Physical Sciences and Mathematics Commons^™

The Construction Of Khovanov Homology, Shiaohan Liu

Master's Theses

Knot theory is a rich topic in topology that studies the how circles can be embedded in Euclidean 3-space. One of the main questions in knot theory is how to distinguish between different types of knots efficiently. One way to approach this problem is to study knot invariants, which are properties of knots that do not change under a standard set of deformations. We give a brief overview of basic knot theory, and examine a specific knot invariant known as Khovanov homology. Khovanov homology is a homological invariant that refines the Jones polynomial, another knot invariant that assigns a Laurent …

Complex Dimensions Of 100 Different Sierpinski Carpet Modifications, Gregory Parker Leathrum

Master's Theses

We used Dr. M. L. Lapidus's Fractal Zeta Functions to analyze the complex fractal dimensions of 100 different modifications of the Sierpinski Carpet fractal construction. We will showcase the theorems that made calculations easier, as well as Desmos tools that helped in classifying the different fractals and computing their complex dimensions. We will also showcase all 100 of the Sierpinski Carpet modifications and their complex dimensions.

The Biological, Physical And Chemical Response Of The Little Creek Watershed To The 2020 Czu Lighting Complex Fire, Natalie Fontana

Master's Theses

This post-fire study was conducted to characterize and observe fire induced changes in physical habitat parameters, water-quality conditions and macroinvertebrate assemblages in the Little Creek watershed, a tributary to Scotts Creek located in Cal Poly’s Swanton Pacific Ranch in Davenport, California. Pre-fire data was collected by a Cal Poly student, John Hardy, for his 2017 thesis. Post-burn bioassessment surveys for this study were repeated at four of the same study sites used by Hardy to provide comparisons to the California Stream Condition Index via a modified version of the State of California’s Surface Water Ambient Monitoring Program protocol. Macroinvertebrates were …

Interactive Water Vortex Exhibit, Simon Way, Emily Laing, Roqaya Naseri, Makenzie Kan

Mechanical Engineering

The San Luis Obispo Children’s Museum requested an interactive water vortex exhibit to both engage and entertain inquisitive guests, ages two to eight. The goal was to design and manufacture an exhibit that would educate its users on the fluid mechanics behind water vortices. They activate the mechanics by spinning a wheel, which is perceived as the catalyst to manipulate the flow of water to successfully create a whirlpool. Our team has created an interactive display that will enlighten young minds, providing the museum with an educational exhibit which shares a concept not currently taught by any other. Our project …

Soil Burn Severity And Environmental Covariate Effects On Soil Health Two Years Postfire In The Sierra Nevada, Julie A. Lewis

Master of Science in Environmental Sciences and Management Projects

Wildfires have been steadily increasing in both size and severity in recent decades. This global trend is most evident in California, especially the North Coast and Sierra Nevada. Although these trends are rising, there is little known about the effects of these wildfires on forest soils. Soil is the 2nd largest C sink on the planet, and the largest terrestrial bank. Without understanding the implication of rising wildfire severities on these soils, we cannot understand how to help protect this resource in the future. Due to the rapid increase in wildfire size and intensity, there is little known about the …

Temporal And Spectral Analysis Of 1es 2344+514 In Two Flaring States Observed By Veritas, Connor Poggemann

Physics

VERITAS observed the bright blazar 1ES 2344+514 during two flaring periods, one from Dec. 17 to Dec. 18, 2015 (MJD 57373-57374) with a peak flux of ~60% of the Crab and another from Nov. 28 to Dec. 3, 2021 (MJD 59546-59551) with a peak flux of ~20% of the Crab. This blazar, located at a redshift of z = 0.044, is classified as an extreme high-frequency-peaked BL Lacertae object (HBL). It is known to be variable, including several previous day-scale flares: Whipple on Dec. 20, 1995, VERITAS on Dec. 7, 2007, and MAGIC on Aug. 11, 2016. The VERITAS near-nightly …

The Tidal Prism, Viable Eelgrass Habitat, And The Effects Of Sea Level Rise In Morro Bay, Kaden A. Caliendo

Master's Theses

The tidal prism, or the volume of water exchanged from the sea to an estuary from mean low to mean high tide, influences system hydrodynamics and ecological functioning. Since 1884, the tidal prism in Morro Bay, California has been estimated to be decreasing over time due to sedimentation from upstream practices. What is the current tidal prism in Morro Bay and how will that change with sea level rise? How will eelgrass respond to rising sea levels?

For this study, inexpensive tidal gauges were deployed at four locations in Morro Bay from March to August 2023 to measure spatially varying …

Clueless: Revolutionizing Sustainable Fashion And Combating Overconsumption, Tanya Ravichandran

Graphic Communication

“Clueless” revolutionizes sustainable fashion by combating wardrobe overconsumption and the industry’s carbon footprint, using AI to suggest personalized outfits from existing wardrobes tailored to weather and wear history. It enhances user engagement through features like outfit ‘shuffle’ and provides insights into wardrobe utilization and carbon impact.

It’s more than an app; it’s a step towards a greener wardrobe and a healthier planet.

Effects Of Arbuscular Mycorrhizal Fungi Inoculation And Cover Crop On Soil Carbon Dynamics And Microbial Communities In A Mediterranean Lemon Orchard., Anna Rodriguez-Paiatsyka

Master of Science in Environmental Sciences and Management Projects

Plant-associated fungi such as arbuscular mycorrhizal fungi (AMF) have the potential to sequester carbon (C), improve soil aggregation, and promote plant health. Due to multiple benefits of AMF to plant and soil health, AMF has gained much attention leading to a rapidly expanding market in mycorrhizal bio-stimulants intended to improve crop yield, root development, and soil health in horticultural crops, including citrus. However, there is limited information on how to inoculate a mature citrus orchard, and how inoculation of a mature orchard with AMF affects C sequestration. In this study, we planted a cover crop inoculated with AMF in a …

Using Remote Sensing To Determine Riparian Resilience In Beaver Dammed Versus Un-Dammed Corridors Following Whiplash Weather, Sophie Charlotte Valérie Aubry

Master of Science in Environmental Sciences and Management Projects

Beaver complexes slow and store water allowing for riparian growth which in turn fosters biodiversity, retains carbon, and enhances resistance to fires and drought. Given the benefits associated with beaver complexes and the potential they have for climate mitigation, California hopes to reintroduce beavers and restore their habitat throughout the state. However, the impact of high peak flow events on beaver complexes and their adjacent riparian corridors is less understood and requires more documentation at various spatial scales. To better understand the potential beavers may have as climate change mitigators it is important to understand beaver complex resiliency following a …

Foundations Of Memory Capacity In Models Of Neural Cognition, Chandradeep Chowdhury

Master's Theses

A central problem in neuroscience is to understand how memories are formed as a result of the activities of neurons. Valiant’s neuroidal model attempted to address this question by modeling the brain as a random graph and memories as subgraphs within that graph. However the question of memory capacity within that model has not been explored: how many memories can the brain hold? Valiant introduced the concept of interference between memories as the defining factor for capacity; excessive interference signals the model has reached capacity. Since then, exploration of capacity has been limited, but recent investigations have delved into the …

Nanoparticles And The Environment: Biopolymer Grafted Cellulose And Screen-Printed Carbon Nanotube Composites, Dominique Henry Porcincula

Master's Theses

A host of environmental issues will define the state of the environment in the 21^st century, with plastic pollution and water shortages among them. While solutions to these problems require large-scale, multipronged solutions, one way we can address them is through material innovation and the use of nanoparticles.

In the first project, we address the issue of plastic pollution by creating nanocomposites of biodegradable polymers (PLA and PCL) with cellulose nanofibrils. Here, PLA and PCL are grafted from the surface of cellulose nanofibrils via ring-opening polymerization of cyclic ester monomers. Polymer-grafted cellulose (PGC) is characterized with structural analysis, solubility …

Smartphone Based Object Detection For Shark Spotting, Darrick W. Oliver

Master's Theses

Given concern over shark attacks in coastal regions, the recent use of unmanned aerial vehicles (UAVs), or drones, has increased to ensure the safety of beachgoers. However, much of city officials' process remains manual, with drone operation and review of footage still playing a significant role. In pursuit of a more automated solution, researchers have turned to the usage of neural networks to perform detection of sharks and other marine life. For on-device solutions, this has historically required assembling individual hardware components to form an embedded system to utilize the machine learning model. This means that the camera, neural processing …

Assessing Environmental Impact Of The Built Environment By Adopting Life Cycle Design: Using Swanton Pacific Ranch As A Case Study, Hope E. Springer

Master of Science in Environmental Sciences and Management Projects

To combat the carbon emissions contributed to the atmosphere by the built environment, it is imperative that low-embodied-carbon materials choices be prioritized throughout the building design process. To achieve this, this professional project creates an Excel-based, open source, and user-friendly tool for the construction sector to make design decisions that prioritize the sustainability of structures, as one such tool does not currently exist. The use of OpenLCA software and the EcoInvent34 database are utilized to calculate the environmental impact of 25 different building materials, as well as energy and electricity consumption. Swanton Pacific Ranch (SPR) in Santa Cruz County is …

Greenhouse Gas Emissions And Fire Behavior Impacts Following California Fuel Treatments, Lindsay M. Senechal

Master of Science in Environmental Sciences and Management Projects

Fuel treatments are being increasingly applied across California landscapes as communities struggle to recover from wildfire disasters nationwide. Increased funding for treatments stems from grants under CARB’s Greenhouse Gas Reduction Fund and funding requires reports accounting the yielded benefits from these fuel treatments. Using data from real-world local scale fuel treatments, I used the forest simulation model FVSFEE and fire behavior software IFTDSS to quantify GHG emission benefits and fire behavior impacts 70 years after treatment. Results suggest that fuel treatments do not yield significant GHG benefits, and fire behavior impacts (conditional flame length) are minimal but overall show slight …

The Methods Of Communication And Education Used To Train Forest And Fire Personnel Through The Swanton Pacific Ranch, Christine Brittney Johnson

Master of Science in Environmental Sciences and Management Projects

California does not have a cohesive curriculum for educating and training forest and fire professionals. The Swanton Pacific Ranch Fuels Management Training Program is Cal Fire affiliated and provides online and in person training to assist in equipping fire and forest professionals throughout California with the necessary skills to be successful fire and forest practitioners and managers. An exit survey was offered to all workshop participants after the Swanton workshop concluded. The survey was answered by 331 Swanton workshop participants to assess the effectiveness of the training program, the educational practices used to teach participants, and what factors of a …

Environmental Controls On Soil Organic Matter Fractions In Post-Fire Landscapes, Alexis Heuer

Master of Science in Environmental Sciences and Management Projects

In the past few decades, the world’s climate is being altered by anthropogenic forces such as the increase in carbon dioxide (CO2) emissions due to fossil fuel combustion (Paraschiv and Paraschiv, 2020). In California, the impacts of increased CO2 concentrations have created longer fire seasons, warmer temperatures, and increased lightning strikes which allow for wildfires to become more frequent, severe, and larger in scale (Westerling et al., 2006). Wildfires of this magnitude result in acceleration of landscape scale processes such as erosion and aggregation which in turn affects soil organic matter (SOM), the basis of soil health (Gonz´alez-P´erez et al., …

Establishing A Monitoring Framework To Evaluate Impacts Of Grazing Exclusion And Inform Restoration At Santa Rita Ranch, Annie Booth, Annie Booth

Master of Science in Environmental Sciences and Management Projects

Santa Rita Ranch is a 1,750-acre cattle ranch in Templeton, California, that was privately owned and continuously grazed for the past 70 years. In 2021, The Land Conservancy of San Luis Obispo (LCSLO) acquired the property, and in the winter of 2022, they built a fence that bisects the ranch, excluding the cattle from 800 acres to preserve the riparian habitat. The LCSLO is currently defining the ecological baseline for the ranch to inform future management decisions. Given that cattle grazing has many environmental tradeoffs, they wanted to establish a long-term monitoring study to understand how relieving the pressures of …

Fire Effects On Soil Organic Matter In The Creek Fire, Gracie E. Doolin

Master of Science in Environmental Sciences and Management Projects

Wildfires have increased in frequency and severity over the past few decades due to the increased concertation of CO2 emissions from anthropogenic influence. Soil carbon (C) sequestration has been identified as a climate change mitigation strategy; however, the influx of large-scale wildfires has accelerated landscape processes such as erosion, reducing soil aggradation, and soil C and nitrogen (N) protection. This trend is highlighted by the Creek Fire that occurred in September 2020 and burned 379,895 acres in the Sierra National Forest. This research is designed to close the knowledge gap regarding the impact of burn severity on soil organic matter …

Identifying The Stream Depletion Paradox By Monitoring A Stream’S Response To Aquifer Pumping From Neighboring Wells, James Klueber

Master of Science in Environmental Sciences and Management Projects

Current groundwater models utilize a constant head (Dirichlet) boundary condition which assumes stream stage is fixed and does not experience any drawdown in the event of pumping from an interconnected aquifer despite the presence of stream depletion. Therefore, constant head boundary implies that streams and lakes in a groundwater model behave as an infinite supply of water when aquifer pumping occurs. This study aimed to determine if a stream located in the California Central Coast experiences drawdown and depletion when pumping occurs within an aquifer-stream system. This was achieved by measuring stream stage, aquifer water levels, stream discharge, and the …

Pumping-Induced Drawdown Of Streams In Proximity To Agricultural Wells, Sara Alina Sternberg

Master of Science in Environmental Sciences and Management Projects

In the context of unprecedented drought and aquifer overdraft in California, understanding surface water and groundwater connectivity have become increasingly important. While there is a clear understanding of how wells induce drawdown in aquifers (Theis, 1935; Hantush, 1965), secondary effects on local streams have not fully been considered. Current mathematical models targeting aquifer drawdown do not address stream drawdown response in aquifer-stream systems with strong connectivity; instead, they assume the stream to be a constant head boundary. In the drought-stricken and summer-dry climate of California, streams often run dry for months out of the year, which is currently not reflected …

Functional Nanocomposite Coatings For Use In Food Packaging, Camden N. Webb

Master's Theses

Plastics are a class of materials known for their cost and property advantages, increasing significantly in their usage worldwide. Unfortunately, these benefits come with an increasingly concerning environmental impact. A combination of inadequate disposal options and combinations of materials have led to environmental disasters that will impact generations. One of the worst areas for plastic waste is food packaging. Plastic as a material generally excels at durability and longevity, but as food packaging, it outlives its intended purpose by several orders of magnitude. This leads to plastic food packaging materials sitting in landfill or leading to the environment for hundreds …

Covalent Adaptable Networks For Wood Coatings, Jachin Boaz Clarke

Materials Engineering

Wood swells and shrinks causing problems with seasonal humidity. Applying thick coatings of reactive finishes based on cross-linked polyurethane, epoxy, or polyesters can slow moisture-vapor exchange. However, the use of thick coatings leads to cracking and crazing sooner than thin finishes. This research proposes the addition of 3.3 mol % triazabicyclodecene, a conventionally used covalent adaptable network catalyst, in a commercially available polyester-based wood coating. The self-healing of the wood coating is tested using DMA stress relaxation and compression molding. The result from DMA renders inconclusive and compression molding indicates the novel wood coating oxidizes at elevated temperatures. The wood …

Optimizing Solid Thermal Storage In Insulated Solar Electric Cookers, Stefan Avramov

Physics

Insulated Solar Electric Cookers, more commonly known by their acronym ISECookers, are an alternative to biomass cooking. The ISECooker in its simplest form is a solar panel connected to a heating element, in contact with a cooking pot in an insulated chamber. An aluminum puck can be heated as solid thermal storage (STS) for increased power and night time cooking. Power was limited to about 500 W by the interface between the STS and cookpot. Powdered graphite and silver were separately applied to increase thermal flow. However, the powdered graphite decreased the thermal flow, while powdered silver decreased the temperature …

Learning The Game: Implementations Of Convolutional Networks In Automated Strategy Identification, Cameron Klig

Master's Theses

Games can be used to represent a wide variety of real world problems, giving rise to many applications of game theory. Various computational methods have been proposed for identifying game strategies, including optimized tree search algorithms, game-specific heuristics, and artificial intelligence. In the last decade, systems like AlphaGo and AlphaZero have significantly exceeded the performance of the best human players in Chess, Go, and other games. The most effective game engines to date employ convolutional neural networks (CNNs) to evaluate game boards, extract features, and predict the optimal next move. These engines are trained on billions of simulated games, wherein …

Representations From Group Actions On Words And Matrices, Joel T. Anderson

Master's Theses

We provide a combinatorial interpretation of the frequency of any irreducible representation of Sn in representations of Sn arising from group actions on words. Recognizing that representations arising from group actions naturally split across orbits yields combinatorial interpretations of the irreducible decompositions of representations from similar group actions. The generalization from group actions on words to group actions on matrices gives rise to representations that prove to be much less transparent. We share the progress made thus far on the open problem of determining the irreducible decomposition of certain representations of Sm × Sn arising from group actions on matrices.

Exploring The Mass To Light Ratio Of Massive Galaxies With The Rubin Dp0 Preview Dataset, Denvir Joy Higgins

Physics

The Vera C. Rubin Observatory will perform the 10-year long Legacy Survey of Space and Time expected to begin in 2024. LSST will cover the Southern Hemisphere, collecting over two million images with an 8.4-meter telescope and 3200-pixel camera. In collaboration with the scientific community and based on the Outer Rim Simulation \citep{heit19}, the Rubin Observatory released a simulated dataset (DP0) of the data that is expected to be in hand at the 5-year mark. Using this simulated dataset, I have explored the number and luminosity of the most massive local galaxies. Using a sample of the brightest, closest galaxies …

A Monte-Carlo Simulation Of Gamma Rays In A Sodium Iodide Detector, Ben Kessler

Physics

Gamma rays principally interact with matter through Compton scattering, photoelectric effect, pair production, and triplet production. The focus of this simulation is to study the theoretical energy spectrum created by gamma rays from a Cesium-137 source, which produces gamma photons with an energy of 0.662 MeV. At this energy level, most interactions are results of Compton scatters and the photoelectric effect. Therefore, this simulation only models those two effects on gamma rays. Using Monte Carlo methods and the Metropolis algorithm to sample the probability distributions of the two effects allowed for the simulation of gamma rays in a Sodium Iodide …

Diffusion-Driven Aggregation Of Particles In Quasi-2d Membranes, Oscar Gullickson Rausis

Physics

Many biological membranes can be modeled as two-dimensional (2D) viscous fluid sheets surrounded by three-dimensional (3D) fluids of different viscosity. Such membranes are dubbed quasi-2D as they exhibit properties of both 2D and 3D fluids. The Saffman length is a parameter that describes the energy exchange between the membrane and bulk fluids and controls the cross-over from 2D to 3D hydrodynamics. We aim to model diffusion-driven aggregation of particles embedded in a quasi-2D membrane. It is known that hydrodynamic interactions between solute particles significantly reduce their aggregation rate in 3D fluids. It is expected that in quasi-2D membranes the reduction …

Optimization Of Flagellar Locomotion In The Low Reynolds Number Regime, Aidan M. Trodden, Aidan M. Trodden

Physics

This report investigates the computational and theoretical techniques - modeled by E. Lauga and C. Eloy - used to optimize the shape of an activated flagellum for enhanced cell motility. Cell motility is ubiquitous and has a large affect on biological systems such as marine life ecosystems, reproduction, and infection. The physical principles governing flagellar propulsion are explored using computational fluid dynamics simulations, mathematical modeling, and the sequential quadratic programming (SQP) optimization algorithm. Through iterative refinement, we can identify optimized flagellar shapes that would minimize the energetic cost dependent on a single dimensionless sperm numbers (Sp). The computation of the …