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.

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.

While core-collapse supernovae (CCSNe) are some of the most energetic events in the universe and are responsible for creating the heavy elements we see today, there still remains much to learn regarding the CCSN mechanism. The challenge arises primarily due to the fact that characterizing these events requires a thorough understanding of the simultaneous effects of particle, nuclear, and gravitational physics. The interdisciplinary nature of these events, however, also means that CCSNe are some of few astrophysical events capable of producing electromagnetic, neutrino, as well as gravitational-wave (GW) signals observable with current and future detectors. In this thesis, we analyze the neutrino and GW signals from the largest and longest-running suite of three-dimensional CCSN simulations to date. We first analyze the neutrino signals from each model across three different species to understand how information regarding each stage of the CCSN process as well as the properties of the progenitor star can be extracted from the neutrino luminosity and radiated energy. We study the biases associated with observing neutrinos from a CCSN event from one line of sight, and find that these biases generally grow with time and progenitor mass. We then discuss detection prospects of the neutrino signal by convolving the neutrino fluxes from each model with neutrino detector sensitivities. Next, we analyze the corresponding GW signal and again discuss how CCSN stages and progenitor properties can be gleaned from the GW strain and radiated energy, as well as highlight the possibility of detecting the predicted ``gravitational-wave memory'' effect. We then quantify the detection prospects of the GW signal by calculating signal-to-noise, detection ranges, and detection rates for all of our models with current and future GW detectors. Finally, we leverage the "multimessenger'' nature of CCSN events by comparing the neutrino and GW signals to develop strategies to increase the detection efficiency of the GW signal as well as to place constraints on the nuclear equation-of-state. Overall, the goal of this thesis is to begin developing a theoretical framework to interpret and extract information concerning the CCSN mechanism, progenitor properties, and even open questions in fundamental physics from the next nearby CCSN event.

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.

The Standard Model of particle physics provides a solid theoretical framework for fundamental particles and their interactions, delivering predictions consistent with many experimental results. However, it fails to explain certain observed phenomena, motivating searches for Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC) at CERN. The Compact Muon Solenoid (CMS) experiment studies the 13.6 TeV proton-proton collisions delivered by the LHC, requiring an efficient trigger system to select interesting events out of a collision rate of 40 million per second. This thesis investigates the development, performance, and implementation of a manual cut-based clustering algorithm, clusterjet, designed to improve sensitivity to highly boosted jet topologies at the Level-1 (L1) trigger. Monte Carlo simulations of highly boosted Higgs bosons decaying into bottom quark-antiquark pairs, along with Zero Bias data from Run 3, are used to assess the algorithm’s physics performance. The proposed clusterjet trigger shows improved efficiency and resolution at high transverse momentum compared to existing L1 algorithms, accepting more events in the target high-pT region. However, latency studies using VIVADO HLS suggest that clusterjet does not meet the strict timing requirements for L1 implementation. Future work may focus on overcoming FPGA timing constraints and exploring alternative clustering approaches.

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.

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.

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.

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.

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.

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.

Interpreting gravitational wave (GW) signals from compact binary mergers hinges on the accuracy of numerical relativity (NR) simulations. With the proposed space-based Laser Interferometer Space Antenna (LISA) and other next-generation detectors on the horizon, there is a growing need for more accurate GW predictions as observational sensitivity pushes into more complex parameter regimes. In this work, we investigate the impact of the slow start lapse (SSL) gauge condition, proposed by Zachary Etienne, in moving-puncture simulations of binary black hole (BBH) mergers using the Z4c formulation to solve the Einstein field equations (EFEs). The SSL technique modifies the lapse evolution condition by introducing a damping term that delays the formation of the sharp lapse feature, which is responsible for significant numerical errors in BBH simulations. Using AthenaK—an open-source, performance-portable astrophysics code that leverages GPU computing—we simulate the evolutions of a single black hole (BH), a BBH head-on collision, and a quasicircular BBH system to assess the effects of SSL when paired with Z4c formulation. We also examine its impact on the performance of the apparent horizon (AH) finder AHFinderDirect in these cases. We find that SSL significantly reduces Hamiltonian and momentum-constraint violations—by up to two orders of magnitude in the wavezone—suppresses spurious early-time oscillations in the extracted GWs, and improves convergence behavior. Specifically, analysis of AHFinderDirect diagnostics shows that SSL ensures the continued convergence of the irreducible mass of the BHs as resolution increases. These results indicate that SSL offers meaningful improvements to the accuracy of puncture simulations with Z4c formulation, just as it does for those using the BSSN formulation as demonstrated by Etienne, thereby supporting the development of more precise waveform models for the next era of GW astronomy.

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.

Liquid crystals, which are materials with properties between that of a liquid and a crystal, are commonplace from phone screens to biological systems. Of special interest are active nematic liquid crystals, which are made up of particles that constantly inject energy into the system. This causes active turbulence, a type of chaotic dynamics in fluids driven by activity that is characterized by unpredictable flows, vortices, and the creation and annihilation of topological defects. Active nematics can be described by a small number of macroscopic parameters, including the elasticity and activity. However, these parameters are difficult to measure due to spatial fluctuations and sensitivity to initial conditions which results from turbulence. This thesis uses a neural network developed by Colen et al. (2021) to estimate elasticity and activity given only director field data of Myxococcus xanthus, a soil bacteria that behaves on a large scale as an active nematic liquid crystal.

We study the phenomenon of nonfactorization in 1 + 1 dimensional quantum gravity through the lens of Jackiw-Teitelboim (JT) gravity and its dual construction as an SL(2, R)+ BF theory. After constructing the classical and quantum Hilbert space, we derive the Schwarzian boundary dynamics, interpreting their residual symmetries as underpinning boundary entanglement and nonfactorization. From the Euclidean path integral perspective, we note how nonfactorization manifests as contributions from connected bulk moduli to the topological expansion. In Lorentzian signature, we analyze nonfactorization via entanglement in the Thermofield Double state |TFD(β)⟩and discuss further the restrictions Lorentzian physics may impose on valid bulk moduli. Acknowledging these limitations, we outline a construction of the Saad–Shenker–Stanford matrix integral which realizes Euclidean JT gravity as dual to a nonperturbative, ensemble-averaged boundary theory. To clarify the role of the ensemble in resolving the chaotic dynamics of JT gravity, we develop a fine-grained construction of the JT path integral which incorporates the full spectra of Schwarzian dynamics. Our discussion refines the multiple mechanisms of chaos in JT gravity, though we stress the need for further nonperturbative developments to clarify the relationships between JT gravity, ensemble averaging, and quantum complexity.

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.

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.

A central challenge in biophysics is to find the general principles underlying universal biological structures. Here, we focus on genetic networks, fundamental regulatory units that control gene expression. Inherent in the notion of control is the idea that genetic networks transmit information, and, in some limits, this can be quantified using information theory. A large body of theoretical and experimental work suggests that some genetic networks are tuned close to optimality, such that they transmit the maximum possible amount of information given a set of physical constraints and irreducible sources of noise. Following this principle, here we optimize information transmission in a class of idealized genetic networks. We explore the optimal network structures and derive a scaling relation for the information transmission in terms of the relevant biological parameters. Counterintuitively, this scaling suggests that the optimal strategy is to deploy a large number of noisy channels. Additionally, we find that the system should have a preponderance of weak binding interactions. Next, we show that the optimal solutions are surprisingly stable to a wide range of biologically relevant perturbations. Finally, we connect the predictions of the model to experimental data. Our model represents a step towards understanding the structure and reliability of large genetic networks.

Tantalum superconducting resonators have demonstrated state-of-the-art performance with long coherence times and high quality factors, motivating further study into the sources of microwave loss that limit their performance. An investigation into these sources reveals that two-level systems (TLSs) dominate loss at low powers and temperatures, but at higher temperatures there is an additional source of microwave loss arising from dissipation due to vortex motion. This microwave loss has been observed to reduce in dirty limit films where the mean free path lis shorter than the coherence length ξ, due to defects and roughness pinning vortices and preventing motion-induced dissipation. These results have been replicated with manufactured artificial defects in clean limit films (l >> ξ) where a pattern of holes with lattice parameter a is fabricated on the resonators. However, this additional patterning increases TLS loss at grain boundaries and edges, motivating further research into pinning pattern design. In this study, we vary the lattice parameter a with a fixed hole diameter d to identify the limits of artificial pinning. We first deposit films and verify that we are in the clean limit through magnetoresistance, x-ray diffraction, surface measurements, and imaging. We then fabricate multiple patterns, and compare the effectiveness of vortex pinning through quality factor measurements conducted at millikelvin temperatures. We estimate theoretically that a0 ≈200µm, and find that for a= 300µm the vortices are fully unpinned, but there is no additional microwave loss from defect patterning. We suggest patterns for future research in order to better probe the depinning transition and partially pinned regime.

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.