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DOE OSTI2023

Real-space solution to the electronic structure problem for nearly a million electrons

We report a Kohn–Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20 nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix–vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh–Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Chemistry↗

DOE OSTI2022

Low-energy moiré phonons in twisted bilayer van der Waals heterostructures

We develop a low-energy continuum model for phonons in twisted moiré bilayers, based on a configuration-space approach. In this approach, interatomic force constants are obtained from density functional theory (DFT) calculations of untwisted bilayers with various in-plane shifts. This allows for efficient computation of phonon properties for any small twist angle, while maintaining DFT-level accuracy. Based on this framework, we show how the low-energy phonon modes, including interlayer shearing and layer-breathing modes, vary with the twist angle. As the twist angle decreases, the frequencies of the low-energy modes are reordered and the atomic displacement fields corresponding to phonon eigenmodes break translational symmetry, developing periodicity on the moiré length scale. Here, we demonstrate the capabilities of our model by calculating the phonon properties of three specific structures: bilayer graphene, bilayer molybdenum disulfide (MoS 2 ), and molybdenum diselenide-tungsten diselenide (MoSe 2 -WSe 2 ).

2-dimensional systems↗

DOE OSTI2022

Role of non-Gaussian quantum fluctuations in neutrino entanglement

The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams and obtain the exact phase space explored by this system using the Husimi quasiprobability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one- and two-neutrino entropy. In addition, we propose an approximate phase-space method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and time-dependent Hamiltonians in the nonadiabatic regime.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2024

Phase-space methods for neutrino oscillations: Extension to multibeams

The phase-space approach (PSA), which was originally introduced in Lacroix [] to describe neutrino flavor oscillations for interacting neutrinos emitted from stellar objects is extended to describe arbitrary numbers of neutrino beams. The PSA is based on mapping the quantum fluctuations into a statistical treatment by sampling initial conditions followed by independent mean-field evolution. A new method is proposed to perform this sampling that allows treating an arbitrary number of neutrinos in each neutrino beams. We validate the technique successfully and confirm its predictive power on several examples where a reference exact calculation is possible. We show that it can describe many-body effects, such as entanglement and dissipation induced by the interaction between neutrinos. Due to the complexity of the problem, exact solutions can only be calculated for rather limited cases, with a limited number of beams and/or neutrinos in each beam. The PSA approach considerably reduces the numerical cost and provides an efficient technique to accurately simulate arbitrary numbers of beams. Examples of PSA results are given here, including up to 200 beams with time-independent or time-dependent Hamiltonians. We anticipate that this approach will be useful to bridge exact microscopic techniques with more traditional transport theories used in neutrino oscillations. It will also provide important reference calculations for future quantum computer applications where other techniques are not applicable to classical computers. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Lorentzian OPE inversion formula: A geometric perspective

We give a new perspective on the Lorentzian operator product expansion inversion formula [S. Caron-Huot, Analyticity in spin in conformal theories, .; D. Simmons-Duffin, D. Stanford, and E. Witten, A spacetime derivation of the Lorentzian OPE inversion formula, .], building on [P. Agarwal , companion paper, Embedding space approach to Lorentzian CFT amplitudes and causal spherical functions, .]. We introduce an “auxiliary” fourpoint function that can be related to the traditionally defined ones via a Radon transform. The Mellin amplitudes associated with this auxiliary function can be shown to be equivalent to the conventional partial wave amplitudes. This has the intuitive geometrical meaning of a generalization of the projection-slice theorem. Published by the American Physical Society 2025

Agarwal, Pulkit (ORCID:0000000346581691)↗

DOE OSTI2025

Topological Phenomena in Artificial Quantum Materials Revealed by Local Chern Markers

A striking example of frustration in physics is Hofstadter’s butterfly, a fractal structure that emerges from the competition between a crystal’s lattice periodicity and the magnetic length of an applied field. Current methods for predicting the topological invariants associated with Hofstadter’s butterfly are challenging or impossible to apply to a range of materials, including those that are disordered or lack a bulk spectral gap. Here, in this work, we demonstrate a framework for predicting a material’s local Chern markers using its position-space description and validate it against experimental observations of quantum transport in artificial graphene in a semiconductor heterostructure, inherently accounting for fabrication disorder strong enough to close the bulk spectral gap. By resolving local changes in the system’s topology, we reveal the topological origins of antidot-localized states that appear in artificial graphene in the presence of a magnetic field. Moreover, we show the breadth of this framework by simulating how Hofstadter’s butterfly emerges from an initially unpatterned 2D electron gas as the system’s potential strength is increased and predict that artificial graphene becomes a topological insulator at the critical magnetic field. Overall, we anticipate that a position-space approach to determine a material’s Chern invariant without requiring prior knowledge of its occupied states or bulk spectral gaps will enable a broad array of fundamental inquiries and provide a novel route to material discovery, especially in metallic, aperiodic, and disordered systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Skyrme–Hartree–Fock–Bogoliubov mass models on a 3D mesh: IIb. Fission properties of BSkG2

Large-scale models of nuclear structure are currently the only way to provide consistent datasets for the many properties of thousands of exotic nuclei that are required by nucleosynthesis simulations. In [W. Ryssens et al., Eur. Phys. J. A 58, 246 (2022)], we recently presented the new BSkG2 model based on an energy density functional of the Skyrme type. Relying on a flexible three-dimensional coordinate representation of the nucleus, the model takes into account both triaxial deformation and time-reversal symmetry breaking. BSkG2 achieves a state-of-the-art global description of nuclear ground state (g.s.) properties and reproduces in particular the known masses with a root-mean-square (rms) deviation of 678 keV. Moving beyond g.s. properties, the model also reproduces all empirical values for the primary and secondary barriers as well as isomer excitation energies of actinide nuclei with rms deviations below 500 keV, i.e. with unprecedented accuracy. Here we discuss in detail the extension of our framework to the calculation of the fission barriers of 45 actinide nuclei, including odd-mass and odd-odd systems. We focus in particular on the impact of symmetry breaking which is key to the accuracy of the model: we allow systematically for axial, reflection and time-reversal symmetry breaking. The effect of the latter on the fission properties of odd-mass and odd-odd nuclei is small, but we find that allowing for shapes with triaxial or octupole deformation, as well as shapes with both, is crucial to achieving this accuracy. Here, the numerical accuracy of our coordinate space approach, the variety of nuclear configurations explored and the simultaneous successful description of fission properties and known masses makes BSkG2 the tool of choice for the large-scale study of nuclear structure.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Duality and form factors in the thermally deformed two-dimensional tricritical Ising model

The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional E_7 E 7 Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , in either phase are accompanied by associated disorder operators, \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) . Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For \sigma(x) σ ( x ) and \sigma'(x) σ ′ ( x ) , the equations are identical in form and are parameterised by the values of the one-particle form factors of the two lightest \mathbb{Z}_2 ℤ 2 odd particles. Similarly, the equations for \mu(x) μ ( x ) and \mu'(x) μ ′ ( x ) have identical form and are parameterised by two elementary form factors. Using the clustering property, we show that these four sets of solutions are eventually not independent; instead, the parameters of the solutions for \sigma(x)/\sigma'(x) σ ( x ) / σ ′ ( x ) are fixed in terms of those for \mu(x)/\mu'(x) μ ( x ) / μ ′ ( x ) . We use the truncated conformal space approach to confirm numerically the derived expressions of the matrix elements as well as the validity of the \Delta Δ -sum rule as applied to the off-critical correlators. We employ the derived form factors of the order and disorder operators to compute the exact dynamical structure factors of the theory, a set of quantities with a rich spectroscopy which may be directly tested in future inelastic neutron or Raman scattering experiments.

Cortes Cubero, Axel↗

DOE OSTI2022

Role of non-gaussian quantum fluctuations in neutrino entanglement

The flavor evolution of neutrinos in environments with large neutrino number densities is an open problem at the nexus of astrophysics and neutrino flavor physics. Among the many unanswered questions pertaining to this problem, it remains to be determined whether neutrino-neutrino coherent scattering can give rise to nontrivial quantum entanglement among neutrinos, and whether this can affect the flavor evolution in a meaningful way. To gain further insight into this question, here we study a simple system of two interacting neutrino beams, and obtain the exact phase-space explored by this system using the Husimi quasi-probability distribution. We observe that the entanglement induced by the coupling leads to strong delocalization in phase-space with largely non-Gaussian quantum fluctuations. The link between the neutrino entanglement and quantum fluctuations is illustrated using the one- and two-neutrino entropy. In addition, we propose an approximate phase-space method to describe the interacting neutrinos problem, where the exact evolution is replaced by a set of independent mean-field evolutions with a statistical sampling of the initial conditions. The phase-space approach provides a simple and accurate method to describe the gross features of the neutrino entanglement problem. Applications are shown using time-independent and time-dependent Hamiltonians in the non-adiabatic regime.

Patwardhan, Amol↗

NASA NTRS1972

High intensity solar cell radiometer

Device can be employed under high intensity illumination conditions such as would occur in a close-solar-approach space mission or in monitoring high intensity lamps. Radiometer consists of silicon solar cells with thin semi-transparent coatings of aluminum deposited on the front surfaces to permit transmission of small percentage of light and reflect the remainder.

Brandhorst, H. W.↗

NASA NTRS1981

On various treatments of potential equations at shocks

The potential equation that governs transonic inviscid flowfields is elliptic in subsonic regions and hyperbolic in supersonic regions. The transition from supersonic to subsonic flow may occur either continuously or across a surface of discontinuity known as a shock. Because of the changing type of governing equation and the presence of the surfaces of discontinuity, special treatments of the governing equations are needed at shocks to preserve mass conservation and to ensure satisfaction of the governing equation. In the so-called shock-capturing techniques, shocks are captured by smearing the discontinuity over several mesh cells in the computational domain. Most existing conservative schemes conserve mass flux throughout the flowfield, including shock boundaries; however, they also introduce zero-order errors in the approximation to the governing equation. It is shown that the zero-order errors, which do not diminish as the mesh spacing approaches zero, can cause discrepancies in the prediction of shock strength and location. These parameters are extremely sensitive features of transonic inviscid flowfield calculations. It is also shown that the zero-order errors can be avoided by developing higher-order schemes that properly model the governing equation at shocks.

Chen, L. T.↗

NASA NTRS1981

Modeling of the aircraft in-trail-following task during profile descent

The cockpit display of traffic information (CDTI) system concepts enable the pilot to observe the surrounding air traffic pattern. The impact of such a system is far reaching in terms of improved safety, pilot and controller workload, and aircraft fuel efficiency. One direct payoff is the ability to distribute the ATC workload to the pilot in such tasks as merging and spacing. The CDTI application of spacing approach aircraft in the terminal area is addressed. In-trail-following/CDTI experiments were performed using realistic cockpit simulators and profile descent approach scenarios. Based on collected experimental simulator data, pilot models were developed which include state estimation, decision making and flight control aspects. These models were coupled with models of aircraft and CDTI equipment to study the dynamic phenomena and stability of strings of aircraft along various approach patterns.

Goka, T.↗

NASA NTRS1986

Modeling, estimation and identification methods for static shape determination of flexible structures

This paper outlines methods for modeling, identification and estimation for static determination of flexible structures. The shape estimation schemes are based on structural models specified by (possibly interconnected) elliptic partial differential equations. The identification techniques provide approximate knowledge of parameters in elliptic systems. The techniques are based on the method of maximum-likelihood that finds parameter values such that the likelihood functional associated with the system model is maximized. The estimation methods are obtained by means of a function-space approach that seeks to obtain the conditional mean of the state given the data and a white noise characterization of model errors. The solutions are obtained in a batch-processing mode in which all the data is processed simultaneously. After methods for computing the optimal estimates are developed, an analysis of the second-order statistics of the estimates and of the related estimation error is conducted. In addition to outlining the above theoretical results, the paper presents typical flexible structure simulations illustrating performance of the shape determination methods.

Rodriguez, G.↗

NASA NTRS1987

Potential surfaces for O atom-polymer reactions

Ab initio quantum chemistry methods are used to study the energetics of interactions of O atoms with organic compounds. Polyethylene (CH2)n has been chosen as the model system to study the interactions of O(3P) and O(1D) atoms with polymers. In particular, H abstraction is investigated and polyethylene is represented by a C3 (propane) oligomeric model. The gradient method, as implemented in the GRADSCF package of programs, is used to determine the geometries and energies of products and reactants. The saddle point, barrier geometry is determined by minimizing the squares of the gradients of the potential with respect to the internal coordinates. To correctly describe the change in bonding during the reaction at least a two configuration MCSCF (multiconfiguration self consistent field) or GVB (generalized valence bond) wave function has to be used. Basis sets include standard Pople and Dunning sets, however, increased with polarization functions and diffuse p functions on both the C and O atoms. The latter is important due to the O(-) character of the wave function at the saddle point and products. Normal modes and vibrational energy levels are given for the reactants, saddle points and products. Finally, quantitative energetics are obtained by implementing a small CAS (complete active space) approach followed by limited configuration interaction (CI) calculations. Comparisons are made with available experimental data.

Laskowski, B. C.↗

NASA NTRS1987

Collision detection for spacecraft proximity operations

Collision Detection for Spacecraft Proximity Operations This thesis describes the development of a new collision detection algorithm to be used when two spacecraft are operating in the same vicinity. The two spacecraft are modelled as unions of convex polyhedra, where the polyhedron resulting from the union may be either convex or nonconvex. The relative motion of the two spacecraft is assumed to be such that one vehicle is moving with constant linear and angular velocity with respect to the other. The algorithm determines if a collision is possible and, if so, predicts the time when the collision will take place. The theoretical basis for the new collision detection algorithm is the C-function formulation of the configuration space approach recently introduced by researchers in robotics. Three different types of C-functions are defined that model the contacts between the vertices, edges, and faces of the polyhedra representing the two spacecraft. These C-functions are used to formulate three "collision" conditions. The first of these conditions limits the points representing potential collisions to the zeros of the C-functions. The new algorithm is fundamentally a search for the smallest zero of any C-function that satisfies the second and third collision conditions. The C-functions are shown to be transcendental functions of time for the assumed trajectory of the moving spacecraft. The zeros of these functions cannot be expressed in dosed form. Therefore, numerical search procedures are developed to find aLl of the zeros of a C-function in specified bounded intervals of time. These bounded intervals of time are found by examining the second and third collision conditions. The capabilities of the new algorithm are demonstrated for several example cases. These include examples of collisions determined by zeros of each of the three different types of C-functions. In addition to predicting the time of first contact of the polyhedra, the algorithm identifies the features of the two polyhedra that are touching at this time. The new collision detection algorithm is the first such algorithm that is capable of solving the collision detection problem exactly for the case where the moving object has constant linear and angular velocities. This is a significant improvement on previous collision detection algorithms described in the literature. In particular, the ability to handle constant angular velocity represents a more realistic type of rotational motion than those which have been used in other algorithms.

Robin M Vaughan↗

NASA NTRS1985

Finite-time arbitrary-motion unsteady cascade airfoil theory for helicopter rotors in hover

A complete and detailed derivation of finite-time arbitrary-motion cascade theory is presented for both Laplace and frequency domains. This theory includes the effect of returning wakes for both single- and multibladed rotors. The generalized cascade lift-deficiency function (CLDF) is shown to be consistent with the generalized Theodorsen lift-deficiency function when the wake spacing approaches infinity or when the reduced frequency tends to infinity. This function predicts correct zero-reduced-frequency limit. Accurate and efficient numerical procedures are presented for the evaluation of the CLDF. Numerical examples comparing the CLDF with Loewy's lift deficiency function in frequency domain are presented. Accurate Pade approximants of the CLDF are constructed using a Bode-plot approach which allows for complex poles.

Dinyavari, M. A. H.↗

NASA NTRS1988

Design of automation tools for management of descent traffic

The design of an automated air traffic control system based on a hierarchy of advisory tools for controllers is described. Compatibility of the tools with the human controller, a key objective of the design, is achieved by a judicious selection of tasks to be automated and careful attention to the design of the controller system interface. The design comprises three interconnected subsystems referred to as the Traffic Management Advisor, the Descent Advisor, and the Final Approach Spacing Tool. Each of these subsystems provides a collection of tools for specific controller positions and tasks. This paper focuses primarily on the Descent Advisor which provides automation tools for managing descent traffic. The algorithms, automation modes, and graphical interfaces incorporated in the design are described. Information generated by the Descent Advisor tools is integrated into a plan view traffic display consisting of a high-resolution color monitor. Estimated arrival times of aircraft are presented graphically on a time line, which is also used interactively in combination with a mouse input device to select and schedule arrival times. Other graphical markers indicate the location of the fuel-optimum top-of-descent point and the predicted separation distances of aircraft at a designated time-control point. Computer generated advisories provide speed and descent clearances which the controller can issue to aircraft to help them arrive at the feeder gate at the scheduled times or with specified separation distances. Two types of horizontal guidance modes, selectable by the controller, provide markers for managing the horizontal flightpaths of aircraft under various conditions. The entire system consisting of descent advisor algorithm, a library of aircraft performance models, national airspace system data bases, and interactive display software has been implemented on a workstation made by Sun Microsystems, Inc. It is planned to use this configuration in operational evaluations at an en route center.

Erzberger, Heinz↗

NASA NTRS1989

Design of automated system for management of arrival traffic

Erzberger, Heinz↗