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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Orbital design of flat bands in non-line-graph lattices via line-graph wave functions

Line-graph (LG) lattices are known for having flat bands (FBs) from the destructive interference of Bloch wave functions encoded in only lattice symmetry. In this work, we develop a generic atomic/molecular orbital design principle for FBs in non-LG lattices. Based on linear combination of atomic orbital theory, we demonstrate that the underlying wave-function symmetry of FBs in a LG lattice can be transformed into the atomic/molecular orbital symmetry in a non-LG lattice. We illustrate such orbital-designed topological FBs in three 2D non-LG, square, trigonal, and hexagonal lattices, where the designed orbitals faithfully reproduce the corresponding lattice symmetries of checkerboard, kagome, and diatomic-kagome lattices, respectively. Interestingly, systematic design of FBs with a high Chern number is also achieved based on the same principle. Fundamentally our theory enriches the FB physics; practically, it significantly expands the scope of FB materials, since most materials have multiple atomic/molecular orbitals at each lattice site, rather than a single s orbital mandated in graph theory and generic lattice models.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1981

Theory and applications of optimal control in aerospace systems

This AGARD graph addresses the advances effected in the theory and design of modern optimal guidance and control systems, in the following areas: Part I: Theory, Part II: Design Techniques, Part III: Applications and should provide an aid in the application of these modern techniques. This AGARD graph was prepared at the request of the Guidance and Control Panel of AGARD.

Pieter Kant↗
DOE OSTI2021

Non-Hermitian topological states in 2D line-graph lattices: evolving triple exceptional points on reciprocal line graphs

Non-Hermitian (NH) topological states, such as the doubly-degenerate nodes dubbed as exceptional points (EPs) in Bloch band structure of 2D lattices driven by gain and loss, have attracted much recent interest. We demonstrate theoretically that in the three-site edge-centered lattices, i.e. the so-called line-graph lattices, such as kagome lattice which is a line graph of hexagonal lattice, there exist three types of triply-degenerate EPs evolving intriguingly on another set of line graphs in the reciprocal space. A single TEP (STEP) with ±1/3 topological charge moves faithfully along the edges of reciprocal line graphs with varying gain and loss, while two STEPs merge distinctively into one unconventional orthogonal double TEP (DTEP) with ±2/3 charge at the vertices, which is characterized with two ordinary self-orthogonal eigenfunctions but one surprising 'orthogonal' eigenfunction. Differently, in a modified line-graph lattice with an off-edge-center site, the ordinary coalesced state of DTEPs emerges with three identical self-orthogonal eigenfunctions. Such NH states and their evolution can be generally realized in various artificial systems, such as photonic and sonic crystals, where light and sonic vortex beams with different fractional twisting can be found. Our findings shed new light on fundamental understanding of gapless topological states in NH systems in terms of creation and evolution of high-order EPs, and open up new research directions to further link line graph and flow network theory coupled with topological physics, especially under non-equilibrium gain/loss conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Recent developments in rotary-wing aerodynamic theory

Current progress in the computational analysis of rotary-wing flowfields is surveyed, and some typical results are presented in graphs. Topics examined include potential theory, rotating coordinate systems, lifting-surface theory (moving singularity, fixed wing, and rotary wing), panel methods (surface singularity representations, integral equations, and compressible flows), transonic theory (the small-disturbance equation), wake analysis (hovering rotor-wake models and transonic blade-vortex interaction), limitations on computational aerodynamics, and viscous-flow methods (dynamic-stall theories and lifting-line theory). It is suggested that the present algorithms and advanced computers make it possible to begin working toward the ultimate goal of turbulent Navier-Stokes calculations for an entire rotorcraft.

Johnson, W.↗
DOE OSTI2024

Holographic tensor networks with bulk gauge symmetries

Abstract Tensor networks are useful toy models for understanding the structure of entanglement in holographic states and reconstruction of bulk operators within the entanglement wedge. They are, however, constrained to only prepare so-called “fixed-area states” with flat entanglement spectra, limiting their utility in understanding general features of holographic entanglement. Here, we overcome this limitation by constructing a variant of random tensor networks that enjoys bulk gauge symmetries. Our model includes a gauge theory on a general graph, whose gauge-invariant states are fed into a random tensor network. We show that the model satisfies the quantum-corrected Ryu-Takayanagi formula with a nontrivial area operator living in the center of a gauge-invariant algebra. We also demonstrate nontrivial,n-dependent contributions to the Rényi entropy and Rényi mutual information from this area operator, a feature shared by general holographic states.

Physics↗
NASA NTRS2009

Necessary and Sufficient Conditions for Attitude Estimation in Fractionated Spacecraft Systems

This paper addresses the problem of attitude estimation in fractionated spacecraft clusters. Each module in the cluster may have either a star-tracker, a relative attitude sensor, or both. Using results in nonlinear ob- servability theory, we provide graph-theoretic sufficient conditions for the attitude of every module to be observable. In particular we show that the attitude of every module in the cluster can be observed if every module has either a star tracker with non-collinear stars, or there is a path through the sensing network from a module with a star tracker to the module without a star tracker, and each of the relative measurements along the path has either multiple non-collinear beacons or a single beacon that is not parallel to the rotation vector of the target module.

Blackmore, Lars↗
DOE OSTI2020

Thermochemical Data Fusion Using Graph Representation Learning

Large databases are required for “Big Data” applications in catalysis and materials science. Thermochemical databases can be created by combining data from various sources and by correcting low-fidelity datasets to higher accuracy with minimal computation. To achieve this “data fusion”, thermochemical quantities of interest, calculated at various levels of density functional theory (DFT), need to be mapped to the same, high levels of theory. In this work, a graph theoretical, statistical framework is proposed for such tasks. Subgraph frequencies are shown to provide a natural representation for learning these fusion maps. The maps are linear and are learnt with automated descriptor selection. Using a dataset of as few as ~1% from the QM9 database of 133,885 molecules, these models can predict multiple thermochemical quantities at a higher level of theory with an accuracy of 1 kcal/mol. Here, the method is explainable, generalizable, and provides a diagnostic tool for outlier identification

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Cluster bootstrap for cosmological correlators

We show that cosmological wavefunction coefficients associated with n-site chain and loop graphs for a cubic scalar theory in de Sitter spacetime have symbol alphabets given by subsets of A 2n−2 and B 2n−1 cluster variables, respectively, and satisfy the associated cluster adjacency properties. The key step in proving this is identifying a precise connection between graph “tubings” that appear in the kinematic flow equation and polygon “triangulations” that encode the combinatorics of cluster compatibility. Our results imply that cosmological wavefunction coefficients in a general power-law FRW cosmology satisfy cluster adjacency to all orders in the ϵ expansion around the de Sitter limit. We use this information as bootstrap input to show that de Sitter symbols for n ≤ 4 are uniquely determined by simple physical constraints.

differential and algebraic geometry↗
DOE OSTI2020

Building bases of loop integrands

We describe a systematic approach to the construction of loop-integrand bases at arbitrary loop-order, sufficient for the representation of general quantum field theories. We provide a graph-theoretic definition of ‘power-counting’ for multi-loop integrands beyond the planar limit, and show how this can be used to organize bases according to ultraviolet behavior. This allows amplitude integrands to be constructed iteratively. We illustrate these ideas with concrete applications. In particular, we describe complete integrand bases at two loops sufficient to represent arbitrary-multiplicity amplitudes in four (or fewer) dimensions in any massless quantum field theory with the ultraviolet behavior of the Standard Model or better. We also comment on possible extensions of our framework to arbitrary (including regulated) numbers of dimensions, and to theories with arbitrary mass spectra and charges. At three loops, we describe a basis sufficient to capture all ‘leading-(transcendental-)weight’ contributions of any four-dimensional quantum theory; for maximally supersymmetric Yang-Mills theory, this basis should be sufficient to represent all scattering amplitude integrands in the theory — for generic helicities and arbitrary multiplicity.

1/NExpansion↗
DOE OSTI2024

Dimer piling problems and interacting field theory

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large- N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS1965

Notes on System Theory, Volume VII

System theory - matrices, feedback control system, network synthesis, set theory, stability, shift registers, coding, theorem proving, polynomial roots, channels, and signal flow graphs

FEEDBACK CONTROL SYSTEM↗
DOE OSTI2020

Almost-Rigidity of Frameworks

Here, we extend the mathematical theory of rigidity of frameworks (graphs embedded in d-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes continuously it must remain inside a small ball, a property we call “almost-rigidity”; (II) any other framework with the same edge lengths must lie outside a much larger ball; (III) if the framework deforms by some given amount, its edge lengths change by a minimum amount; (IV) there is a nearby framework that is prestress stable, and thus rigid. The conditions can be tested efficiently using semidefinite programming. The test is a slight extension of the test for prestress stability of a framework, and gives analytic expressions for the radii of the balls and the edge length changes. Examples illustrate how the theory may be applied in practice, and we provide an algorithm to test for rigidity or almost-rigidity. We briefly discuss how the theory may be applied to tensegrities. © 2020 Wiley Periodicals LLC.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Roles of initial condition and vortex pairing in jet noise

Sound generation by vortex pairing in circular and elliptic cold-air jets at Mach 0.15-0.35 is investigated experimentally, with a focus on the effects of initial conditions. The results are presented in graphs and interpreted using the theory of vortex sound proposed by Moehring (1978) and vortex-filament models of jet coherent structure. Tripping the nozzle boundary layer is shown to (1) preempt formation of shear-layer vortices, (2) remove the sound they produce in later pairing, and (3) increase the diffusion of coherent vorticity in the vortex rings. Hence pairing noise should not be significant in practical jets, which are initially turbulent.

Bridges, J. E.↗
DOE OSTI2022

Graph identification of proteins in tomograms ( GRIP‐Tomo )

Abstract In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three‐dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo‐multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single‐domain protein native topologies as well as distinct single‐domain proteins from multimeric complexes within noisy volumes.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Hidden zeros of the cosmological wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr(ϕ 3 ) amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

Cosmological models↗