Physical Sciences and Mathematics Commons^™

Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou

Dissertations, Theses, and Capstone Projects

Atomic delocalization due to nuclear quantum effects (NQE) remains poorly understood in low-temperature liquids near the glass state and during vitrification. Many liquids can be described accurately by treating their nuclei as classical particles, but this approximation fails for light elements such as He and H₂, small hydrogen-containing molecules such as water, and systems in which zero-point motion or isotope-substitution effects are important. Developing a general thermodynamic and statistical-mechanical description of such liquids has been challenging. This dissertation extends the potential energy landscape (PEL) formalism, originally developed for classical liquids and glasses, to liquids that obey quantum mechanics and exhibit …

Mapping The Water Quality Of Jamaica Bay, New York (1996-2024): Principal Component Analysis And K-Means Clustering, Sneha Srivastava

Dissertations, Theses, and Capstone Projects

Jamaica Bay, located along the southeastern coast of New York City, acts as a biodiverse estuary of wetlands, meadows, and salt marsh islands. The purpose of this study is to analyze the water quality conditions of the region over time, comparing locations around the bay to identify hyperlocal features that influence larger trends in the hydrological system. Ten variables were used as water quality indicators, including total Kjeldahl nitrogen, salinity, pH, Secchi disk depth, and total phosphorus, among others, across five stations in the bay, between 1994 and 2024. After data cleaning and standardization methods were applied, principal component analysis …

Rethinking Road Racing Standards: Comparing New York Road Runners Race Results To Running Industry Standards, Jennie Coughlin

Dissertations, Theses, and Capstone Projects

Running has undergone a third boom in participation since 2020, driven largely by people seeking fitness options that were outside and socially distanced during the COVID-19 pandemic. Social media has also allowed runners from groups that did not traditionally participate to find community. As the road racing population has expanded to include more people, some road racing industry standards have not kept up. This project assesses what the road racing community looks like and measures industry standards against the community of participants to see what changes in those standards would be needed to make them inclusive for all participants.

To …

Self-Organized Criticality In Biased Activated Random Walk, Joshua Meisel

Dissertations, Theses, and Capstone Projects

We demonstrate many of the conjectured universality and self-organized criticality (SOC) properties of the interacting particle system Activated Random Walk (ARW) in the setting of one-dimensional biased walks, as formulated for instance in Levine and Silvestri’s 2024 survey. Namely, there exists the same limiting critical state for two finite ARW models, as well as for the infinite model as the density approaches its critical value from below. Many of the desired properties hold, including heavy-tailed avalanches, but spatial correlations decay exponentially fast, a deviation from the SOC paradigm. Nonetheless, the obtained decay rate vanishes with the bias. Since the critical …

Applications Of Entanglement In Quantum Information, Nada Ali

Dissertations, Theses, and Capstone Projects

Entanglement is the resource that most sharply distinguishes quantum information processing from its classical counterpart, and this thesis examines it from two complementary directions: how it can be detected and quantified, and how it, together with the broader machinery of quantum correlations, interference, and measurement, can be put to use. We first study two simple, measurable conditions that detect bipartite entanglement, and show that the extent to which either is violated yields a lower bound on the negativity of a state. The bound is established for two qubits, extended to systems of arbitrary finite dimension, and sharpened when partial knowledge …

Behind The Score: The Influence Of Neighborhood Policy Contexts On New York Regents Exam Performance Across New York City Public High Schools, Philip J. Kovacevic

Dissertations, Theses, and Capstone Projects

This study used a two-level hierarchical linear model (HLM) to test whether New York City neighborhood zoning and land-use characteristics independently predict school-level performance on the New York State Regents Examinations, after controlling for school demographic and organizational characteristics, and Regents mean scores, both drawn from the NYC DOE's Regents Exam Results file (NYC Public Schools InfoHub, 2024). Using NYC Primary Land Use Tax Lot Output (PLUTO) 2025 data, a Neighborhood Educational Quality (NEQ) index was built for each of the city’s 42 community districts by combining the commercial floor area ratio (CommFAR) and the proportion of lots zoned residential …

Cavity Optomechanics Via Mechanically Induced Coupling Of Optical Modes, Satyam S. Jha

Dissertations, Theses, and Capstone Projects

This thesis introduces a transverse, symmetry-breaking mode of optomechanical coupling that departs from the conventional dispersive and dissipative interactions, taking its motivating platform from whispering-gallery-mode (WGM) resonators, where a mechanical displacement lifts the near-degeneracy of azimuthal mode pairs and couples them. After reviewing the standard optomechanical model and the sideband-cooling phenomenology it underlies, we derive the Hamiltonian for the transverse-coupling system and first study its Hamiltonian dynamics, without drive or dissipation. Recast in terms of Schwinger pseudospin operators, the model exhibits a Hamiltonian Hopf bifurcation separating stable and unstable dynamical regimes. In the stable regime, the mechanical nonlinearity permits controlled …

Quaternionic Analogues Of Zagier’S Sums Of Binary Quadratic Forms, Ajmain A. Yamin

Dissertations, Theses, and Capstone Projects

Let K be the real numbers R, complex numbers C or quaternions H. Let O ⊂ K be a full rank discrete Euclidean subring of K. We investigate certain functions F_{k,Δ,O} : K → R indexed by positive integers k, Δ with k odd. When K = R or C, these functions recover Zagier’s sums of binary quadratic forms and Karabulut’s sums of binary Hermitian forms respectively. When K = H, the F_{k,Δ,O} functions are new quaternionic analogues of Zagier's sums whose definition involves sums of binary Hamiltonian forms as defined by Parkkonen-Paulin.

We prove that for fixed "weight" k …

Model-Theoretic Arguments In Philosophy, Peter Susanszky

Dissertations, Theses, and Capstone Projects

This dissertation is on model-theoretic arguments in philosophy, especially those of Quine, Davidson, and Putnam. In the first part, to ground the debate, I give a rigorous introduction to the salient parts of first-order model theory. I start the second part by giving an introduction to Quine's philosophy, and how the model-theoretic arguments fit into it. After considering how Donald Davidson adopted the Quinean lesson, I move on to Putnam's model-theoretic arguments. Putnam's spin on these model-theoretic considerations significantly departs from Quine and Davidson, while retaining many of the core ideas. Most importantly, I argue that the target of Putnam's …

The Role Of External Factors In Shaping Carbohydrate Conformational Landscapes, Murat Yaman

Dissertations, Theses, and Capstone Projects

Carbohydrates (glycans) are among the most structurally diverse biomolecules and participate in a wide range of biological processes, including molecular recognition, cell adhesion, immune response, host-pathogen interactions, and cellular signaling. Their biological functions are governed by a complex interplay between sequence, stereochemistry, conformational flexibility, and environmental factors. However, the structural heterogeneity and dynamic nature of glycans present significant challenges for both experimental characterization and theoretical modeling. In particular, the relationships between glycan structure, conformational dynamics, and the resulting potential energy surfaces remain incomplete.

This dissertation investigates how external factors modulate the potential energy surfaces of carbohydrates through a combination of …

Mesoscopic Scaling Of Microwave Transmittance And Disorder-Induced Alignment, Israel Kurtz

Dissertations, Theses, and Capstone Projects

This thesis presents microwave measurements and numerical simulations of wave propagation and transmission through random mesoscopic waveguides. We analyze the scaling of mesoscopic microwave conductance, including departures from Ohm’s law near channel openings, which are frequencies at which new propagating modes enter the system, and the evolution of modal phase alignment within the medium, which leads to the observed diversity of transmission eigenvalues. We extend the transmission matrix formalism to all sample depths using the flux matrix, which relates the flux amplitude within the sample to the incident flux, and decompose the flux at each sample depth into forward- and …

Ultrafast Spectroscopy Of Organic Materials In Strong Light–Matter Interaction And Terahertz Optics, Kamyar Rashidi

Dissertations, Theses, and Capstone Projects

Ultrafast spectroscopy is a powerful tool for investigating phenomena that occur on extremely short timescales and for probing ultrabroadband spectral responses enabled by its ultrashort laser pulses. These capabilities are essential for advancing both the fundamental understanding of light–matter interactions and the development of next-generation optoelectronic technologies. The first part of this thesis investigates the ultrafast dynamics of organic exciton–polaritons and their application to controlling molecular excited-state processes using momentum-resolved pump–probe spectroscopy. A major challenge in these systems is the dark-state problem, where photoexcitation predominantly populates long-lived excitonic reservoir states that obscure the in trinsic dynamics of the hybrid light–matter …

Complementing Topographic Wetness With Sentinel-2 Phenological Indices To Map Soil Moisture Gradients In A Snowmelt-Driven Mountain Floodplain, Edward Turk

Master's Projects and Capstones

Soil moisture in mountain floodplains varies over a few meters, far finer than ground-based sensors or coarse satellite images resolve; conventional optical and microwave methods sense only the top few centimeters, missing the root zone that governs plant function and biogeochemistry. Similarly, topography-derived moisture variations miss micro-heterogeneities in moisture related to intrinsic soil heterogeneity and/or the root zone. This has important implications for our ability to characterize local hotspots of biogeochemical reactions, like those related to the generation of methane. In this work, we read vegetation as a proxy for the subsurface, using Sentinel-2 land-surface phenology to infer root-zone moisture, …

Exposing And Addressing Machine Learning Brittleness Through Constraint Solving, Muyeed Ahmed

Dissertations

Machine Learning (ML) implementations are fundamentally brittle: nondeterministic, inconsistent, and prone to overfitting; however, constraint solving can be used to systematically expose, quantify, and address this brittleness.

This dissertation first establishes that widely-used implementations of popular ML algorithms are nondeterministic (producing different outputs on the same input, across different runs) and inconsistent (different implementations of the same algorithm producing different outputs on the same input). This is more prevalent in Unsupervised Learning (UL) implementations where, due to the lack of a ground truth, subtle execution errors can go unnoticed and are difficult to verify. Nondeterminism and inconsistency also introduce security …

Development Of Ultrafast Protein Digestion And Standards Free Quantitation Methods For Mass Spectrometric Analysis, Praneeth Ivan Joel Fnu

Dissertations

A wide variety of biologically important molecules, such as enzymes, antibodies, hormones, transporters and receptors are proteins by composition and they play key roles in biological functions such as cellular regulation, communication, metabolism and physiological function. Protein dysfunctions and abnormalities are associated with numerous diseases, making proteins critical targets for understanding disease mechanisms and developing therapeutic interventions. Protein-based therapeutics such as monoclonal antibodies, hormones and vaccines gained popularity due to their high specificity, efficacy, and ability to treat complex diseases that are often difficult to address with small-molecule drugs.

Given the important role of proteins in a variety of biological …

The Inverse Elasto-Acoustic Problem, Patrick Grice

Dissertations

A stable and numerically efficient boundary integral method formulation of the elasto-acoustic problem is presented, based on Fourier analysis. The method generalizes well to multiple scattering. The Frechet derivative of the elasto-acoustic problem with respect to shape perturbations is derived, and geometric flow theory is used to design stable numerical methods for the simulation of moving boundaries. The shape derivative is used to define a regularized Gauss-Newton algorithm for shape fitting of elasto-acoustic scatterers.

Geometric Convergence And State-Space Decompositions For Stochastic Gradient Descent Markov Chains, Philip Zaleski

Dissertations

No abstract provided.

Solar Wind - Magnetosphere - Ionosphere Coupling Processes Through Small-Scale Magnetic Flux Ropes, Youra Shin

Dissertations

Small-scale magnetic flux ropes (SMFRs) in the solar wind are examined to determine their properties in the near-Earth upstream region and their effects on geospace. Although SMFRs are observed frequently in the solar wind, their statistical behavior near Earth and their role in solar wind-magnetosphere-ionosphere coupling remain insufficiently constrained. In this dissertation, an automated Grad-Shafranov reconstruction technique is applied to magnetic field and plasma measurements from MMS and Wind, and ionospheric responses are investigated using geomagnetic indices and SuperDARN observations. During the survey period, MMS has an apogee of approximately 25-29 R_E. This orbital configuration allows the near-Earth …

Spider Biodiversity And Insecticide Sensitivity Across Active And Restored Cranberry Bogs On Nantucket, Tyler J. Kulak

Graduate Masters Theses

Spiders are one of the most diverse groups of organisms on the planet with over 53,000 species described as of 2026. They provide a suite of ecosystem services including their regulation of problematic pests in agricultural systems, appearing in high biomasses across a breadth of ecological niches. While beneficial as pest regulators, they are also susceptible to the same management techniques as pest organisms and are especially vulnerable to chemical control. Cranberry production in Massachusetts likely benefits from spider ecosystem services, but diversity research on spiders in these systems is limited. This study compares the diversity of spider populations from …

A Variational Algorithm For Preparing Superoptimal Thermal States For Quantum Thermometric Measurement Adaptable To Nisq Hardware, Nicholas Donatelli

Graduate Masters Theses

The conditional thermal state (CTS) is a probe-specific quantum thermal state that is known to outperform the Gibbs state in quantum thermometric measurements at sufficiently low temperatures. This thesis introduces a variational quantum algorithm designed to prepare the CTS on quantum computing hardware which optimizes the angular parameters of the quantum gates that comprise the ansatz circuit and, for the one-qubit case, minimizes relative infidelity of the output state with the known CTS. Using noiseless numerical simulations (SPSA with Qiskit), attempting to prepare the CTS yielded relative infidelities with the known CTS on the order of $10^{-5}$ for most parameter …

Toward The Study Of Photon Dynamics In Non-Separable Spacetimes, Kara Nelson

Graduate Masters Theses

Black holes provide a unique laboratory for testing general relativity in the strong-field regime through observations such as black hole images and gravitational wave signals. Comparing theoretical predictions with these observations requires accurate numerical models of photon trajectories. This thesis develops and validates a generalized ray-tracing framework for computing null geodesics in stationary, axisymmetric spacetimes. Unlike many existing ray-tracing methods, the framework does not rely on metric separability or analytic solutions, allowing it to be applied to both separable and non-separable spacetimes. The framework is validated by reproducing known Schwarzschild and Kerr results and is applied to a quasi-Kerr spacetime …

Electrolyte Development And Interfacial Reactions At Multivalent Metal Anode For Next Generation Energy Storage Systems, Leslie Gates

Graduate Masters Theses

The increasing demand for safe, sustainable, and high-performance energy storage systems has driven significant interest in multivalent-ion batteries, including aluminum, magnesium, and zinc-based systems. These technologies have attracted attention due to their high theoretical energy densities, natural abundance, low cost, and environmentally benign nature. However, their development remains hindered by a limited fundamental understanding of electrolyte development and interfacial processes at the electrode–electrolyte interface, where complex electrochemical interactions govern battery performance and stability.

This thesis investigates electrode–electrolyte interactions in both a novel aluminum electrolyte and divalent magnesium and zinc systems. Beginning with the development and characterization of a novel aluminum …

Microrheological Characterization Of Collagen-I Extracellular Matrix Remodeling During Tr146 Tumor Spheroid Invasion And Ppix-Mediated Photodynamic Therapy, Himantha Dilshan Saldonge

Graduate Masters Theses

Oral squamous cell carcinoma (OSCC) invasion is strongly regulated by interactions between tumor cells and the surrounding extracellular matrix (ECM). However, localized ECM mechanical changes during tumor invasion and after photodynamic therapy (PDT) remain insufficiently understood. This study mainly investigated: time-dependent viscoelastic remodeling of collagen-I ECM during TR146 tumor cell invasion, visualization of time-dependent TR146 tumor cell invasion and post-PDT response using live/dead fluorescence imaging, and the direct effect of PpIX-mediated PDT on the viscoelastic properties of spheroid-free collagen-I ECM. Three-dimensional TR146 spheroids were generated using a non-adherent agarose-based method, surrounded by a basement-membrane-like Matrigel layer, and embedded in 3.0 …

Symmetry Breaking And Restoration In The Grasshopper Ising Model, Aradh Bisarya

Graduate Masters Theses

Distance-selective interactions in Ising systems give rise to a range of rich and unexpected phenomena. A notable example is the so-called Grasshopper Ising model, a conserved spin Ising model with interactions only between spins at a fixed distance. This model is the discrete version of the following mathematical problem: A grasshopper lands at a random point on a planar lawn of area one. It then makes one jump of fixed distance in a random direction. What lawn shape maximizes the probability that the grasshopper lands on the lawn after the jump? The solution to this problem, corresponding to the ground …

Symmetric Informationally Complete Positive Operator Valued Measures Minimize P-Norm Difference Between Quantum And Classical Probability Rules, Austin Monaghan

Graduate Masters Theses

Experimental violations of Bell's inequality demonstrate quantum theory's incompatibility with a local hidden-variable formulation. Simply put, either 1) measurements performed at one point in space may instantaneously influence far away systems ("spooky action at a distance") or 2) measurement outcomes are not the result of pre-existing properties. The act of measurement takes part in the very creation of the outcomes. If we reject condition 1 as a valid assumption, how can we interpret the significance of condition 2 i.e. no local parameters?  In QBism, condition 2 arises from something deeper: that the Born rule expresses a nonclassical condition for connecting …

Infrared Detectability Of Whale Species And Behaviors To Enhance Automatic Detection For Real-Time Vessel Strike Avoidance, Laura J. Howes

Graduate Masters Theses

Real-time detection of large whales at sea is critical for mitigating serious injury and mortality from ship strikes and other human activities such as seismic surveys, especially for endangered species such as the critically endangered North Atlantic Right Whale (Eubalaena glacialis). Traditional marine mammal observers are limited by environmental conditions and human factors, necessitating a robust, 24-hour solution. This study investigates the efficacy of a novel onboard detection tool infrared (IR) technology to detect whale blows and body parts. While IR is a promising advancement, its performance under varying sea conditions (e.g., fog, humidity) and its ability to …

Synthesizing Viscoelasticity: Living Polymers, Micro-Macro Relations, And Paths For Resolution, Adam M. Hasler

Graduate Masters Theses

This thesis investigates the relationship between macroscopic rheological signals and underlying microscopic dynamics in complex fluids, specifically focusing on ”living polymers” within the cetyltrimethylammonium bromide (CTAB) and sodium salicylate (NaSal) surfactant system. The research addresses the inverse parameterization problem, demonstrating how bulk measurements like zero-shear viscosity can mask fundamentally different physical topologies, such as purely cylindrical, reptating micelles versus highly branched networks. Through the successful synthesis of viscoelastically ”degenerate” samples, the study utilizes an array of characterization techniques including frequency sweeps, Large Amplitude Oscillatory Shear (LAOS) to resolve these unique underlying states. Furthermore, the work explores further avenues of study …

The Sliding Aperture Transform: A Mathematical Method Applied To Radiation-Induced Dlts Capacitance Transients, Md Abu Bakkar Siddique

Graduate Masters Theses

This thesis presents the Sliding Aperture Transform (SLAPt), a novel mathematical technique for extracting exponential argument and pre-factor  from experimental data. The method transforms measured waveforms into an inverse-domain representation where exponential decay processes appear as distinct peaks, simplifying data analysis and reducing the effects of baseline offsets and noise. The technique is here applied to time dependent capacitance transients associated with irradiated and non-irradiated silicon pn junction diodes. The technique is further developed and applied to positive argument exponentials using an axillary function. This allows forward bias  current-voltage measurements, and forward pulse-bias current transient measurements to be SLAP analyzed, …

Modeling Kinetics Of 5-Aminolevulinic Acid-Induced Protoporphyrin Ix Accumulation For Optimal Photodynamic Therapy, Priscilla Melebor

Graduate Masters Theses

Photodynamic therapy (PDT) is a minimally invasive treatment that uses light-activated photosensitizers to selectively destroy diseased tissue through the generation of reactive oxygen species. However, conventional in vitro models often fail to accurately reproduce the pharmacokinetics of photosensitizer accumulation and clearance observed in vivo. This study investigated protoporphyrin IX (PpIX) accumulation following 5-aminolevulinic acid (ALA) exposure under physiologically relevant conditions using two-dimensional (2D) monolayers and three-dimensional (3D) spheroids. By comparing continuous ALA exposure with transient exposure followed by ALA washout, this work provides a more biologically relevant framework for studying PpIX kinetics and optimizing photodynamic therapy.

Informationally Complete Measurements In Quantum Theory: Implementation, Geometry, And Correlations, Sachin Gupta

Graduate Doctoral Dissertations

Informationally complete measurements provide a bridge between the operational and geometric structure of quantum theory. They allow quantum states to be reconstructed from measurement probabilities. This thesis studies informationally complete measurements from two complementary perspectives: their physical implementation and their role in the probabilistic reconstruction of quantum theory.

The first part develops a symmetry-driven Naimark extension for rank-one Weyl- Heisenberg covariant Projective Operator-Valued Measures (POVMs) in arbitrary finite dimension. Since every element of such a POVM is generated from a single fiducial state by the Weyl-Heisenberg displacement operators, the full measurement inherits a strong covariance structure. We show that this …