Physical Sciences and Mathematics Commons^™

Echolocation On Manifolds, Kerong Wang

Honors Theses

We consider the question asked by Wyman and Xi [WX23]: ``Can you hear your location on a manifold?” In other words, can you locate a unique point x on a manifold, up to symmetry, if you know the Laplacian eigenvalues and eigenfunctions of the manifold? In [WX23], Wyman and Xi showed that echolocation holds on one- and two-dimensional rectangles with Dirichlet boundary conditions using the pointwise Weyl counting function. They also showed echolocation holds on ellipsoids using Gaussian curvature.

In this thesis, we provide full details for Wyman and Xi's proof for one- and two-dimensional rectangles and we show that …

Self-Quenching Of Carbon Monoxide In The Presence Of Noble Gases, Madeline V. Hinkle

Honors Theses

Precise rate coefficients for the vibrational relaxation pathways of CO(v)-CO in the presence of Ar and Kr have been determined through the work of this thesis. This work was motivated by the need to find a more cost-effective alternative to using xenon as a bath gas, which has increased significantly in price in the past few years. Similar experiments within this lab at Bucknell have been conducted in the past using argon, which can be used in the same manner as xenon but comes at a much lower price, but the experiments yielded inferior results compared to those using xenon. …

The Precedence-Constrained Quadratic Knapsack Problem, Changkun Guan

Honors Theses

This thesis investigates the previously unstudied Precedence-Constrained Quadratic Knapsack Problem (PC-QKP), an NP-hard nonlinear combinatorial optimization problem. The PC-QKP is a variation of the traditional Knapsack Problem (KP) that introduces several additional complexities. By developing custom exact and approximate solution methods, and testing these on a wide range of carefully structured PC-QKP problem instances, we seek to identify and understand patterns that make some cases easier or harder to solve than others. The findings aim to help develop better strategies for solving this and similar problems in the future.

Computationally Modeling The Human-Structure Interaction Response Of An Occupied Cantilevered Structure, Brennan Smith

Honors Theses

There is a limited understanding of the impact that passive human occupants have on a dynamic structural system, referred to as Human-Structure Interaction (HSI). Cantilevers are naturally prone to excessive vibrations due to their long unsupported spans, and cantilevered structures such as those commonly found in the seating area of a stadium facility or concert hall are designed to support a high density of occupancy.

This study determined that HSI in cantilevered structures can be modeled using a simple two-degree-of-freedom system. The results of the model were validated by data that was collected on a small-scale laboratory structure intentionally designed …

Centers Of N-Degree Poncelet Circles, Georgia Corbett

Honors Theses

Given a circle inscribed in a polygon inscribed in the unit circle, if one connects all the vertices with line segments we get a family of circles called a package of Poncelet circles, due to its connection to a theorem of Poncelet. We are interested in where the centers of the Poncelet circles can be. Specifically, we have shown that if one of the circles in the Poncelet package is centered at 0, then all of the circles must be centered at 0 as well. This was proven by Spitkovsky and Wegert in 2021 using elliptic integrals but we …

Evaluating Field Evidence Of Fine-Grained Sediment Abrasion In Gravel-Bedded Rivers: A Case Study Of The Lillooet And Suiattle Rivers In The Cascade Volcanic Arc (British Columbia, Canada, And Washington, Usa), Devin T. Johnson

Honors Theses

Steep, gravel-bedded rivers are important sites for studying gravel abrasion, where material transported as bed load experiences size reduction and rounding due to grain-to-grain collisions. Studying fine sediment (diameter) abrasion and grain shape changes in fluvial systems is more challenging due to difficulties in quantifying sediment shape at this scale, but it is assumed that fine particles traveling in suspension do not experience abrasion. Improvements in particle characterization technology now allow for the accurate, rapid quantification of particle shape for sediments as fine as 0.8 μm through dynamic image analysis. Here we use the Camsizer X2 (CX2) to test the …

The Implementation Of Augmented Reality And Low Latency Protocols In Musical Instrumental Collaborations, Qixiao Zhu

Honors Theses

Past projects involving musical software have been completely virtual, while these software do well in entertainment and education, there is the question of whether these software are playable to the same extent as physical musical instruments. The software presented in this paper, "AR Jam", utilizes various software and hardware tools to form a networked mixed reality system for the users to play music on. The intention of this project is to seek new ways to explore more playable musical instruments in the digital world. The paper presents the software's implementation, challenges such as optimization problems of the synthesizer, and the …

Deposited Cigarette Smoke As A Driver Of Oxidation And Partitioning Processes On Indoor Surfaces, April Hurlock

Honors Theses

Despite the large amount of time that individuals spend indoors during their lives, very little attention was paid to the chemistry that occurs on indoor surfaces until recently. Although not visible to the naked eye, physical and chemical processes, such as partitioning and oxidation, are occurring on virtually every indoor surface in a typical household. Indoor pollutants, ranging from skin oils to environmental cigarette smoke, drive a lot of these processes. The transformation of indoor surfaces by indoor pollutants can increase chemical exposure risks as new irritants or carcinogens can be introduced to the surfaces. In this thesis, I describe …

Graphs, Adjacency Matrices, And Corresponding Functions, Yang Hong

Honors Theses

Stable polynomials, in the context of this research, are two-variable polynomials like $p(z_1,z_2) = 2 - z_1 - z_2$ that are guaranteed to be non-zero if both input variables have an absolute value less than one in the complex plane. Stable polynomials are used in a variety of mathematical fields, thus finding ways to construct stable polynomials is valuable. An important property of these polynomials is whether they have boundary zeros, which are points in the complex plane where the polynomial equals zero and both variables have an absolute value of 1. Overall, it is challenging to find stable polynomials …

Long-Range And Chaotic Active Mixing Of Swimming Microbes In A Vortex Chain Flow, Nghia Le

Honors Theses

We present experiments studying the motion and active mixing of swimming mi- crobes in laminar, vortex-dominated fluid flows. We are testing a theory that predicts the existence of swimming invariant manifolds (SwIMs) - invisible, one-way barriers blocking the paths of self-propelled tracers in the flow in one direction. We also pro- pose that the SwIMs together can form chute structures in three-dimensional phase space that facilitate cross-vortex transport of the microbes. We also observe evidence of how these structures promote long-range transport at different non-dimensional velocities (microbe’s velocity relative to flow velocity). Long-range transport is quan- tified by measuring the …

Selective Melt Recrystallization Of Acetaminophen Polymorphs Through Environmental Control, Eleanor Lowe

Honors Theses

Polymorphism is the ability for a molecule to crystallize into multiple different structures in the solid state. The preparation of one polymorph over another is practically important to pharmaceutical development, as properties of polymorphs can vary and impact the drug delivery method. Polymorph outcomes depend heavily on the environment in which the crystal is nucleated, or initially formed. Acetaminophen, the active ingredient in Tylenol, is one example of a polymorphic compound. Here we use acetaminophen as a model system to better understand primary factors controlling polymorph selection and interconversion. We hypothesize a specific atmospheric environmental factor plays large role in …

Particle Swarm Optimization For High Rigidity Spectrometer, Yicheng Wang

Honors Theses

The goal of this project is to find reliable parameter settings for a multi-dimensional global optimizer to optimize the performance of a large acceptance ion optical system for the requirements of nuclear physics experiments. We develop and test the Particle Swarm Optimization (PSO), a global optimization algorithm designed for continuous multi-dimensional problems, on a large acceptance particle beam separator, the High Rigidity Spectrometer (HRS) at the Facility for Rare Isotope Beams (FRIB), which is a laboratory specializing in the production and experimental study of short-lived nuclear matter. We split the HRS into two sections, the High-Transmission Beamline (HTBL) and the …

Evaluating The Relationship Between Floodplain Topography And Channel Avulsion: Evidence From The Devonian Catskill Formation, North-Central Pennsylvania, Usa, Molly O'Halloran

Honors Theses

Topographic complexity on floodplains can route flow, control sediment dispersal, and influence channel behavior, but studying floodplain-channel interactions in modern rivers is challenging because of human modifications and the short timescales of observable data. This project assesses the link between different types of floodplain microtopography and avulsion style in the Devonian Catskill Formation, north-central Pennsylvania, where thick stacks of fluvial strata provide a lengthy record of channel-floodplain interaction. Using a combination of field observations and computer modeling, this study identifies sedimentary features indicative of floodplain complexity and analyzes their impact on avulsion style at fourteen Catskill Formation outcrops.

Based on …

A Contraction Based Approach To Tensor Isomorphism, Anh Kieu

Honors Theses

Tensor isomorphism is a hard problem in computational complexity theory. Tensor isomorphism arises not just in mathematics, but also in other applied fields like Machine Learning, Cryptography, and Quantum Information Theory (QIT). In this thesis, we develop a new approach to testing (non)-isomorphism of tensors that uses local information from "contractions" of a tensor to detect differences in global structures. Specifically, we use projective geometry and tensor contractions to create a labelling data structure for a given tensor, which can be used to compare and distinguish tensors. This contraction labelling isomorphism test is quite general, and its practical potential remains …

Environmental Racism In Baltimore: A Geographical Study Into The Connections Between Environmental Toxins And Public Health, Genevieve Block

Honors Theses

An investigation into the relationship between environmental toxins and environmental racism in Baltimore City, Maryland.

Perceptually Improved Medical Image Translations Using Conditional Generative Adversarial Networks, Anurag Vaidya

Honors Theses

Magnetic resonance imaging (MRI) can help visualize various brain regions. Typical MRI sequences consist of T1-weighted sequence (favorable for observing large brain structures), T2-weighted sequence (useful for pathology), and T2-FLAIR scan (useful for pathology with suppression of signal from water). While these different scans provide complementary information, acquiring them leads to acquisition times of ~1 hour and an average cost of $2,600, presenting significant barriers. To reduce these costs associated with brain MRIs, we present pTransGAN, a generative adversarial network capable of translating both healthy and unhealthy T1 scans into T2 scans. We show that the addition of non-adversarial …

Crystalline Architecture And Stratigraphy Of Coral Skeletal Density Banding: A Geobiological Record Of Changing Coral Reef Ecology, Kyle Fouke

Honors Theses

Coral skeletal density banding (CSDB), composed of alternating high density band (HDB) and low density band (LDB) layers that comprise the CaCO₃ (aragonite) skeleton of scleractinian corals, are used as chronometers for global paleoclimatic reconstructions of sea surface temperature (SST). Scleractinian coral skeletons have been intensively studied for centuries with detail analysis of the macro- and microscale skeletal structure to establish taxonomic and evolutionary relationships of coral species, mechanisms of biomineralization, and seafloor physical, chemical and biological alteration (diagenesis) of the skeleton. This study is the first to determine the crystalline architecture of HDBs and CSDB stratigraphic …

Sedimentological, Architectural, And Paleoenvironmental Analysis Of The Fluvial Upper Devonian Catskill Formation, North-Central Pennsylvania, Usa, Matylda Zaklicki

Honors Theses

During the Late Devonian time period, sediments eroded from the Acadian mountains were transported westward and deposited in fluvial environments, but the morphology of the rivers, avulsion style, and controls on basin infilling remain unclear. This study assesses the sedimentology, channel geometry, stratigraphic architecture, and avulsion style of the paleochannels and floodplains of the uppermost 80 meters of the Catskill Formation near Blossburg, Pennsylvania, using field-based lithofacies observations, high-resolution panoramic photographs, and terrestrial lidar scanning.

Upper Catskill Formation strata at Blossburg Middle consist of sandy channel and muddy floodplain deposits. Floodplain deposits were categorized into either proximal floodplain deposits or …

Linked-Cluster Expansions For Lattice Spin Models, Yuyi Wan

Honors Theses

Similar to various series expansions that are used to approximate mathematical func- tions, the linked-cluster expansion is an approximation method that allows us to approach the actual values of a very large physical system’s different physical quan- tities by systematically studying smaller systems embedded in this larger system. The main concept in linked-cluster expansion, weight, represents the additional con- tribution to a certain physical quantity by increasing the system size by one unit. These weights are used to eventually build up the result on a larger system. In our case, we focus on the partition function, a quantity that can …

Fluvial Sedimentology And Architecture Of Two Latest Devonian Lower Huntley Mountain Formation Outcrops, North-Central Pennsylvania, Usa, Evan W. Filion

Honors Theses

Thick successions of river deposits accumulated in the north-central Pennsylvania region of the Appalachian foreland basin during Late Devonian time (~380-360 Ma). The properties and morphologies of these paleorivers are not well characterized. Latest Devonian tectonic, climatic, and eustatic controls on river dynamics and basin infilling also remain unclear. This study assesses the sedimentology, facies architecture, paleochannel depths, and grain size of a 133 m thick section of fluvial strata exposed across two outcrops, Blossburg South (older) and Blossburg West (younger), mapped as lower Huntley Mountain Formation near Blossburg, Pennsylvania. Field-based lithofacies observations, high-resolution panoramic photography, terrestrial lidar scanning, and …

Ethics, Privacy And Data Collection: A Complex Intersection, Matthew S. Brown

Honors Theses

The technology around us enables incredible abilities such as high-resolution video calls and the ability to stay connected with everyone we care about through social media. This technology also comes with a hidden cost in the form of data collection.

This work explores what privacy means and how users understand what data social media companies collect and monetize. This thesis also proposes a more ethical business model that addresses privacy concerns from an individual perspective.

Positivity Among P-Partition Generating Functions Of Partially Ordered Sets, Nate Lesnevich

Honors Theses

We find necessary and separate sufficient conditions for the difference between two labeled partially ordered set's (poset) partition generating functions to be positive in the fundamental basis. We define the notion of a jump sequence for a poset and show how different conditions on the jump sequences of two posets are necessary for those posets to have an order relation in the fundamental basis. Our sufficient conditions are of two types. First, we show how manipulating a poset's Hasse diagram produces a poset that is greater according to the fundamental basis. Secondly, we also provide tools to explain posets that …

Late Devonian Sedimentary Record Of Appalachian Tectonics And Erosion: Geochronology And Geochemistry Of Detrital Muscovite And Zircon From Central Pennsylvania Strata, Cole T. Gardner

Honors Theses

Foreland basin sediment deposition in North-Central Pennsylvania during Late Devonian time records erosion of hinterland source terranes exhumed during regional plate convergence, including the collisional Acadian orogeny. The Catskill clastic wedge preserves a coarsening-upwards stratigraphic succession from marine to fluvial environments associated with sediment progradation and sea-level regression, yet depositional timescales and quantitative provenance data are largely unconstrained.

Detailed facies analysis of eight outcrops spanning >2 km of stratigraphy in Lycoming Co., Pennsylvania documents distinct upsection changes, interpreted to reflect changes in depositional environments consistent with previous sedimentology of the Catskill clastic wedge. Stratigraphy displays a transition from nearshore marine …

Contextualizing Sexual Assault Data Collection On College Campuses: A Socio-Technical Approach, Anushikha Sharma

Honors Theses

Sexual assault is a rampant issue on college campuses in the United States. Colleges and universities use a variety of survey instruments to collect data regarding sexual assault as a means to improve campus culture, policies, and resources. These instruments contain a wealth of associated information in the form of metadata, that is, data about data.

This project takes a human-centered socio-technical approach to understanding the data collection processes associated with sexual assault, specifically, on the campus of Bucknell University. By identifying the underlying metadata within the data collection processes, this research contextualizes and critiques the process of data collection, …

Bridging Act-R And Project Malmo, Developing Models Of Behavior In Complex Environments, David M. Schwartz

Honors Theses

Cognitive architectures such as ACT-R provide a system for simulating the mind and human behavior. On their own they model decision making of an isolated agent. However, applying a cognitive architecture to a complex environment yields more interesting results about how people make decisions in more realistic scenarios. Furthermore, cognitive architectures enable researchers to study human behavior in dangerous tasks which cannot be tested because they would harm participants. Nonetheless, these architectures aren’t commonly applied to such environments as they don’t come with one. It is left to the researcher to develop a task environment for their model. The difficulty …

Launch-Explore-Summarize In High School Calculus, Nate Mattis

Honors Theses

Current research on high school calculus instruction indicates that students often possess a procedural knowledge of differentiation and integration as opposed to a conceptual knowledge (Orton, 1983; Ferrini-Mundy & Graham, 1994). Given the prominence of traditional lecture and textbook-based calculus classes in the United States, students are not always given the opportunity to expand their conceptual knowledge of essential calculus concepts. This project introduces calculus students to a more active and communal method of teaching: Launch-Explore-Summarize (LES) (CMP, n.d.). This methodology places students at the center of their learning and emphasizes inquiry-based thinking during a class. Specifically, two LES lessons …

Extensions Of The Morse-Hedlund Theorem, Eben Blaisdell

Honors Theses

Bi-infinite words are sequences of characters that are infinite forwards and backwards; for example "...ababababab...". The Morse-Hedlund theorem says that a bi-infinite word f repeats itself, in at most n letters, if and only if the number of distinct subwords of length n is at most n. Using the example, "...ababababab...", there are 2 subwords of length 3, namely "aba" and "bab". Since 2 is less than 3, we must have that "...ababababab..." repeats itself after at most 3 letters. In fact it does repeat itself every two letters. …

On A Problem Of Burnside, Matthew Mizuhara

Honors Theses

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner.

NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

Utilization Of Probabilistic Models In Short Read Assembly From Second-Generation Sequencing, Matthew W. Segar

Honors Theses

With the advent of cheaper and faster DNA sequencing technologies, assembly methods have greatly changed. Instead of outputting reads that are thousands of base pairs long, new sequencers parallelize the task by producing read lengths between 35 and 400 base pairs. Reconstructing an organism’s genome from these millions of reads is a computationally expensive task. Our algorithm solves this problem by organizing and indexing the reads using n-grams, which are short, fixed-length DNA sequences of length n. These n-grams are used to efficiently locate putative read joins, thereby eliminating the need to perform an exhaustive search over all possible read …

Verifying Harder's Conjecture For Classical And Siegel Modular Forms, David Sulon

Honors Theses

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form.

Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.