Digital Commons Network^™

Electronic Detection Of Ultra Cold Neutral Plasma, Nirakar Poudel

Honors Theses

The project was started with an objective to investigate the effect of radio fre- quency absorption in Ultra Cold Neutral Plasmas (UNPs). The plasma oscillation is density dependent and can be excited by using external radio frequency field. A homodyne circuit is used to detect direct absorption of the radio frequency waves. The radio frequency waves are applied to conducting meshes which lie on either side of the plasma. The meshes are effectively a capacitor, which together with inherent circuit resistance constitute a high pass filter. A small part of the gain and phase shift of the filter depend on …

The Radon Transform And The Mathematics Of Medical Imaging, Jen Beatty

Honors Theses

Tomography is the mathematical process of imaging an object via a set of finite slices. In medical imaging, these slices are defined by multiple parallel X-ray beams shot through the object at varying angles. The initial and final intensity of each beam is recorded, and the original image is recreated using this data for multiple slices. I will discuss the central role of the Radon transform and its inversion formula in this recovery process.

From Pond To Pump: Microalgae As A Feedstock For Biodiesel, Anna H. Leavitt

Honors Theses

The global reliance on fossil fuels is an unsustainable practice that has led to the depletion of finite resources and the accumulation of greenhouse gases in the atmosphere, leading to global climate change (Demirbas 2010). Transportation accounts for about a third of carbon dioxide (CO2) emissions in the United States. Demand for oil continues to increase and resources are becoming more uncertain. Increased production of renewable fuels such as biofuels can help ease the dependence on fossil fuels. Although interest and production in biofuels has been increasing in the past decade, current feedstocks do not meet efficiency needs and some …

Odd Or Even: Uncovering Parity Of Rank In A Family Of Rational Elliptic Curves, Anika Lindemann

Honors Theses

Puzzled by equations in multiple variables for centuries, mathematicians have made relatively few strides in solving these seemingly friendly, but unruly beasts. Currently, there is no systematic method for finding all rational values, that satisfy any equation with degree higher than a quadratic. This is bizarre. Solving these has preoccupied great minds since before the formal notion of an equation existed. Before any sort of mathematical formality, these questions were nested in plucky riddles and folded into folk tales. Because they are so simple to state, these equations are accessible to a very general audience. Yet an astounding amount of …

Geodynamic Constraints On The Flow Of Samoan-Plume Mantle Into The Northern Lau Basin, Nathan Katsiaficas

Honors Theses

The northernmost portion of the Lau basin, South Pacific, features numerous geochemical and geophysical anomalies. These include: (1) a strong latitudinal gradient in the trace element and isotopic (Sr-Nd-Pb) enrichment of basalts erupted along the various back-arc spreading centers (BASCs) within the basin, (2) high 3He/4He (up to 28 times RA, where RA, the ratio in Earth's atmosphere, is 1.4 x 10-6) in basalts erupted along some portions of the BASCs (e.g., Rochambeau Bank), and (3) the presence of trench-parallel shear-wave splitting near the Tonga arc. The occurrence of these anomalies has been attributed to the southward flow of mantle …

A Web Application In Rest: The Design, Implementation, And Evaluation Of A Web Application Based On RePresentational STate TRansfer, William O’Brien

Honors Theses

It is no secret the Internet has evolved at an alarming rate since its public debut in the early 90s. What began as a simple way for users to publish files has evolved into a platform for impressively complex interactive applications. Now, applications once restricted to a single operating system are made available to all through advancements in browser technology and libraries. For a long time, Adobe has offered Photoshop as a far from trivial image editing program for around $100 to the Windows and Mac platforms. Recently, a web application emulating Photoshop’s features has been made freely available to …

Recurrence Relations, Fractals, And Chaos: Implications For Analyzing Gene Structure, Sarah. M. Harmon

Honors Theses

The “chaos game” is a well-known algorithm by which one may construct a pictorial representation of an iterative process. The resulting sets are known as fractals and can be mathematically characterized by measures of dimension as well as by their associated recurrence relations. Using the chaos game algorithm, is it possible to derive meaningful structure out of our own genetic encoding, and that of other organisms? In this paper, I will present one method of applying the chaos game to biological data and subsequently will discuss both the mathematical and biological implications of the results.

Isometries And Spontaneous Lorentz Violation In General Relativity, Greg Merritt

Honors Theses

General Relativity, or GR, is a theory which describes gravity as a manifestation of the curvature of space and time. While the other three fundamental forces in nature are represented as field theories, GR is a geometric theory. In the search for a way to reconcile the field theories for the electromagnetic, strong, and weak forces with the gravitational force, a logical place to start is by re-expressing GR as a field theory. In doing so, we find that the theory contains a number of symmetries. When we solve the equations in GR, we find that by choosing certain solutions …

Cameras, Satellites, And Surveys: A Multi-Platform Approach To Monitoring Lake Conservation Behavior, Daniel D. Homeier

Honors Theses

Shoreline buffers are essential to maintaining lake water quality and there are numerous methods for their assessment. There is uncertainty in the benefits and drawbacks of different shoreline buffer assessment methods. In this study I explore three methods of remotely assessing shoreline buffers in the Belgrade Lakes Region of Maine: household surveys, geotagged shoreline photos, and satellite imagery. By comparing these three methods I will evaluate their accuracy and applicable scale when used to assess the presence and quality of shoreline buffers.

I used both parametric and non-parametric analysis to (1) evaluate the relative accuracy of 154 household surveys in …

Examination Of Spatial Variations In Recrystallization Mechanisms In Quartz, Emma N. Beck

Honors Theses

S-C mylonites form as a result of non-coaxial deformation in ductile shear zones. Planes of weakness develop and delineate two domains, the S and the C Each of these domains accommodates variable amounts of strain. Sample WMSZ-188 exhibits subgrain rotation (SGR) recrystallization in the C domains, and grain boundary migration (GBM) recrystallization in the S domains. This partitioning of recrystallization mechanisms indicates either: (1) strain-rate partitioning during a single deformation event; or (2) a second, lower-temperature deformation event that over-printed the C domains. This study tests these two hypotheses. Optical and EBSD analyses were used to look for evidence of …