School of Physics (SoP)The School of Physics at Georgia Tech is well known for its high academic standards and stands among the top ranked schools. It offers a dynamic environment for research and education in many areas of physics.http://hdl.handle.net/1853/60712023-02-09T07:26:45Z2023-02-09T07:26:45ZGeometric modeling of biological and robotic locomotion in highly damped environmentsZhong, Baxihttp://hdl.handle.net/1853/702072023-01-23T21:50:12Z2022-12-14T00:00:00ZGeometric modeling of biological and robotic locomotion in highly damped environments
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.
2022-12-14T00:00:00ZZhong, BaxiBiological 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.Novel and improved algorithms for the contraction of 2D tensor networksLan, Wangweihttp://hdl.handle.net/1853/701742023-01-23T21:50:06Z2022-12-08T00:00:00ZNovel and improved algorithms for the contraction of 2D tensor networks
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.
2022-12-08T00:00:00ZLan, WangweiTensor 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 opticsWei, Bochaohttp://hdl.handle.net/1853/701712023-01-23T21:50:06Z2022-12-07T00:00:00ZMiniature atomic beams and its application in quantum optics
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.
2022-12-07T00:00:00ZWei, BochaoThe 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.Non-inertial Undulatory Locomotion Across ScalesDiaz Cruz, Kelimarhttp://hdl.handle.net/1853/701602023-01-23T21:50:04Z2022-12-13T00:00:00ZNon-inertial Undulatory Locomotion Across Scales
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.
2022-12-13T00:00:00ZDiaz Cruz, KelimarLocomotion 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.