, are defined as the components mathematical self-efficacy and mathematical value, both represented as dependent variables in the study. 4 independent variables were studied as potential influences regarding mathematical motivation beliefs. The variables included parental influences, teacher influences, mathematical anxiety, and the environment/setting. This research was conducted using 2 high schools in a rural area in East Mississippi. The 1st high school was predominantly African American …

Pubh 7090 A - Selected Topics In Public Health: Advanced Infectious Disease Epidemiology, Isaac Chun-Hai Fung

Jiann-Ping Hsu College of Public Health Syllabi

This course covers the use of mathematical and computational approaches to study infectious diseases. We will discuss models that address both the dynamics of infectious disease spread through populations and the dynamics of pathogens inside an infected individual. Students will learn how to build and analyze models for a variety of human and animal diseases. We will look at the impact of interventions on disease outcomes. Students will learn how to interpret results of modeling studies to make informed public health policy decisions.

An Application Of Mathematical Morphology Operators As Features Extraction Method For Low Speed Slew Bearing Condition Monitoring, Wahyu Caesarendra, Dwi B. Wibowo, Mochammad Ariyanto, Joga D. Setiawan

Faculty of Engineering and Information Sciences - Papers: Part A

This paper presents a new application of mathematical morphology (MM) operators for low speed slew bearing condition monitoring. The MM operators were used as a signal processing step and feature extraction method for bearing vibration signals. Four basic MM operators; erosion, dilation, closing and opening, were studied. This paper also investigates another potential MM operator, namely gradient operator. Two common time domain features in bearing condition monitoring, namely root mean square (RMS) and kurtosis, were extracted from the processed signal. The study shows that the changes in bearing condition can be clearly detected from the extracted features (RMS and kurtosis) …

A Mathematical Framework Of Human Thought Process: Rectifying Software Construction Inefficiency And Identifying Characteristic Efficiencies Of Networked Systems Via Problem-Solution Cycle, Jonathan Sarbah-Yalley

Master's Theses

Problem

The lack of a theory to explain human thought process latently affects the general perception of problem solving activities. This present study was to theorize human thought process (HTP) to ascertain in general the effect of problem solving inadequacy on efficiency.

Method

To theorize human thought process (HTP), basic human problem solving activities were investigated through the vein of problem-solution cycle (PSC). The scope of PSC investigation was focused on the inefficiency problem in software construction and latent characteristic efficiencies of a similar networked system. In order to analyze said PSC activities, three mathematical quotients and a messaging wavefunction …

Mathematical Modelling Of Highway Traffic Policies, Benjamin Squire, John-Paul Mann, Nathan Minor

Symposium Of University Research and Creative Expression (SOURCE)

Extensive research has been done to model and simulate traffic flow in order to answer valuable questions in the implementation of different traffic policies. A major open question is whether or not the stay right except to pass rule is an efficient traffic policy in terms of traffic flow and safety. We develop a particle-interaction based model which stems from how cars react and make decisions using locally restricted knowledge and observe how snapshots of these processes over a large closed continuous road govern the dynamics of the overall traffic flow. Through computer simulation, we observe and analyze the difference …

Analysis Of Adiabatic Trapping For Quasi-Integrable Area-Preserving Maps, Armando Bazzani, Christopher Frye, Massimo Giovannozzi, Cédric Hernalsteens

Faculty Bibliography 2010s

Trapping phenomena involving nonlinear resonances have been considered in the past in the framework of adiabatic theory. Several results are known for continuous-time dynamical systems generated by Hamiltonian flows in which the combined effect of nonlinear resonances and slow time variation of some system parameters is considered. The focus of this paper is on discrete-time dynamical systems generated by two-dimensional symplectic maps. The possibility of extending the results of neo-adiabatic theory to quasi-integrable area-preserving maps is discussed. Scaling laws are derived, which describe the adiabatic transport as a function of the system parameters using a probabilistic point of view. These …

The Heisenberg Relation - Mathematical Formulations, Richard V. Kadison, Zhe Liu

Faculty Bibliography 2010s

We study some of the possibilities for formulating the Heisenberg relation of quantum mechanics in mathematical terms. In particular, we examine the framework discussed by Murray and von Neumann, the family (algebra) of operators affiliated with a finite factor (of infinite linear dimension).

Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Attractive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder

Faculty Bibliography 2010s

Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation (NLS) modeling attractive Bose-Einstein condensates (BECs) in a small potential are obtained via a form of nonlinear perturbation. The focus here is on perturbations to the bright soliton solutions due to small potentials which either confine or repel the BECs: under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of the bright solitons. Importantly, we do not need to assume that the nonlinearity is small, as we perform a sort of nonlinear perturbation by allowing the zeroth-order perturbation term to be governed by a …

Stationary Solutions For The 2+1 Nonlinear Schrodinger Equation Modeling Bose-Einstein Condensates In Radial Potentials, Kristina Mallory, Robert A. Van Gorder

Faculty Bibliography 2010s

Stationary solutions for the 2 + 1 cubic nonlinear Schrodinger equation modeling Bose-Einstein condensates (BEC) in a small potential are obtained via a form of perturbation. In particular, perturbations due to small potentials which either confine or repel the BECs are studied, and under arbitrary piecewise continuous potentials, we obtain the general representation for the perturbation theory of radial BEC solutions. Numerical results are also provided for regimes where perturbative results break down (i.e., the large-potential regime). Both repulsive and attractive BECs are considered under this framework. Solutions for many specific confining potentials of physical relevance to experiments on BECs …

A Squeeze-Like Operator Approach To Position-Dependent Mass In Quantum Mechanics, Héctor M. Moya-Cessa, Francisco Soto-Eguibar, Demetrios N. Christodoulides

Faculty Bibliography 2010s

We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schrodinger equation may then be applied to find the respective eigenvalues and eigenfunctions. As an example, we consider a position-dependent-mass that leads to the integrable Morse potential and therefore to well-known solutions.

Continuous And Discrete Schrodinger Systems With Parity-Time-Symmetric Nonlinearities, Amarendra K. Sarma, Mohammad-Ali Miri, Ziad H. Musslimani, Demetrios N. Christodoulides

Faculty Bibliography 2010s

We investigate the dynamical behavior of continuous and discrete Schrodinger systems exhibiting parity-time (PT) invariant nonlinearities. We show that such equations behave in a fundamentally different fashion than their nonlinear Schrodinger counterparts. In particular, the PT-symmetric nonlinear Schrodinger equation can simultaneously support both bright and dark soliton solutions. In addition, we study a discretized version of this PT-nonlinear Schrodinger equation on a lattice. When only two elements are involved, by obtaining the underlying invariants, we show that this system is fully integrable and we identify the PT-symmetry-breaking conditions. This arrangement is unique in the sense that the exceptional points are …

Modelling The Rejection Of N-Nitrosamines By A Spiral-Wound Reverse Osmosis System: Mathematical Model Development And Validation, Takahiro Fujioka, Stuart J. Khan, James A. Mcdonald, Annalie Roux, Yvan Poussade, Jorg E. Drewes, Long D. Nghiem

SMART Infrastructure Facility - Papers

A mathematical model was developed based on the irreversible thermodynamic principle and hydro- dynamic calculation to predict the rejection of N-nitrosamines by spiral-wound reverse osmosis (RO) membrane systems. The developed model is able to accurately describe the rejection of N-nitrosamines under a range of permeate flux and system recovery conditions. The modelled N-nitrosamine rejections were in good agreement with values obtained experimentally using a pilot-scale RO filtration system. Simulation from the model revealed that an increase in permeate flux from10 to 30L/m2h led to an increase in the rejection of low molecular weight N-nitrosamines such as N-nitrosodimethylamine (NDMA) (from31% to …

An Advanced Mathematical Model And Its Experimental Verification For Trilayer Conjugated Polymer Actuators, Chuc Nguyen, Gursel Alici, Gordon G. Wallace

Faculty of Engineering and Information Sciences - Papers: Part A

This paper describes the establishment of an enhanced mathematical model and an inversion-based controller based on the proposed model for a trilayer conjugated polymer actuator that will steer a cochlear implant through a 3-D structure. The multilayer electroactive polymer actuator that operates in air will suit many biomedical applications. We propose to use viscoelastic models for the conducting polymer and membrane layers of the actuator so that its mechanical properties can be incorporated into the actuator more accurately. The proposed model accurately predicts the frequency response of the electrical admittance and curvature of the conjugated polymer actuators, and its efficacy …

A Mathematical Analysis Of A Membrane Bioreactor Containing A Sludge Disintegration System, Mark Nelson, Thomas Yue

Faculty of Engineering and Information Sciences - Papers: Part A

The activated sludge process is widely used to treat domestic and industrial wastewater. A significant drawback of this process is the production of "sludge", the disposal of which can comprise a significant proportion of the total operating costs of a wastewater treatment plant. We analyze the steady-state operation of a membrane bioreactor system (MBR) incorporating a sludge disintegration unit (SDU) to reduce sludge production. We provide a qualitative understanding of the model by finding analytically the steady-state solutions of the model and determining its stability as a function of the residence time. In practice a target value of the mixed …

Stationary Solutions For The 1+1 Nonlinear Schrodinger Equation Modeling Repulsive Bose-Einstein Condensates In Small Potentials, Kristina Mallory, Robert A. Van Gorder

Faculty Bibliography 2010s

Stationary solutions for the 1 + 1 cubic nonlinear Schrodinger equation modeling repulsive Bose-Einstein condensates (BEC) in a small potential are obtained through a form of nonlinear perturbation. In particular, for sufficiently small potentials, we determine the perturbation theory of stationary solutions, by use of an expansion in Jacobi elliptic functions. This idea was explored before in order to obtain exact solutions [Bronski, Carr, Deconinck, and Kutz, Phys. Rev. Lett. 86, 1402 (2001)], where the potential itself was fixed to be a Jacobi elliptic function, thereby reducing the nonlinear ODE into an algebraic equation, (which could be easily solved). However, …

Scaling Laws And Accurate Small-Amplitude Stationary Solution For The Motion Of A Planar Vortex Filament In The Cartesian Form Of The Local Induction Approximation, Robert A. Van Gorder

Faculty Bibliography 2010s

We provide a formulation of the local induction approximation (LIA) for the motion of a vortex filament in the Cartesian reference frame (the extrinsic coordinate system) which allows for scaling of the reference coordinate. For general monotone scalings of the reference coordinate, we derive an equation for the planar solution to the derivative nonlinear Schrodinger equation governing the LIA. We proceed to solve this equation perturbatively in small amplitude through an application of multiple-scales analysis, which allows for accurate computation of the period of the planar vortex filament. The perturbation result is shown to agree strongly with numerical simulations, and …

A Mathematical Function To Represent S-Shaped Relationships For Geotechnical Applications, Martin D. Liu, K J. Xu, Suksun Horpibulsuk

Faculty of Engineering and Information Sciences - Papers: Part A

In this paper a new mathematical function is proposed for describing the S-shape relationship in both normal x and y scale and the semi-logarithmic x and y scale. Basic features of the proposed function have been demonstrated. The proposed function has then been used to simulate the S-shape relationship for seven categories of engineering phenomena. It is seen that the proposed mathematical function has a great potential for representing various S-shape relationships and provides a powerful tool for characterising properties of materials or response of systems; it is thus useful for further numerical analysis.

Sludge Formation In The Activated Sludge Process: Mathematical Analysis, Asma O. M Alharbi, Mark I. Nelson, Annette L. Worthy, Harvinder S. Sidhu

Faculty of Engineering and Information Sciences - Papers: Part A

One drawback associated with the activated sludge process is the production of 'sludge'. The expense for treating excess sludge can account for 50-60% of the running costs of a plant. Traditional methods for disposing of excess sludge, which include incineration, the use of landfill sites and dumping at sea are becoming increasingly regulated worldwide due to concerns about the presence of potentially toxic elements in it. Furthermore, a combination of the limited amount of land available for landfill, particularly in urban areas, with stringent legislation has seen the economic costs of using landfill sites increasing sharply. Thus there is a …

Applying Mathematical Model To Simplify The Procession Of Pipeline Route Selection, Jianli Liu, Shuqing Yang, Joseph Wiltshire

Faculty of Engineering and Information Sciences - Papers: Part A

Now there are many pipelines to deliver liquid-like water diversions in the world. Optimal route for pipeline transportation is a major concern for engineers, economists, and decision makers. Pipeline route selection is governed by many factors such as the shortest distance between supply and demand points, constructability, affordability, environmental impacts, and approachability. There are many methods developed for the pipeline route selection like Gestalt method, land suitability mapping techniques, geographic information systems (GIS), imaging technologies for pipeline mapping with the use of airborne lidar, etc. But these methods, though robust in translating physical constraints into feasible alternatives for route location, …

A Mathematical Model For The Biological Treatment Of Industrial Wastewater In A Reactor Cascade, Rubayyi Turki Alqahtani, Mark I. Nelson, Annette L. Worthy

Associate Professor Annette Worthy

Many industrial processes, particularly in the food industry, produce slurries or wastewaters containing high concentrations of biodegradable organic materials. Before these contaminated wastewaters can be discharged the concentration of the biodegradable organic pollutant must be reduced. One way to do this is to pass the wastewater through a bioreactor containing biomass which grows through consumption of the pollutant. Anaerobic conditions are often favoured for the processing of waste materials with high levels of biodegradable organic pollutants as these can be removed with low investment and operational costs. We investigate the steady state effluent concentration leaving a cascade of two reactors. …

A Mathematical Model For The Biological Treatment Of Industrial Wastewaters In A Cascade Of Four Reactors, Annette L. Worthy, Mark I. Nelson, Rubayyi Turki Alqahtani

Associate Professor Annette Worthy

Many industrial processes, particularly in the food industry, produce slurriesor wastewaters containing high concentrations of biodegradable organicmaterials. Before these contaminated wastewaters can be dischargedthe concentration of these pollutants must be reduced. A method which has beenextensively employed to remove biodegradable organic matter is biologicaltreatment. In this process the wastewater (or slurry) is passed through abioreactor containing biomass which grows through consumption of thepollutants.The industrial treatment of wastewaters typically employs a reactor cascade.In a reactor cascade of n reactors the effluent stream from the ith reactor inthe cascade acts as the feed stream for the (i+1)th reactor, i.e. the nextreactor. The …

Mathematical Modelling In Nanotechnology, Ngamta Thamwattana, James M. Hill

Dr Ngamta Thamwattana

The interaction of nano particles with conventional materials dramatically changes all the physical parameters, which usually characterize the bulk material. The nano particles constitute highly reactive isolated sites to the extent that it leads to a change in the electronic structure of the nano composite, and accordingly all the physical properties, such as thermal, mechanical and electrical properties become different from those of the bulk material. To successfully exploit nano composites as components and devices, this fundamental shift of physical properties must be properly understood and accurately modelled. While experimentation is crucial, a theoretical understanding is also necessary and with …

Unifying Model Of Driven Polymer Translocation, T. Ikonen, A. Bhattacharya, T. Ala-Nissila, W. Sung

Faculty Bibliography 2010s

We present a Brownian dynamics model of driven polymer translocation, in which nonequilibrium memory effects arising from tension propagation (TP) along the cis side subchain are incorporated as a time-dependent friction. To solve the effective friction, we develop a finite chain length TP formalism, based on the idea suggested by Sakaue [Phys. Rev. E 76, 021803 (2007)]. We validate the model by numerical comparisons with high-accuracy molecular dynamics simulations, showing excellent agreement in a wide range of parameters. Our results show that the dynamics of driven translocation is dominated by the nonequilibrium TP along the cis side subchain. Furthermore, by …

Spectral Analysis Of Certain Schrodinger Operators, Mourad E.H. Ismail, Erik Koelink

Faculty Bibliography 2010s

The J-matrix method is extended to difference and q-difference operators and is applied to several explicit differential, difference, q-difference and second order Askey-Wilson type operators. The spectrum and the spectral measures are discussed in each case and the corresponding eigenfunction expansion is written down explicitly in most cases. In some cases we encounter new orthogonal polynomials with explicit three term recurrence relations where nothing is known about their explicit representations or orthogonality measures. Each model we analyze is a discrete quantum mechanical model in the sense of Odake and Sasaki [J. Phys. A: Math. Theor. 44 (2011), 353001, 47 pages].

Orthogonal Basic Hypergeometric Laurent Polynomials, Mourad E.H. Ismail

Faculty Bibliography 2010s

The Askey-Wilson polynomials are orthogonal polynomials in x = cos theta, which are given as a terminating (4)phi(3) basic hypergeometric series. The non-symmetric Askey-Wilson polynomials are Laurent polynomials in z = e(i theta), which are given as a sum of two terminating (4)phi(3)'s. They satisfy a biorthogonality relation. In this paper new orthogonality relations for single (4)phi(3)'s which are Laurent polynomials in z are given, which imply the non-symmetric Askey-Wilson biorthogonality. These results include discrete orthogonality relations. They can be considered as a classical analytic study of the results for non-symmetric Askey-Wilson polynomials which were previously obtained by affine Hecke …

Unstaggered-Staggered Solitons In Two-Component Discrete Nonlinear Schrodinger Lattices, Boris A. Malomed, D. J. Kaup, Robert A. Van Gorder

Faculty Bibliography 2010s

We present stable bright solitons built of coupled unstaggered and staggered components in a symmetric system of two discrete nonlinear Schrodinger equations with the attractive self-phase-modulation nonlinearity, coupled by the repulsive cross-phase-modulation interaction. These mixed modes are of a "symbiotic" type, as each component in isolation may only carry ordinary unstaggered solitons. The results are obtained in an analytical form, using the variational and Thomas-Fermi approximations (VA and TFA), and the generalized Vakhitov-Kolokolov (VK) criterion for the evaluation of the stability. The analytical predictions are verified against numerical results. Almost all the symbiotic solitons are predicted by the VA quite …

Exact Solution For The Self-Induced Motion Of A Vortex Filament In The Arc-Length Representation Of The Local Induction Approximation, Robert A. Van Gorder

Faculty Bibliography 2010s

We review two formulations of the fully nonlinear local induction equation approximating the self-induced motion of the vortex filament (in the local induction approximation), corresponding to the Cartesian and arc-length coordinate systems. The arc-length representation put forth by Umeki [Theor. Comput. Fluid Dyn. 24, 383 (2010)] results in a type of 1 + 1 derivative nonlinear Schrodinger (NLS) equation describing the motion of such a vortex filament. We obtain exact stationary solutions to this derivative NLS equation; such exact solutions are a rarity. These solutions are periodic in space and we determine the nonlinear dependence of the period on the …