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At least 379 records · Page 21

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

Jain, Abhinandan↗

Comprehensive Modeling and Analysis of Rotorcraft Variable Speed Propulsion System With Coupled Engine/Transmission/Rotor Dynamics

This project develops comprehensive modeling and simulation tools for analysis of variable rotor speed helicopter propulsion system dynamics. The Comprehensive Variable-Speed Rotorcraft Propulsion Modeling (CVSRPM) tool developed in this research is used to investigate coupled rotor/engine/fuel control/gearbox/shaft/clutch/flight control system dynamic interactions for several variable rotor speed mission scenarios. In this investigation, a prototypical two-speed Dual-Clutch Transmission (DCT) is proposed and designed to achieve 50 percent rotor speed variation. The comprehensive modeling tool developed in this study is utilized to analyze the two-speed shift response of both a conventional single rotor helicopter and a tiltrotor drive system. In the tiltrotor system, both a Parallel Shift Control (PSC) strategy and a Sequential Shift Control (SSC) strategy for constant and variable forward speed mission profiles are analyzed. Under the PSC strategy, selecting clutch shift-rate results in a design tradeoff between transient engine surge margins and clutch frictional power dissipation. In the case of SSC, clutch power dissipation is drastically reduced in exchange for the necessity to disengage one engine at a time which requires a multi-DCT drive system topology. In addition to comprehensive simulations, several sections are dedicated to detailed analysis of driveline subsystem components under variable speed operation. In particular an aeroelastic simulation of a stiff in-plane rotor using nonlinear quasi-steady blade element theory was conducted to investigate variable speed rotor dynamics. It was found that 2/rev and 4/rev flap and lag vibrations were significant during resonance crossings with 4/rev lagwise loads being directly transferred into drive-system torque disturbances. To capture the clutch engagement dynamics, a nonlinear stick-slip clutch torque model is developed. Also, a transient gas-turbine engine model based on first principles mean-line compressor and turbine approximations is developed. Finally an analysis of high frequency gear dynamics including the effect of tooth mesh stiffness variation under variable speed operation is conducted including experimental validation. Through exploring the interactions between the various subsystems, this investigation provides important insights into the continuing development of variable-speed rotorcraft propulsion systems.

DeSmidt, Hans A.↗

Machine learning-based multidomain processing for texture-based image segmentation and analysis

Atomic and molecular resolved atomic force microscopy (AFM) images offer unique insights into materials' properties such as local ordering, molecular orientation, and topological defects, which can be used to pinpoint physical and chemical interactions occurring at the surface. Utilizing machine learning for extracting underlying physical parameters increases the throughput of AFM data processing and eliminates inconsistencies intrinsic to manual image analysis, thus enabling the creation of reliable frameworks for qualitative and quantitative evaluation of experimental data. Here, we present a robust and scalable approach to the segmentation of AFM images based on flexible pre-selected classification criteria. The usage of supervised learning and feature extraction allows us to retain the consideration of specific problem-dependent features (such as types of periodical structures observed in the images and the associated numerical parameters: spacing, orientation, etc.). We highlight the applicability of this approach for the segmentation of molecular resolved AFM images based on the crystal orientation of the observed domains, automated selection of boundaries, and collection of relevant statistics. Finally, we outline a general strategy for machine learning-enabled analysis of nanoscale systems exhibiting periodic order that could be applied to any analytical imaging technique

36 MATERIALS SCIENCE↗

Collaborative Computing Support for Analysis Facilities Exploiting Software as Infrastructure Techniques

Prior to the public release of Kubernetes it was difficult to conduct joint development of elaborate analysis facilities due to the highly non-homogeneous nature of hardware and network topology across compute facilities. However, since the advent of systems like Kubernetes and OpenShift, which provide declarative interfaces for building fault-tolerant and self-healing deployments of networked software, it is possible for multiple institutes to collaborate more effectively since resource details are abstracted away through various forms of hardware and software virtualization. In this whitepaper we will outline the development of two analysis facilities: "Coffea-casa" at University of Nebraska Lincoln and the "Elastic Analysis Facility" at Fermilab, and how utilizing platform abstraction has improved the development of common software for each of these facilities, and future development plans made possible by this methodology.

97 MATHEMATICS AND COMPUTING↗

Magnetic dilution effect and topological phase transitions in (Mn 1- x Pb x )Bi 2 Te 4

We report, as the first intrinsic antiferromagnetic topological insulator, MnBi 2 Te 4 has provided a material platform to realize various emergent phenomena arising from the interplay of magnetism and band topology. Here, by investigating (Mn 1-x Pb x )Bi 2 Te 4 (0 ≤ x ≤ 0.82) single crystals via the x-ray, electrical transport, magnetometry and neutron measurements, chemical analysis, external pressure, and first-principles calculations, we reveal the magnetic dilution effect on the magnetism and band topology in MnBi 2 Te 4 . With increasing x, both lattice parameters a and c expand linearly by around 2%. All samples undergo the paramagnetic to A-type antiferromagnetic transition with the Néel temperature decreasing lineally from 24 K at x = 0 to 2 K at x = 0.82. Our neutron data refinement of the x = 0.37 sample indicates that the ordered moment is 4.3(1)μ B /Mn at 4.85 K and the amount of the Mn Bi antisites is negligible within the error bars. Isothermal magnetization data reveal a slight decrease of the interlayer plane-plane antiferromagnetic exchange interaction and a monotonic decrease of the magnetic anisotropy due to diluting magnetic ions and enlarging the unit cell. For x = 0.37, the application of external pressures enhances the interlayer antiferromagnetic coupling, boosting the Néel temperature at a rate of 1.4 K/GPa and the saturation field at a rate of 1.8 T/GPa. Furthermore, our first-principles calculations reveal that the band inversion in the two end materials, MnBi 2 Te 4 and PbBi 2 Te 4 , occurs at the Γ and Z point, respectively, while two gapless points appear at x = 0.44 and x = 0.66, suggesting possible topological phase transitions with doping.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Quantum Filtering and Analysis of Multiplicities in Eigenvalue Spectra

Fine-grained spectral properties of quantum Hamiltonians, including both eigenvalues and their multiplicities, provide useful information for characterizing many-body quantum systems as well as for understanding phenomena such as topological order. Extracting such information with small additive error is #BQP-complete in the worst case. In this work, we introduce QFAMES (quantum filtering and analysis of multiplicities in eigenvalue spectra), a quantum algorithm that efficiently identifies clusters of closely spaced dominant eigenvalues and determines their multiplicities under physically motivated assumptions, which allows us to bypass worst-case complexity barriers. QFAMES also enables the estimation of observable expectation values within targeted energy clusters, providing a powerful tool for studying quantum phase transitions and other physical properties. We validate the effectiveness of QFAMES through numerical demonstrations, including its applications to characterizing quantum phases in the transverse-field Ising model and estimating the ground-state degeneracy of a topologically ordered phase in the two-dimensional toric code model. We also generalize QFAMES to the setting of mixed initial states. Our approach offers rigorous theoretical guarantees and significant advantages over existing subspace-based quantum spectral analysis methods, particularly in terms of the sample complexity and the ability to resolve degeneracies.

97 MATHEMATICS AND COMPUTING↗

Topology optimization of additively manufactured fluidic components free of internal support structures

This report integrates projection-based approaches for implementing overhang constraints with fluid topology optimization to design additively manufactured fluidic components that do not require internal support structures. Internal support structures are challenging, potentially impossible to remove in complex fluid networks, yet would degrade fluidic performance if left within the part. This presents a major challenge in coupling topology optimization with additive manufacturing in the design of fluid components. The proposed approach leverages past work in overhang constraints for solid mechanics, including projection formulations and adjoint sensitivity analysis, and considers incompressible Navier–Stokes equations for laminar fluid flow. The approach is demonstrated on 2D and 3D fluid topology optimization problems to minimize pressure drop and constrain mass flow rates in pipes and manifolds. Resulting designs are crisp, logical, satisfy performance constraints, and satisfy overhang constraints, eliminating the need for internal support structures.

42 ENGINEERING↗

Photoinduced Dirac semimetal in ZrTe5

Abstract Novel phases of matter with unique properties that emerge from quantum and topological protection present an important thrust of modern research. Of particular interest is to engineer these phases on demand using ultrafast external stimuli, such as photoexcitation, which offers prospects of their integration into future devices compatible with optical communication and information technology. Here, we use MeV Ultrafast Electron Diffraction (UED) to show how a transient three-dimensional (3D) Dirac semimetal state can be induced by a femtosecond laser pulse in a topological insulator ZrTe 5 . We observe marked changes in Bragg diffraction, which are characteristic of bond distortions in the photoinduced state. Using the atomic positions refined from the UED, we perform density functional theory (DFT) analysis of the electronic band structure. Our results reveal that the equilibrium state of ZrTe 5 is a topological insulator with a small band gap of ~ 25 meV, consistent with angle-resolved photoemission (ARPES) experiments. However, the gap is closed in the presence of strong spin-orbit coupling (SOC) in the photoinduced transient state, where massless Dirac fermions emerge in the chiral band structure. The time scale of the relaxation dynamics to the transient Dirac semimetal state is remarkably long, τ ~ 160 ps, which is two orders of magnitude longer than the conventional phonon-driven structural relaxation. The long relaxation is consistent with the vanishing density of states in Dirac spectrum and slow spin-repolarization of the SOC-controlled band structure accompanying the emergence of Dirac fermions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Observability and Estimation of Distributed Space Systems via Local Information-Exchange Networks

Spacecraft formation flying involves the coordination of states among multiple spacecraft through relative sensing, inter-spacecraft communication, and control. Most existing formation-flying estimation algorithms can only be supported via highly centralized, all-to-all, static relative sensing. New algorithms are proposed that are scalable, modular, and robust to variations in the topology and link characteristics of the formation exchange network. These distributed algorithms rely on a local information exchange network, relaxing the assumptions on existing algorithms. Distributed space systems rely on a signal transmission network among multiple spacecraft for their operation. Control and coordination among multiple spacecraft in a formation is facilitated via a network of relative sensing and interspacecraft communications. Guidance, navigation, and control rely on the sensing network. This network becomes more complex the more spacecraft are added, or as mission requirements become more complex. The observability of a formation state was observed by a set of local observations from a particular node in the formation. Formation observability can be parameterized in terms of the matrices appearing in the formation dynamics and observation matrices. An agreement protocol was used as a mechanism for observing formation states from local measurements. An agreement protocol is essentially an unforced dynamic system whose trajectory is governed by the interconnection geometry and initial condition of each node, with a goal of reaching a common value of interest. The observability of the interconnected system depends on the geometry of the network, as well as the position of the observer relative to the topology. For the first time, critical GN&C (guidance, navigation, and control estimation) subsystems are synthesized by bringing the contribution of the spacecraft information-exchange network to the forefront of algorithmic analysis and design. The result is a formation estimation algorithm that is modular and robust to variations in the topology and link properties of the underlying formation network.

Fathpour, Nanaz↗

Design optimization of lightweight automotive seatback through additive manufacturing compression overmolding of metal polymer composites

With the growing demand for enhanced automotive fuel efficiency and environmental sustainability, there is a need for lightweighting automotive components through innovative design and manufacturing processes. Here, this study leverages a combination of numerical iterative design optimization and hybrid additive manufacturing–compression molding (AM-CM) technique for metal polymer composites to lightweight an automotive seatback. The AM-CM process enables robust mechanical interlocking between metals and composites, boasting high stiffness and strength with low overall density. Replacing metallic components with such metal polymer composites allows for comparable mechanical performance while significantly reducing the overall weight. First, the automotive seatback design space is reduced to critical load carrying regions using topology optimization and high stress concentration areas are identified using finite element analysis. Next, a lightweight metal polymer subcomponent is designed for a high stress concentration region. The full seatback frame with spatially heterogeneous material-specific design is then iteratively optimized to enable enhanced stiffness with minimal weight. Overall, the automotive seatback frame designed with location-specific metal, polymer, and metal polymer composite materials weighs 20% less than the metal-only design while exhibiting similar stiffness.

36 MATERIALS SCIENCE↗

Surrogate-assisted optimization under uncertainty for design for remanufacturing considering material price volatility

Remanufacturing is a well-established end-of-life (EOL) strategy that promises significant savings in energy and carbon emissions. However, the current design practices are not remanufacturing-inclusive, i.e., the majority of products are designed for a single life cycle. As a result, potential products that can sustain multiple life cycles are deprived of additional benefits of being designed for remanufacturing, such as reduced material usage, lower cost, and improved environmental impact. Moreover, the uncertainty in design, material selection, and economics are not considered to produce remanufacturable designs. Accordingly, this research proposes a design for remanufacturing (DfRem) framework that accounts for design uncertainty and material price volatility. The framework systematically explores the design space, performs design optimization under uncertainty, followed by topology optimization to provide additional mass savings, and finally, a price volatility analysis for plausible design material choices. The candidate designs are evaluated based on their design mass, material price volatility, failure mode characteristics, carbon footprint, and embodied energy impacts. The proposed framework's utility is demonstrated via the use of an engine cylinder head case study subjected to thermo-mechanical loads along with fatigue and wear failure. Considering grey cast iron and aluminum alloy as the design material choices, it was found that the cast iron design reduced the initial design mass by 6% as opposed to a 5% decrease for aluminum. On the other hand, about 8% area of the cast iron design failed due to fatigue, compared to 3% for aluminum. Here, we further observed that although the aluminum design provided better mechanical performance than the cast iron design, this material was more expensive and volatile in price.

36 MATERIALS SCIENCE↗

Atomic scale crystal field mapping of polar vortices in oxide superlattices

Polar vortices in oxide superlattices exhibit complex polarization topologies. Using a combination of electron energy loss near-edge structure analysis, crystal field multiplet theory, and first-principles calculations, we probe the electronic structure within such polar vortices in [(PbTiO 3 ) 16 /(SrTiO 3 ) 16 ] superlattices at the atomic scale. The peaks in Ti L-edge spectra shift systematically depending on the position of the Ti 4+ cations within the vortices i.e., the direction and magnitude of the local dipole. First-principles computation of the local projected density of states on the Ti 3d orbitals, together with the simulated crystal field multiplet spectra derived from first principles are in good agreement with the experiments.

36 MATERIALS SCIENCE↗

Computational prediction of ferromagnetic 𝐴⁢𝑇 6 ⁢𝑋 6 kagome compounds

We present a systematic high-throughput density-functional-theory investigation of the structural and magnetic stability of 312 substitutional compounds in the magnetic kagome 𝐴⁢𝑇 6⁢ 𝑋 6 family. Our screening confirms the stability of many previously reported structures and predicts several additional stable candidates. Within collinear spin configurations, we find that Fe-based systems predominantly adopt antiferromagnetic ground states, whereas Mn-based analogs exhibit a more balanced distribution between ferromagnetic and antiferromagnetic order. For compounds exhibiting several nearly degenerate collinear configurations, we analyze the nature of their magnetic ground states, assess the possible emergence of noncollinear order, and discuss the limitations and uncertainties inherent to standard density-functional approaches. Our electronic structure analysis further reveals that predicted ferromagnetic kagome systems display characteristic features of topological metals, with rich magnetic configurations that can be tuned by chemical substitution. Altogether, these ferromagnetic kagome compounds constitute a broad and still largely unexplored materials platform for the emergence of exciting magnetotransport phenomena.

Density functional calculations↗

Computing Edge States without Hard Truncation

We present a numerical method which accurately computes the discrete spectrum and associated bound states of semi-infinite Hamiltonians which model electronic “edge” states localized at boundaries of one- and two-dimensional crystalline materials. The problem is nontrivial since arbitrarily large finite “hard” (Dirichlet) truncations of the Hamiltonian in the infinite bulk direction tend to produce spurious bound states partially supported at the truncation. Our method, which overcomes this difficulty, is to compute the Green's function of the semi-infinite Hamiltonian by imposing an appropriate boundary condition in the bulk direction; then, the spectral data is recovered via Riesz projection. We demonstrate our method's effectiveness by studies of edge states at a graphene zig-zag edge in the presence of defects modeled both by a discrete tight-binding model and a continuum PDE model under finite difference discretization. Our method may also be used to study states localized at domain wall-type edges in one- and two-dimensional materials where the edge Hamiltonian is infinite in both directions; we demonstrate this for the case of a tight-binding model of distinct honeycomb structures joined along a zig-zag edge. Here, we expect our method to be useful for designing novel devices based on precise wave-guiding by edge states.

97 MATHEMATICS AND COMPUTING↗

A new partitioning strategy for efficient re-analysis of large structural systems

A computational procedure is presented for the reanalysis of large unsymmetric structural systems. The procedure is based on a novel partitioning strategy in which the responses of both the original and modified structures are approximated by symmetric and antisymmetric response vectors, each obtained by using only a fraction of the degrees of freedom of the discrete model of the structure. The procedure is applied to linear static analysis of framed structures. Design modifications consisted of removing members, resulting in topologically unsymmetric structures. The efficient application of the procedure on sequential computers as well as on multiprocessor computers is discussed, and its effectiveness is demonstrated by means of two numerical examples.

Noor, Ahmed K.↗

Test and evaluation of load converter topologies used in the Space Station Freedom Power Management and distribution DC test bed

Power components hardware in support of the Space Station Freedom dc Electrical Power System were tested. One type of breadboard hardware tested is the dc Load Converter Unit, which constitutes the power interface between the electric power system and the actual load. These units are dc to dc converters that provide the final system regulation before power is delivered to the load. Three load converters were tested: a series resonant converter, a series inductor switchmode converter, and a switching full-bridge forward converter. The topology, operation principles, and tests results are described, in general. A comparative analysis of the three units is given with respect to efficiency, regulation, short circuit behavior (protection), and transient characteristics.

Lebron, Ramon C.↗

Test and evaluation of load converter topologies used in the Space Station Freedom power management and distribution dc test bed

Power components hardware in support of the Space Station freedom dc Electric Power System were tested. One type of breadboard hardware tested is the dc Load Converter Unit, which constitutes the power interface between the electric power system and the actual load. These units are dc to dc converters that provide the final system regulation before power is delivered to the load. Three load converters were tested: a series resonant converter, a series inductor switch-mode converter, and a switching full-bridge forward converter. The topology, operation principles, and test results are described, in general. A comparative analysis of the three units is given with respect to efficiency, regulation, short circuit behavior (protection), and transient characteristics.

Lebron, Ramon C.↗