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Full-Text Articles in Physical Sciences and Mathematics

Artificial Intelligence And Translation: Exploring Current Applications, Limitations And Future Potential Of Language Models Through Japanese-English Translation, Loklin Elias Nord Mar 2027

Artificial Intelligence And Translation: Exploring Current Applications, Limitations And Future Potential Of Language Models Through Japanese-English Translation, Loklin Elias Nord

Undergraduate Theses, Capstones, and Recitals

This thesis highlights the recent improvements and capabilities of Large Language Models (LLMs), specifically their ability to produce translations between different languages. The continued up-scaling of model sizes has led to breakthroughs in the level of their observed intelligence, allowing them to produce translations that are similar in quality to highly skilled human translators. However, to facilitate the reasoning processes that LLMs now possess, their demand for computational power and the supporting hardware and resources has increased proportionally. Considering the impacts of this technology on the environment, energy resources, and its accessibility, my research explores the possibilities of smaller, highly …


Computational Studies Of Triplet State Formation In Zinc Dipyrrin Complexes, Reuben Kwabla Adigbli Dec 2026

Computational Studies Of Triplet State Formation In Zinc Dipyrrin Complexes, Reuben Kwabla Adigbli

Electronic Theses and Dissertations

Zinc dipyrromethene complexes are promising earth-abundant photosensitizers due to their strong visible-light absorption and tunable excited states. To rationally design them for photocatalysis and photodynamic therapy, a molecular-level understanding of triplet-state formation is needed, but details of intersystem crossing remain unclear. To study the effect of π-extension, we synthesized an indole-substituted zinc dipyrrin complex: the dipyrromethane ligand was prepared from indole and mesitaldehyde, oxidized to the dipyrromethene, then coordinated with zinc. DFT and TD-DFT calculations determined ground and excited-state geometries and energies in different solvents, modeled absorption spectra, and visualized charge distributions. The results show how solvent polarity shifts energies …


Wildfire And Fuel Treatments In Utah: A Practical Guide And Outcomes From An Oak-Maple Ecosystem, Annie E. Prescott Dec 2026

Wildfire And Fuel Treatments In Utah: A Practical Guide And Outcomes From An Oak-Maple Ecosystem, Annie E. Prescott

All Graduate Theses and Dissertations, Fall 2023 to Present

Wildfire is a natural part of Utah’s landscapes, but as wildfires become more extreme and communities continue to expand into wildland areas, it is increasingly important to understand how wildfires behave and how their negative effects can be mitigated. One way to reduce wildfire risks and protect life, property, and ecosystem services is through fuel treatments — actions that reduce the amount and arrangement of flammable vegetation through mechanical removal, wildland fire, or other methods.

Information on wildfire behavior and fuel treatments is abundant but often scattered, ecosystem-specific and difficult to access. In addition, most research in the Western U.S. …


Toward Optimizing Fruit Production In Utah Soils: Apple Salt Tolerance Screening And Tart Cherry Fertility Management, Kaitlin Dabbs Dec 2026

Toward Optimizing Fruit Production In Utah Soils: Apple Salt Tolerance Screening And Tart Cherry Fertility Management, Kaitlin Dabbs

All Graduate Theses and Dissertations, Fall 2023 to Present

Fruit production in Utah can be challenging due to local climate and soil conditions. Tart cherries and apples are major fruit crops in Utah, and improvements to these cropping systems would be beneficial for farmers and local consumers. Two experiments were conducted to evaluate desired improvements for these crops. The first study looked for salt tolerance in ten new apple rootstocks. Salty soils can be found throughout the state limiting the land suitable for apple production. When grown in salty soils apple trees often have reduced growth and production potential. A specialized drip irrigation system was constructed in a greenhouse …


Extending Geometric Acoustic Ray Tracing To Multi-Room Environments: A Case Study On Gunshot Sound Transmission Between Adjacent Rooms, Tyler Ton Dec 2026

Extending Geometric Acoustic Ray Tracing To Multi-Room Environments: A Case Study On Gunshot Sound Transmission Between Adjacent Rooms, Tyler Ton

Theses and Dissertations

Accurate localization of gunshots in multi-room building environments remains a challenging problem in acoustic forensics and public safety applications. Existing approaches model sound propagation within a single room, neglecting the transmission of acoustic energy through walls and other building materials. This thesis presents a study on modeling multi-room gunshot acoustic transmission, combining geometric ray tracing with structural acoustic transmission-loss modeling to generate impulse responses for two horizontally adjacent rooms separated by a shared wall, providing a foundation for future inter-room gunshot localization work. The proposed system uses GSound-SIR, a geometric acoustics engine, to simulate sound propagation in both of the …


A Fundamental Study Of Fatty Acid Ionic Liquids And Their Effects On Biomolecules, Achismita Dutta Sep 2026

A Fundamental Study Of Fatty Acid Ionic Liquids And Their Effects On Biomolecules, Achismita Dutta

Theses and Dissertations

Fatty acid ionic liquids (FAILs) are a class of ionic liquids (ILs) with relatively low toxicity and potential applications in biological systems. This study examined the interactions of tetramethylguanidinium decanoate, tetramethylguanidinium octanoate, choline decanoate, and choline octanoate with lipid membranes, proteins, and nucleic acids. Membrane leakage experiments using model lipid vesicles showed that decanoate-based FAILs produced greater membrane permeabilization than octanoate-based analogues, consistent with their higher membrane permeability. These effects were stronger for the ILs than for decanoate alone and occurred below the critical micelle concentration (CMC), suggesting that micelle formation may not be essential for membrane disruption. The ability …


A Hybrid Rule-Based And Large Language Model Framework For Extracting Acronym–Definition Pairs From Scientific Literature, Petro Skrypnyk Sep 2026

A Hybrid Rule-Based And Large Language Model Framework For Extracting Acronym–Definition Pairs From Scientific Literature, Petro Skrypnyk

Theses and Dissertations

Authors of scientific papers rely heavily on acronyms and often use them without defining them, making the literature harder to read and index. This thesis develops and evaluates a hybrid rule-based and large language model (LLM) framework that extracts acronym–definition pairs from scientific PDF documents. It extends an earlier Rowan University system that combined a regular-expression parser with a single LLM on 200 papers. That system showed that neither the parser nor the LLM alone is sufficient for accurate extraction of the pairs. The framework is a fully automated pipeline from PDF input to scored results. It compares four LLM …


Potential Energy Landscape Formalism For Quantum Liquids, Yang Zhou Sep 2026

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 …


Catalytic Synthesis Of Protoberberine Alkaloids And Their Evaluation As Selective Dopamine Receptor Ligands, Ashok Reddy Gudipally Sep 2026

Catalytic Synthesis Of Protoberberine Alkaloids And Their Evaluation As Selective Dopamine Receptor Ligands, Ashok Reddy Gudipally

Dissertations, Theses, and Capstone Projects

Dopamine regulates motor control, cognition, reward, motivation, and neuroendocrine signaling. Disruption of dopaminergic neurotransmission is closely linked to central nervous system disorders, including Parkinson’s disease, schizophrenia, addiction, and related neuropsychiatric conditions. Because these functions are mediated by multiple dopamine receptor subtypes with distinct roles in physiology and disease, the discovery of subtype-selective ligands remains an important goal in neuropharmacology. Within this context, protoberberine alkaloids, particularly tetrahydroprotoberberines (THPBs), are attractive molecular frameworks because they combine structural complexity with broad biological relevance, including measurable activity in CNS-related diseases. Prior work from our laboratory and others established (–)-stepholidine (1.60) as an important lead …


Model-Theoretic Arguments In Philosophy, Peter Susanszky Sep 2026

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 …


Exposing And Addressing Machine Learning Brittleness Through Constraint Solving, Muyeed Ahmed Aug 2026

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 Aug 2026

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 Aug 2026

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 Aug 2026

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 Aug 2026

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 RE. This orbital configuration allows the near-Earth …


A Variational Algorithm For Preparing Superoptimal Thermal States For Quantum Thermometric Measurement Adaptable To Nisq Hardware, Nicholas Donatelli Aug 2026

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 …


Modeling Kinetics Of 5-Aminolevulinic Acid-Induced Protoporphyrin Ix Accumulation For Optimal Photodynamic Therapy, Priscilla Melebor Aug 2026

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.


The Sliding Aperture Transform: A Mathematical Method Applied To Radiation-Induced Dlts Capacitance Transients, Md Abu Bakkar Siddique Aug 2026

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, …


Spider Biodiversity And Insecticide Sensitivity Across Active And Restored Cranberry Bogs On Nantucket, Tyler J. Kulak Aug 2026

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 …


Toward The Study Of Photon Dynamics In Non-Separable Spacetimes, Kara Nelson Aug 2026

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 …


Synthesizing Viscoelasticity: Living Polymers, Micro-Macro Relations, And Paths For Resolution, Adam M. Hasler Aug 2026

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 …


Microrheological Characterization Of Collagen-I Extracellular Matrix Remodeling During Tr146 Tumor Spheroid Invasion And Ppix-Mediated Photodynamic Therapy, Himantha Dilshan Saldonge Aug 2026

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 Aug 2026

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 Aug 2026

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 Aug 2026

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 …


Electrolyte Development And Interfacial Reactions At Multivalent Metal Anode For Next Generation Energy Storage Systems, Leslie Gates Aug 2026

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 …


Motor Imagery Eeg Decoding For Brain-Computer Interfaces: Structured Representation, Transfer, And Drift, Yiming Shen Aug 2026

Motor Imagery Eeg Decoding For Brain-Computer Interfaces: Structured Representation, Transfer, And Drift, Yiming Shen

Graduate Doctoral Dissertations

Motor imagery EEG decoding is often summarized by the accuracy of a final classifier, but the classifier is only the last stage of the pipeline. Before classification, the signal has already been shaped by preprocessing, feature extraction, source-session organization, and adaptation. This dissertation studies how feature representation, source-session transfer, and drift shape reliable MI-EEG decoding for brain-computer interfaces.

It first studies within-session decoding on public MI-EEG datasets using nested validation that keeps preprocessing, feature fitting, and model selection inside the training folds. This analysis separates gains from feature representation from gains due to nonlinear classification, and relates both comparisons to …


Dynamics Of Swimming Microorganisms At Structured Liquid Crystal Interfaces, Vajra Sabhapathy Badha Aug 2026

Dynamics Of Swimming Microorganisms At Structured Liquid Crystal Interfaces, Vajra Sabhapathy Badha

Graduate Doctoral Dissertations

Active matter systems are self-driven units that consume energy to generate motion and mechanical stresses, producing non-equilibrium states of broad physical significance. Examples include synthetic microswimmers and migrating cells. Motile bacteria are a widely studied biological example because their self-propelled motion, hydrodynamic interactions, and collective organization are strongly coupled to local environmental conditions. Their swimming is sensitive to interfacial viscoelasticity, ordering, confinement, and hydrodynamic boundary effects, making them useful for investigating how interfaces regulate active biological motion. Because bacterial accumulation and attachment at interfaces are central to colonization and biofilm formation, these interactions are relevant to both active matter physics …


Informationally Complete Measurements In Quantum Theory: Implementation, Geometry, And Correlations, Sachin Gupta Aug 2026

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 …


The Grasshopper's Journey To The Bloch Sphere, David Llamas Aug 2026

The Grasshopper's Journey To The Bloch Sphere, David Llamas

Graduate Doctoral Dissertations

The Grasshopper Problem asks a simple geometric question. A grasshopper lands on a lawn of fixed area and jumps a fixed distance in a random direction. What shape of lawn maximizes the probability that the grasshopper remains on the lawn after jumping? The jump rule is rotationally symmetric, but the best lawns do not have to be. This dissertation studies how that symmetry breaking occurs, maps the continuum problem to a novel constrained spin system, and uses the spherical Grasshopper Problem to compare quantum singlet correlations with classical local models.

For planar lawns, boundary-integral and perturbative calculations explain why the …