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ItemAbstract and Physical Effects of Curvature on Dynamics of Extended Body Systems(Georgia Institute of Technology, 2023-12-07) Day, BrianThe presence of intrinsic curvature of an ambient space influences the dynamics of point particles moving through it as typically considered in applications of differential geometry in physical contexts, such as general relativity. We aim to utilize the mathematics of differential geometry to instead consider the collective curvature effects on extended body systems in some generic curved space. To this end we develop a mathematical framework which serves as the foundation of a general dynamics solver numerical toolkit in which users can simulate the dynamics of discrete extended body systems in generic curved spaces. Through analyzing the dynamics of such extended body systems we recognized a relationship between deformation of the body during its dynamics as a result of the ambient curvature. This led us to expand our mathematical model of extended bodies to include deformable bodies. We find that such deformable bodies can generate collective motion via deforming their body even in a ambient space lacking curvature. This is due to the presence of an abstract notion of curvature defined on the configuration space of the system via considering the system as being described by a mathematical object known as a fiber bundle. This revelation allows us to discuss the dynamics of such deformable control systems using the ideas of geometric mechanics. In particular, we consider recasting our system in a geometric mechanics framework to address the question of determining optimal controls of how to deform the system so as to minimize some cost function. This is based on considering the optimization problem as a variational problem whose solutions correspond to optimal controls of the system. We develop this variational approach into a numerical toolkit acting as the foundation of a more general purpose optimization toolkit for deformable control systems described by fibers bundles.
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ItemBiomolecules' conformational changes studied by simulations and enhanced sampling(Georgia Institute of Technology, 2023-11-17) Pang, Yui TikBiomolecules, ranging from small molecules like vitamins to proteins, play critical roles in sustaining cellular functions. Their functionality is closely tied to their ability to undergo conformational changes in response to environmental conditions or binding events. In drug design, understanding the conformational flexibility of small molecules is crucial. Small molecules can undergo conformational changes that affect their interactions with target proteins. This understanding is vital for predicting drug behavior and interactions in biological systems. Proteins, which are central to various biological processes, have intricate conformational dynamics. They can shift between various conformations to fulfill their functions, from subtle side chain rearrangements to extensive structural changes. Misfolded proteins can lead to diseases, making the study of protein conformational changes critical in both understanding biological processes and developing therapies. Molecular dynamics simulations offer a powerful tool for studying biomolecular dynamics. These simulations allow for precise control and measurement of various aspects of biomolecular systems, providing insights into their structural dynamics. However, some biological processes occur on long timescales, necessitating enhanced sampling techniques to accelerate simulations and capture rare events. In this thesis, we investigated three distinct biomolecular systems: capsid assembly modulator AT130, passenger domain of pertactin, and SARS-CoV-2 spike protein. Employing advanced simulation techniques and enhanced sampling methods, we delved into the intricate behaviors of these biomolecules, each representing a unique aspect of biological complexity. During this exploration, I also updated the open-source parameterization tool, Force Field Toolkit, to accommodate the novel sigma-hole particle (LP) introduced in CGenFF 4.0. Our research spanned a range of scales and complexities, showcasing the adaptability and relevance of simulations and enhanced sampling approaches in the study of diverse biological systems.
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ItemOn the Generalization of Shadowing to Fluid Turbulence: Practical Methods For Quantifying Dynamical Similarity(Georgia Institute of Technology, 2023-07-31) Pughe-Sanford, Joshua L.Chaos is an intrinsic property of many real world systems, impacting a number of today's open research questions. While many chaotic systems have known governing equations and are deterministically “solved,” we still lack a comprehensive framework for predicting, controlling, and simply making sense of such systems. And while recent advances in technology allow us to explore these systems through direct numerical simulation better than ever before, the need for an insightful theoretical framework is still very much alive. Such a framework exists in a subset of chaotic systems, known as Axiom A chaotic systems. As a result, Axiom A systems are understood quite well. However, the requirements for a system to be Axiom A are quite strict, and the overlap between systems that are Axiom A and those that are physically significant is quite small. A very important concept in Axiom A systems is the notion of shadowing, which allows the chaotic dynamics to be decomposed piecewise-in-time in terms of much easier to analyze solutions known as periodic orbits. Periodic orbits are solutions to the governing equations that, unlike chaos, repeat in time. Their compactness make periodic orbits very simple objects to manipulate, both numerically and theoretically. This decomposition ultimately results in a predictive theory of Axiom A systems both deterministically and statistically. In this dissertation, we seek to generalize the concept of shadowing to a broader class of (non Axiom A) chaotic systems, specifically, fluid turbulence. Although recent studies suggest that Exact Coherent Structures—e.g., repeating solutions to the Navier-Stokes equation—are descriptive of turbulence, it is an open question whether they are to turbulence what periodic orbits are to Axiom A chaos. Here, we propose a generalized method for quantifying shadowing and discuss the generalized nature of shadowing in turbulence. Our results suggest that an axiom A framework for chaos may be more generalizable than previously thought.
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ItemAchieving a Quantum Simulator in Ultracold Fermionic Systems(Georgia Institute of Technology, 2023-07-30) Xiong, FengReal world material systems often have properties with roots in quantum mechanics which we are interested in. Studying such systems by classical models is often unsuitable, being either ineffective or inefficient. The general approach is utilizing laser cooled and trapped atoms as quantum simulators. This thesis presents our study of ultracold quantum gases of Li-6, signifying our progress in building a quantum simulator and providing a platform for conducting quantum simulation experiments. First, we demonstrate the achievement of quantum degeneracy in the form of molecular Bose-Einstein condensates (mBECs) of Li-6 in its lowest and second lowest two hyperfine state pairs by an all-optical method. We employ mostly standard techniques, but also introduce several unique features in our hardware system. Then, by preparing a degenerate Fermi gas of Li-6 in a mixture of its second lowest two hyperfine states and measuring its spin susceptibility in the BEC-BCS crossover, we study the “pseudogap” effects and compare it to the high-Tc cuprates. We develop a novel radiofrequency method to map the mixture to an RF-dressed basis. Imbalances are created between thermally equilibrium RF-dressed states, from which the spin susceptibilities are extracted over the interaction strength-temperature phase diagram. The results of such measurements for gases in the strongly interacting regions are compared to a mean-field model, to the ideal Fermi gas model, and to experimental results from several other publications. Lastly, we implement a 1D optical lattice and tune the single particle dispersion relation through dynamically modulating the lattice by Floquet engineering. The driving signal is modulated through an IQ modulator fed to two AOMs. By loading a molecular BEC of Li-6 pairs into the shaken lattice, we achieve coupling between the first two energy bands resulting in a double-well dispersion. The major result of our observations is that the sample under the inverted dispersion bifurcates into two soliton-like peaks in the momentum space. While in the position space, a density corrugation is formed in the condensate, which is caused by the two bifurcated wave peaks with opposing momentum beginning to separate. We have not yet fully understood the mechanism behind this phenomenon. For now, we model the result semi-classically by the Gross-Pitaevskii equation, from which the numerical simulations match reasonably well with the experimental results.
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ItemPhysics-Inspired Machine Learning of Partial Differential Equations(Georgia Institute of Technology, 2023-07-30) Golden, Matthew RyanThis dissertation discusses the Sparse Physics-Informed Discovery of Empirical Relations (SPIDER) algorithm, which is a technique for data-driven discovery of governing equations of physical systems. SPIDER combines knowledge of symmetries, physical constraints like locality, the weak formulation of differential equations, and sparse regression to construct mathematical models of spatially extended physical systems. SPIDER is a valuable tool in synthesizing scientific knowledge as demonstrated by its applications. First, libraries of terms are constructed using available physical fields. The symmetries of a system allow libraries to be projected into independently transforming spaces, known as irreducible representations. This breaks relations down into their indivisible parts; each minimal physical relation is learned independently to reduce implicit bias. A library of nonlinear functions is constructed for each irreducible representation of interest. Second, each library term is evaluated in the weak formulation. SPIDER is aimed at experimental systems with inherently noisy data making accurate estimation of derivatives difficult. The weak formulation solves this problem: library terms are integrated over spacetime domains with flexible weight functions. Integration by parts can avoid numerical differentiation in many situations and increases robustness to noise by orders of magnitude. Clever weight functions can remove discontinuities and even entirely remove unobserved fields from analysis. Third, a sparse regression algorithm can find parsimonious relations ranging from dominant balances to multi-scale quantitatively accurate relations. Applications to direct numerical simulation of 3D fluid turbulence and experimental 2D active nematic turbulence are presented. SPIDER recovered complete mathematical models of both systems. The active nematic system is of particular interest; SPIDER identified a 2D description contradicting widely accepted theoretical descriptions used for over a decade. SPIDER facilitated the discovery of a new physical constraint on the fluid flow.
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ItemDynamics of debris disks and young planetary systems(Georgia Institute of Technology, 2023-07-25) Moore, Nathaniel W. H.Debris disks are gas-poor structures of dust which orbit around their host star. These disks are the leftover remnants of planetary formation and can hold important clues in understanding the evolution and history of planetary systems. Distinct features in a disk’s morphology can elucidate the architecture of an underlying planetary system or indicate the signatures of past close encounters with flyby stars. In this thesis I discuss both our Solar System debris disk, as well as that of an exoplanetary system: HD106906. Specifically, I use signs in the inclination distribution of the Kuiper Belt in our own Solar System to constrain the environment of our Solar System’s stellar birth cluster. I also use observations of unique features in the debris disk surrounding HD106906 to constrain its evolutionary history and propose a unique formation theory for this unusual system. My results provide a link between the present configuration of a system’s debris disk and the dynamical history of the system itself. Beyond debris disks, I then explore the role of planetary orbital dynamics on habitability. I considered an external perturber on young planetary systems through the dynamical mechanism known as evection resonance and discuss the implications that this mechanism may have in increasing the habitability of planets in such systems.
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ItemResonant and Secular Evolution of Three Body Systems – With Applications on Planetary Systems and Gravitational Wave Sources(Georgia Institute of Technology, 2023-07-24) Bhaskar, Hareesh GauthamThis work focuses on the gravitational interactions of astrophysical systems. In particular, we focus on the triple system dynamics, including mildly hierarchical three body secular dynamics, as well as precession induced resonances of binaries under the perturbation of a third companion. We apply our theoretical investigations of these physical processes to wide-orbit planetary systems and black hole binaries embedded in AGN disks. More specifically, we consider the secular dynamics of a test particle in a mildly-hierarchical configuration. We find the limit within which the secular approximation is reliable, present resonances and chaotic regions using surface of sections, and characterize regions of phase space that allow large eccentricity and inclination variations. Finally, we apply the secular results to the outer solar system. We focus on the distribution of extreme trans-neptunian objects (eTNOs) under the perturbation of a possible outer planet (Planet-9), and find that in addition to a low inclination Planet-9, a polar or a counter-orbiting one could also produce pericenter clustering of eTNOs, while the polar one leads to a wider spread of eTNO inclinations. Beyond the secular mildly hierarchical triple dynamics, we also propose a novel pathway through which compact binaries could merge due to eccentricity excitation, including in a near coplanar configuration. Mechanisms have been proposed to enhance the merger rate of stellar mass black hole binaries, such as the von Zeipel-Lidov-Kozai mechanism (vZLK). However, high inclinations are required in order to greatly excite the eccentricity and to reduce the merger time through vZLK. Specifically, a compact binary migrating in an AGN disk could be captured in a precession-induced resonance, when the apsidial and nodal precession rates of the binary are commensurable to the orbital period around the supermassive black hole. We find 8 such resonances upto quardupole order of the Hamiltonian. We show that if a binary is captured in these resonances and is migrating towards the companion, it can experience large eccentricity and inclination variations. Eccentricity is excited when the binary sweeps through the resonance which happens only when it migrates on a timescale 10-100 times the libration timescale of the resonance. Libration timescale decreases as the mass of the disk increases. The eccentricity excitation of the binary can reduce the merger timescale by a factor up to $10^{3−5}$.
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ItemElectromagnetic and Gravitational Wave Signatures of Massive Black Hole Binaries in Merger Galaxies(Georgia Institute of Technology, 2023-05-16) Li, KunyangMotivated by observational searches for potential gravitational-wave (GW) signals from massive black binary (MBHB) coalescences, we developed a model to describe orbital evolution of MBHBs. In this thesis, we use the model developed to determine how the properties of the merger remnant galaxy and the orbital configuration of MBHs affect the likelihood for and timescale to a coalescence. By varying galactic properties and orbital configurations of MBHBs in the model, we built a parameter space that contains 40,000 model galaxies, spans a wide range in initial orbital eccentricities and includes both prograde and retrograde orbits. We used these models to acquire a comprehensive view of how different types of orbital decay mechanisms impact the MBHB evolution. We estimated the LISA detection rates for different binary orbital configurations in the absence and presence of radiation feedback and explored the properties of MBHBs that are most likely to be detected as GW sources by applying the model on MBH pairs from the IllustrisTNG simulation. Finally, we use the model to quantify the electromagnetic (EM) detectability of dual active galactic nuclei (dAGNs). By tracking how the EM detectability varies with galaxy and orbital properties, we provided a convenient way to select dAGN candidates that evolve into GW sources. These kinds of predictions will be crucial for the future and present EM and GW observatories, for they will indicate where to look for possible MBH coalescences or the most detectable dAGNs.
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ItemBiophysical Constraints of Multicellularity: Building a Darwinian Material(Georgia Institute of Technology, 2023-04-27) Day, Thomas CooperThe evolution of multicellularity fundamentally changed life on Earth, resulting in successful and impactful lineages that continue to permeate and change the planet. Yet its origins, usually buried in the deep past, have remained unclear. For example, it is unknown how multicellular traits arise and emerge as repeatable and heritable. It is also unclear how spatial patterns of cell differentiation arise from undifferentiated origins. One camp of study has investigated the emergence of these traits from a genetic point of view. This camp is interested in how group-level genes are created, and then encoded into a multicellular genome. But, there is also a growing understanding that physical considerations play an outstanding role in shaping incipient multicellularity. Here, we use this biophysical viewpoint to investigate how physical constraints arise in freshly multicellular groups, and how these constraints may enable or limit subsequent adaptation and evolution. We show that some properties of multicellularity, that are historically considered difficult to achieve, can freely emerge without needing group-level genes. First, we review the many ways that cells can physically attach, and introduce a helpful classification scheme based upon their mechanical function: intercellular bonds can either be reformable after breaking, or they can be nonreformable. We investigate some of the downstream consequences of attaching cells from either one of these two classes, arguing that non-reformable bonds may bestow inherent advantages to a biological material, naturally producing some of the key features necessary to partake in evolution by natural selection, without any need for group level genes. Second, we consider one of the consequences of self-assembling cells via cell attachments: how are cells organized absent a developmental program? We find, through a combination of experiments and simulations, that, no matter the starting intercellular bond class, random noise resulting from cell birth and death processes result in a distribution of cell organization that is repeatable and predictable. In other words, there is a universal ``ground state'' of multicellular organization, that not only exists but repeatably reproduces itself, with the potential to effect any multicellular trait that relies upon cell packing. Therefore, heritable group-level traits can be generated simply by attaching cells together, without the need for developmental programs. After these two chapters, we turn our attention to investigating the evolution of spatially-patterned multicellularity. A fundamental prerequisite to achieving spatial patterning is for nascent multicellular organisms to become large, yet it is currently unknown if organisms can achieve such large size \textit{de novo}. Here, we experimentally show that initially microscopic organisms, without developmental plans, can achieve macroscopic size, on the order of millimeters, by evolving a mechanism that enables large size: material toughness. We uncover a novel biophysical adaptation, the entanglement of separate branches of cells, that evolved \textit{de novo} to achieve this material toughness. Later, we explore (through experiments, simulations, and theory) how entanglement might arise in general for growing systems, finding that entanglement is a relatively easy emergent biophysical phenomenon for any multicellular group with nonreformable, branching cell structures. Since these structures are rampant in both extant and fossil multicellularity, we suggest that physical entanglement may be a hitherto underappreciate mechanism for achieving group toughness, that can evolve without any need for group-level development. Taken together, we have thus shown that some key characteristics of multicellular life, including characteristics necessary for its origins, may freely emerge from physical considerations. We suggest that by considering more biophysical challenges for nascent multicellularity, we may yet find solutions to problems that were previously considered unsolvable.
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ItemTime-Variability and Primordial Black Hole Evaporation: Astrophysical Neutrino Studies(Georgia Institute of Technology, 2023-04-26) Dave, Pranav MayankOur current understanding of the universe stems from observations across the electromagnetic spectrum as well as additional messengers, such as gravitational waves, cosmic rays, and neutrinos. Particularly, we have observed a high-energy astrophysical diffuse neutrino flux using the IceCube Neutrino Observatory at the South Pole for the past 10 years. However, the specific sources that contribute to this flux are not known. More recently, IceCube reported evidence of neutrino emission from the nearby AGN and Seyfert II galaxy NGC 1068. In this work, I present a new method to ask: Is NGC 1068 a time-variable neutrino source? By applying this method to an identical data sample that was used to report the evidence of emission, I conclude that the neutrino emission from NGC 1068 is consistent with a steady source. This new method can be applied to future candidate point sources observed by IceCube and serves as a source characterization tool. Hawking radiation elegantly unifies quantum field theory, general relativity, and thermodynamics. Primordial Black Holes (PBHs) offer a way to directly observe Hawking radiation as the hole evaporates over the age of the universe. No evidence for Hawking radiation or PBHs has been reported yet and PBHs have been extensively studied as Dark Matter (DM) candidates in the past. In this work, I present a search for high-energy neutrino emission from an individual PBH that is evaporating in our local universe using data collected by IceCube. This is the first time high-energy neutrinos have been used to search for Hawking radiation from an evaporating PBH. Due to null detection in this search, I present an upper limit to the PBH evaporation density rate and compare it to existing limits from gamma-ray telescopes.