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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1980

Hamiltonian indices and rational spectral densities

Several (global) topological properties of various spaces of linear systems, particularly symmetric, lossless, and Hamiltonian systems, and multivariable spectral densities of fixed McMillan degree are announced. The study is motivated by a result asserting that on a connected but not simply connected manifold, it is not possible to find a vector field having a sink as its only critical point. In the scalar case, this is illustrated by showing that only on the space of McMillan degree = /Cauchy index/ = n, scalar transfer functions can one define a globally convergent vector field. This result holds both in discrete-time and for the nonautonomous case. With these motivations in mind, theorems of Bochner and Fogarty are used in showing that spaces of transfer functions defined by symmetry conditions are, in fact, smooth algebraic manifolds.

Byrnes, C. I.↗
NASA NTRS1984

Geometric interpretations of the Discrete Fourier Transform (DFT)

One, two, and three dimensional Discrete Fourier Transforms (DFT) and geometric interpretations of their periodicities are presented. These operators are examined for their relationship with the two sided, continuous Fourier transform. Discrete or continuous transforms of real functions have certain symmetry properties. The symmetries are examined for the one, two, and three dimensional cases. Extension to higher dimension is straight forward.

Campbell, C. W.↗
NASA NTRS1991

Molecular dynamics and quasidynamics simulations of the annealing of bulk and near-surface interstitials formed in molecular-beam epitaxial Si due to low-energy particle bombardment during deposition

The relaxation, diffusion, and annihilation of split and hexagonal interstitials resulting from 10 eV Si irradiation of (2x1)-terminated Si(100) are investigated. Molecular dynamics and quasidynamics simulations, utilizing the Tersoff many-body potential are used in the investigation. The interstitials are created in layers two through six, and stable atomic configurations and total potential energies are derived as a function of site symmetry and layer depth. The interstitial Si atoms are allowed to diffuse, and the total potential energy changes are calculated. Lattice configurations along each path, as well as the starting configurations, are relaxed, and minimum energy diffusion paths are derived. The results show that the minimum energy paths are toward the surface and generally involved tetrahedral sites. The calculated interstitial migration activation energies are always less than 1.4 eV and are much lower in the near-surface region than in the bulk.

Kitabatake, M.↗
NASA NTRS1991

High-performance multiprocessor architecture for a 3-D lattice gas model

The lattice gas method has recently emerged as a promising discrete particle simulation method in areas such as fluid dynamics. We present a very high-performance scalable multiprocessor architecture, called ALGE, proposed for the simulation of a realistic 3-D lattice gas model, Henon's 24-bit FCHC isometric model. Each of these VLSI processors is as powerful as a CRAY-2 for this application. ALGE is scalable in the sense that it achieves linear speedup for both fixed and increasing problem sizes with more processors. The core computation of a lattice gas model consists of many repetitions of two alternating phases: particle collision and propagation. Functional decomposition by symmetry group and virtual move are the respective keys to efficient implementation of collision and propagation.

Lee, F.↗
NASA NTRS1994

Some Aspects of the Implementation of Double Group Symmetry and Electron Correlation in Molecular 4-Component Calculations

The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.

Dyall, Kenneth G.↗
NASA NTRS2007

General Forms of Wave Functions for Dipositronium, Ps2

The consequences of particle interchange symmetry for the structure of wave functions of the states of dipositronium was recently discussed by the author [I]. In the present work, the methodology is simply explained, and the wave functions are explicitly given.

Schrader, D.M.↗
NASA NTRS1986

Radiative transfer in a sphere illuminated by a parallel beam - An integral equation approach

The problem of multiple scattering of nonpolarized light in a planetary body of arbitrary shape illuminated by a parallel beam is formulated using the integral equation approach. There exists a simple functional whose stationarity condition is equivalent to solving the equation of radiative transfer and whose value at the stationary point is proportional to the differential cross section. The analysis reveals a direct relation between the microscopic symmetry of the phase function for each scattering event and the macroscopic symmetry of the differential cross section for the entire planetary body, and the interconnection of these symmetry relations and the variational principle. The case of a homogeneous sphere containing isotropic scatterers is investigated in detail. It is shown that the solution can be expanded in a multipole series such that the general spherical problem is reduced to solving a set of decoupled integral equations in one dimension. Computations have been performed for a range of parameters of interest, and illustrative examples of applications to planetary problems as provided.

Shia, R.-L.↗
NASA NTRS1979

The utilization of abelian point group symmetry in the graphical unitary group approach to the calculation of correlated electronic wavefunctions

A procedure is described for the utilization of abelian point group symmetry in the graphical unitary group approach (GUGA) to calculations of correlated electronic wavefunctions. The procedure is based on a recursively computed set of symmetry dependent counting indices, and results in the separate numbering, without gaps, of the Gelfand states (configuration functions) belonging to each symmetry species

Shavitt, I.↗
NASA NTRS1982

Asymptotic freedom in solids - A theorem

A cusp theorem is proved that relates the zero-separation value and slope of two-particle position correlation functions in quantum many-body systems with Coulombic interactions. The theorem is independent of the particle type and symmetry of the wave function. Its proof uses only the integral form of the Schroedinger equation and the continuity and exponential decay of the wave function. It is used to derive a sum rule for the electron-gas structure factor and an exact statement about the screening of point charges. Applications to atomic-orbital-based calculations for H2 and metallic H are described.

Carlsson, A. E.↗
DOE OSTI2025

SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born–Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wave function ansatz that includes both nuclear and electronic coordinates. Furthermore, this strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.

Chemical calculations↗
DOE OSTI2024

Hidden magnetism and split off flat bands in the insulator metal transition in VO 2

Transition metal d -electron oxides with an odd number of electrons per unit cell are expected to form metals with partially occupied energy bands, but exhibit in fact a range of behaviors, being either insulators, or metals, or having insulator-metal transitions. Traditional explanations involved predominantly electron-electron interactions in fixed structural symmetry. The present work focuses instead on the role of symmetry breaking local structural motifs. Viewing the previously observed V-V dimerization in VO 2 as a continuous knob, reveals in density functional calculations the splitting of an isolated flat band from the broad conduction band. This leads past a critical percent dimerization to the formation of the insulating phase while lowering the total energy. In VO 2 this transition is found to have a rather low energy barrier approaching the thermal energy at room temperature, suggesting energy-efficient switching in neuromorphic computing. Interestingly, sufficient V-V dimerization suppresses magnetism, leading to the nonmagnetic insulating state, whereas magnetism appears when dimerization is reduced, forming a metallic state. This study opens the way to design novel functional quantum materials with symmetry breaking-induced flat bands.

Chemistry↗
DOE OSTI2024

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in d-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the 〈σσϵσσ〉 correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff ∆ ⩽ ∆cutoff. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Structure Sensitive Reaction Kinetics of Chiral Molecules on Intrinsically Chiral Surfaces

Enantiospecific heterogeneous catalysis utilizes chiral surfaces to resolve enantiomers via structure sensitive surface chemistry. The catalyst design challenge is the identification of chiral surface structures that maximize enantiospecificity. Herein, we develop data driven models for the enantiospecificity of tartaric acid reactions on chiral Cu(hkl) R&S surfaces. Measurements of enantiospecific rate constants were obtained by using curved Cu(hkl) R&S surfaces that enable kinetic measurements on hundreds of chiral surface orientations. One model uses feature vectors derived from generalized coordination numbers to capture the local structure around Cu atoms exposed by the Cu(hkl) R&S surfaces. The second model introduces the use of chiral cubic harmonic functions to capture the symmetry constraints of the face-centered cubic Cu structure. The model using 58 generalized coordination numbers has a fitting error similar to that of the model using only 5 cubic harmonic functions. The two models predict maxima in the enantiospecificity on surfaces with very similar surface orientations. The models developed in this work are applicable for any enantiospecific reaction happening on any chiral material with a cubic lattice structure, opening the way to understanding the surface structure sensitivity of the enantiospecific reaction kinetics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

An Exact Separation of the Spin-Free and Spin-Dependent Terms of the Dirac-Coulomb-Breit Hamiltonian

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

Dyall, Kenneth G.↗
DOE OSTI2025

Bootstrapping the 3d Ising stress tensor

We compute observables of the critical 3d Ising model to high precision by applying the numerical conformal bootstrap to mixed correlators of the leading scalar operators σ and ϵ, and the stress tensor T μν . We obtain new precise determinations of scaling dimensions (∆ σ , ∆ ϵ ) = (0.518148806(24), 1.41262528(29)) as well as OPE coefficients involving σ, ϵ, and T μν . We also describe several improvements made along the way to algorithms and software tools for the numerical bootstrap.

Conformal and W Symmetry↗
DOE OSTI2026

Magnetization orientation-dependent Shubnikov-de Haas oscillations in ferromagnetic Weyl semimetal Co 3 Sn 2 S 2

We report a study of Shubnikov–de Haas oscillations in high-quality single crystals of ferromagnetic Weyl semimetal Co 3 Sn 2 S 2 . The Fermi surfaces resolved in our experiments are three-dimensional and reflect an underlying trigonal crystallographic symmetry. Combined with density functional calculations, we identify that multiple Fermi surfaces in the system—of both electron and hole nature—arise from the energy dispersion of the (spin-orbit gapped) mirror-protected nodal rings. We observe an evolution of the Fermi surfaces with in-plane magnetic fields, in contrast to field perpendicular to the kagome lattice planes, which has little effect. Viewed alongside the easy-axis anisotropy of the system, our observation reveals an evolution of the electronic structure of Co 3 Sn 2 S 2 —including the Weyl points—with the ferromagnetic moment orientation. Through the case study of Co 3 Sn 2 S 2 , our results provide concrete experimental evidence of an anisotropic interplay via spin-orbit coupling between the magnetic degrees of freedom and electronic band singularities, which has long been expected in semimetallic and metallic magnetic systems.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Tensor-polarized parton density in the 𝑁 → Δ transition from the large-𝑁 𝑐 light-cone wave function

The tensor-polarized parton density is defined by the forward matrix element of a partonic operator in the 𝑁 → Δ transition. In this work, we investigate it by employing the large-𝑁 𝑐 light-cone wave function derived from the mean-field approach. The mean-field picture is based on low-energy effective dynamics in the large-𝑁 𝑐 limit, where the baryon wave function is formulated in the rest frame. By exploiting the covariance of the mean-field solution, we derive the corresponding large-𝑁 𝑐 light-cone wave function—decomposed unambiguously into 3⁢𝑄 , 5⁢𝑄 , 7⁢𝑄 , and higher Fock components—in the infinite momentum frame. Evaluating the overlap of these wave functions, we derive an overlap representation of the tensor-polarized parton density in the 𝑁 → Δ transition and find that the leading contribution arises from the 5⁢𝑄 Fock sector. This indicates that the tensor-polarized parton density directly probes the genuine 5⁢𝑄 component and is governed by chiral dynamics. Our numerical analysis shows that the 𝑁 → Δ tensor-polarized parton density is suppressed, consistent with standard large-𝑁 𝑐 expectations. Finally, we establish connections among the tensor-polarized parton density, the generalized parton distribution 𝐻 𝑋 , and the energy-momentum tensor form factor 𝐹 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Accessing bands with extended quantum metric in kagome Cs 2 Ni 3 S 4 through soft chemical processing

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs 2 Ni 3 S 4 to CsNi 3 S 4 , we see a two orders of magnitude drop in the room temperature resistance. However, CsNi 3 S 4 is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin.

Science & Technology - Other Topics↗