Physical Sciences and Mathematics Commons^™

The Mystery Of The Non-Transitive Grime Dice, Nicholas Pasciuto

Undergraduate Review

No abstract provided.

The Characterization Of Vectors In RN With The Haar Property, Terrence Kelleher

Undergraduate Review

Introduction:
As modern communication becomes more digital than ever, infrastructure tries to maintain an equal pace. Unfortunately, this is not always possible. Therefore, computer scientists and mathematicians alike have endeavored to invent ways to store, send and retrieve data, even if transmitted signals are severely damaged. One such way is by using what is called an error-correcting code, or an ECC. An ECC is a method of encoding information such that a signal that possesses a message can be significantly altered and still be decoded. There are many different types of ECCs. The type that is of interest in this …

Deriving The Dyer-Roeder Equation From The Geodesic Deviation Equation Via The Newman-Penrose Null Tetrad, Aly Aly

Undergraduate Review

In this paper we examine the geodesic deviation equation using the Newman-Penrose (N-P) formalism for a flat Friedmann-Lemaitre-Robertson-Walker(FLRW) metric [Carroll,S. (2004), Ryden, B. (2003), Newman Penrose(1962)]. We solved the geodesic deviation equation for angular diameter distance, using the relevant N-P components, and the resulting expression was the Dyer-Roeder equation of cosmology [Ryden, B. (2003)] [Schneider et al.(1992)]. This leads us to believe that we can apply the N-P formalism to a perturbed FLRW metric and find a solvable equation for angular diameter distance [Kling Campbell(2008)]. The perturbed FLRW metric incorporates clumps of matter into a metric that is on average …

Dynamics Of Climate Change: Explaining Glacier Retreat Mathematically, Robert Guillette

Undergraduate Review

Climate change is an important topic that has become extremely relevant this day and age. The world’s climate is undergoing monumental shifts with over two-thirds of the estimated 150 glaciers existing in 1850 disappearing by 1980. The melting of glaciers offers tangible evidence of broader environmental changes as they respond directly to long-term trends in temperature, precipitation, and solar radiation. Since the study of glacier retreat provides a barometer of climate change, it is important to better understand the effects of climatic factors on glaciers. In my project I created a mathematical model for the melting of glaciers and used …

Size-Frequency Distribution Of Orbitolina Texana Foraminifera, Jeremy Foote

Undergraduate Review

This study examined size-frequency distributions for an extinct Cretaceous-age benthic foraminifera called Orbitolina Texana in order to determine the health of this foram community during the time of accumulation. Forams were collected from limestone outcrops of the Glen Rose Formation in central Texas. Based on paleontological and sedimentological evidence, Orbitolina Texana are interpreted to be a shallow water (<10 m) benthic organism that was most abundant in back-reef environments. Sizefrequency distributions were generated from the diameters of 4,245 Orbitolina Texana fossils. The results indicate that the Orbitolina Texana population is characterized by a Gaussian (normal) size distribution. Size-frequency distributions of fossilized foraminifera in the stratigraphic record are controlled by two principle variables; environmental controls that affect the biology of the organisms (e.g., environmental stressors, like food availability and ambient conditions) and sedimentological controls that affect how the organisms are distributed (e.g., hydrodynamic parameters, like waves and currents). Based on a sedimentological characterization of the host limestone including lack of high-energy sedimentary structures, high mud content and back-reef position on the depositional profile, hydrodynamic parameters are interpreted to not have exerted a significant effect on the distribution of the forams preserved in the rock record. As such, the biological controls are interpreted to be the dominate control on the foram sizefrequency distribution. Therefore, the Gaussian (normal) size distribution suggests that the mortality rate is independent of size/age, which is classified as Type II survivorship. As this result is consistent with similar taxon, the results indicate that this Orbitolina Texana population was a healthy biologic community, despite the low biologic diversity observed in the Glen Rose Formation.

A Mathematical Analysis Of A Game Of Craps, Yaqin Sun

Undergraduate Review

The game of craps is an extremely popular game offered by casino operators. There are some 40 different types of bets that one can place each time the game is played. One of the best bets from a player’s point of view is the Pass Line bet. The probability of winning a Pass Line bet is almost the same as the probability of losing (²⁴⁴⁄₄₉₅ versus ²⁵¹⁄₄₉₅) as we will derive rigorously in this article. Since the “house” has such a small advantage over the players, many players possess the illusion that they have …

The Archbishop's Odyssey, Leonard Sprague

Undergraduate Review

For centuries, scholars have analyzed a collection of problems that, nowadays, has been defined as NP-complete. Currently, NP-complete problems have no known efficient solutions. The Clay Mathematics Institute has offered a reward of one million dollars for a solution. The problem of finding Hamilton paths and cycles has been shown to be in this category. Knight’s tours, where the knight must visit every square of a chessboard exactly once, are examples of Hamilton paths and cycles.

This research revolves around the creation of a new branch of the tour problems, through a new piece: the Archbishop. Chess Grandmaster Jose Capablanca …

Applying Green Chemistry Principles In The Electrophilic Bromination Of Indole-3-Acetic Acid, Kyle Murphy

Undergraduate Review

The goals of green chemistry are to reduce or eliminate the use of hazardous reagents, prevent the synthesis of toxic products and byproducts, and improve the overall efficiency of chemical reactions. Green chemistry is incredibly important today as chemical products are produced and used around the world, resulting in the use and generation of hazardous chemicals, and unintended consequences to human health and the environment. Figure 1 shows the 12 Principles of Green Chemistry1, developed by Paul Anastas and John Warner, which provide the framework for a sustainable future in the design of more efficient technologies to produce consumer products …

A Strategic Analysis For Small Hydro Power (Shp) Development In Himachal Pradesh, India, Steven Spicer

Undergraduate Review

In addition to India currently being the second most populated country in the world, economists at Goldman Sachs have listed India as one of the five BRICS countries (Brazil, Russia, India, China, and South America) projected to be most dominant economies by 2050. In spite of the rapid growth in India’s economy, there are still many serious issues affecting the majority of its people. The US Energy Information Administration reports that roughly 25% of India’s 1.2 billion people are living without access to electricity; which translates to 300 million citizens without power (EIA, 2013). Various estimates put India’s energy supply …

Research Brief: Applying Green Chemistry Principles Towards The Sustainable Synthesis Of Biodiesel From Waste Vegetable Oil, Brandon Ackley

Undergraduate Review

In 2011, the U.S. consumed over 18 million barrels per day of refined petroleum products and biofuels; almost 22% of global petroleum consumption. This includes oil used for transportation, electricity, and production of consumer products. More than half of this oil was imported from foreign countries, and in his 2006 State of the Union Address President Bush warned that, “We have a serious problem, America is addicted to oil, which is often imported from unstable parts of the world”. With the need for new energy sources more apparent than ever, serious research is needed to further the advancement of alternative …

Who Wants To Play Sadisticube?, Danica Baker

Undergraduate Review

Logic puzzles and games are popular amongst many people for the purpose of entertainment. They also provide intriguing questions for mathematical research. One popular game that has inspired interesting research is Rubik’s Cube. Researchers at MIT have investigated the Rubik’s Cube to find the maximum number of moves, from any starting position, needed to win the game [6]. Another logic puzzle that has recently become very popular is Sudoku. Sudoku is a Japanese number game where a 9x9 grid is set up with a few numbers scattered on the grid. Mathematicians have been investigating Sudoku, exploring questions such as the …

Hydropower Development In Himachal Pradesh: A Stakeholder Equity Analysis, Eliott Rousseau

Undergraduate Review

Seen as the champion of green energy to some and environmentally disastrous to others, hydropower is a multifaceted issue. As it continues to be developed in India, some of the most remote locations and vulnerable people are being affected. This paper holistically examines the process of hydropower development in rural Himachal Pradesh. The locus of this study is tribal region of Bharmour Tehsil within Chamba District of Himachal Pradesh, India. Aspects pertaining to project commission, the consent process, and government sponsored rural development schemes are examined, with emphasis given to equity among rural stakeholders. The nature of this project was …

Environmental Considerations Of Small-Scale Hydroelectric Power Plants In Himachal Pradesh, India, Darwin Werthessen

Undergraduate Review

The need for increased energy production in India is high priority and hydroelectric power has been identified as having the greatest potential for achieving energy independence. The Indian government has continually created more streamlined methods for efficient implementation of hydroelectric facilities with an emphasis on small-scale (<25 MW) and micro (<5 MW) facilities in the more remote regions. Himachal Pradesh has effectively achieved one hundred percent electrification due to these initiatives and realized some of the most successful development in the nation with respect to rural electrification and improved infrastructure such as roads, schools, and hospitals. Hydroelectricity, and especially that produced through run of the river type systems, is generally embraced as a renewable source of energy by many established standards. Small scale run of the river facilities are also heralded for the minimal impact to the environment. However, with increased development and construction in continually industrializing areas, measurable human impacts have increased felt within the environment and ecosystems. Several studies and papers published by the Indian government, as well as the state government of Himachal Pradesh, identify these impacts as low to nonexistent. In contrast, a growing number of studies refute this claim and deserve consideration. There is a diversity of opinion on this subject. Some secondary sources indicate minimal to non-existent environmental impacts stemming from projects less than 25 MW, considered as Small Hydro Power (SHP); while other sources express significant concern. Interviews with government officials and researchers in the Indian states of Himachal Pradesh and Uttarakhand as well as in the capital city of Delhi revealed a wide range of views. This paper presents observations and argues for greater exploration of these issues through future research.

Delineation And Characterization Of The Furnace Brook Watershed In Marshfield, Massachusetts: Potential Impact Of Water Supply Extraction, Erik Croll

Undergraduate Review

The Furnace Brook watershed in Marshfield, Massachusetts supplies a coastal community of 25,132 residents with nearly 45% of its town water supply (Marshfield 2012a). As in many other coastal communities, development pressure in Marshfield has increased in recent years, creating a growing demand for freshwater extraction. It has been observed, however, that portions of the stream and Furnace Pond disappear entirely at certain times of year, generally between June and August, depending on the rate of groundwater extraction. This has created a conflict between protecting the designated wetland areas and meeting public pressure for water resources, even within what is …

The Effect Of Hydrochloric Acid Strength On The Nanometer-Scale Dissolution Topography Of Calcite Crystal Surfaces, Jennifer Fruzzetti

Undergraduate Review

The physico-chemical mechanisms by which rock-forming minerals dissolve in natural fluids are controlled by a number of environmental factors. In this study, we investigate dissolution mechanisms by observing how the nanometer-scale surface topography of calcite is affected by the acidity of etching solutions. Here we report atomic force microscope (AFM) observations of calcite crystal surfaces both before and after chemical etching for 10 seconds in 0.01%, 0.1%, and 1.0% HCl solutions. AFM observations show that unetched, freshly-cleaved calcite {10ī4} crystal surfaces are characterized by flat layers separated by steps oriented parallel to calcite cleavage planes. Calcite {10ī4} crystal surfaces etched …

Modeling Plaque Aggregation On The Neuronal Network, Thomas Howard

Undergraduate Review

Alzheimer’s disease is a condition linked to plaque aggregation in the brain. Despite being the focus of many studies, current treatments are of questionable significance in the overall improvement of a patient’s condition. In recent years, computer models have been used to better understand complex biological systems and simulate the effects of various treatments. In the following paper we present a mathematical model studying the effects of plaque aggregation on the neuronal pathways of the human brain. To create our mathematical model we employ tools from the theory of dynamical systems and stochastic processes, and simulate the passage of a …

Exploring Diagonals In The Calkin-Wilf Tree, Matthew Gagne

Undergraduate Review

For centuries, people have been interested in patterns. Even in that which appears random, humans have been trying to understand the underlying order of things. Mathematicians throughout time have studied many phenomena, including infinite sequences of numbers and have been able, at times, to see structure. Many have found the satisfaction, even joy, of discovering patterns in sequences. A typical way to describe this is by a recursive formula. A recursive definition defines a term in the sequence using the previous terms in the sequence. Even more satisfying than a recursive formula is a closed formula. With this, one can …

Computer Programming To Advance Gravitational Lensing, Alex Roche

Undergraduate Review

The purpose of this research was to create a computer code that would numerically test a Poisson equation relating the mass distribution of a lens galaxy cluster to weak gravitational shear. Einstein’s theory of general relativity predicts that space-time is bent by massive objects, and in weak gravitational lensing, galaxy clusters act as lenses. The observable result is that galaxies far behind the gravitational lens will appear slightly more elliptical than they actually are. The ellipticity of the background galaxies is quantifiable and is directly related to the weak gravitational shear, and the shear is used to determine the mass …

A Greener Disney, Cidalia Pina

Undergraduate Review

Disney brings nature and environmental issues to the forefront with its non-confrontational approach to programming meant for children. This opportunity raises awareness and is relevant to growing environmental concerns. However this awareness is just a cursory start, there is an imbalance in their message and effort with that of their carbon footprint. The important eco-messages that Disney presents are buried in fantasy and unrealistic plots. As an entertainment giant with the world held magically captive, Disney can do more, both in filmmaking and as a corporation, to facilitate a greener planet.

Sedimentary Petrology And Provenance Of The Teddy Creek Group Sw Montana, Renee Holt

Undergraduate Review

A previously undocumented sequence of sedimentary rocks has been identified within SW Montana and informally named the Teddy Creek Group (TCG). This project focuses on the field relations, mineral compositions, and textures of these rocks to determine their origin and relationship to the more regionally extensive Cenozoic Renova Formation.

Development Of Biomarkers For Endocrine Disrupting Compounds In The Fathead Minnow, Pimephales Promelas, Tara Frare

Undergraduate Review

Organic waste compounds (OWC’s) are an environmental concern that can have adverse effects on humans, animals, and the environment. Ethinyl estradiol (EE2) is one common OWC and is an active ingredient in oral birth control pills. The presence of EE2 in aquatic environments and drinking water can be linked to decreased fertility and altered physiology in fish. I am developing Q-PCR biomarkers to detect changes in fish at low concentrations before adverse effects occur at higher concentrations. RNA was extracted from twenty fathead minnows that had not been exposed to OWC’s and will be used to synthesize cDNA. Thus far …

Analyzing The Galois Groups Of Fifth-Degree And Fourth-Degree Polynomials, Jesse Berglund

Undergraduate Review

It is known that the general equations of fourth-degree or lower are solvable by formula and general equations of fifth-degree or higher are not. To get an understanding of the differences between these two types of equations, Galois theory and Field theory will be applied. The Galois groups of field extensions will be analyzed, and give the solution to the query “What is the difference between unsolvable fifth-degree equations and fourth-degree equations?”

Analysis Of The “Travelling Salesman Problem” And An Application Of Heuristic Techniques For Finding A New Solution, Mateusz Pacha-Sucharzewski

Undergraduate Review

In 1832, a German travelling salesman published a handbook describing his profession. Sadly, his name is unknown; he only stated that the book was written by “one old travelling salesman.” However, he has come down in history thanks to a rather simple and quite obvious observation. He pointed out that when one goes on a business trip, one should plan it carefully; by doing so, one can “win” a great deal of time and increase the trip’s “economy.” Two centuries later, mathematicians and scientists are still struggling with what is now known as the “Travelling Salesman Problem” (TSP).

Stable Isotopic Constraints Of The Turpan Basin In Northwestern China, Allen J. Schaen

Undergraduate Review

Stable isotopic analysis of sedimentary rocks can be used to reconstruct past geologic changes in the elevation and climate of topographic features such as mountain ranges and plateaus. The Tibetan Plateau is an ideal field laboratory for conducting this type of study because of the Plateau’s extreme topographic relief and relatively recent geologic growth. Here we present oxygen and carbon isotope compositions from a suite of sedimentary rock samples taken from the western Turpan Basin in northwestern China. This area of the basin collects sediment from weathering and erosion of the Bogda Shan located to the north. The goal of …

The Invasive Asian Shore Crab, A Dominant Species On Southeastern Massachusetts Beaches: A Cause For Concern, Kimberly Westgate

Undergraduate Review

The non-native Asian shore is becoming a dominant species in southeastern Massachusetts beaches. A study was conducted to test whether environmental conditions across beaches in southeastern Massachusetts had an effect on the crab species inhabiting those areas. Although this was the main focus, it was found that the invasive Asian shore crab has had an ecological impact on the native crab populations. Six southeastern Massachusetts beaches (Scituate Beach, Plymouth Beach, Mass Trust Estuary, Ellisville Harbor, Gooseberry Island, and Sandwich Marsh) were visited and crab species were counted in measured sites, generally two sites pe r beach. Crab species found were …

Solar Observations During A Solar Minimum Using A Small Radio Telescope, Gary Forrester

Undergraduate Review

The Sun is currently in a quiescent phase called solar minimum. We used Bridgewater State College’s (B.S.C.’s) Small Radio Telescope (SRT) to observe solar radio emission during this quiet phase and correlated our data to solar X-ray data readily available through the National Oceanic and Atmospheric Administration (NOAA). Previous observations made during a period of high solar activity (solar maximum) using one of M.I.T.’s SRTs showed that some solar radio and X-ray events were correlated, while others were not. We made observations during solar minimum and found one event where there was a correlation between radio and X-ray emission.

Regional Vs. Local Impact Of Wind On Glaciers In The Andes Mountains, Derek Ferris

Undergraduate Review

Northern Peru will face critical water resource issues in the near future as permanent ice in the Andes Mountains continues to rapidly melt. Ironically, the melt-water from these glaciers supports the culture of 100s of thousands of people living at lower elevations, particularly during the dry season, and predictions suggest some glaciers may be gone in less than 100 years. The impact of local warming of “U” shaped valleys running down the dryer western slope of the Andes range is largely disregarded in current climate model predictions because of the complexity of simulating the complex topography. Studies that compare the …

A Two-Dimensional, Linear–Elastic Model To Explain Radial Extensional Fractures, Pantheon Fossae, Caloris Basin, Mercury, Brianne Mcdonough

Undergraduate Review

In this study, two-dimensional linear elasticity theory is used to model the lithospheric stress field that produces radial extensional fractures observed at Pantheon Fossae in the Caloris Basin of Mercury. These fractures were imaged by the MESSENGER mission flyby of Mercury on January 14, 2008 and show radial fractures extending outward from a 40-kilometer impact crater named Apollodorus. Recent studies have proposed several different mechanisms to explain these fractures, including magmatic processes, central basin uplift, and stresses produced by the formation of the impact crater itself.

EΠi + 1=0: The History & Development, Dawne Charters-Nelson

Undergraduate Review

I have on occasion run across the equation in books, articles and in conversation with other mathematicians. In each of these encounters the person alluded to a fascination with this equation which links the five most important constants in the whole of analysis:

• 0 = The additive identity
• 1 = The multiplicative identity
• π = The circular constant
• e = The base of the natural logarithms
• i = The imaginary unit

Being a novice mathematician, I wondered how all these fundamental constants could end up in one equation and what it meant. Along with this thought came the realization that …

An Optical Scalar Approach To Weak Gravitation Lensing, Louis Bianchini

Undergraduate Review

We assume a thick gravitational lens governed by a Baltz n=1 matter density model. From the gravitational potential we then derive expressions for a Weyl tensor component and Ricci tensor component. A perturbative approach is taken to solve for the convergence and shear as given by Sach’s equation. By applying the geodesic deviation equation to a bundle of light rays with our expressions for the optical scalars we are able to derive expressions for the image shape and size at any point along the path from source to observer, in the case of an axially symmetric lens and source.