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Creasing In Thick Hemispherical Shells As A Model For Foveal Formation, Indigo Skye Peppard May 2025

Creasing In Thick Hemispherical Shells As A Model For Foveal Formation, Indigo Skye Peppard

Undergraduate Honors Theses

This research experimentally investigates creasing behavior on the inner surface of hemispherical shells with the ultimate goal of modelling the formation of the foveal pit, a sharp surface deformation present in the retina of the eye of many animals. Creasing is a phenomenon observed in hyperelastic materials and is characterized by sharply localized surface deformations that appear at ~35% compressive strain. The foveal pits of anoles (small iguanian lizards) are funnel-shaped and resemble creases when cut along the central axis. Furthermore, during foveal pit formation the anole eye contracts around 35% along this same axis. Given these similarities we believe …


Topological And Optical Properties Of Two-Dimensional Materials, Haonan Wang May 2025

Topological And Optical Properties Of Two-Dimensional Materials, Haonan Wang

Arts & Sciences Graduate Student Theses and Dissertations

Recent advances in condensed matter physics have revealed a wide range of novel quantum phenomena in two-dimensional (2D) materials. The discovery of unique topological, magnetic, and optical properties in solids has greatly expanded our understanding of quantum phases in electronic structures. As more material systems are proposed theoretically and realized experimentally, our research focuses on uncovering and explaining these phenomena through effective models and first-principles calculations. First, we explore topological mosaic patterns in moiré superlattices—structures composed of periodic, spatially distinct domains, each with different topological properties. These domains give rise to periodic edge states along domain walls. We explore the …


X-Ray Polarization Of Accreting Stellar-Mass Black Holes Through Accretion States, Nicole Rodriguez Cavero May 2025

X-Ray Polarization Of Accreting Stellar-Mass Black Holes Through Accretion States, Nicole Rodriguez Cavero

Arts & Sciences Graduate Student Theses and Dissertations

In recent years, X-ray polarization has opened up a new window into our understanding of astrophysical sources. Among them are accreting stellar-mass black holes, which play a key role in testing the behavior of matter in extreme gravitational environments. These sources can be observed in different states of the accretion cycle, predominantly in the soft and hard states. Every state is dominated by a combination of thermal disk, coronal, or reflected emission—each type containing different information about the environment around the black hole that can be understood through polarization. Polarimeters such as the Imaging X-ray Polarimetry Explorer and XL-Calibur allow …


Computational Design Of Potent Sirna For Braf Oncogene Silencing For Enhancing Cancer Therapy, Muhammad Hermawan Widyananda, Ricadonna Raissa May 2025

Computational Design Of Potent Sirna For Braf Oncogene Silencing For Enhancing Cancer Therapy, Muhammad Hermawan Widyananda, Ricadonna Raissa

Karbala International Journal of Modern Science

The discovery of oncogenic BRAF mutations has prompted the development of inhibitors, yet resistance remains widespread. A more effective strategy involves targeting BRAF mRNA with siRNA to overcome resistance to BRAF inhibitors. This study aims to design potent siRNA for BRAF oncogene silencing using a computational approach. The full coding sequence of BRAF was retrieved from the NCBI database and potential siRNAs were predicted using the Ui-Tei, Reynolds, and Amarzguioui rules. Identified siRNAs were further analyzed using various prediction systems and parameters, including their interaction with the hAgo2 protein. The results identified that seven siRNAs (siRNA 23, siRNA 24, siRNA …


Characterization Of A Magnetically Contained Hot Filament Plasma Source With A Wide-Sweeping Langmuir Probe, Jonas Rowan May 2025

Characterization Of A Magnetically Contained Hot Filament Plasma Source With A Wide-Sweeping Langmuir Probe, Jonas Rowan

Doctoral Dissertations and Master's Theses

Ionospheric plasma research in the Space and Atmospheric Instrumentation Laboratory’s Space Plasma Chamber has been hindered by the lack of a suitable plasma diagnostic instrument and understanding of its hot-filament plasma source. This thesis describes efforts made to remedy both problems. A wide-range Sweeping Langmuir Probe was developed with a ±35 V sweeping range to fully analyze ion and electron saturation regions in the entire IV curve. A method was derived to estimate the chamber source’s filament temperatures. The new Langmuir probe was integrated into a refurbished automated system designed in Python to measure plasma parameters for various chamber conditions, …


First-Principles Studies Of Excited-State Properties In Large-Scale Systems, Du Li May 2025

First-Principles Studies Of Excited-State Properties In Large-Scale Systems, Du Li

Arts & Sciences Graduate Student Theses and Dissertations

Density Functional Theory (DFT) is widely used as a powerful tool for studying the electronic structure of materials. However, due to the local or semilocal nature of exchange-correlation functionals, such as the local density approximation and generalized gradient approximation functional, DFT often underestimates the electronic band gap. Many-body perturbation theory (MBPT) within the GW approximation provides more accurate quasiparticle energies calculation by incorporating many-electron screening effects. Additionally, solving the Bethe-Salpeter Equation (BSE) allows for a detailed analysis of excitonic effects in optical spectra. Despite their accuracy, GW-BSE calculations are computationally expensive, particularly for large-scale systems such as defects and substrate-supported …


First-Principles Studies Of Electrical Polarization Effects In Ferroelectrics, Antiferroelectrics And Defects, Louis Alaerts May 2025

First-Principles Studies Of Electrical Polarization Effects In Ferroelectrics, Antiferroelectrics And Defects, Louis Alaerts

Dartmouth College Ph.D Dissertations

Over the last few decades, density functional theory (DFT) has emerged as a formidable tool in the field of computational material science. Not only has it become a complementary method approach to experiments by rationalizing the many complex properties of materials but its formidable predictive power can also be used to identify the most promising candidates for specific applications. Point defects in semiconductors have become an important platform for the development of quantum networks due to their ability to act as spin-photon interfaces. Spectral diffusion, the broadening of the optical emission line, can significantly impact the performance of these defect-based …


Entanglement-Enhanced Metrology With Superconducting Circuits, Xingrui Song May 2025

Entanglement-Enhanced Metrology With Superconducting Circuits, Xingrui Song

Arts & Sciences Graduate Student Theses and Dissertations

Circuit quantum electrodynamics provides a unique platform for investigating fundamental physics and practical quantum applications. In this thesis, I introduce the superconducting circuit platform from a foundational perspective. Drawing inspiration from quantum electrodynamics and utilizing the analog of closed time-like curves, this work achieves quantum enhancement over classical strategies. Specifically, I investigate agnostic phase estimation protocol and the associated approaches that leverage quantum entanglement to optimally estimate an unknown rotation angle without requiring prior knowledge of the rotation axis. This work not only demonstrates a proof of concept for a type of entanglement-assisted metrology but also highlights intriguing quantum effects. …


Tunable Optical Beam Focusing Using Static Water Droplets On An Electrospun Polymer Fiber, Marco Laurence M. Budlayan, Dina C. Palangyos, Jonathan N. Patricio, Susan D. Arco, Raphael A. Guerrero May 2025

Tunable Optical Beam Focusing Using Static Water Droplets On An Electrospun Polymer Fiber, Marco Laurence M. Budlayan, Dina C. Palangyos, Jonathan N. Patricio, Susan D. Arco, Raphael A. Guerrero

Physics Faculty Publications

This work explores the use of static water microdroplets on a microfiber to vary the width of an optical beam. Varying the water droplet volume changes the beam width without replacing any optical components. A surface derived from glass deposited with polyvinyl chloride (PVC) microfibers via electrospinning was used to sustain the droplet shape on the surface. Scanning electron microscopy revealed the presence of randomly intertwined microfibers with diameters of less than 3 µm which afforded the surface a hydrophobic property. A decrease in the optical transmittance of the films and an increase in the water contact angle were also …


Abel Inversion Comparison Of Geant4 Simulation And Ozone Production Using Cavity Ringdown Spectroscopy In Nitrogen/Oxygen Mixtures In The Presence Of Alpha Radiation, Sidney John Gautrau May 2025

Abel Inversion Comparison Of Geant4 Simulation And Ozone Production Using Cavity Ringdown Spectroscopy In Nitrogen/Oxygen Mixtures In The Presence Of Alpha Radiation, Sidney John Gautrau

Dissertations

The effects of radioactive materials on atmospheric gases have been a topic of interest for years. Radioactive materials ionize the surrounding air, and subsequent reactions lead to molecules such as ozone and nitrogen oxides. The presence of these species above background levels can be used as a marker for radioactive materials which has desirable defense applications like remote detection of radioactive materials. The molecules created in the presence of radioactive materials have been quantified in literature using G-values, which is the number of molecules of a product produced per 100 eV of deposited energy. In this work, Cavity Ringdown Spectroscopy …


The Search For Slow Particles And Magnetic Monopoles With Nova, John Clark May 2025

The Search For Slow Particles And Magnetic Monopoles With Nova, John Clark

Poster Presentations

Singular magnetic poles, north or south, have been theorized to exist for hundreds of years. In the modern day, the elusive singular magnetic pole still remains undiscovered. The appearance of this particle would help confirm many Grand Unified Theories, GUTs, and revolutionize our understanding of some of the fundamental forces of the universe. Fermilab's NOvA collaboration is working on ways to screen and detect magnetic monopoles and other slow-moving particles coming from outer space alongside their main mission to study neutrinos. The aim of this work is to determine and improve the Far Detector’s efficiency at identifying slow moving particles. …


Thin-Film Optical Filters For Selective Transmission And Black-Body Reflection In Pyroelectric Energy Systems., Cedric Cruz Silva May 2025

Thin-Film Optical Filters For Selective Transmission And Black-Body Reflection In Pyroelectric Energy Systems., Cedric Cruz Silva

Electronic Theses and Dissertations

Essential to pyroelectric energy systems is the ability for a pyroelectric material to achieve high temperatures rapidly. In pursuit of augmenting this process, several thin-film optical filters were designed for transmitting laser excitation in the near-infrared region, while simultaneously reflecting black-body radiation for pyroelectric materials. Designs include a classical Fabry-Perot structure with gold and tantalum pentoxide, an induced transmittance filter with silica, hafnia, and gold, and an indium-tin-oxide filter with silica, alumina, and ITO. Performance varies depending on the design. The Fabry-Perot filter experimentally showed a maximum transmittance of 42% at 1.04 μm and an infrared reflectance of 98%. The …


Performance Optimization Of A 1:10 Scale Radio-Controlled Car Through Aerodynamic And Mechanical Enhancements, George Kerner May 2025

Performance Optimization Of A 1:10 Scale Radio-Controlled Car Through Aerodynamic And Mechanical Enhancements, George Kerner

Celebrating Scholarship and Creativity Day (2018-)

Changes in the performance of a 1/10 scale radio-controlled car due to various mechanical and aerodynamic modifications were investigated. The car’s mechanical performance was evaluated by measuring lap times on custom figure-eight and oval tracks to assess handling. A straight 60-foot track was used to measure acceleration times. Mechanical modifications included a low-center-of-gravity chassis, a higher power motor, and wider street tires to optimize suspension, drivetrain, and grip. Aerodynamic enhancements included the integration of front and rear spoilers, a diffuser, and an undertray all designed using Autodesk Fusion. All aerodynamic components were 3D printed and mounted to the vehicle for …


Search For A Diffuse Flux Of Photons With Energies Above Tens Of Pev At The Pierre Auger Observatory, A. Abdul Halim, P. P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, B. Fick, K. Nguyen, D. Nitz, Et Al. May 2025

Search For A Diffuse Flux Of Photons With Energies Above Tens Of Pev At The Pierre Auger Observatory, A. Abdul Halim, P. P. Abreu, M. Aglietta, I. Allekotte, K. Almeida Cheminant, A. Almela, B. Fick, K. Nguyen, D. Nitz, Et Al.

Michigan Tech Publications

Diffuse photons of energy above 0.1 PeV, produced through the interactions between cosmic rays and either interstellar matter or background radiation fields, are powerful tracers of the distribution of cosmic rays in the Galaxy. Furthermore, the measurement of a diffuse photon flux would be an important probe to test models of super-heavy dark matter decaying into gamma-rays. In this work, we search for a diffuse photon flux in the energy range between 50 PeV and 200 PeV using data from the Pierre Auger Observatory. For the first time, we combine the air-shower measurements from a 2 km2 surface array consisting …


Rotation Errors Due To Field Quantization For Simultaneously Driven Atoms, Hunter Lindemann May 2025

Rotation Errors Due To Field Quantization For Simultaneously Driven Atoms, Hunter Lindemann

Graduate Theses and Dissertations

If we want to physically implement qubits by using two level atoms within a cavity, then certain single-qubit gates (such as the X-gate) can be performed by bathing the atoms in an electromagnetic field from a laser. If the average photon count n̄ of the field greatly exceeds the number of N qubits, then the slight fluctuations of the field's phase and amplitude are mostly negligible. However, such a strong field might require more energy than what is desirable for the setup. If a weaker field is used in which phase and amplitude fluctuations might be noticeable, then the …


Signal Modeling Of High Purity Germanium Detectors, Brooke Parker Thibodeau May 2025

Signal Modeling Of High Purity Germanium Detectors, Brooke Parker Thibodeau

Honors Scholar Theses

Pulse shape analysis can be used to analyze radiation incident on a semiconductor diode detector. Finite element analysis (FEA) can be used to simulate high purity germanium detectors with user-specified geometry, impurity concentration, and bias voltage. Subsequent streamline calculation can be used to conduct pulse shape analysis for single and multiple site gamma-ray interactions within the detector volume. Cross sections of the detector can be visualized by contour plots of the electric field, drift velocity magnitude, and collection time, as well as t30 and t90 rise-time values.


Flow Field Surrounding Bluegill (Lepomis Macrochirus) During Suction-Feeding, Jensine Caroline Coggin May 2025

Flow Field Surrounding Bluegill (Lepomis Macrochirus) During Suction-Feeding, Jensine Caroline Coggin

Electronic Theses and Dissertations

Suction-feeding is a common method for capturing prey by aquatic organisms and contributed to the diversification of fishes by enabling them to consume a wide range of prey. Suction-feeding is a complex fish-fluid interaction governed by various hydrodynamic forces: inertia, unsteady, viscous, and pressure gradients. These forces are described by the coupling between the flow physics equations (Navier-Stokes) and the dynamic behavior of the fish (motion and forces). However, the distribution of the pressure field that drives this process, and the extent to which suction-feeding is three-dimensional, remain underexplored. I estimated the pressure within the flow field surrounding the mouth …


The Search For Slow Particles And Magnetic Monopoles With Nova, John Clark May 2025

The Search For Slow Particles And Magnetic Monopoles With Nova, John Clark

Honors Theses

Singular magnetic poles, north or south, have been theorized to exist for hundreds of years. In the modern day, the elusive singular magnetic pole still remains undiscovered. The appearance of this particle would help confirm many Grand Unified Theories, GUTs, and revolutionize our understanding of some of the fundamental forces of the universe. Fermilab's NOvA collaboration is working on ways to screen and detect magnetic monopoles and other slow-moving particles coming from outer space alongside their main mission to study neutrinos. The aim of this work is to determine and improve the Far Detector’s efficiency at identifying slow moving particles. …


Can Neutron Star Mergers Alone Reproduce R-Process Enrichment In Ultra-Faint Dwarf Halos?, Christine Gyure May 2025

Can Neutron Star Mergers Alone Reproduce R-Process Enrichment In Ultra-Faint Dwarf Halos?, Christine Gyure

Honors Theses

Neutron star mergers (NSMs) are the only confirmed source of the r-process responsible for heavy element formation. However, there are concerns about the extent to which NSMs can enrich small dwarf galaxies arising from either a strong natal kick velocity or substantial merger time. We present the results of a novel analytic model investigating the impact of these two distributions, represented respectively by a Maxwellian and power law, and their accompanying parameters on chemical enrichment in ultra-faint dwarf halos. We find that our model reproduces the observed enrichment fractions in these small dwarf galaxies for a variety of parameter combinations, …


An Integrative Approach To Einstein’S Field Equations Of General Relativity For High School Students, Christina M. Aintablian May 2025

An Integrative Approach To Einstein’S Field Equations Of General Relativity For High School Students, Christina M. Aintablian

Senior Honors Theses

Einstein’s Field Equations form the foundation of the theory of General Relativity, describing the interdependence of mass-energy and spacetime curvature, where curvature gives rise to gravity. However, the complexity of these equations makes them difficult for high school students to grasp. The mathematical framework of General Relativity is introduced step by step, beginning with relative motion and culminating in a discussion of complex phenomena that challenge modern physics. Each explanation intertwines core concepts of relativity with pre-established mental models to enhance learning. Through the use of figures, analogies, narratives, and thought experiments, a structured framework is developed to make relativity …


Physics Embedded Neural Network: A Novel Data-Free Numerical Method For Solving Computational Physics Problems, Pawan Gaire May 2025

Physics Embedded Neural Network: A Novel Data-Free Numerical Method For Solving Computational Physics Problems, Pawan Gaire

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A novel approach for solving partial differential equations (PDEs) using neural networks for scientific computing is introduced. The proposed approach, referred to as physics-embedded neural network (PENN), features a unique architecture that incorporates the PDE and boundary conditions information directly within the final fully-connected layer of the feed-forward neural network (NN). The key aspect of PENN is the parallel numerical embedding of a differential equation associated with physical problems within the activation function of the network’s final layer. This integration leads to a new class of computational solvers competitive with classical methods like the Finite Element Method (FEM) and capable …


Revealing Hidden Histories: A Multi-Sensor Aerial Survey For Detecting Unmarked Burials At Sinking Spring Cemetery, Abingdon, Va, Noah Hall May 2025

Revealing Hidden Histories: A Multi-Sensor Aerial Survey For Detecting Unmarked Burials At Sinking Spring Cemetery, Abingdon, Va, Noah Hall

Electronic Theses and Dissertations

The Sinking Spring Cemetery, established in 1773 in Abingdon, Virginia, spans 11 acres and is divided by a road. The 9-acre southern section was reserved for white church members. Enslaved individuals and free people of color were buried in the smaller northern section, where few headstones remain today. This study aimed to map the unmarked graves using thermal, multispectral, and Light Detection and Ranging (LiDAR) sensors deployed on unmanned aerial systems. Graves were characterized by subtle topographic depressions mapped by LiDAR and cooler radiant temperature anomalies in thermal imagery. Thermal data collected at different times of the day and year …


Impact Of Shear Flow On Marine Biofilms Using Hyperspectral Imaging, Shantanu Mahesh Kore May 2025

Impact Of Shear Flow On Marine Biofilms Using Hyperspectral Imaging, Shantanu Mahesh Kore

All Theses

Various microbial communities in marine biofilms cause biofouling on submerged surfaces, posing challenges to marine industries. Despite their ecological and economic importance, biofilms' biomechanical and biochemical responses to hydrodynamic shear stress are insufficiently understood, particularly in dynamic flow conditions. To fill this gap, our study uses an innovative fiber-optic hyperspectral imaging (HSI) system and a supercontinuum laser source to examine marine biofilms' structure, composition, and detachment behavior at different shear stress levels.

To detect spectral and spatial heterogeneity in live biofilms without labeling, we created a custom imaging pipeline that captures reflectance spectra in the 600-850 nm range, targeting microbial …


Divergence-Free Smoothed Particle Hydrodynamics In A Stream Digital Twin, Austin Hartley May 2025

Divergence-Free Smoothed Particle Hydrodynamics In A Stream Digital Twin, Austin Hartley

All Theses

Digital Twins (DT) are being explored by the South Carolina (SC) water community to simulate how SC streams will flow at various water levels. Currently, a DT called Gilligan simulates these streams utilizing weakly-incompressible Smoothed Particle Hydrodynamics (SPH). This method does not strictly enforce incompressibility, which leads to unrealistic water flows and unwanted visual artifacts that require post-processing effects to hide. To address these problems and simulate more realistic water flows, the Gilligan stream logic is updated and a state-of-the-art SPH method that enforces incompressibility—Divergence-Free SPH (DFSPH)—is implemented within the Gilligan framework. DFSPH is able to make use of two …


Automated Radiotherapy Treatment Planning For Breast Cancer: A Robust To Ol For Global Deployment, Hana Baroudi May 2025

Automated Radiotherapy Treatment Planning For Breast Cancer: A Robust To Ol For Global Deployment, Hana Baroudi

Dissertations and Theses (Open Access)

Breast cancer incidence continues to rise worldwide, particularly in low- and middle-income countries, where limitations in resources already constrain access to timely care. Radiotherapy is a cornerstone of breast cancer management, proven to significantly lower both recurrence and mortality. However, a growing shortage of radiation staff worldwide threatens the prompt delivery of these treatments.This thesis proposes an automated solution to address the limited accessibility of radiotherapy planning in breast cancer management by developing an end-to-end automated treatment planning model and evaluating its performance and limitations across diverse patient populations.

An automated contouring model was trained using data from 104 whole-breast …


Development Of Lineal Energy Spectrum-Based Biological Effects Models For Protons, Joseph M. Decunha, Fada Guan, David Grosshans, Zhongxing Liao, Dragan Mirkovic, Oleg Vassiliev, Radhe Mohan May 2025

Development Of Lineal Energy Spectrum-Based Biological Effects Models For Protons, Joseph M. Decunha, Fada Guan, David Grosshans, Zhongxing Liao, Dragan Mirkovic, Oleg Vassiliev, Radhe Mohan

Dissertations and Theses (Open Access)

In this dissertation, methods are developed and described to allow for the rapid calculation of microdosimetric spectra (specifically, lineal energy) for protons. SuperTrack, a GPU-accelerated tool for calculation of microdosimetric spectra was developed and is capable of computing lineal energy spectra up to 5000x faster than using Geant4 directly. Proton lineal energy spectra generated by SuperTrack are indistinguishable from those generated by Geant4. With SuperTrack, large libraries of lineal energy spectra for monoenergetic protons spanning 0-300 MeV have been developed. The proton lineal energy spectra calculated by SuperTrack have been compared to experimental measurements made by a tissue equivalent proportional …


Molecular Insights: Advances In Single Molecule And Single Particle Detection For Analysis Of Chemical, Physical, And Biological Phenomena, James Ethan Batey May 2025

Molecular Insights: Advances In Single Molecule And Single Particle Detection For Analysis Of Chemical, Physical, And Biological Phenomena, James Ethan Batey

Chemistry & Biochemistry Undergraduate Honors Theses

This thesis is focused on recent advancements made in the field of chemical imaging, optical microscopy, and recent developments that have improved spatial, temporal, or spectral resolution or have made certain techniques more accessible and cost effective for their wider adoption. This thesis is organized based on the systems of interest we studied with each new technique. Although, it is important to note that many of the methods here can be used with a multitude of systems even if not explicitly mentioned. The first chapter of this thesis will discuss the current state of chemical imaging, common terminology, and important …


Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton May 2025

Growth, Cladding, And Characterization Of Single Crystal Optical Fiber: The Next Evolution In Directed Energy Systems, Allen Benton

All Dissertations

High-power fiber lasers are steadily increasing in maximum power and rapidly approaching theoretical maximum power output from a single fiber aperture. The low thermal conductivity of silica fibers is an inherent limitation to the dissipation of heat from the fiber core, and the buildup of heat within the laser gain media is the principal driver of transverse mode instability within fiber systems. This limitation necessitates the exploration of alternate fiber host materials. Due to their high thermal conductivity, excellent transmission range, ability to host most of the optically active rare earth ions, and success as bulk laser materials, single-crystalline YAG …


A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis May 2025

A System And Method For Measuring Spatially Varying Surface Appearances With A Study Of Feathers, Jessica Baron-Lis

All Dissertations

Real-world materials, particularly biological structures such as feathers exhibit complex appearances that vary spatially across their surfaces. The field of computer graphics provides a means of understanding such surfaces through material modeling which uses both analytical models and data acquired from light-surface interactions. There are many efforts within the past decade in measuring materials for graphics, but common limitations in these works include not accounting for spatially varying properties and reliance on neural networks and synthetic datasets.

Feathers from modern birds present diverse appearances due to how light interacts with their unique hierarchical microstructures. Variations in those structures lead to …


Conservation Laws For Asymptotically Perfect Fluid Spacetimes, Lyle Arnett Jr. May 2025

Conservation Laws For Asymptotically Perfect Fluid Spacetimes, Lyle Arnett Jr.

All Graduate Theses and Dissertations, Fall 2023 to Present

In physics, conservation laws, like those for energy or momentum, are powerful tools that help us understand how systems evolve and interact. In general relativity, where spacetime itself is curved by matter and energy, defining such conservation laws becomes especially subtle and complex. Traditional methods rely on idealized conditions like empty space or special symmetries, which limit their usefulness in more realistic, dynamic settings such as an expanding universe.

This dissertation explores a modern mathematical framework, developed by Iyer and Wald, that allows conservation laws to be derived directly from the equations governing spacetime. Using this approach, I examine not …