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 397 records · Page 22

Intermodal transfer in temporal discrimination

This study determined if training for accuracy in temporal discrimination would transfer across sensory modalities. A fractionation method was used in which subjects bisected the durations of acoustic and visual signals at three standard intervals (6, 12, and 18 sec). Absolute error was the performance index. Half of the subjects were trained with acoustic stimuli and then tested in vision; the remainder were trained in vision and tested in audition. Similar negatively accelerated acquisition functions were noted for both modalities. Positive intermodal transfer, characterized by symmetry across modalities, was obtained at all standard durations. The results were considered to provide support for the notion that a common mechanism underlies temporal discriminations in different sensory systems.

Warm, J. S.↗

Photoabsorption in formaldehyde

Theoretical studies of the vertical electronic dipole excitation and ionization spectra in molecular formaldehyde are reported. The investigations relied on configuration-interaction calculations and moment-theory techniques. A double-zeta basis of contracted Gaussian-lobe functions supplemented with appropriate polarization and bond functions was used to construct Fock spectra in C(2 nu) symmetry for certain states near the ground state equilibrium geometry. The ionization energies, discrete vertical transition frequencies, and oscillator strengths for occupied and vertical Fock orbitals are in general accord with experimental determinations and other theoretical calculations. Stieltjes and Chebyshev vertical electronic photoionization profiles were calculated and found to be in good agreement with appropriately averaged photoionization-mass spectrometric measurements of the cross section for parent H2CO(+) ion production.

Langhoff, P. W.↗

Laminar boundary layer on cone in supersonic flow at large angle of attack

The laminar boundary-layer flow about a circular cone at large angles of attack to a supersonic stream has been analyzed in the plane of symmetry by a method applicable in general to the flow about conical bodies. At the bottom of the cone, velocity profiles were obtained showing the expected tendency of the boundary layer to become thinner on the under side of the cone as the angle of attack is increased. At the top of the cone, the analysis failed to yield unique solutions except for small angles of attack. Beyond a certain critical angle of attack, boundary-layer flow does not exist in the plane of symmetry, thus indicating separation. This critical angle is presented as a function of Mach number and cone vertex angle.

Moore, Franklin K↗

Model checking

Automatic formal verification methods for finite-state systems, also known as model-checking, successfully reduce labor costs since they are mostly automatic. Model checkers explicitly or implicitly enumerate the reachable state space of a system, whose behavior is described implicitly, perhaps by a program or a collection of finite automata. Simple properties, such as mutual exclusion or absence of deadlock, can be checked by inspecting individual states. More complex properties, such as lack of starvation, require search for cycles in the state graph with particular properties. Specifications to be checked may consist of built-in properties, such as deadlock or 'unspecified receptions' of messages, another program or implicit description, to be compared with a simulation, bisimulation, or language inclusion relation, or an assertion in one of several temporal logics. Finite-state verification tools are beginning to have a significant impact in commercial designs. There are many success stories of verification tools finding bugs in protocols or hardware controllers. In some cases, these tools have been incorporated into design methodology. Research in finite-state verification has been advancing rapidly, and is showing no signs of slowing down. Recent results include probabilistic algorithms for verification, exploitation of symmetry and independent events, and the use symbolic representations for Boolean functions and systems of linear inequalities. One of the most exciting areas for further research is the combination of model-checking with theorem-proving methods.

Dill, David L.↗

A New Fitting Procedure for the Blended He I 1083 nm Multiplet

The He I 1083 nm multiplet is a powerful tool for observing the outer solar atmosphere but is difficult to analyze because the lines are weak, highly variable, and spectrally blended, both internally and with other neighboring solar and telluric lines. After separation from nearby spectral features, two components of the He I multiplet are resolved. Fitting these lines with two unconstrained Gaussian profiles always gives a ratio of major to minor component of less than half the value which would be expected for optically thin lines. One possibility for explaining the discrepancy between the weakness of the lines and the ratio of the spectral components is to assume that the line formation regions are concentrated in laterally unresolved, optically thick structures with small filling factor. However, we present here a least-squares fitting technique using cubic splines with fixed breakpoints with the constraint that the blend is the sum of three identically shaped profiles shifted in wavelength according to the atomic structure of the blend and weighted by the corresponding statistics weights, in agreement with optically thin line formation. The basis functions for the fitting procedure have no built-in spectral symmetry or shape. The resulting underlying profiles tend to be asymmetric with excess absorption to the blue, consistent with formation by "hot" and "cool" spatial elements within the observed volume, with the hotter regions having differential motion toward the observer. The results agree well with NASA/XSO Spectromagnetograph observations in quiet sun and coronal holes. Partial funding of this research was provided through the NASA Sun-Earth Connection SR&T program.

Jones, H. P.↗

Finite-Temperature Quantum Matter with Rydberg or Molecule Synthetic Dimensions

Synthetic-dimension platforms offer unique pathways for engineering quantum matter. We compute the phase diagram of a many-body system of ultracold atoms (or polar molecules) with a set of Rydberg states (or rotational states) as a synthetic dimension, where the particles are arranged in real space in optical microtrap arrays and interact via dipole-dipole exchange interaction. Using mean-field theory, we find three ordered phases—two are localized in the synthetic dimension, predicted as zero-temperature ground states, and one is a delocalized phase. We characterize them by identifying the spontaneously broken discrete symmetries of the Hamiltonian. We also compute the phase diagram as a function of temperature and interaction strength for both signs of the interaction. For system sizes with more than six synthetic sites and attractive interactions, we find that the thermal phase transitions can be first or second order, which leads to a tricritical point on the phase boundary. Furthermore, by examining the dependence of the tricritical point and other special points of the phase boundary on the synthetic dimension size, we shed light on the physics for thermodynamically large synthetic dimension.

74 ATOMIC AND MOLECULAR PHYSICS↗

Local Sn Dipolar-Character Displacements behind the Low Thermal Conductivity in SnSe Thermoelectric

The local atomic structure of SnSe was characterized across its orthorhmbic-to-orthorhombic structural phase transition using x-ray pair distribution function analysis. Substantial Sn displacements with a dipolar character persist in the high symmetry high temperature phase, albeit with a symmetry different from that of the ordered displacements below the transition. The analysis implies that the transition is neither order-disorder nor displacive, but rather a complex crossover. Robust ferro-coupled SnSe intra-layer distortions suggest a ferroelectric-like instability as the driving force. Furthermore, these local symmetry-lowering Sn displacements are likely integral to the ultra-low lattice thermal conductivity mechanism in SnSe.

36 MATERIALS SCIENCE↗

The Fraternal Twins of Quartet O4(+)

Eleven stationary geometries of quartet O4(+) have been studied by ab initio methods. The geometries were optimized at the Complete Active Space Self-Consistent Field (CASSCF) level of theory and the energies were calculated by the multiconfigurational second order pertubation method (CASPT2), using Double-Zeta Plus polarization (DZP), Triple-Zeta Plus Double Polarization (TZ2P), average Atomic Natural Orbital (ANO) (5s4p2d) and average ANO (6s5p3d2f) basis sets. The rectangular and trans-planar structures are found to be the most stable, with an energy barrier to conversion between the two at the threshold of dissociation. Both have a delocalized hole and are stable relative to separated 02 and 02(+)by 11.0 and 11.5 kcal/mol for the rectangular and the 2 trans-planar structure, respectively, compared with the experimentally deduced energy in the range of 9.2 to 10.8 kcal/mol. The adiabatic ionization potentials of 04 and 02 are computed to be 11.67 and 12.21 eV, while experimental values are 11.66 and 12.07 eV, respectively. The vibrational frequencies have been computed for all degrees of freedom at the CASSCF level of theory. Symmetry breaking is found to be a particular problem in the computation of the antisymmetric stretch frequency for the delocalized structures at the CASSCF level of theory. Attempts to rectify these problems using the restricted active space self-consistent field (RASSCF) method leads to additional difficulties, but further analysis yields insight into the symmetry breaking and problems with earlier calculations. Finally, a nonorthogonal configuration interaction (CI) calculation based on the interaction of localized CASSCF wave functions using the Complete Active Space State Interation (CASSI) method leads to a balanced treatment of the antisymmetric stretch which is free from symmetry breaking. The study explains the four most prominent absorption frequencies observed in the partially unassigned IR spectrum of O4(+) isolated in solid neon as the antisymmetric OO stretch, and the combination band of the symmetric and antisymmetric 00 stretch of both the rectangular and trans-planar structures.

Lindh, Roland↗

X-ray study of ferroic octupole order producing anomalous Hall effect

Recently found anomalous Hall, Nernst, magnetooptical Kerr, and spin Hall effects in the antiferromagnets Mn 3 X (X = Sn, Ge) are attracting much attention for spintronics and energy harvesting. Since these materials are antiferromagnets, the origin of these functionalities is expected to be different from that of conventional ferromagnets. Here, we report the observation of ferroic order of magnetic octupole in Mn 3 Sn by X-ray magnetic circular dichroism, which is only predicted theoretically so far. The observed signals are clearly decoupled with the behaviors of uniform magnetization, indicating that the present X-ray magnetic circular dichroism is not arising from the conventional magnetization. We have found that the appearance of this anomalous signal coincides with the time reversal symmetry broken cluster magnetic octupole order. Our study demonstrates that the exotic material functionalities are closely related to the multipole order, which can produce unconventional cross correlation functionalities.

36 MATERIALS SCIENCE↗

Higgs potential from instantons

We propose that the Higgs potential, a key element in our understanding of nature, is partially generated by the instantons of new confining dynamics, perhaps from a hidden sector. In this picture, while the Higgs itself is a fundamental field, it controls the strength of the nonperturbative interactions that give rise to its potential. This setup can be realized in “Twin Higgs” hierarchy models, where the twin strong dynamics confines at or above the weak scale, but large quantum corrections to the Higgs potential are avoided. We examine a simple setup in which this instanton contribution is augmented by a quartic term, which is sufficient for a realistic electroweak symmetry breaking mechanism. The minimum of the potential is given by the Lambert 𝑊 0 function, with these assumptions. We discuss the predictions of this model and how it may be tested through measurements of the Higgs self coupling. Given the connection with nontrivial dynamics, one may also consider the prospects of accessing hidden sector states at colliders; this seems to be typically challenging in our setup. Symmetry restoration in the early Universe in this scenario is briefly examined. We also comment on the possible connection of our general setup with recent work on the physics of field space end points.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Impact of symmetry breaking and spin-orbit coupling on the band gap of halide perovskites

Halide perovskite (HP) materials have recently emerged as a class of semiconductors with immense promise for various optoelectronic applications, ranging from solar cells to light-emitting diodes. One of the unique attributes of HPs is their tunable band gaps with different factors governing their value. Furthermore, the first factor is related to relativistic corrections [“mass-Darwin,” connected to the ns 2 lone pairs, and spin-orbit coupling (SOC)] that induce an orbital shift or degeneracy splitting, resulting in a band-gap reduction. The second factor involves the structural configuration: in HPs the local symmetry of each Wyckoff position tends to be broken, inducing an opening of the band gap. Based on high-throughput density functional theory calculations, this paper systematically studies a possible self-cancelation on the band-gap correction for HPs when the polymorphous configuration—structural effects—and the SOC—electronic effects—are included. Our results indicate that the nature of interplay between SOC and symmetry breaking (SB) is that they are independent decoupling effects to describe the band-gap magnitude in halide perovskites. As a result of that, we observe a transitivity of the band-gap description; i.e., if we know the band gap of halide perovskites without SB and SOC, we can independently add the effects of band-gap reduction due to SOC and band-gap opening due to SB, regardless of the order in which these effects are considered.

14 SOLAR ENERGY↗

In-plane quasi-single-domain BaTiO 3 via interfacial symmetry engineering

The control of the in-plane domain evolution in ferroelectric thin films is not only critical to understanding ferroelectric phenomena but also to enabling functional device fabrication. However, in-plane polarized ferroelectric thin films typically exhibit complicated multi-domain states, not desirable for optoelectronic device performance. Here we report a strategy combining interfacial symmetry engineering and anisotropic strain to design single-domain, in-plane polarized ferroelectric BaTiO 3 thin films. Theoretical calculations predict the key role of the BaTiO 3 /PrScO 3 (110) O substrate interfacial environment, where anisotropic strain, monoclinic distortions, and interfacial electrostatic potential stabilize a single-variant spontaneous polarization. A combination of scanning transmission electron microscopy, piezoresponse force microscopy, ferroelectric hysteresis loop measurements, and second harmonic generation measurements directly reveals the stabilization of the in-plane quasi-single-domain polarization state. This work offers design principles for engineering in-plane domains of ferroelectric oxide thin films, which is a prerequisite for high performance optoelectronic devices.

36 MATERIALS SCIENCE↗

Mirror symmetry breaking and lateral stacking shifts in twisted trilayer graphene

Here, we construct a continuum model of twisted trilayer graphene using ab initio density-functional-theory calculations, and we apply it to address twisted trilayer electronic structure. Our model accounts for moiré variation in site energies, hopping between outside layers, and hopping within layers. We focus on the role of a mirror symmetry present in ABA graphene trilayers with a middle layer twist. The mirror symmetry is lost intentionally when a displacement field is applied between layers, and unintentionally when the top layer is shifted laterally relative to the bottom layer. We calculate two band-structure characteristics that are directly relevant to transport measurements, namely the Drude weight and the weak-field Hall conductivity. We relate them via the Hall density to assess the influence of the accidental lateral stacking shifts currently present in all experimental devices on electronic properties. Finally, we comment on the role of the possible importance of accidental lateral stacking shifts for superconductivity in twisted trilayers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Anomalies of cosmic anisotropy from holographic universality of great-circle variance

We examine all-sky cosmic microwave background temperature maps on large angular scales to compare their consistency with two scenarios: the standard inflationary quantum picture, and a distribution constrained to have a universal variance of primordial curvature perturbations on great circles. The latter symmetry is not a property of standard quantum inflation, but may be a symmetry of holographic models with causal quantum coherence on null surfaces. Since the variation of great-circle variance is dominated by the largest angular scale modes, in the latter case the amplitude and direction of the unobserved intrinsic dipole (that is, the ℓ = 1 harmonics) can be estimated from measured ℓ = 2, 3 harmonics by minimizing the variance of great-circle variances including only ℓ = 1, 2, 3 modes. It is found that including the estimated intrinsic dipole leads to a nearly-null angular correlation function over a wide range of angles, in agreement with a null anti-hemispherical symmetry independently motivated by holographic causal arguments, but highly anomalous in standard cosmology. Simulations are used here to show that simultaneously imposing the constraints of universal great-circle variance and the vanishing of the angular correlation function over a wide range of angles tends to require patterns that are unusual in the standard picture, such as anomalously high sectorality of the ℓ = 3 components, and a close alignment of principal axes of ℓ = 2 and ℓ = 3 components, that have been previously noted on the actual sky. The precision of these results appears to be primarily limited by errors introduced by models of Galactic foregrounds.

79 ASTRONOMY AND ASTROPHYSICS↗

Extending a 10‐node composite tetrahedral finite element for solid mechanics

Abstract We propose to extend the composite tetrahedral finite element first introduced by Thoutireddy et al. (2002) and recently reformulated by Ostien et al. (2016). We generalize the gradient operator and mass matrix to curved domains through analytical expressions weighted by subtetrahedra Jacobians. Optimal integration weights are constructed to increase the accuracy of Gaussian quadrature. We preserve the variational structure of the formulation through a new five‐field functional with additional, independent fields for the Jacobian and the pressure. This approach not only obviates volumetric locking but also yields symmetry. A deleterious soft mode, common to both the quadratic and composite tetrahedral element with constant pressure formulations is effectively stabilized through a novel convex energy penalty function. Numerous numerical examples spanning a patch test to the impact of a Taylor bar demonstrate the accuracy, robustness, and convergence of the extended composite tetrahedral element for application to structural metals.

Foulk III, James W.↗

Learning broken symmetries with approximate invariance

Recognizing symmetries in data allows for significant boosts in neural network training, which is especially important where training data are limited. In many cases, however, the exact underlying symmetry is present only in an idealized dataset, and is broken in actual data, due to asymmetries in the detector, or varying response resolution as a function of particle momentum. Standard approaches, such as data augmentation or equivariant networks fail to represent the nature of the full, broken symmetry, effectively overconstraining the response of the neural network. We propose a learning model which balances the generality and asymptotic performance of unconstrained networks with the rapid learning of constrained networks. This is achieved through a dual-subnet structure, where one network is constrained by the symmetry and the other is not, along with a learned symmetry factor. In a simplified toy example that demonstrates violation of Lorentz invariance, our model learns as rapidly as symmetry constrained networks but escapes its performance limitations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗