Search NASA⌕ Search

SEARCH · Search NASA

Results for “Symmetry functions”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 91 records · Page 5

Measuring Galactic dark matter through unsupervised machine learning

ABSTRACT Measuring the density profile of dark matter in the Solar neighbourhood has important implications for both dark matter theory and experiment. In this work, we apply autoregressive flows to stars from a realistic simulation of a Milky Way-type galaxy to learn – in an unsupervised way – the stellar phase space density and its derivatives. With these as inputs, and under the assumption of dynamic equilibrium, the gravitational acceleration field and mass density can be calculated directly from the Boltzmann equation without the need to assume either cylindrical symmetry or specific functional forms for the galaxy’s mass density. We demonstrate our approach can accurately reconstruct the mass density and acceleration profiles of the simulated galaxy, even in the presence of Gaia-like errors in the kinematic measurements.

Astronomy & Astrophysics↗

Anisotropic Fano resonance in the Weyl semimetal candidate LaAlSi

Topological Weyl semimetal (WSM) is a solid-state realization of chiral Weyl fermions, whose phonon behaviors provide in-depth knowledge of their electronic properties. In this work, anisotropic Fano resonance is observed in a type-II WSM candidate LaAlSi by polarized Raman spectroscopy. The asymmetric line shape occurs for the $B^2_1$ phonon mode of LaAlSi only for 488- and 532-nm laser excitations but not for 364-, 633-, and 785-nm excitations, suggesting the excitation selectivity. The asymmetry, frequency, and linewidth of the $B^2_1$ phonon mode, along with the spectral background, all show fourfold rotational symmetry as a function of the polarization angle in the polarized Raman spectra. While the shift of Raman frequency in a metal or semimetal is typically attributed to Kohn anomaly, here we show that the anisotropic frequency shift in LaAlSi cannot be explained by the effect of Kohn anomaly, but potentially by the anisotropic scattering background of Fano resonance. Origins of the excitation-energy dependence and anisotropic behavior of the Fano resonance are discussed by the first-principles calculated electronic band structure and phonon dispersion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Flow field measurements for cylindrical configurations in a hypersonic wind tunnel: Windward and leeward flow fields

Windward and leeward measurements were made for a variety of simulated infinite cylinders exposed to hypersonic streams over an angle of attack from 30 deg to 90 deg. For the range of conditions included in the study, the following conclusions are made: (1) Swept cylinder theory provides a reasonable correlation of the measured laminar heat transfer rates from the plane of symmetry. (2) The boundary layer transition criteria in the plane of symmetry are a function of the transverse curvature. (3) Relaminarization of the circumferential boundary layer for a right circular cylinder was observed at the highest Reynolds number tested. (4) The effect of leeside geometry on the average heat transfer rate can be correlated with a single geometric parameter which is dependent on the location of separation. (5) The relationship of leeward heating to angle of attack is virtually linear for each cross section. (6) No systematic effect of free stream Reynolds number was observed.

Bertin, J. J.↗

On the characteristics of caloric nystagmus in healthy persons

The asymmetry of reflex activity of labyrinths and directional preponderance of the reaction were studied on healthy persons subjected to caloric tests. Calorization with hot water was accompanied by less pronounced reactions in all parameters of nystagmus than analogous indices at cold water stimulation. The symmetry of labyrinth function shifted to the right in individuals with greater activity of the left central vestibular formations, analogous to right handedness behavior. It is concluded that asymmetry of reflex nystagmus in healthy persons can be due to a certain preponderance of functional activity in structures of the left hemisphere of the brain.

Bodo, D.↗

Missile impact craters (White Sands Missile Range, New Mexico) and applications to lunar research: Contributions to astrogeology

Craters in natural materials at White Sands Missile Range, N. Mex., were produced by the impact of high-velocity to hypervelocity missiles traveling along oblique trajectories with kinetic energies between 2.1 and 81 × 1014 ergs. The oblique impacts produce craters 2 to 10 m across with morphologies and ejecta that are bilaterally symmetrical with respect to the plane of the missile trajectory. Rims are high and the amount of ejecta large in down-trajectory and lateral directions, whereas rims are low to nonexistent and ejecta thin to absent up-trajectory. Symmetry development and modifications of the symmetry are a function of target material, local topography, and angle of impact. Seven mappable units can be recognized in and around the craters. Three of these are ejecta: thick ejecta near the crater, thin to discontinuous ejecta at greater distances, and scattered ejecta at the greatest distances to the limit of throwout. These ejecta units may be absent on the up-trajectory side; if present, they are rarely as thick or continuous as on other sides of the crater. Three units are target materials: undeformed target material exposed in local patches through thin to discontinuous ejecta and everywhere between the fragments of scattered ejecta, tilted and broken target material exposed in upper crater walls, and shattered and fractured target material exposed on the up-trajectory crater wall. The seventh unit is slope material composed of talus and fallback within the crater. Development, character, and exposure of these units varies chiefly with the target material. Ejecta from the craters is chiefly broken but relatively undeformed target material that may range in size from very fine grained debris to large blocks. Where the target is porous, significant amounts of the ejecta are composed of sheared and compressed fragments, some coated with dark layers of mixed projectile pieces, powder, and fused metal mixed with crushed target material. For layered targets, the original stratigraphic sequence is crudely preserved and in inverted order in thick ejecta. Secondary impact craters are produced by the impact of ejected fragments when the surrounding surface materials are sufficiently weak. A wide variety of secondary impact crater relations may result. Secondary craters nearest the primary crater have blocks in them that are larger than or the same size as the crater they produced. Farther from the primary crater, the fragments are generally smaller than the secondary crater and are ejected from it. Excavation of four craters revealed a mixed breccia beneath the crater floor composed of missile pieces, sheared and compressed target material, and crushed debris. Banded, disaggregated target material and nonmixed breccia surrounded the mixed breccia, and these breccias were surrounded by a zone of conjugate fractures. Beneath the ejecta on the lateral and down-trajectory crater flanks, the target materials were tilted upward and broken. Up-trajectory, open fractures and downward displacement occurred in two of the craters. No displacement was observed for the other two. Beneath the down-trajectory rims of craters with distinct layering, overturned synclines were observed. Missile breakup and behavior during cratering are a function of target and missile properties. Missile breakup depends on missile velocity and is most extensive at high velocities, where the missile is fragmented, powdered, and partly fused. Burial of missile or its fragmented, powdered, and fused remains is greatest for porous targets and least for dense cohesive targets. For very porous targets, camouflet structures containing the fragmented missile may form. Least squares fit to the data on craters in dry to moist targets indicate V(a) = 10^(-11.433)E(p)^(1.205) where V(a) is the volume of the apparent crater and E(p) is the kinetic energy of the missile. This equation is consistent with expectations of the equations relating apparent depth and radius to kinetic energy. Extrapolation of displaced masses and kinetic energies for laboratory impacts with sand and rock converge near 10^(15) to 10^(16) ergs, where the extrapolations are near the data on missile impact craters, corrected for impact angle. Displaced masses of craters produced by missile impacts and by chemical explosives with small scaled depths of burial are about the same when the kinetic energies of the missiles (corrected for angle of impact) are equal to the TNT equivalent energy of the explosive. The problem of equivalent scaled depth of burst for an impact crater is complicated and not entirely resolved, however. Both missile impact craters and chemical explosive craters in water-saturated targets are larger than their counterparts in dry to moist materials. Data collected during the study of missile impact craters have helped resolve a number of problems in lunar research: (1) the soillike nature of lunar surface materials was predicted, (2) sizes of craters produced by artificial impacts were correctly predicted, (3) certain features imaged by Surveyor were found to be analogous to features associated with missile impact craters, {4) missile impacts were used in support of the Apollo passive seismic experiment, (5) craters seen in Apollo orbital photographs were found to be similar to some missile impact craters, (6) missile impact craters supplied data on sample collection and crater phenomenology used in training astronauts, and (7) some returned lunar samples are similar to coated, sheared, and compressed fragments ejected from missile impact craters.

H. J. Moore↗

Fuel spray measurements with an imaging-type spray analyzer

The application of an imaging-type, automated spray analysis system to measurements of fuel sprays requires consideration of a number of significant factors both in its use and in the interpretation of the data. These factors are reviewed and a procedure developed for one such instrument is described. The procedure involves optical scans along the optic axis of the system and an appropriate mathematical inversion scheme for interpretation of the results. The system is nominally capable of yielding the local size distribution function and the total number density at points along the optic axis for droplets from about 10 to 500 microns. No assumptions regarding the form of the size distribution function or the symmetry of the spray are required.

Skifstad, J. G.↗

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.↗

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.↗

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.↗

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.↗

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.↗

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.↗

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators 〈σσϵσσ〉 in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff ∆ ⩽ ∆ cutoff . We then compute several OPE coefficients involving ϵ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Magnetic crystalline-symmetry-protected axion electrodynamics and field-tunable unpinned Dirac cones in EuIn 2 As 2

Knowledge of magnetic symmetry is vital for exploiting nontrivial surface states of magnetic topological materials. EuIn 2 As 2 is an excellent example, as it is predicted to have collinear antiferromagnetic order where the magnetic moment direction determines either a topological-crystalline-insulator phase supporting axion electrodynamics or a higher-order-topological-insulator phase with chiral hinge states. Here, we use neutron diffraction, symmetry analysis, and density functional theory results to demonstrate that EuIn 2 As 2 actually exhibits low-symmetry helical antiferromagnetic order which makes it a stoichiometric magnetic topological-crystalline axion insulator protected by the combination of a 180° rotation and time-reversal symmetries: $C_2 × \mathcal{T} =$ 2'. Surfaces protected by 2' are expected to have an exotic gapless Dirac cone which is unpinned to specific crystal momenta. All other surfaces have gapped Dirac cones and exhibit half-integer quantum anomalous Hall conductivity. We predict that the direction of a modest applied magnetic field of $μ_0H ≈$ 1 to 2 T can tune between gapless and gapped surface states.

36 MATERIALS SCIENCE↗

Information content of the differences in the charge radii of mirror nuclei

Differences in the charge radii of mirror nuclei have been recently suggested to contain information on the slope of the symmetry energy L. To test this hypothesis, we perform statistical correlation analysis using quantified energy density functionals that are consistent with our previous knowledge on global nuclear observables such as binding energies and charge radii. We conclude that the difference in charge radii between a mirror pair, $ΔR$$^{mir}_{ch}$, is an inferior isovector indicator compared to other observables, such at the neutron skin or electric dipole polarizability α D . In particular, this quantity correlates poorly with both the neutron skin and L. Here, we demonstrate that $ΔR$$^{mir}_{ch}$ is influenced by pairing correlations in the presence of low-lying proton continuum in the proton-rich mirror-partner nucleus. Considering the large theoretical uncertainties on $ΔR$$^{mir}_{ch}$, we conclude that the precise data on mirror charge radii cannot provide a stringent constraint on L.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A chiral switchable photovoltaic ferroelectric 1D perovskite

Spin and valley degrees of freedom in materials without inversion symmetry promise previously unknown device functionalities, such as spin-valleytronics. Control of material symmetry with electric fields (ferroelectricity), while breaking additional symmetries, including mirror symmetry, could yield phenomena where chirality, spin, valley, and crystal potential are strongly coupled. Here we report the synthesis of a halide perovskite semiconductor that is simultaneously photoferroelectricity switchable and chiral. Spectroscopic and structural analysis, and first-principles calculations, determine the material to be a previously unknown low-dimensional hybrid perovskite (R)-(-)-1-cyclohexylethylammonium/(S)-(+)-1 cyclohexylethylammonium) PbI 3 . Optical and electrical measurements characterize its semiconducting, ferroelectric, switchable pyroelectricity and switchable photoferroelectric properties. Temperature dependent structural, dielectric and transport measurements reveal a ferroelectric-paraelectric phase transition. Circular dichroism spectroscopy confirms its chirality. The development of a material with such a combination of these properties will facilitate the exploration of phenomena such as electric field and chiral enantiomer–dependent Rashba-Dresselhaus splitting and circular photogalvanic effects

36 MATERIALS SCIENCE↗

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.↗

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.↗