Physical Sciences and Mathematics Commons^™

Entropy Production In A Fluid-Solid System Far From Thermodynamic Equilibrium, Bong Jae Chung, Blas Ortega, Ashuwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Abstract.: The terminal orientation of a rigid body in a moving fluid is an example of a dissipative system, out of thermodynamic equilibrium and therefore a perfect testing ground for the validity of the maximum entropy production principle (MaxEP). Thus far, dynamical equations alone have been employed in studying the equilibrium states in fluid-solid interactions, but these are far too complex and become analytically intractable when inertial effects come into play. At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive. In our past work, we have shown that the MaxEP is a …

Characterizing The "Realistic-Ness" Of Word Problems In Secondary Mathematics Textbooks, Mary L. Dalton

Theses, Dissertations and Culminating Projects

Word problems are an integral part of any secondary mathematics curriculum and one purpose has been to prepare students for the real-world – for everyday events as well as workplace problem-solving. Prior literature suggests that word problems have not met this objective, in part, because the textbook problems do not mirror the kinds of problems commonly found in real life situations.

In this dissertation, I investigate a sample of word problems from two contemporary non-traditional textbooks to uncover the aspects that may influence if and how the problems might be used in the classroom. I utilize a qualitative content analysis …

Identification Of Dynamic Outliers, Kangkana Sarmah Baruah

Theses, Dissertations and Culminating Projects

Several methods for performing the identification of outliers are described when dealing with functional data. The methods studied include prediction intervals for detection of dynamic functional outliers as well as related methods from the functional data literature. A comparison of methods is performed using metrics for dynamic outlier identification. Simulations and applications to environmental studies illustrate the applicability of the methods. Results obtained from simulation and application to real dataset suggest that Dynamic Function-on-Function Regression is a preferable method for detecting dynamic outliers. This method can detect outliers at a very high identification rate. Identification rate of dynamic outliers increases …

Spin Viscosity Effects In Planar Ferrofluid Couette Flow Of Ferrofluids, LucíA Cataldo Ottieri

Theses, Dissertations and Culminating Projects

Previous studies of planar Couette flow of ferro-fluids in a transverse time-independent external magnetic field are extended to include the effects by spin diffusion. We numerically study the modification in the internal rotation of particles in a colloidal ferro-fluid. In particular, we consider a ferro-fluid between two concentric cylinders, and apply a radial magnetic field inversely proportional to the radial variable. We consider the influence of shear effects by assuming a constant magnetic field while varying the rotation rate of the inner cylinder, and the effects of the balance between shear and magnetic stresses by varying the values of the …

Stochastic Improvisation Of Jazz Solos, Tevin Rouse

Theses, Dissertations and Culminating Projects

We propose using stochastic methods to generate new Jazz solos in the style of an artist of interest. To accomplish this, we implement several Markov models that use an artist’s known solos in order to mimic their pitch selection tendencies. Construction of two unique solos were generated for each artist considered as well as analysis of the characteristics the solos possessed in comparison to the artist’s original solo. This software implementation seeks to offer a new method for creating computer music compositions.

Constructing Magic Squares Of Squares Modulo Certain Prime Numbers, Nicholas Ryan Bilynsky

Theses, Dissertations and Culminating Projects

A magic square is a square table of numbers such that each row, column, or diagonal adds up to the same sum. This research is inspired by an open question posed by Martin Labar in 1984. The open question states: “Can a 3 x 3 magic square be constructed using nine distinct perfect squares?” Though unsolved, this question sheds light on the existence of a Magic Square of Squares modulo a prime number p. For over two thousand years, many mathematicians have looked at these magical properties. In this thesis, the focus is on certain prime numbers p in the …

Quantum Mechanics For Non-Hermitian Hamiltonians With Pt Symmetries, Gustavo D. Duarte

Theses, Dissertations and Culminating Projects

Quantum Mechanics is an axiomatic theory. One of its axioms states that every observable of a physical system is associated with a Hermitian operator allowing the reality of the energy spectrum and a complete set of eigenfunctions. Furthermore, because of the Hermicity imposed on the observable described by the Hamiltonian H, the time evolution of the system is preserved. In recent years, researchers have shown that the Hermicity requirement may be relaxed by a weaker condition described by the combined actions of P and T symmetries on the operator. Under this new regimen some non-Hermitian Hamiltonians have real spectra such …

Joint Modelling Of Longitudinal Measurements And Time-To-Event Data : Application To Hiv Study, Mirna Walid Halawani

Theses, Dissertations and Culminating Projects

Longitudinal and survival data are frequently collected in biomedical studies. The research questions of interest in these studies often require separate analysis of the outcomes. But in many occasions interest also lies in studying their association structures, such as in biomarker research, where the clinical studies are designed to identify biomarkers with strong prognostic capabilities for event time outcomes. In the separate analyses, a linear mixed-effects model is used for modeling the longitudinal data to study the changing trend of the response overtime when controlling some covariates and a survival model is used to model the time-to-event data. A common …

Partitioning Random Graphs Into Monochromatic Components, Deepak Bal, Louis Debiasio

Department of Mathematics Facuty Scholarship and Creative Works

Erdős, Gyàrfàs, and Pyber (1991) conjectured that every r-colored complete graph can be partitioned into at most r – 1 monochromatic components; this is a strengthening of a conjecture of Lovàsz (1975) and Ryser (1970) in which the components are only required to form a cover. An important partial result of Haxell and Kohayakawa (1995) shows that a partition into r monochromatic components is possible for sufficiently large r-colored complete graphs. We start by extending Haxell and Kohayakawa’s result to graphs with large minimum degree, then we provide some partial analogs of their result for random graphs. In particular, we …

Metastable States In Terminal Orientation Of Hinged Symmetric Bodies In A Flow, Doralia Castillo, Bong Jae Chung, Klaus Schnitzer, Karina Soriano, Haiyan Su, Ashuwin Vaidya

Department of Mathematics Facuty Scholarship and Creative Works

Symmetric bodies such as cylinders and spheroidal bodies, in their terminal stable states, are long known to have their long axis align themselves perpendicular to the direction of the flow. This property has been confirmed in primarily sedimentation based theoretical, experimental and numerical techniques and the transition to a terminal stable state is believed to coincide with the onset of significant inertial effects in the flow. However, the threshold at which this transition occurs is yet unknown. We conduct modified experiments with hinged bodies and a CFD study to examine the nature of the transition of prolate spheroids and cylinders …

The Maximum Number Of Complete Subgraphs Of Fixed Size In A Graph With Given Maximum Degree, Jonathan Cutler, A. J. Radcliffe

Department of Mathematics Facuty Scholarship and Creative Works

In this article, we make progress on a question related to one of Galvin that has attracted substantial attention recently. The question is that of determining among all graphs G with n vertices and Δ(G) ≤ r, which has the most complete subgraphs of size t, for t≥3. The conjectured extremal graph is aKr+1 ∪ Kb, where n = a(r + 1) + b with 0 ≤ b ≤ r. Gan et al. (Combin Probab Comput 24(3) (2015), 521–527) proved the conjecture when a ≤ 1, and also reduced the general conjecture to the case t = 3. We prove …

On The Three Dimensional Interaction Between Flexible Fibers And Fluid Flow, Bogdan Nita, Ryan Allaire

Department of Mathematics Facuty Scholarship and Creative Works

In this paper we discuss the deformation of a flexible fiber clamped to a spherical body and immersed in a flow of fluid moving with a speed ranging between 0 and 50 cm/s by means of three dimensional numerical simulation developed in COMSOL . The effects of flow speed and initial configuration angle of the fiber relative to the flow are analyzed. A rigorous analysis of the numerical procedure is performed and our code is benchmarked against well established cases. The flow velocity and pressure are used to compute drag forces upon the fiber. Of particular interest is the behavior …

Freedericksz Transition In Nematic Liquid Crystal Couette Flow, Arup Mukherjee

Department of Mathematics Facuty Scholarship and Creative Works

This article investigates the effects of an external magnetic field on the Freedericksz transition for an elastically anisotropic nematic liquid crystal sample occupying the annular region between two concentric cylinders in relative (slow) rotation. Assuming both azimuthal and radial magnetic fields and strong anchoring conditions for the liquid crystal director perpendicular to the surface of the cylinders, we investigate and characterize the differences in the director distortions and the critical field value for the onset of the transition.

Adult Learners, Learning Disabilities, And Mathematics : A Case Study, Marguerite Sheehan Flood

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand how mathematics is taught at a small, liberal arts college that self-advertised as accommodating diverse learners. A qualitative case study was conducted on the mathematics program at Waterview College. Waterview College is unique in that almost half of their students self-identify with a disability, including learning disabilities (LD). The number of students with learning disabilities that attend college is increasing; therefore it is important for mathematics instructors to understand and accommodate diverse learners. The data for this research were collected using one-on-one instructor interviews, classroom observations, and student focus group interviews. The …