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ItemProgramming Mechanics in Knitted Materials, Stitch by Stitch Data Repository(Georgia Institute of Technology, 2024-02) Singal, Krishma ; Dimitriyev, Michael S. ; Gonzalez, Sarah E. ; Cachine, Alexander P. ; Quinn, Sam ; Matsumoto, Elisabetta A.
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ItemExperimental Data for "Spatial constraints and stochastic seeding subvert microbial arms race"(Georgia Institute of Technology, 2024-01) Copeland, Raymond ; Zhang, Christopher ; Hammer, Brian K. ; Yunker, Peter J.This item is the experimental data for figures 7 and 8 of the paper titled "Spatial constraints and stochastic seeding subvert microbial arms race" which was accepted at PLOS computational biology.
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ItemData for the publication "Pressure control of magnetic order and excitations in the pyrochlore antiferromagnet MgCr2O4"(Georgia Institute of Technology, 2024-01) Mourigal, MartinMgCr2O4 is one of the best-known realizations of the pyrochlore-lattice Heisenberg antiferromagnet. The strong antiferromagnetic exchange interactions are perturbed by small further-neighbor exchanges such that this compound may in principle realize a spiral spin liquid (SSL) phase in the zero-temperature limit. However, a spin Jahn-Teller transition below TN≈13 K yields a complicated long-range magnetic order with multiple coexisting propagation vectors. We present neutron scattering and thermo-magnetic measurements of MgCr2O4 samples under applied hydrostatic pressure up to P=1.7 GPa demonstrating the existence of multiple close-lying nearly degenerate magnetic ground states. We show that the application of hydrostatic pressure increases the ordering temperature by around 0.8 K per GPa and increases the bandwidth of the magnetic excitations by around 0.5 meV per GPa. We also evidence a strong tendency for the preferential occupation of a subset of magnetic domains under pressure. In particular, we show that the k=(0,0,1) magnetic phase, which is almost negligible at ambient pressure, dramatically increases in spectral weight under pressure. This modifies the spectrum of magnetic excitations, which we interpret unambiguously as spin waves from multiple magnetic domains. Moreover, we report that the application of pressure reveals a feature in the magnetic susceptibility above the magnetostructural transition. We interpret this as the onset of a short-range ordered phase associated with k=(0,0,1), previously not observed in magnetometry measurements.
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ItemRaw data and simulation code for "Quantum-to-classical crossover in generalized spin systems – the temperature-dependent spin dynamics of FeI2"(Georgia Institute of Technology, 2024-01) Mourigal, MartinSimulating quantum spin systems at finite temperatures is an open challenge in many-body physics. This work studies the temperature-dependent spin dynamics of a pivotal compound, FeI2, to determine if universal quantum effects can be accounted for by a phenomenological renormalization of the dynamical spin structure factor S(q,ω) measured by inelastic neutron scattering. Renormalization schemes based on the quantum-to-classical correspondence principle are commonly applied at low temperatures to the harmonic oscillators describing normal modes. However, it is not clear how to extend this renormalization to arbitrarily high temperatures. Here we introduce a temperature-dependent normalization of the classical moments, whose magnitude is determined by imposing the quantum sum rule, i.e. ∫dωdqS(q,ω)=NSS(S+1) for NS dipolar magnetic moments. We show that this simple renormalization scheme significantly improves the agreement between the calculated and measured S(q,ω) for FeI2 at all temperatures. Due to the coupled dynamics of dipolar and quadrupolar moments in that material, this renormalization procedure is extended to classical theories based on SU(3) coherent states, and by extension, to any SU(N) coherent state representation of local multipolar moments.
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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.