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All sources NASA NTRS DOE OSTI

DOE OSTI2020

Optical analogues to the equatorial Kerr–Newman black hole

Optical analogues to black holes allow the investigation of general relativity in a laboratory setting. Previous works have considered analogues to Schwarzschild black holes in an isotropic coordinate system; the major drawback is that required material properties diverge at the horizon. We present the dielectric permittivity and permeability tensors that exactly reproduce the equatorial Kerr–Newman metric, as well as the gradient-index material that reproduces equatorial Kerr–Newman null geodesics. Importantly, the radial profile of the scalar refractive index is finite along all trajectories except at the point of rotation reversal for counter-rotating geodesics. Construction of these analogues is feasible with available ordinary materials. A finite-difference frequency-domain solver of Maxwell’s equations is used to simulate light trajectories around a variety of Kerr–Newman black holes. For reasonably sized experimental systems, ray tracing confirms that null geodesics can be well-approximated in the lab, even when allowing for imperfect construction and experimental error.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Path-Based Dictionary Augmentation: A Framework for Improving $k$ -Sparse Image Processing

In this study, we have previously shown that augmenting orthogonal matching pursuit (OMP) with an additional step in the identification stage of each pursuit iteration yields improved $k$ -sparse reconstruction and denoising performance relative to baseline OMP. At each iteration a “path” or geodesic, is generated between the two dictionary atoms that are most correlated with the residual and from this path a new atom that has a greater correlation to the residual than either of the two bracketing atoms is selected. Here, we provide new computational results illustrating improvements in sparse coding and denoising on canonical datasets using both learned and structured dictionaries. The two methods of constructing a path are investigated for each dictionary type: the Euclidean geodesic formed by a linear combination of the two atoms and the 2-Wasserstein geodesic corresponding to the optimal transport map between the atoms. We prove here the existence of a higher-correlation atom in the Euclidean case under assumptions on the two bracketing atoms and introduce algorithmic modifications to improve the likelihood that the bracketing atoms meet those conditions. Although, we demonstrate our augmentation on OMP alone, in general it may be applied to any reconstruction algorithm that relies on the selection and sorting of high-similarity atoms during an analysis or identification phase.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Feasibility investigation of integrated optics Fourier transform devices

The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.

Verber, C. M.↗

NASA NTRS1993

Design and evaluation of a foam-filled hat-stiffened panel concept for aircraft primary structural applications

Geodesically stiffened structures are very efficient in carrying combined bending, torsion, and pressure loading that is typical of primary aircraft structures. They are also very damage tolerant since there are multiple load paths available to redistribute loads compared to prismatically stiffened structures. Geodesically stiffened structures utilize continuous filament composite materials which make them amenable to automated manufacturing processes to reduce cost. The current practice for geodesically stiffened structures is to use a solid blade construction for the stiffener. This stiffener configuration is not an efficient concept and there is a need to identify other stiffener configurations that are more efficient but utilize the same manufacturing process as the solid blade. This paper describes a foam-filled stiffener cross section that is more efficient than a solid-blade stiffener in the load range corresponding to primary aircraft structures. A prismatic hat-stiffener panel design is then selected for structural evaluation in uni-axial compression with and without impact damage. Experimental results for both single stiffener specimens and multi-stiffener panel specimens are presented. Finite element analysis results are presented that predict the buckling and postbuckling response of the test specimens. Analytical results for both the element and panel specimens are compared with experimental results.

Ambur, Damodar R.↗

DOE OSTI2025

Towards Full ‘Galilei General Relativity’: Gravitational Kinematics in Bargmann Spacetimes

Because of the strict separation of mass and energy in Galilei physics, a Galilei-invariant tensor formalism is most at home in a 5-dimensional extended spacetime associated with the Bargmann-Galilei (traditionally ‘Bargmann’) group, a central extension of the Galilei group that explicitly exhibits the transformation properties of kinetic energy. While not necessary for a tensor formalism fully embodying Poincaré physics, a similar central extension of the Poincaré group to the Bargmann-Poincaré group may illuminate a path towards a strong-field ‘Galilei general relativity’. Here the Bargmann metric is generalized to curved spacetime by extending the usual 1+3 (traditionally ‘3+1’) formalism of general relativity on 4-dimensional spacetime to a 1+3+1 formalism, whose spacetime kinematics is shown to be consistent with that of the usual 1+3 formalism. On Bargmann spacetime, tensor laws governing the motion of an elementary classical material particle and the dynamics of a simple fluid reference the foliation of spacetime in a manner that partially reverts the Einstein perspective (accelerated fiducial observers, and geodesic material particles and fluid elements) to a Newton-like perspective (geodesic fiducial observers, and accelerated material particles and fluid elements subject to a gravitational force).

Cardall, Christian [ORNL] (ORCID:000000020086105X)↗

DOE OSTI2022

Hyperbolic string vertices

The string vertices of closed string field theory are subsets of the moduli spaces of punctured Riemann surfaces that satisfy a geometric version of the Batalin-Vilkovisky master equation. We present a homological proof of existence of string vertices and their uniqueness up to canonical transformations. Using hyperbolic metrics on surfaces with geodesic boundaries we give an exact construction of string vertices as sets of surfaces with systole greater than or equal to L with L ≤ 2 arcsinh 1. Intrinsic hyperbolic collars prevent the appearance of short geodesics upon sewing. The surfaces generated by Feynman diagrams are naturally endowed with Thurston metrics: hyperbolic on the vertices and flat on the propagators. For the classical theory the length L is arbitrary and, as L → ∞hyperbolic vertices become the minimal-area vertices of closed string theory

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Quantum gravity fluctuations in the timelike Raychaudhuri equation

We consider a timelike geodesic congruence in the presence of perturbative quantum fluctuations of the spacetime metric. We calculate the change in the volume of a bundle of geodesics due to such fluctuations and thereby obtain a quantum-gravitationally modified timelike Raychaudhuri equation. Quantum gravity generically increases the convergence of congruences and the production of caustics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Quantum-gravitational null Raychaudhuri equation

Abstract We consider a congruence of null geodesics in the presence of a quantized spacetime metric. The coupling to a quantum metric induces fluctuations in the congruence; we calculate the change in the area of a pencil of geodesics induced by such fluctuations. For the gravitational field in its vacuum state, we find that quantum gravity contributes a correction to the null Raychaudhuri equation which is of the same sign as the classical terms. We thus derive a quantum-gravitational focusing theorem valid for linearized quantum gravity.

Physics↗

DOE OSTI2020

SO(3)-invariance of informed-graph-based deep neural network for anisotropic elastoplastic materials

This work examines the frame-invariance (and the lack thereof) exhibited in simulated anisotropic elasto-plastic responses generated from supervised machine learning of classical multi-layer and informed-graph-based neural networks, and proposes different remedies to fix this drawback. The inherent hierarchical relations among physical quantities and state variables in an elasto-plasticity model are first represented as informed, directed graphs, where three variations of the graph are tested. While feed-forward neural networks are used to train path-independent constitutive relations (e.g., elasticity), recurrent neural networks are used to replicate responses that depends on the deformation history, i.e. or path dependent. In dealing with the objectivity deficiency, we use the spectral form to represent tensors and, subsequently, three metrics, the Euclidean distance between the Euler Angles, the distance from the identity matrix, and geodesic on the unit sphere in Lie algebra, can be employed to constitute objective functions for the supervised machine learning. In this, the aim is to minimize the measured distance between the true and the predicted 3D rotation entities. Following this, we conduct numerical experiments on how these metrics, which are theoretically equivalent, may lead to differences in the efficiency of the supervised machine learning as well as the accuracy and robustness of the resultant models. Neural network models trained with tensors represented in component form for a given Cartesian coordinate system are used as a benchmark. Our numerical tests show that, even given the same amount of information and data, the quality of the anisotropic elasto-plasticity model is highly sensitive to the way tensors are represented and measured. The results reveal that using a loss function based on geodesic on the unit sphere in Lie algebra together with an informed, directed graph yield significantly more accurate rotation prediction than the other tested approaches.

42 ENGINEERING↗

DOE OSTI2025

Collisionless zonal-flow dynamics in quasisymmetric stellarators

The linear collisionless plasma response to a zonal-density perturbation in quasisymmetric stellarators is studied, including the geodesic-acoustic-mode oscillations and the Rosenbluth–Hinton residual flow. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become non-existent in quasi-helically symmetric configurations when the effective safety factor in helical-angle coordinates is small. Compared with concentric-circular tokamaks, the Rosenbluth–Hinton residual is also found to be multiplied by a geometric factor $\mathcal {C}$ that arises from the flux-surface-averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for $\mathcal {C}$ , which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the global gyrokinetic particle-in-cell code GTC, and good agreement with the theoretical Rosenbluth–Hinton residual level is achieved when the quasisymmetry error is small enough.

Zhu, Hongxuan (ORCID:0000000198446972)↗

DOE OSTI2020

Extended harmonic mapping connects the equations in classical, statistical, fluid, quantum physics and general relativity

Abstract One potential pathway to find an ultimate rule governing our universe is to hunt for a connection among the fundamental equations in physics. Recently, Ren et al. reported that the harmonic maps with potential introduced by Duan, named extended harmonic mapping (EHM), connect the equations of general relativity, chaos and quantum mechanics via a universal geodesic equation. The equation, expressed as Euler–Lagrange equations on the Riemannian manifold, was obtained from the principle of least action. Here, we further demonstrate that more than ten fundamental equations, including that of classical mechanics, fluid physics, statistical physics, astrophysics, quantum physics and general relativity, can be connected by the same universal geodesic equation. The connection sketches a family tree of the physics equations, and their intrinsic connections reflect an alternative ultimate rule of our universe, i.e. , the principle of least action on a Finsler manifold.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

The tortoise and the hare: a causality puzzle in AdS/CFT

Here, we pose and resolve a holographic puzzle regarding an apparent violation of causality in anti-de Sitter (AdS)/conformal field theory. If a point in the bulk of AdS moves at the speed of light, the boundary subregion that encodes it may need to move superluminally to keep up. With AdS 3 as our main example, we prove that the finite extent of the encoding regions prevents a paradox. We show that the length of the minimal-size encoding interval gives rise to a tortoise coordinate on AdS that measures the nonlocality of the encoding. We use this coordinate to explore circular and radial motion in the bulk before passing to the analysis of bulk null geodesics. For these null geodesics, there is always a critical encoding where the possible violation of causality is barely avoided. We show that in any other encoding, the possible violation is subcritical.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Expanding on the double copy in null Fermi coordinates

We propose a Weyl classical double copy for a Fermi normal coordinate expansion around null geodesics. To leading order in this ‘Penrose expansion’, we recover a previously proposed double copy of the Penrose limit. For spacetimes with an exact double copy, this Penrose limit double copy is extended to all orders. For spacetimes without such a double copy, generic obstructions appear at second subleading order beyond the Penrose limit. We thus argue that for any spacetime, near any null geodesic there is a classical double copy structure at least up to first subleading order in the Penrose expansion. Lastly, we point out a difficulty in identifying an appropriate flat space to extend our results to the Kerr–Schild double copy, related to the generic incompatibility between Kerr–Schild and Penrose–Güven gauge.

Chawla, Samarth [Arizona State University, Tempe, ↗

DOE OSTI2022

Plasma shape effects on the Alfvén eigenmode spectrum through Alfvén slow-magnetosonic wave coupling

In this report the effect of the plasma shaping (triangularity and elongation) on the continuous spectrum, frequency gaps, and number of eigenmodes is studied. The plasma shaping affects the coupling between Alfvén and slow magnetosonic waves via the geodesic magnetic curvature and the plasma pressure. The Alfvén-slow coupling creates a large number of new gaps in the continuous spectrum below the Alfvén frequency where discrete modes can reside. In ideal magnetohydrodynamic simulations a large number (a few hundred or more) of potential eigenmodes are found. The number of eigenmodes is correlated with the maximum geodesic curvature and a minimum number of possible discrete eigenmodes is found at a negative triangularity of -0.3. It is hypothesized that these possible eigenmodes form a low amplitude and dense discrete spectrum, which can be studied experimentally.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A classical, non-singular, bouncing universe

We present a model for a classical, non-singular bouncing cosmology without violation of the null energy condition (NEC). The field content is General Relativity plus a real scalar field with a canonical kinetic term and only renormalizable, polynomial-type self-interactions for the scalar field in the Jordan frame. The universe begins vacuum-energy dominated and is contracting at t=-∞. We consider a closed universe with a positive spatial curvature, which is responsible for the universe bouncing without any NEC violation. An Rφ 2 coupling between the Ricci scalar and the scalar field drives the scalar field from the initial false vacuum to the true vacuum during the bounce. The model is sub-Planckian throughout its evolution and every dimensionful parameter is below the effective-field-theory scale M P , so we expect no ghost-type or tachyonic instabilities. This model solves the horizon problem and extends co-moving particle geodesics to past infinity, resulting in a geodesically complete universe without singularities. We solve the Friedman equations and the scalar-field equation of motion numerically, and analytically under certain approximations.

Astronomy & Astrophysics↗

DOE OSTI2020

Quantum fields, geometric fluctuations, and the structure of spacetime

Quantum fluctuations of the vacuum stress-energy tensor are highly non-Gaussian, and can have unexpectedly large effects on spacetime geometry. In this paper, we study a two-dimensional dilaton gravity model coupled to a conformal field, in which the distribution of vacuum fluctuations is well understood. In this model, the fluctuations of the matter field are responsible for the fluctuations of the geometry itself. Here, by analyzing the geodesic deviation in this model, we show that a pencil of massive particles propagating on this fuzzy spacetime eventually converges and collapses. This is consistent with our earlier analysis of null geodesics in [Phys. Rev. Lett. 107, 021303 (2011)].

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Effective Field Theory for Extreme Mass Ratio Binaries

We derive an effective field theory describing a pair of gravitationally interacting point particles in an expansion in their mass ratio, also known as the self-force (SF) expansion. The 0SF dynamics are trivially obtained to all orders in Newton’s constant by the geodesic motion of the light body in a Schwarzschild background encoding the gravitational field of the heavy body. The corrections at 1SF and higher are generated by perturbations about this configuration—that is, the geodesic deviation of the light body and the fluctuation graviton—but crucially supplemented by an operator describing the recoil of the heavy body as it interacts with the smaller companion. Using this formalism we compute new results at third post-Minkowskian order for the conservative dynamics of a system of gravitationally interacting massive particles coupled to a set of additional scalar and vector fields.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Historic Submarine Landslides in the Northern Gulf of Mexico

This dataset provides a set of polygons representing the zone of depletion for historic submarine landslides (also referred to as mass transport deposits) within four regions of the US Exclusive Economic Zone in the northern Gulf of Mexico. Landslides were digitized by geologists and spatial scientists at the National Energy Technology Laboratory by visually interpreting landslide boundaries from a seismic-derived, high resolution bathymetric hillshade provided by the Bureau of Ocean and Energy Management (BOEM, 2017). A portion of the landslide features are derived from other spatial sources including the Seismic Water Anomalies dataset by BOEM (2016) as well as from McAdoo et al., 2000 and Twichell et al, 2005. The scale that landslides depletion areas can be interpreted at is limited by the spatial resolution of the gridded bathymetry, which is 12.192 meters (BOEM, 2017). For each landslide feature in the dataset, geometry metrics were calculated including geodesic area (km2) and geodesic perimeter (km) using the North America Albers Equal Area Conic projected coordinate system. The same geometry metrics were calculated for the four inventory regions.

DOE↗