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College of Sciences

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School of Biological Sciences

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School of Chemistry and Biochemistry

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School of Earth and Atmospheric Sciences

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School of Mathematics

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School of Physics

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Geometric modeling of biological and robotic locomotion in highly damped environments

(Georgia Institute of Technology, 2022-12-14) Zhong, Baxi

Biological systems can use seemingly simple rhythmic body and limb undulations to traverse their complex natural terrains. We are particularly interested in the regime of locomotion in highly damped environments, which we refer to as geometric locomotion. In geometric locomotion, the net translation is generated from properly coordinated self-deformation to counter the drag forces, as opposed to inertia-dominated systems where inertial forces dominate over frictional forces (thus coasting/gliding is possible). The scope of geometric locomotion include locomotors with diverse morphologies across scales in various environments. For example, at the macroscopic scale, legged animals such as fire salamanders (S. salamandra), display high maneuverability by properly coordinating their body bending and leg movements. At the microscopic scale, nematode worms, such as C. elegans, can manipulate body undulation patterns to facilitate effective locomotion in diverse environments. These movements often require proper coordination of animal bodies and/or limbs; more importantly, such coordination patterns are environment dependent. In robotic locomotion, however, the state-of-the-art gait design and feedback control algorithms are computationally costly and typically not transferable across platforms and scenarios (body-morphologies and environments), thus limiting the versatility and performance capabilities of engineering systems. While it is challenging to directly replicate the success in biological systems to robotic systems, the study of biological locomotors can establish simple locomotion models and principles to guide robotics control processes. The overarching goal of this thesis is to (1) connect the observations in biological systems to the optimization problems in robotics applications, and (2) use robotics as tools to analyze locomotion behaviors in various biological systems. In the last 30 years, a framework called “geometric mechanics” has been developed as a general scheme to link locomotor performance to the patterns of “self-deformation”. This geometric approach replaces laborious calculation with illustrative diagrams. Historically, this geometric approach was limited to low degree-of-freedom systems while assuming an idealized contact model with the environment. This thesis develops and advances the geometric mechanics framework to overcome both of these limitations; and thereby generates insight into understanding a variety of animal behaviors as well as controlling robots, from short-limb elongate quadrupeds to body-undulatory multi-legged centipedes in highly-damped environments.
Non-inertial Undulatory Locomotion Across Scales

(Georgia Institute of Technology, 2022-12-13) Diaz Cruz, Kelimar

Locomotion is crucial to behaviors such as predator avoidance, foraging, and mating. In particular, undulatory locomotion is one of the most common forms of locomotion. From microscopic flagellates to swimming fish and slithering snakes, this form of locomotion is a remarkably robust self-propulsion strategy that allows a diversity of organisms to navigate myriad environments. While often thought of as exclusive to limbless organisms, a variety of locomotors possessing few to many appendages rely on waves of undulation for locomotion. In inertial regimes, organisms can leverage the forces generated by their body and the surrounding medium's inertia to enhance their locomotion (e.g., coast or glide). On the other hand, in non-inertial regimes self-propulsion is dominated by damping (viscous or frictional), and thus the ability for organisms to generate motion is dependent on the sequence of internal shape changes. In this thesis, we study a variety of undulating systems that locomote in highly damped regimes. We perform studies on systems ranging from zero to many appendages. Specifically, we focus on four distinct undulatory systems: 1) C. elegans, 2) quadriflagellate algae (bearing four flagella), 3) centipedes on terrestrial environments, and 4) centipedes on fluid environments. For each of these systems, we study how the coordination of their many degrees of freedom leads to specific locomotive behaviors. Further, we propose hypotheses for the observed behaviors in the context of each of these system's ecology.
Active defects in flat and curved spaces

(Georgia Institute of Technology, 2022-12-13) Nambisan, Jyothishraj

The interaction and dynamics of topological defects have inspired numerous studies across physics over centuries. They manifest as salient features in liquid crystalline materials, as regions where the underlying director field is undefined. Liquid crystals can be intrinsically driven out of equilibrium via an energy input at the level of the constituent particles, thus forming a unique class of non-equilibrium systems, known as active liquid crystals. In this thesis, we explore the rich phenomenology of topological defects observed in the microtubule-kinesin active nematic system, confined to surfaces of different topology and varying curvature. In 2D flat space, we observe short-range ferromagnetic alignment of +1/2 defects, mediated by -1/2 defects in between. This is primarily driven by passive elastic mechanisms, as confirmed via hydrodynamic simulations of active and passive liquid crystals. However, the system does not develop any long-range or quasi-long-range order over time. The qualitative features of defect-defect correlations are found to be independent of defect density. In curved space experiments, we observe a clear preference for the orientation of defects and persistent long-range order detected on highly curved regions of toroidal drops. This is a remarkable confirmation that curvature, and gradients of it, have a major role in intrinsically biasing the alignment of defects. This is in stark contrast to random, isotropic defect orientations found in locally flat regions. We then propose an idealized mechanism of defect alignment subject to curvature gradients, which is currently being inspected via agent-based simulations of an active multi-defect system. The observation of surface curvature as an aligning field is much more fundamental than recent works in similar systems, where patterned substrates and external fields have been used to align defects and create order. We also present the first experimental confirmation of hyperuniformity in an active system of topological defects. Originally conceived from the mathematical study of point patterns, hyperuniform systems are characterized by the suppression of large-scale fluctuations in the number (or density) of particles like a perfect crystal, while being isotropic like a liquid that has no long-range spatial or orientational order. Our discovery is unique, as it is the entire system that is hyperuniform, and not any specific snapshot or microstate of it. We quantify the degree of hyperuniformity using existing tests in literature and contrast the results with randomly distributed and manually dragged point patterns. The origins of hyperuniformity is found to be connected to the intrinsic creation-annihilation mechanisms of the defects and the constant average number of defects, even in the active turbulent state. The confirmation of hyperuniformity in our system also contrasts with giant number fluctuations, that are generally seen as a hallmark of active matter. Overall, our work explores the rich interplay of activity, topology and curvature in a liquid crystalline system and how topological defects interact to develop correlations and orientational order subject to the governing factors. More generally, our work provides an exciting test bed with associated techniques to study active matter in a controlled experimental setting.
Novel and improved algorithms for the contraction of 2D tensor networks

(Georgia Institute of Technology, 2022-12-08) Lan, Wangwei

Tensor network algorithms are important numerical tools for studying quantum many-body problems. However, the high computational costs have prevented its applications in two-dimensional (2D) systems. In this thesis, we discussed our work on more efficient contractions of 2D tensor networks. In particular, for 2D statistical mechanics, we propose a modified form of a tensor renormalization group algorithm for evaluating partition functions of classical statistical mechanical models on 2D lattices. This algorithm coarse-grains only the rows and columns of the lattice adjacent to a single core tensor at each step, such that the lattice size shrinks linearly with the number of coarse-graining steps as opposed to shrinking exponentially as in the usual tensor renormalization group (TRG). However, the cost of this new approach only scales as O(χ4) in terms of the bond dimension χ, significantly cheaper than the O(χ6) cost scaling of TRG, whereas numerical benchmarking indicates that both approaches have comparable accuracy for the same bond dimension χ. In 2D quantum mechanics, we propose a pair of approximations that allows the leading order computational cost of contracting an infinite projected entangled-pair state (iPEPS) to be reduced from O(χ3D6) to O(χ3D3) when using a corner-transfer approach. The first approximation involves (i) reducing the environment needed for truncation of the boundary tensors (ii) relies on the sequential contraction and truncation of bra and ket indices, rather than doing both together as with the established algorithm. Our benchmark results are comparable to the standard iPEPS algorithm. The improvement in computational cost enables us to perform large bond dimension calculations, extending its potential to solve challenging problems.
Miniature atomic beams and its application in quantum optics

(Georgia Institute of Technology, 2022-12-07) Wei, Bochao

The utilization of thermal atoms can enable further miniaturization and scalability of atomic devices and facilitate more applications of quantum information science in daily life. Thermal atomic beams can be easily generated and maintained compared with cold atoms. They also offer a longer coherence time and transverse Doppler-free interaction compared with thermal vapor. However, thermal atomic beams are rarely utilized in small-scale atomic devices. This thesis discussed novel approaches to generate miniature atomic beams and demonstrated their application in the field of quantum optics. The properties of our miniature atomic beam devices were characterized. Then, we studied the combination of our chip-scale atomic beams with nanophotonic resonators to achieve strong coupling in the cavity QED field. Master equation simulations were implemented to understand the dynamics, expected signal, and constraints of this platform. Efficient edge couple was demonstrated to couple free space laser beam to the chip. Besides the field of cavity QED, slow single atoms in our miniature atomic beams were isolated from our thermal atomic beam. Photon statistics from single atoms in our atomic beam were measured and studied theoretically. High values of the second-order and third-order correlation functions were found, which indicate its potential to be a source of photon pairs or triplets. Our observations showed the prospect of a bottom-up approach to building a thermal quantum system with trackable slow single atoms in an atomic beam.
Transport-Enabled Qubit Operations with Trapped Ions

(Georgia Institute of Technology, 2022-10-19) Tinkey, Holly Nicole

Trapped ion systems are a strong candidate for quantum information processing due to the long lifetimes of their internal electronic states, which can be treated as a two-level quantum system called a qubit. Trapped ions and atoms are unique among other physical quantum information platforms because their position is not fixed, and they can be spatially manipulated with electric fields. This characteristic is widely used in logic-passive operations such as ion loading and transport between different regions in a trap, but it is not often actively incorporated into qubit manipulations. This thesis describes research into techniques that take advantage of transport operations to produce one- and two-qubit operations on two co-trapped calcium-40 ions. The first technique involves single-ion addressing achieved via sequences of laser pulses and modulations of the confining electric field potential; I describe my contributions to lowering the motional heating during the potential modulations and applying the single-ion addressing technique to perform quantum process tomography. The second transport-enhanced technique is the first demonstration of a two-qubit entangling gate performed on ions during transport, and I outline the experimental methods used to characterize and tailor the transport to achieve entanglement during the interaction.
Hybridization and dehybridization of short oligonucleotides

(Georgia Institute of Technology, 2022-10-10) Hart, Derek Jordan

DNA duplex separation and formation underlie our most fundamental genetic processes. One of the most powerful tools for exploring these binding and unbinding reactions is single-molecule force spectroscopy. This method applies tension to a single DNA strand and observes the change in its extension or kinetics with a microscope. However, these experiments typically study longer DNA molecules (>10 bp) subject to higher forces (>10 piconewtons); hence, the behavior of short DNA subject to weak forces is not well understood. In particular, it is not clear whether statistical chain models ordinarily used to explain force spectroscopy data are applicable at these small scales. To remedy this, we focused solely on short DNA duplexes (<10 bp) subject to very weak forces (< 10 piconewtons). For this purpose, we used two tools: an experimental technique called single-molecule fluorescence resonance energy transfer (smFRET), and the coarse-grained DNA simulation code oxDNA. The experiments implemented a simple, high-throughput DNA assay, dubbed “DNA bows”, which exploit the bending rigidity of DNA to exert very weak forces on short DNA strands. With this method, we demonstrate that weak force accelerates the hybridization and dehybridization of short oligonucleotides from 2 to 6 piconewtons, contradicting the predictions of simple chain models. We next used oxDNA to investigate how the extension of short DNA changes with force throughout its binding and unbinding transitions. Regardless of force, we find that the transition state of an oligoduplex is at least as extended as its bound state, in agreement with our experiments. We also find that extension is a poor reaction coordinate at 3 piconewtons and below. These results establish the nature of DNA duplex transitions at the force and length scales relevant to DNA biology as well as emerging DNA nanotechnologies.
Characterizing the bending and twisting mechanics of DNA and its mismatches

(Georgia Institute of Technology, 2022-08-31) Ryan, Michael Lee

DNA holds enormous power over cellular processes, genetic expression, reproduction, and as a consequence life in general. While many genetic interactions are studied and manipulated, in an ideal world we would understand DNA at a physical level and build up all interactions from first principles. The more we know about the theromechanics of this semi-flexible polymer, the greater control we have over it to correct mistakes, utilize it as a tool, or fortify it from degradation. In the interest of exploring this molecule and its intrinsic properties, we target it with bending and torsional stress. In our bending studies, we design small DNA molecules capable of bending into tight loops. Measuring the rates of this cyclization and de-cyclization process gives insight on how rigid the helical backbone is for matched nucleotides and mismatched pairs. We find that matched nucleotides resist helical deformation to a much greater degree than mismatches. We take this a step further and explore bending anisotropy for all of these pairs and mispairs. It is clear in our experimental results that nucleotide pairs have a preferred bending direction and that anisotropy should be considered more relevant than the current field treats it. We also take a novel approach at twisting DNA with a horizontal variant of magnetic tweezers, which we hope to combine with fluorescence to merge two powerful DNA probing techniques. We confirm the viability of this new tweezing technique by reproducing plectonemic hat curves, which are well studied. A fluorescent study of these molecules confirms our tweezing results. In this twisting study, we also developed a new technique using CRISPR to create extremely long, torsionally constrained molecules that show preliminary success.
Evidence for the dynamical relevance of relative periodic orbits in turbulence

(Georgia Institute of Technology, 2022-08-01) Crowley, Christopher J.

Despite a long and rich history of scientific investigation, fluid turbulence remains one of the most challenging problems in science and engineering. One of the key outstanding questions concerns the role of coherent structures that describe frequently observed patterns embedded in turbulence. It has been suggested, but not proven, that coherent structures correspond to unstable, recurrent solutions of the governing equations of fluid dynamics. In this thesis, I present the first experimental evidence that three-dimensional turbulent flow mimics the spatial and temporal structure of multiple such solutions episodically but repeatedly. These results provide compelling evidence that coherent structures, grounded in the governing equations, can be harnessed to predict how turbulent flows evolve.
Topological Properties of SU(n) Fermions

(Georgia Institute of Technology, 2022-07-30) Yau, Man Hon

Ultra-cold fermions loaded in optical lattices have become ideal systems to study related electronic phase diagrams and transport properties, because they provide a clean and well controlled playground to change various lattice parameters and external fields at the turn of a knob. It is now possible to create artificial magnetic fields in optical lattices that mimic electronic materials exhibiting integer and fractional quantum Hall effects. The synthetic magnetic flux values created in optical lattices are sufficiently large to allow for the experimental exploration of the intricacies of Harper’s model and the Hofstadter butterfly, as well as the experimental determination of Chern numbers. For ultracold fermions in optical lattices, artificial magnetic fields enable studies of topological insulators that break time-reversal symmetry, such as quantum Hall systems, while artificial spin-orbit fields allow for studies of topological insulators that do not break time-reversal symmetry, such as quantum spin Hall systems. Both types of topological insulators are characterized by Berry curvatures and Chern numbers, which have been measured experimentally using time-of-flight techniques, inspired by theoretical proposals, and using dynamics of the center of mass of the atomic cloud, also motivated by theoretical work. However, studies of ultracold fermions may go beyond the quantum simulation of spin-1/2 topological insulators under typical condensed matter conditions, because artificial magnetic, spin-orbit, and Zeeman fields may be adjusted independently. The thesis develop the topological properties and discuss the quantum Hall responses of SU(N) fermions in two-dimensional lattices, when artificial magnetic flux and color-orbit coupling are present.