This thesis explores the biophysical mechanisms underlying gas exchange and pore formation in avian eggs. Drawing from biological data and applying principles from diffusion theory, chemical physics, and applied mathematics, we develop a comprehensive model of gas transport through complex pore geometries. With a diffusive resistance framework, we show that gas conductance is related to both internal pore geometry and density of pore openings on the egg surface. Using this, we derive a novel criterion for the number of pores at which gas flux saturates. Pore branching is shown to reduce access resistance without high cost to internal resistance, and is thus proposed as an explanation for steep scaling of functional pore area with egg size. Finally, we review previous frameworks of eggshell and pore formation, and build on this work by advancing a novel theory of pore formation. We propose that the organic matrix in the palisade layer plays a central role in shaping pores during shell calcification. Together, these analyses deepen our understanding of avian developmental physiology.

This thesis investigates the physics performance, trigger efficiency, and Field Programmable Gate Array (FPGA) implementation of machine learning (ML)-based algorithms for Lorentz-boosted 𝐻 → 𝑏̄𝑏 tagging within the CMS Level-1 Trigger (L1T) under Phase-1 conditions. The proposed algorithm, WOMBAT (Wide Object ML Boosted Algorithm Trigger), comprises a high-performance Master Model (W-MM) and a quantized, FPGA-synthesizable Apprentice Model (W-AM), benchmarked against the standard Single Jet 180 and the custom rule-based JEDI (Jet Event Deterministic Identifier) triggers.

All algorithms process calorimeter trigger primitive data to localize boosted 𝐻 → 𝑏̄𝑏 jets. Outputs are post-processed minimally to yield real-valued (𝜂, 𝜙) jet coordinates at trigger tower granularity.

Trigger rates are evaluated using 2023 CMS ZeroBias data (0.64 fb^(−1)), with efficiency assessed via a Monte Carlo sample of 𝐻 → 𝑏̄𝑏 offline re-constructed AK8 jets. W-MM achieves a 1 kHz rate at an offline jet 𝑝𝑇 threshold of 146.8 GeV, 40.6 GeV lower than Single Jet 180, while maintaining comparable signal efficiency. W-AM reduces the threshold further to 140.4 GeV, with reduced efficiency due to fixed-output constraints and limited multi-jet handling.

FPGA implementation targeting the Xilinx Virtex-7 XC7VX690T confirms that W-AM meets resource constraints with a pre-place-and-route latency of 22 clock cycles (137.5 ns). In contrast, JEDI requires excessive resource usage and a 56-cycle latency, surpassing the 14-cycle L1T budget.

These results underscore trade-offs between physics performance and hardware constraints: W-MM offers the highest tagging performance but exceeds current FPGA capacity; W-AM is deployable with reduced efficiency; JEDI remains deployable with moderate efficiency but increased latency. Originally developed for Run-3 CMS L1T, WOMBAT serves as a proof-of-concept for Phase-2 triggers, where hardware advances will enable online deployment of more sophisticated ML-based L1T systems.

This work examines three closely interrelated ideas: functional minimization, trajectory optimization, and optimal control. The term trajectory optimization typically describes offline path planning under known dynamics. On the other hand, optimal control typically denotes an optimization problem with feedback, requiring dynamic minimization of a time-dependent loss. Both problems can be understood as subsets of a broader class of functional minimization problems whereby a solution f∗ is sought to minimize a loss functional L : f → R. I cover a wide range of techniques in optimal control, ranging from classical ideas rooted in variational calculus to more modern approaches based on reinforcement learning and differentiable physics. My work revolves around two principal problems: the Brachistochrone, upon which I base much of my discussion of variational techniques, and an original control problem (the Rocket Problem) defined in Section 3. I implement three distinct computational solutions to the Rocket Problem: direct control policy optimization, a neural network controller, and a reinforcement learning agent trained via Proximal Policy Optimization. The first two approaches leverage a novel differentiable solver while the last takes a more generic approach to sequential decision problems.

El Niño events are major expressions of the El Niño Southern Oscillation (ENSO), with significant impacts on precipitation and temperature patterns both over the Pacific and globally. Traditional frameworks for understanding ENSO dynamics, such as sea surface temperature anomalies (SSTAs), fail to fully capture the mechanisms of El Niño onset, progression, and termination. Building on the moist static energy (MSE) framework developed by Neelin and Held (1987), this paper applies a gross moist instability (GMI) lens to reanalysis and climate model data to better understand the spatial and temporal evolution of El Niño. Neelin and Held’s precipitation approximation is a function of net vertical energy flux, gross moist stability, and vertical specific humidity gradient. This approximation highlights the importance of gross moist stability in capturing convective processes that SSTAs alone cannot resolve. In comparing model and reanalysis data, we find that the spatial patterns of GMI anomaly and precipitation anomaly are consistent in the reanalysis data, but not the model data. The precipitation anomaly for the model data matches the observed behaviour, but GMI anomaly does not. We use Neelin and Held’s approximation for precipitation which includes the variable GMI to assess what might be causing this discrepancy.

We find that the precipitation approximation is a good predictor of the spatial behaviour of actual precipitation in the model and reanalysis data and is particularly strong over the Niño 4 and equatorial region. While the spatial pattern is strong, the predicted precipitation consistently underestimates the magnitude of precipitation. We attribute the underestimation to the approximation not including horizontal exports of moisture which likely contribute significantly toward this error. By decomposing the precipitation approximation, we find that the main driver of predicted precipitation is energy convergence. Gross moist stability plays a less significant role and specific humidity plays the smallest role in driving precipitation. This suggests that while there might be some compensation between variables in the precipitation approximation, the model precipitation follows the observed pattern because energy convergence, and not GMI, is the main driver.

We then compare the spatial correlation coefficients between variables of the flux adjusted climate model and the reanalysis data. We find that the years with elevated SSTs during El Niño events (late Y0 and early Y+1) have slightly higher correlation than the year following the event (Y+2) and significantly higher correlation than the year preceding the event (Y-1). Moreover, the correlation is stronger for SSTs and precipitation—both emergent properties of ENSO—than energy convergence and instability—underlying processes that contribute to ENSO behaviour. These results indicate that climate models are tuned to the years with peak El Niño behaviour and likely ignore important ENSO indicators in the years surrounding El Niño events. The results also indicate that the models are tuned to the emergent properties of El Niño events rather than the underlying dynamics causing the events. Our results suggest that better representation of atmospheric convection and energetics in all years around El Niño events, but particularly the year preceding the event, could strengthen the predictive capability of climate models.

Discretization of the Schwinger model is a common testbed to calculate observables in low-dimensional QED. Extending this model to be spatially 2D is more unexplored and might uncover interesting behaviors. A lattice model is constructed first for the Schwinger model as done in this paper by Dempsey et. al [1] and then the model is extended into 2D.

Stochastic resetting -- the strategy of randomly restarting a search process -- has been shown to optimize first-passage times across a large set of physical and biological systems. In this thesis, we apply stochastic resetting to reinforcement learning (RL) agents, aiming to understand its effects on exploration efficiency and learning dynamics. Beginning with a review of stochastic resetting in simple diffusive and random walk systems, we extend these ideas to ε-greedy Q-learning agents operating in a bounded two-dimensional grid environment. Through numerical simulations, we find that despite stochastic resetting not minimizing first-passage times in our simulation geometry, it can still significantly accelerate learning by reducing the number of training steps required to reach optimal policies. We identify characteristic signatures of learning dynamics, such as a sharp spike in episode length relative variance and a universal intersection point across training curves with fixed exploration rate and different resetting rates. Moreover, we demonstrate that even small nonzero resetting rates enhance learning efficiency compared to no resetting. These findings suggest that stochastic resetting may be a broadly applicable tool for accelerating learning processes in both artificial and biological systems and point to potential avenues of further numerical and analytical investigation.

Power systems in the U.S. are evolving rapidly. For the first time in two decades, electricity demand is growing. At the same time, wind and solar have become the cheapest and fastest-growing sources of new electricity generation. To support the flexibility and reliability of this changing grid, large-scale battery storage systems are being deployed across the country. These batteries store excess renewable energy during the day and discharge it when demand peaks in the evening. Battery operators must make decisions about when to charge and when to discharge the system both a day ahead and in real time. In this thesis, I develop methods for making dispatch (charge/discharge) decisions under uncertainty about grid conditions. I begin by creating a battery optimizer using a linear programming method. I conduct two studies with the optimizer using historical data from electricity markets in the U.S. The first study simulates a battery in Texas from 2015 to 2025. I find that on average it earns over half of its yearly revenue on just 27 high-value days—mostly hot days in the summer. The second study compares how batteries with different durations (the time it takes to discharge at max power) perform in various regions of the U.S. Regions with high price volatility like Texas benefit most from batteries. Systems with significant renewable generation also benefit, particularly from batteries with 3- to 4-hour durations. In the final chapter, I develop a new optimizer that uses a stochastic programming framework to better account for price uncertainty. Using the stochastic programming optimizer, batteries generated 16% higher revenues on average than using the linear programming optimizer. This improvement highlights the importance of giving the battery system flexibility to react to changing grid conditions in real time.

Bemfica, Disconzi, Noronha, and Kovtun (BDNK) formulated the first causal and stable theory of viscous relativistic hydrodynamics to first-order in the gradient expansion, providing rigorous proofs of hyperbolicity and well-posedness of the underlying equations of motion over an explicit range of hydrodynamic frames. Since then, there has been several numerical and analytic studies of the BDNK equations, ranging from astrophysical to holographic applications, which have revealed their promise in modeling relativistic flows when viscous, first-order corrections to ideal hydrodynamics are important. In this thesis, we present numerical solutions of the BDNK equations obtained via finite-difference methods for conformal fluids in $4$D Minkowski spacetime. We consider flows with variations in only one spatial dimension in Cartesian coordinates, and flows constrained to the surface of a geometric sphere of radius $R$. We find both in the Cartesian geometry and on the two-sphere that, for a particular choice of smooth, stationary initial data with a gaussian peak in the energy density and a sufficiently large value of the entropy-normalized shear viscosity, our numerical simulations lose convergence as the solution evolves into a regime where the relative magnitude of the viscous to zeroth-order terms in the stress-energy tensor are $O(10)$ and growing, while the weak energy condition is strongly violated (with $u\mu u\nu T\mu \nu =O(-1)$). We present two additional tests of our numerical scheme to Kelvin-Helmholtz-unstable initial data and small, linear fluid perturbations of equilibrium states. We also present a preliminary qualitative comparison between the Euler and BDNK evolution of initial data which, in the inviscid case, eventually evolves into a turbulent regime. Our low-temperature BDNK simulations demonstrate the damping of high-frequency modes in the energy and vorticity densities, preventing the onset of turbulence in the viscous fluid, which, in one of the cases considered, reaches a steady state within the time frame of the simulation.

Fluorescence microscopy techniques are powerful tools for measuring protein kinematics in biological systems and for understanding protein aggregation pathways. In this paper, we discuss the theoretical and mathematical foundations behind several microscopy techniques including fluorescence correlation spectroscopy (FCS), photon counting histograms (PCH) and burst analysis spectroscopy (BAS). Next, we sought to calibrate a custom built confocal fluorescence microscope for future BAS experiments. We estimated the confocal volume using FCS measurements of fluorescent nanobeads and fluorescein dye. While nanobead measurements provided a reasonable preliminary estimate, subsequent experiments with fluorescein produced unexpected results, showing diffusion times similar to those of the nanobeads—an outcome inconsistent with the known molecular properties. We therefore believe there to be a mistake in out experimental setup. Despite extensive troubleshooting, we were unable to determine the source of the error. Further study is needed to determine the error and properly calibrate the microscope before it can be used for future experiments.

This thesis explores the interplay between quantum physics and biological organization across two frontiers: Quantum Biology, where genuine quantum mechanical processes influence macroscopic life, and Quantum-Like systems, where classical systems exhibit mathematical structures formally resembling quantum mechanics. By investigating both domains, I aim to illuminate how quantum principles manifest both directly in biological function and indirectly through emergent organizational patterns. I begin by deriving a generalized Hamiltonian for the Radical Pair Mechanism underlying avian magnetoreception, capturing how hyperfine interactions and Zeeman interactions with the Earth’s magnetic field modulate singlet-triplet interconversion in cryptochrome proteins. Analytical and numerical treatments demonstrate how coherent spin dynamics can influence global navigation behavior, providing a tractable model for quantum biological sensing. Then, I traverse scales and investigate the emergence of Quantum-Like (QL) structures within the human brain. Drawing inspiration from modern whole-brain modeling techniques, particularly Connectome Harmonic Decomposition, I map real neurophysiological data onto QL graphs, constructing a framework where physical brain dynamics are represented by robust, scalable QL state spaces. Together, these investigations suggest that quantum mechanics may not only shape specialized biological functions, but also that classical systems like the brain can mirror quantum architectures, hinting at deeper symmetries between the fundamental and living worlds.

Verifying the dynamical similarity between data-drained deep learning models and the biological circuits they aim to replicate remains a significant challenge. Benchmarking methods that evaluate such models based on their underlying dynamical systems, rather than only their output performance, are thus highly desirable. In this work, we validate and extend one such recently proposed method: the Computation through Dynamics Benchmark (CtD-B). In the context of models that solve the Poisson-clicks task (a perceptual decision-making cognitive task), we test existing CtD-B metrics and find that functional similarity measures — Rate R2 and Dynamical Systems Alignment (DSA/co-BPS) — are robust across models, but representational metrics — State R2 and Cycle-Convergence (Cycle-Con) — are reliable for low-dimensional models. Leveraging dynamical systems theory, we extend the analysis function of the benchmark to consider local similarity: fixed points and timescales in both task-trained (TT) and data-driven (DD) models. Notably, we find that DD models can fit observed data without preserving the characteristic timescales of TT solutions.

Neutral atoms in optical tweezer arrays have been a versatile platform for quantum information processing, simulation, and metrology. In particular, alkaline-earth-like atoms like Sr and Yb have surged as a resourceful choice over the alkalis, with their rich internal structure and metastable 3P0 clock state. On the other hand, alkaline-earth-like atoms have a more complex energy structure due to their two valence electrons and low-lying core-excited states, and require comprehensive spectroscopic study and modeling to fully understand and harness favorable properties. To incorporate all the complex interactions, multichannel quantum defect theory (MQDT) is used. MQDT dates back to the 1970s and has been used to describe inert gases and alkaline-earth atoms. Recent works have developed MQDT models of 174Yb and 171Yb L ≤ 2 Rydberg states, based on laser and rf precision spectroscopy. In this thesis, we present precision spectroscopy and MQDT models of L = 3 and L = 4 Rydberg states. Additionally, measurements of D state polarizabilities and P state lifetimes are presented and discussed.

Tumors are ecologically dynamic systems composed of heterogeneous cell populations in competition for space and resources. Adaptive therapy---a novel therapy regimen with potential use for hormone sensitive cancers---leverages this competition to control therapy-resistant tumors. However, its success relies on understanding the composition of the tumor to better model the interpopulation competition. This thesis combines time-lapse imaging of competing prostate cancer cells with physics-inspired analysis (mean-squared displacement, correlation maps, clustering) to characterize the competitive dynamics between phenotypically distinct prostate cancer cell populations.

Notably, we find that cancer cells exhibit intrapopulation anisotropic ordering. This suggests that cells preferentially align head-to-tail rather than side-by-side, creating a bias in mechanical interactions that can affect tumorigenesis. We also show that competitor abundances dynamically affect carrying capacities and drive preferential cluster growth. Together, these quantitative insights provide a framework for optimizing adaptive therapy based on tumor composition and spatial organization.

I develop a macroeconomic model accounting for global warming using stochastic control to study how climate policies can maximize welfare through incentivizing green capital investment. Mathematically, this system defines a mean-field game, which I represent using nonlinear PDEs resembling equations of motion for classical particles in a physical system. However, this economic system is much harder to solve due to constraints of dynamic optimization and belief consistency. I first rigorously develop stochastic control theory and draw extensive parallels to Lagrangian and Hamiltonian mechanics. I then consider a continuum of economic agents who optimize investment decisions between “green” and “brown” capital types, the latter of which drives increases in a stochastic temperature process that damages capital productivity. I leverage equation-informed neural networks to solve for agent value functions and the evolution of the distributions of economic variables to quantify welfare and climate-transition trajectories under a central-planner economy and a decentralized equilibrium under multiple climate policies. The technical contributions of this thesis include obtaining global solutions for decentralized equilibrium using deep learning, for which I achieve upper bounds of 2 ×10−4 mean- squared error equation loss for the agent value function, close to the median threshold of 1 ×10−4 for reported convergence in three papers inspiring this work; and validating a deep-learning solution of the central-planner economy with 14% mean relative error versus a finite-difference solution and 4% normalized difference from an analytic boundary value. The economic-policy-relevant contributions include quantifying a 2% normalized reduction in agent value from the central-planner economy to the decentralized economy without climate policy and an 8% normalized reduction in agent value from an optimal constant carbon tax to a stochastic tax representing political turnover. My results further suggest that to mitigate weaker incentives under a stochastic carbon tax, a welfare-maximizing government should invest carbon-tax revenue directly into green capital rather than transferring monetary revenue back to the population.

This thesis reviews the Standard Model (SM) of particle physics and explores Beyond the Standard Model (BSM) theories, including supersymmetry, dark sectors, and neutral naturalness, with an emphasis on signatures searchable at particle collider experiments such as long-lived particles and Higgs processes. We examine detector hardware and data-taking software of the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC), focusing on the calorimeters and trigger system. In particular, we discuss the role of model-independent Real-time Anomaly Detection (RAD) in the CMS Level 1 Trigger (L1T) implemented in the Calorimeter Image Convolutional Anomaly Detection Algorithm (CICADA). We evaluate the impact of sectioning calorimeter inputs on CICADA performance and find no significant deviations, suggesting limited importance of spatial context. Furthermore, we carry out a Hyperparameter Optimization (HPO) search over Quantized Neural Networks (QNNs) for novel CICADA architectures, and identify several models with improved performance. This work contributes to the development of RAD for physics discovery at the LHC.

While most studies of self-interacting dark matter (SIDM) focus on short-range interactions dominated by the hard scattering of particles, this thesis explores SIDM dominated by long-range interactions. Specifically, we investigate the implications of long-range interactions within the dark sector, focusing on a dark matter subhalo streaming through the Milky Way. We show that such interactions can give rise to collective phenomena analogous to plasma instabilities in the Standard Model. We characterize the linear growth of these instabilities in the presence of a streaming subhalo, and use particle-in-cell (PIC) simulations to study their non-linear evolution. Our results reveal that the instability induces mixing between the subhalo and the Milky Way background, leading to density fluctuations. These fluctuations could, in principle, perturb stellar orbits, motivating a search for kinematic signatures in ultra-faint dwarf galaxies to constrain this model. Additionally, we propose that the outer layers of the subhalo may undergo an evaporation-like process as a result of this mixing, resulting in a more compact object by the time the subhalo reaches the inner galaxy.

As a unified field theory of mesons and baryons in 3+1 dimensions, the Skyrme Model has proven to represent an interesting formulation to considering nucleons, with crucial connections to Quantum Chromodynamics. The study of cubic arrays of Skyrme solitons (or "skyrmions") in particular underscores a broad array of considerations regarding multi-skyrmion interactions, with key methods to considering potential branches for further investigation regarding these systems. One such direction for further research is the question of lattice structures in R^2, which have experienced a resurgence of interest in light of experimental verification of these 2-dimensional skyrmion lattices. As such, in this paper, we study the properties of square lattice structures of 2-dimensional skyrmions, specifically the cases of those using twisted or periodic boundary conditions. After reviewing the construction of the 2-Dimensional Skyrme model and its properties with regard to the hedgehog ansatz, we determine ansatz forms for the twisted and periodic square lattices as Fourier series which satisfy the overarching symmetries of the system. We then truncate our Fourier expansions to a finite number of terms, plug said expansion into the base energy functional, and determine the Fourier coefficients which minimize the energy per lattice unit while maintaining certain constraints regarding the topological degree over each lattice unit, reflective of the properties stemming from the choice of boundary conditions. From this procedure, we determine that, at various values of the mass-squared parameter µ^2, the square lattice with twisted boundary conditions demonstrates a lower energy per lattice unit than that with periodic boundary conditions. Furthermore, while the periodic square lattice yields a baryon density which converges to an array of full 2D skyrmions in the minimal-energy configuration, the twisted square lattice demonstrates a splitting of the minimal-energy baryon density into half-skyrmions, localized regions where the topological degree is approximately 1/2. We also extend our analysis to include additional terms in the energy functional, specifically an additional four-derivative term and that pertaining to the Dzyaloshinskii-Moriya interaction, whose strength we control via the corresponding coefficients κ and D, respectively. We consider various cases, including (a) κ ≠ 0 while D = 0, (b) κ = 0 while D ≠ 0, and (c) both κ, D ≠ 0. In our analysis of the Dzyaloshinskii-Moriya term in particular, we determine that, as the term coefficient D approaches a critical value D_crit from below (hence acting as an upper bound), the field configuration stretches along the boundaries of the square tessellation. We then finish this paper with some considerations regarding a lattice tessellated by equilateral triangles, and initial steps towards considering this topic.

Excess noise in amplifiers poses a significant limitation on scan rate in the comprehensive search for axion dark matter. For this reason, the quantum-limited parametric amplifier is essential to axion detection experiments. Due to its ability to provide broadband, quantum-limited amplification at hundreds of MHz, the KI-TWPA is the amplifier of choice for low-frequency applications such as the Princeton Axion Search. Despite experimental progress in the use of these devices, a rigorous analytical model for quantum noise does not exist for KI-TWPA systems. In this paper, a simplified quantum noise model for the KI-TWPA is formulated from the ground up, and some basic implications of such a model are discussed.

Transition-metal dichalcogenide monolayers (e.g., WS2, WSe2, MoS2, and MoSe2) have been shown—from both simulations and experiments—to exhibit interesting strain-engineering capabilities in which their optical and electronic properties could be controlled with strain. This paper will discuss the fabrication processes and straining mechanisms for applying large mechanical strain on these monolayers and evaluate their effectiveness through the analyses of photoluminescence and Raman spectroscopy data of a WS2 monolayer under various amounts of tensile strain. Improvements and future experiments are also proposed.

Replica wormholes arise as natural contributions to the gravitational path integral when computing the nth Renyi entropies of density matrices for holographic systems. In this paper, we extend this notion to non-holographic systems by introducing an auxiliary bulk. The auxiliary bulk serves as a space over which we can integrate the symplectic form of the system in the path integral. This allows us to compute partition functions on wormhole topologies. We build on this concept by computing wormhole partition functions for the examples of a particle on a circle and a particle on a group. We also consider a class of geometric states that are obtained by slicing the topologies over which the partition functions are defined. These are the thermal density matrix (obtained by slicing the thermal circle), the TFD state (obtained by purifying the thermal density matrix), and the TMD state (obtained by slicing the partition functions on wormhole topologies). We also show how these wormhole partition functions show up as contributions to the overlaps of generalized TFD states, causing the Hilbert space spanned by them to become finite-dimensional. In an attempt to extend the topology obtained by considering wormholes and extract some notion of geometry from them, we also consider the concept of Krylov state complexity of TFD states \cite{spreadofstates}, which is conjectured to be the dual of the length of a wormhole connecting the left and right Hilbert spaces in holographic systems.