Physics, 1936-2025

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.

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.

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.

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.

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.

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.

Antibody-mediated activation of the complement system depends on the assembly of six immunoglobulin G molecules into a surface-bound hexamer that can ligate the six globular heads of C1q for downstream target cell killing. Experimental studies have shown that antibody valency, target cell surface antigen density, antibody affinity, and hexamer formation strength can all impact hexamer formation. However, a comprehensive picture of the IgG hexamerization regimes is still lacking, as most experiments perturb only one variable at a time. Here, we present a minimal statistical physics model of thermodynamic equilibrium, in which monovalent and bivalent IgG Ab-Ag complexes form on the cell surface and nucleate into hexamers through separate pathways. We probe antibody valency, antibody affinity, antigen density, and hexamer formation strength simultaneously in our model to investigate distinct regimes of hexamer formation. The analytical limits of conserved sum rules and numerical phase diagrams of our model suggest that at moderate antibody affinities, hexamers form at low surface antigen densities through "precursor sampling," where the dominance of free monovalent vs. bivalent complexes is observed. At intermediate density, aggregation kinetics favor bivalent hexamers; however, at saturating density, a "geometric packing limit" may impose a strict ceiling, where monovalent hexamers dominate. Meanwhile, increasing the strength of hexamer formation shifts these transitions to lower antigen densities but does not eliminate the preference for monovalent hexamer formation at high surface antigen densities. The resulting phase diagrams help to reconcile experimental studies on monovalent vs. bivalent hexamer formation and suggest potential design rules to consider for antibody therapeutics that activate complement.

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.

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.

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.

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.

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.

Analyzing the physical properties of particles scattered after high-speed collisions is an important component of particle physics research. But reconstructing particle tracks from the position data of thousands of scattered particles in high-pileup events is a difficult task. Assessing how physically plausible a track formed by a set of points is could serve as the final step in a machine learning pipeline that identifies possible reconstructed tracks, and providing an accurate assessment for the plausibility of the tracks is therefore critical for training earlier steps in the pipeline. Thus, we attempt to create a neural network that can classify sets of position points as part of one track or part of multiple different tracks. To ensure our classifier is robust, we generate the sets of points that do not come from one true track by slightly perturbing a true track, either by randomly moving points by an amount proportional to the deviation of points from a circle fit of the track or by simply swapping out some of the points for one of their nearest neighbors. We then train the neural network on these true and perturbed tracks and try to find the model that can most accurately identify the true tracks, working to ensure that the classifier is effective in the high-momentum regimes that are most relevant for track reconstruction. We find that using transfer learning by first training a model on fake tracks that are easy to identify before training using more difficult fake tracks is markedly more effective than just directly training on the difficult tracks. Using this transfer learning strategy, we create a classifier that has a total momentum-weighted accuracy of 0.6608 on the most difficult category of fake tracks and an area under the receiver operating characteristic curve of 0.7280. Finally, we suggest possible improvements and alternate methods that could improve this performance and move closer to a classifier that can be reliably incorporated into a training pipeline.

Defective Interfering Particles (DIPs) are viruses whose genome has been damaged to a point where they are unable to replicate on their own, however are able to replicate with the help of a non-damaged virus (WT virus).[23] There is mounting evidence that DIPs play a crucial and ubiquitous role during the course of infection for some RNA viruses, which has lead to renewed interest in their interactions with standard viral particles - especially with respect to influenza.[23][4] We examine the ecology between the Influenza A DIPs and standard Influenza A viruses in vitro, through theoretical modeling of influenza replication. We find a simple two parameter model for the competition between standard influenza viruses and influenza DIPs. When this model is fitted to experimental data, it provides evidence that influenza DIPs with a moderate replication advantage are selected for during in vitro passaging experiments.

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.

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.

This thesis is based on work done with the Princeton Field-Reversed Configuration 2 (PFRC-2), a plasma device located at the Princeton Plasma Physics Laboratory (PPPL). This thesis focuses on the examination of x-ray spectra detected via an AmpTek Fast Silicon Drift Detector (SDD). This x-ray emission comes via bremsstrahlung and line radiation from electrons inside the plasma chamber and yields information about electron energy distribution (EED), density, and effective volume of the plasma observed by the detector. The goal is to analyze x-ray emission spectra to inform us about the EED and plasma density responsible for the x-ray emission. An important finding is that the x-ray emission can grow in brightness with increasing average energy in a characteristic time of order 10 ms, far longer than the observed instability time scale (0.1 ms) and estimated energy confinement time scale, also < 0.1 ms. The growth rate is comparable to the classical penetration time, although we have observed it in some cases to be of an order even greater than this time. When the plasma rotates, the x-rays are observed to come in bursts at twice the frequency of the plasma rotation. The detector was operated at the low energy extreme of its published energy range. We report on the efforts needed to make these measurements reliable and informative. Finally, we observe spectra and comment on their behavior as a function of multiple key independent variables. We find x-ray energy to increase with power and exhibit no conclusive correlation between average energy and the presence of a stability-inducing gas puff in the plasma.

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.

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 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.