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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Programmable hyperbolic polaritons in van der Waals semiconductors

Lighting a route for hyperbolic dispersion The propagation of light within a material is usually well defined, with the propagation described by scattering and dispersion. In artificially designed metamaterials and in anisotropic layered materials, the dispersion can be hyperbolic, giving rise to subwavelength confinement of the light. Sternbach et al. show that the hyperbolic dispersion can be optically switched on and off on demand in the layered transition metal dichalcogenide tungsten diselenide (see the Perspective by Deng and Chen). Illuminating the material with ultrafast pulses of sub-bandgap light creates a transient waveguide, resulting in hyperbolic dispersion in the material. The ability to tune the dispersion characteristics on demand using optical pumping is an effective approach for developing ultrafast switching photonic devices and controlling the propagation of light on the nanoscale. Science , this issue p. 617 ; see also p. 572

Science & Technology - Other Topics↗
NASA NTRS1996

Output Tracking for Systems with Non-Hyperbolic and Near Non-Hyperbolic Internal Dynamics: Helicopter Hover Control

A technique to achieve output tracking for nonminimum phase linear systems with non-hyperbolic and near non-hyperbolic internal dynamics is presented. This approach integrates stable inversion techniques, that achieve exact-tracking, with approximation techniques, that modify the internal dynamics to achieve desirable performance. Such modification of the internal dynamics is used (1) to remove non-hyperbolicity which an obstruction to applying stable inversion techniques and (2) to reduce large pre-actuation time needed to apply stable inversion for near non-hyperbolic cases. The method is applied to an example helicopter hover control problem with near non-hyperbolic internal dynamic for illustrating the trade-off between exact tracking and reduction of pre-actuation time.

Devasia, Santosh↗
DOE OSTI2020

Quantum simulation of hyperbolic space with circuit quantum electrodynamics: From graphs to geometry

We show how quantum many-body systems on hyperbolic lattices with nearest-neighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. Here, the underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a table-top quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincaré disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs in the future. Importantly, our analysis reveals that even relatively small discrete hyperbolic lattices emulate the continuous geometry of negatively curved space, and thus can be used to experimentally resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Crystallography of hyperbolic lattices

Hyperbolic lattices are a revolutionary platform for tabletop simulations of holography and quantum physics in curved space and facilitate efficient quantum error correcting codes. Their underlying geometry is non-Euclidean, and the absence of Bloch's theorem precludes the straightforward application of the often indispensable energy band theory to study model Hamiltonians on hyperbolic lattices. Motivated by recent insights into hyperbolic band theory, we initiate a crystallography of hyperbolic lattices. Here we show that many hyperbolic lattices feature a hidden crystal structure characterized by unit cells, hyperbolic Bravais lattices, and associated symmetry groups. Using the mathematical framework of higher-genus Riemann surfaces and Fuchsian groups, we derive a list of example hyperbolic {p,q} lattices and their hyperbolic Bravais lattices, including five infinite families and several graphs relevant for experiments in circuit quantum electrodynamics and topolectrical circuits. This dramatically simplifies the computation of energy spectra of tight-binding Hamiltonians on hyperbolic lattices, from exact diagonalization on the graph to solving a finite set of equations in terms of irreducible representations. The significance of this achievement needs to be compared to the all-important role played by conventional Euclidean crystallography in the study of solids. We exemplify the high potential of this approach by constructing and diagonalizing finite-dimensional Bloch wave Hamiltonians.

2-dimensional systems↗
DOE OSTI2023

A Unification Framework for Euclidean and Hyperbolic Graph Neural Networks

Hyperbolic neural networks have recently gained significant attention due to their promising results on several graph problems including node classification and link prediction. The primary reason for this success is the effectiveness of hyperbolic space in capturing the inherent hierarchy of graph datasets. However, they are limited in terms of generalization, scalability, and have inferior performance when applied to non-hierarchical datasets. In this paper, we take a completely different perspective for modeling hyperbolic networks and answer the following question: is an Euclidean model able to approximate a function or behavior in the hyperbolic space? Extending the universal approximation theory developed for Euclidean models, We draw an analogy from the hyperbolic components to the Euclidean counterparts and conclude that, in order to capture hierarchical features, it is possible to generalize hyperbolic models to be a special case of Euclidean models with the proposed Pseudo-Poincaré technique. We applied our non-linear hyperbolic normalization to the current state-of-the-art homogeneous and multi-relational graph networks and demonstrate significant improvements in performance compared to both Euclidean and hyperbolic counterparts. The primary impact of this work lies in its ability to capture hierarchical features in the Euclidean space, and thus, can replace hyperbolic networks without any loss in performance metrics while simultaneously leveraging the power of Euclidean networks such as interpretability and efficient execution of various model components.

Khatir, Mehrdad↗
DOE OSTI2022

Tunable, Homoepitaxial Hyperbolic Metamaterials Enabled by High Mobility CdO

We report propagating light exhibits hyperbolicity in strongly anisotropic materials where the principal components of the dielectric tensor are opposite in sign. While hyperbolicity occurs naturally in anisotropic polar dielectrics, wherein optical phonons along orthogonal crystal axes are nondegenerate, such optical anisotropy can also be engineered in hyperbolic metamaterials (HMMs): thin film superlattices of alternating dielectric and metallic layers. Contrasted with the severely limited tunability of natural hyperbolic materials, the hyperbolic behavior of HMMs can be tailored significantly both through superlattice design and material selection. However, so far HMMs have suffered from high optical losses, hindering their performance. In this report, broadly tunable (λ = 2–5 µm) Type I and II hyperbolic modes with low losses (quality (Q)-factors up to 19.7) are observed through attenuated total reflectance measurements of monolithic, homoepitaxial superlattices of high- and low-doped cadmium oxide (CdO). Further, the low losses offered by CdO enable the first demonstration of real-space imaging of hyperbolic plasmon polaritons in nanoresonators by scattering-type scanning near-field optical microscopy—previously only possible for hyperbolic phonon polariton materials. Tunable, low-loss CdO HMMs promise designability for applications such as on-chip photonics, super-resolution imaging (hyperlensing), enhanced emission, novel emitter designs, and possibly quantum nanophotonic and time variant metasurfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Dual Optical Hyperbolicity of PdCoO 2 and PdCrO 2 Delafossite Single Crystals

Hyperbolic materials exhibit a very peculiar optical anisotropy with simultaneously different signs of the dielectric tensor components. This anisotropy allows the propagation of exotic surface-wave excitations like hyperbolic phonons and plasmon polaritons. While hyperbolic materials hold promise for applications in subwavelength photonics and enhanced light-matter interactions, their natural occurrence is limited to a few materials, often accompanied by significant dielectric losses and limited hyperbolic spectral bandwidth. Focusing on PdCoO 2 and PdCrO 2 delafossite transition-metal oxides, in this paper unique dual hyperbolic regimes are demonstrated:: one localized around a phonon absorption in the mid-infrared spectral region, and the other extending into the visible range. Both hyperbolic regimes show exceptional properties including low dissipation and high hyperbolic quality factors. These results pave the way for innovative applications of delafossite layered metals in subwavelength photonics, imaging, and sensing.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Machine Learning Moment Closure Models for the Radiative Transfer Equation III: Enforcing Hyperbolicity and Physical Characteristic Speeds

This is the third paper in a series in which we develop machine learning (ML) moment closure models for the radiative transfer equation. In our previous work (Huang et al. in J Comput Phys 453:110941, 2022), we proposed an approach to learn the gradient of the unclosed high order moment, which performs much better than learning the moment itself and the conventional $P_N$ closure. However, while the ML moment closure has better accuracy, it is not able to guarantee hyperbolicity and has issues with long time stability. In our second paper (Huang et al., in: Machine learning moment closure models for the radiative transfer equation II: enforcing global hyperbolicity in gradient based closures, 2021. arXiv:2105.14410), we identified a symmetrizer which leads to conditions that enforce that the gradient based ML closure is symmetrizable hyperbolic and stable over long time. The limitation of this approach is that in practice the highest moment can only be related to four, or fewer, lower moments. In this paper, we propose a new method to enforce the hyperbolicity of the ML closure model. Motivated by the observation that the coefficient matrix of the closure system is a lower Hessenberg matrix, we relate its eigenvalues to the roots of an associated polynomial. Here, we design two new neural network architectures based on this relation. The ML closure model resulting from the first neural network is weakly hyperbolic and guarantees the physical characteristic speeds, i.e., the eigenvalues are bounded by the speed of light. The second model is strictly hyperbolic and does not guarantee the boundedness of the eigenvalues. Several benchmark tests including the Gaussian source problem and the two-material problem show the good accuracy, stability and generalizability of our hyperbolic ML closure model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Possible Realization of Hyperbolic Plasmons in Few-Layered Rhenium Disulfide

Hyperbolic plasmons are a highly desired property in optoelectronics and biomolecular sensing. The necessary condition to realize hyperbolic plasmons is a significant anisotropy of the principal components of the dielectric function, such that at a certain frequency range, one component is negative and the other is positive, i.e., one component is metallic, and the other one is dielectric. Here, we study the effect of anisotropy in ReS 2 , and our theory shows that ReS 2 can host hyperbolic plasmons in the ultraviolet frequency range. The operating frequency range of the hyperbolic plasmons can be tuned with the number of ReS 2 layers. However, we note that the significantly large imaginary part of the macroscopic dielectric response in all layered variants of ReS 2 can result in substantial losses for the hyperbolic plasmons, as in the case with other known hyperbolic materials, with the exception of MoOCl 2 . We also note that ReS 2 hosts ultraviolet hyperbolic plasmons while ZrSiSe, WTe 2 , and CuS nanocrystals host infrared plasmons, providing a novel platform for optoelectronics in the ultraviolet range.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Parallel-in-Time Multigrid Methods for Hyperbolic Problems, with a Focus on the Shallow Water Equations

The coming massive parallelism of exascale computing presents a pressing challenge for the many DOE simulations of time-dependent partial differential equations, which typically use traditional sequential time stepping methods. Since this traditional approach is inherently serial, it presents a sequential bottleneck when moving to exascale computing, because future performance gains will come through greater concurrency, not faster clock speeds. Thus, the goal of this work is to research parallelism in time, i.e., methods that compute multiple time values simultaneously, not sequentially. The focus will be on hyperbolic problems of programmatic interest to DOE, with the goal of enabling scalable simulations of time-dependent hyperbolic problems on future architectures. The difficulty lies in the fact that hyperbolic problems are well-known to be difficult for parallel-in-time methods, with the most common parallel-in-time method, Parareal, diverging in many cases. Here, the chosen methodology for scalably solving these hyperbolic space-time equations is multigrid-reductionin-time (MGRIT), because multigrid (when it works) is a powerful, optimal, and scalable solver for discretized PDEs. To further research in this area, this project will explore a model hyperbolic problem (the shallow water equations) in the context of recent advances (e.g., by Wingate and Haut) in constructing improved coarse time-grid time-propagators by using the slow asymptotic structure of the equations. In particular, we will investigate if such coarse time-propagators offer significant advantages in an MGRIT setting, and explore any broader insights gained into parallel-in-time for hyperbolic problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Parallel-in-Time Integration for Nonlinear Hyperbolic Problems (Final Report)

The work for the subcontract was situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. Over the past two decades, much progress has been made in this area; however, this progress has largely been limited to diffusion-dominated PDEs, with some recent success in scalar linear hyperbolic PDEs. Given the ubiquity of numerical simulations of hyperbolic PDEs throughout the sciences, in particular, nonlinear hyperbolic systems, there is a strong need to develop efficient parallel-in-time techniques for hyperbolic problems beyond simple scalar and linear cases, which is the main topic of this subcontract. The main focus of the work was to further develop and perfect coarse-grid operators for the Multigrid Reduction-inTime (MGRIT) method applied to hyperbolic PDEs that were recently proposed in PhD thesis, based on a modified semi-Lagrangian approach.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Circuit Quantum Electrodynamics in Hyperbolic Space: From Photon Bound States to Frustrated Spin Models

Circuit quantum electrodynamics is one of the most promising platforms for efficient quantum simulation and computation. In recent groundbreaking experiments, the immense flexibility of superconducting microwave resonators was utilized to realize hyperbolic lattices that emulate quantum physics in negatively curved space. Here we investigate experimentally feasible settings in which a few superconducting qubits are coupled to a bath of photons evolving on the hyperbolic lattice. We compare our numerical results for finite lattices with analytical results for continuous hyperbolic space on the Poincaré disk. We find good agreement between the two descriptions in the long-wavelength regime. We show that photon-qubit bound states have a curvature-limited size. We propose to use a qubit as a local probe of the hyperbolic bath, for example, by measuring the relaxation dynamics of the qubit. We find that, although the boundary effects strongly impact the photonic density of states, the spectral density is well described by the continuum theory. We show that interactions between qubits are mediated by photons propagating along geodesics. We demonstrate that the photonic bath can give rise to geometrically frustrated hyperbolic quantum spin models with finite-range or exponentially decaying interaction.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

Parallel-in-Time Methods for Method-of-Lines Discretizations of Nonlinear Hyperbolic PDEs and Systems (Final Report)

The work for the subcontract is situated in the area of parallel-in-time integration for hyperbolic partial differential equations (PDEs). Parallel-in-time integration is an active area of research due to its ability to enable faster numerical simulations for applications throughout many areas of science. The work in this subcontract builds on a variety of results that were obtained, as part of the work performed for Subcontract No. B648355, for the Multigrid Reduction-in-Time (MGRIT) method from [1] applied to hyperbolic PDEs. This subcontract extends these results further to more efficient methods and to the case of method-of-lines discretizations for nonlinear hyperbolic PDES and systems of PDEs. The following is a summary of the research performed and results achieved during milestone periods 1, 2 and 3 by the PI (Hans De Sterck) and Postdoctoral Research Associate (Oliver Krzysik), for required tasks 1-4 (as listed in the Statement of Work): Research over the previous year has been split into three main projects: (i) solution of acoustic equation system; (ii) solution of nonlinear scalar hyperbolic PDEs; (iii) solution of nonlinear hyperbolic systems of PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Off-axis representation of hyperbolic mirror shapes for X-ray beamlines

Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

TiN‐Au/HfO 2 ‐Au Multilayer Thin Films with Tunable Hyperbolic Optical Response

Abstract Hyperbolic metamaterials (HMM) possess significant anisotropic physical properties and tunability and thus find many applications in integrated photonic devices. HMMs consisting of metal and dielectric phases in either multilayer or vertically aligned nanocomposites (VAN) form are demonstrated with different hyperbolic properties. Herein, self‐assembled HfO 2 ‐Au/TiN‐Au multilayer thin films, combining both the multilayer and VAN designs, are demonstrated. Specifically, Au nanopillars embedded in HfO 2 and TiN layers forming the alternative layers of HfO 2 ‐Au VAN and TiN‐Au VAN. The HfO 2 and TiN layer thickness is carefully controlled by varying laser pulses during pulsed laser deposition (PLD). Interestingly, tunable anisotropic physical properties can be achieved by adjusting the bi‐layer thickness and the number of the bi‐layers. Type II optical hyperbolic dispersion can be obtained from high layer thickness structure (e.g., 20 nm), while it can be transformed into Type I optical hyperbolic dispersion by reducing the thickness to a proper value (e.g., 4 nm). This new nanoscale hybrid metamaterial structure with the three‐phase VAN design shows great potential for tailorable optical components in future integrated devices.

Chemistry↗