Physical Sciences and Mathematics Commons^™

Using Mathematical Research Methods To Solve A Problem In Music Theory Instruction, Specifically, The Teaching Of Secondary Dominant Chords, Angela Ulrich

Williams Honors College, Honors Research Projects

The mathematical method for research is used to find a solution to a problem in music theory: understanding and identifying secondary dominant chords. By reviewing and assessing the teaching methods of university professors and theory textbooks, and comparing those findings with student reviews, a new method for teaching the concept is developed. The proposed system incorporates aural, visual, and kinetic exercises to serve every learner. The literature review and sample unit plan are followed by a possible procedure for testing the effectiveness of the new method.

3d Printing Applications Within Spectrophotometry, Eric J. Stanczyk

Williams Honors College, Honors Research Projects

Ultraviolet-visible spectroscopy is a tool used throughout the field of chemistry and in chemical labs across the world. Spectrophotometers are a core technology in analytical chemistry, and are used to obtain accurate data on solution concentration. Unfortunately spectrophotometers can be difficult to obtain due to their high cost and low availability outside of a laboratory; this is especially true in either high school or lower grades where buying a spectrophotometer could be considered unreasonable due to price. There are ways to obtain cheaper spectrophotometers, but they can have a high initial cost or low overall quality. This paper will discuss …

Microstructure And Deformation Mechanism Analysis Of Carbonate Rock Located In An Anticline, Natalie R. Zidd

Williams Honors College, Honors Research Projects

Rock samples were collected from the Tensleep formation in the Seminoe Mountains located in Carbon County, Wyoming. These samples were analyzed to determine the deformation mechanisms operating during small scale displacement faulting. There are three distinct zones included in the sample which includes the undeformed Tensleep, fine grained layers with grain size variation, and porous layers with grain size variation. The microstructures in the fine grained layer were consistent with deformation by crystal plastic deformation mechanisms; whereas, the microstructures in the porous layer were consistent with brittle deformation mechanisms. The microstructures in these rocks are nearly identical to those observed …

The Diameter Of A Rouquier Block, Andrew Mayer

Williams Honors College, Honors Research Projects

For my Honors Research Project, I will be researching special properties of Rouquier blocks that represent the partitions of integers. This problem is motivated by ongoing work in representation theory of the symmetric group. For each integer n and each prime p, there is an object called a Rouquier block; this block can be visualized as a collection of points in a plane, each corresponding to a partition. In this group of points, we say a pair of points is “connected” if certain conditions on the partitions are met. We compare each partition with each other partition, add edges when …

Effects Of Invasion Timing In A One-Dimensional Model Of Competing Species With An Infectious Disease, Eliza Jacops

Williams Honors College, Honors Research Projects

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore …

Wavelet Transform Of Optical Conductivity Of Bi2sr2cacu2o8+X In The Normal And Superconducting State, Patrick Janovick

Williams Honors College, Honors Research Projects

This paper compares the wavelet transform of the optical conductivity of Bi₂Sr₂CaCu₂O_8+x in both the normal and the superconducting state. The wavelet transforms of the normal and superconducting state are also compared with wavelet transforms of the Drude model as well as the Lorentz model. The wavelet transform of the collected data for Bi₂Sr₂CaCu₂O_8+x is similar in shape to the Drude model. The wavelet transform of the collected data in the normal state corresponds to the Drude model with a high scattering rate and the collected …

Diversification And Market Neutral Portfolios In S&P500, Alan S. Agnew

Williams Honors College, Honors Research Projects

Our goal is to investigate strategies to deal with the risks associated with holding asset in the stock market. We first deal with risk of holding a specific stock, by the use of diversification. Later, we’ll attempt to deal with the market risk, which is the risk of entire market going up and down. Data used in this project comes from daily adjusted closing price of stocks listed in the S&P500 index ranging from January 3^rd, 2000 to December 31^st, 2015 and the data is processed using statistical software R.

Sections 2 through 4 of this …

The Changes In Woodlot Land Cover From 1988 To 2006 Within Private/Farmland In Hancock County, Ohio, Louis C. Birchall

Williams Honors College, Honors Research Projects

The amount of woodlots in Ohio have dramatically decreased since the introduction of settlers into the State. The removal of forest for open space, urban areas, fuel and resources was key to this change. Since the development of the economy to a more service based industry in recent years, woodlots have begun to return in certain areas. This research shows the change in woodlot patterns in Hancock County, Ohio from 1988 to 2006.

The analysis was done by classifying the data into 'woodlot' and 'other land use' by using image segmentation and manual editing processes. Accuracy checks were conducted on …

Zipping Towards Stem: Simulation Wind Tunnel, Devon A. Goldberg, Emma Pierson, Brandon Hein, Jeremy Hein, Greg Flohr

Williams Honors College, Honors Research Projects

The simulation wind tunnel program created for this project is implemented within a larger, National Science Foundation funded project titled Zipping Towards STEM: Integrating Engineering Design into the Middle School Physical Science Curriculum. Over the course of the next two years, all Akron Public School 8th grade students will go through the Zipping Towards STEM project curriculum. The students will be exposed to the typical steps of engineering design (computer modeling, simulation, building, and testing) and learn about the fundamentals of aerodynamics through the design of their own Soap Box Derby mini-cars. The virtual wind tunnel will be used …

Black Cloud Randomization Test, Nicholas S. Vanni

Williams Honors College, Honors Research Projects

The Black Cloud Randomization Test looks at a nontraditional question and attempts to answer the question using unique statistics. The purpose of this paper is to apply what has been learned throughout the years and apply this knowledge to a final project. Data for this project follows an emergency room’s on call schedule, as well as the number of traumas that came in during each day shift. The project builds on what has been already learned and helps to open a different way of working with statistics. The project was coded in the R software. With different restrictions, there are …

Comparison Of Option Price From Black-Scholes Model To Actual Values, Matthew J. Krznaric

Williams Honors College, Honors Research Projects

The Black-Scholes model is a widely used method for pricing European-style options in a straightforward way, through the use of calculations and ideal market assumptions. Due to certain unrealistic ideal conditions exercised by the model, The Black-Scholes technique of pricing options may not be entirely accurate in implementation. This paper addresses these problems due to the model limitations, determining how The Black-Scholes method compares to the results when using the actual data. Using a mix of historical S&P500 data and generated normal distributions, we first calculated and graphed option prices through the Black-Scholes formulas. With the help of R, we …

Illustrating Pit Initiation And Evolution In Aluminum Alloys According To A 3-Dimensional Cellular Automata Based Model, Kathryn Stalker

Williams Honors College, Honors Research Projects

The objective of this work is to develop a cellular automata based model of pitting initiation and subsequent three-dimensional evolution of pit shapes. Here, a cellular automaton is a collection of cells, each of which may be in one of two states, metallic or electrolyte, arranged over a grid. Pit initiation is implemented over a 2-dimensional grid representative of the metal surface while pit propagation is resolved over a 3-dimensional grid which describes a subsection of the bulk metal. The size of the bulk metal will be on the order of millimeters, and a layer of electrolyte, in which chloride …

Price Signaling In A Two-Market Duopoly, Matthew Hughes

Williams Honors College, Honors Research Projects

Within any industry, firms typically produce related products over multiple subsequent periods in an attempt to build consumer loyalty and achieve continued sales. Apple releases new iPhones and car companies produce new models every year, relying on consumers believing each new product is of high quality. Firms rely on the spillover effects from previous markets, where firms are able to more easily demonstrate their product's quality to the consumers before purchase. The goal is to find a range of prices which allows the high quality firm to distinguish its type to consumers via the price pH and if spillover effects …

Subgroups Of Finite Wreath Product Groups For P=3, Jessica L. Gonda

Williams Honors College, Honors Research Projects

Let M be the additive abelian group of 3-by-3 matrices whose entries are from the ring of integers modulo 9. The problem of determining all the normal subgroups of the regular wreath product group P=Z₉≀(Z₃ × Z₃) that are contained in its base subgroup is equivalent to the problem of determining the subgroups of M that are invariant under two particular endomorphisms of M. In this thesis we give a partial solution to the latter problem by implementing a systematic approach using concepts from group theory and linear algebra.

Rubber Roads For The Rubber City: Testing The Suitability Of Rubberized Asphalt For Roads In Northeast Ohio, Jessica M. Fraser

Williams Honors College, Honors Research Projects

This research paper explores the benefits of using rubberized asphalt concrete (RAC) versus normal asphalt concrete (NAC) and why it is environmentally important. New road construction and repair of roadways due to potholes are always occurring in Northeast Ohio. Recently, the city of Akron’s transportation budget has increased, which includes projects such as reconstructing asphalt and resurfacing pavements throughout the city of Akron. Using rubberized asphalt may improve the quality of our roads and reduce roadway degradation which will likely save cities money.

Using rubberized asphalt recycles old tires, which do not decompose, and creates a positive use for them …

New Facets Of The Balanced Minimal Evolution Polytope, Logan Keefe

Williams Honors College, Honors Research Projects

The balanced minimal evolution (BME) polytope arises from the study of phylogenetic trees in biology. It is a geometric structure which has a variant for each natural number n. The main application of this polytope is that we can use linear programming with it in order to determine the most likely phylogenetic tree for a given genetic data set. In this paper, we explore the geometric and combinatorial structure of the BME polytope. Background information will be covered, highlighting some points from previous research, and a new result on the structure of the BME polytope will be given.

The Synthesis Of Poly(Propylene Fumarate), Brian N. Fitch

Williams Honors College, Honors Research Projects

Poly(propylene fumarate) is a promising material in the field of bone tissue engineering. A recently described chain growth polymerization was developed for the synthesis of poly(propylene fumarate). This pathway uses the ring-opening polymerization of maleic anhydride and propylene oxide with magnesium ethoxide as an initiator to yield poly(propylene maleate). The poly(propylene maleate) was then isomerized to poly(propylene fumarate) using diethyl amine. In order to scale up the reaction to a 20L reactor, several optimizations of the purification schemes was required. The main optimizations were done to the purification of poly(propylene maleate). Several methods were tested including replacing the water washes …

Diffusive Behavior Of Physically Cross-Linked Hydrogels, Morgan A. Stilke

Williams Honors College, Honors Research Projects

A hydrogel is a water swollen polymeric network that has the potential to transform a variety of biomedical applications because of its biocompatibility and water content. Unfortunately, hydrogels typically have poor mechanical robustness. The majority of the content is water, while the remaining structure consists of a physical network, a covalent network, or a combination of both, yielding strength and toughness. There are several strategies attempted to improve mechanical properties including double network hydrogels comprised of two interpenetrating networks: one being a highly crosslinked sacrificial network and the other being a weakly crosslinked network that maintains reversibility after deformation. However, …

Identification And Quantification Of Zooplankton In Ne Ohio Drinking Water Reservoirs, Michael Vigorito

Williams Honors College, Honors Research Projects

Cyanobacteria, or blue-green algae, are present in most freshwater ecosystems and are usually harmless. When these algae swell in numbers, they release harmful toxins that can be detrimental to animal and human health, and can destroy ecosystems. For this reason, many scientists and engineers have studied these harmful algal blooms in an attempt to predict, prevent, or control them to keep people and ecosystems safe. One of the variables in this investigation is the presence and quantity of zooplankton. These animals could play an important role in the prevalence of cyanobacteria, but more information is needed to determine what that …

Controls On Joint Formation During Glacial Unloading Of The Sharon Sandstone At Gorge Metropark, Akron, Ohio, Abigail N. Ritter

Williams Honors College, Honors Research Projects

The transition between significantly different materials is known to inhibit crack propagation, i.e. automobile glass, machinable ceramics and joints in different lithologies. In order to determine if a significant material transition, or a surface, such as a bedding plane, has a greater impact on inhibiting joint formation, I investigated discontinuous joints that formed during glacial unloading of the Sharon Sandstone, which is exposed at Gorge Metropark in Akron, Ohio. The Sharon Sandstone is a medium grained quartz arenite of Early Pennsylvanian age with significant cross-bedding, and contains many continuous (i.e. through-going), and discontinuous, joints in similar orientations. Stress fields created …

Galvanically Induced/Accelerated Crevice Corrosion, Zachary R. Roland

Williams Honors College, Honors Research Projects

In this thesis, a one dimensional model is developed to investigate the initial stages of corrosion in a fastener assembly consisting of a stainless steel fastener and aluminum 7075 as the plate. Differential equations are formulated and solved to determine the profiles for the potential, the oxygen concentration, and the aluminum ion concentration in the crevice, and also the potential in the bulk electrolyte. This fastener system exhibits galvanic corrosion, pitting corrosion, and crevice corrosion. It is found that the potential decreases monotonically down the length of the crevice, the oxygen concentration decreases exponentially down the length of the crevice, …

Mutagenesis-Based Active-Site Characterization Of The Diabetes Drug Target Mitoneet, Lisa Mickley

Williams Honors College, Honors Research Projects

This project investigates the cluster stability of an outer mitochondrial membrane protein mitoNEET under mutational stress and drug binding analysis. MitoNEET is a part of a class of proteins that coordinate an Fe-S molecule into its tertiary structure. This protein is believed to facilitate the oxidative capacity of the electron transport chain by reversible loss of its coordinated Fe-S molecule. The research of this paper uses site directed protein mutagenesis to selectively alter the three cysteine, one histidine cluster coordination into more common coordination patterns such as two cysteine, two histidine or four cysteine. The ultimate goal is to optimize …

Optimizing Solvent Blends For A Quinary System, Thomas L. Hoy

Williams Honors College, Honors Research Projects

The Department of Polymer Engineering had received a grant from the Keck foundation to produce a process in which hundreds of copolymers can be formulated, synthesized, analyzed and then extrapolated to produce the optimal polymer for the desired material property. This process involves synthesizing approximately fifty polymers in a custom apparatus, none of which necessarily have the same monomer components. This leads to issue of which solvent or blend of solvents to use that would sufficiently dissolve both monomers and the resulting copolymer. If the monomers are not completely dissolved, a homogenous reaction will be impossible and if the copolymer …

Srcmx: A Gui Application For Srcml, Brian Kovacs

Williams Honors College, Honors Research Projects

srcMX is a GUI application that utilizes the srcML command-line tool to convert and display source code using the srcML format. The goal is for srcMX to promote the manipulation and exploration of source code using srcML. I also hope that the user-friendly nature inherent to GUI applications allows srcMX to introduce a larger audience to the many features offered by srcML. The application is written in C++ using the Qt and Qt Quick frameworks.