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At least 1,063 records · Page 59

Higher spin partition functions via the quasinormal mode method in de Sitter quantum gravity

In this note we compute the 1-loop partition function of spin- s s fields on Euclidean de Sitter space S^{2n+1} S 2 n + 1 using the quasinormal mode method. Instead of computing the quasinormal mode frequencies from scratch, we use the analytic continuation prescription L_{\text{AdS}}\to iL_{\text{dS}} L AdS → i L dS , appearing in the dS/CFT correspondence, and Wick rotate the normal mode frequencies of fields on thermal \text{AdS}_{2n+1} AdS 2 n + 1 into the quasinormal mode frequencies of fields on de Sitter space. We compare the quasinormal mode and heat kernel methods of calculating 1-loop determinants, finding exact agreement, and furthermore explicitly relate these methods via a sum over the conformal dimension. We discuss how the Wick rotation of normal modes on thermal \text{AdS}_{2n+1} AdS 2 n + 1 can be generalized to calculating 1-loop partition functions on the thermal spherical quotients S^{2n+1}/\mathbb{Z}_{p} S 2 n + 1 / ℤ p . We further show that the quasinormal mode frequencies encode the group theoretic structure of the spherical spacetimes in question, analogous to the analysis made for thermal AdS in [1-3] .

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

First-Order System Least Squares for the Stokes Equations, with Application to Linear Elasticity

Following our earlier work on general second-order scalar equations, here we develop a least-squares functional for the two- and three-dimensional Stokes equations, generalized slightly by allowing a pressure term in the continuity equation. By introducing a velocity flux variable and associated curl and trace equations, we are able to establish ellipticity in an H(exp 1) product norm appropriately weighted by the Reynolds number. This immediately yields optimal discretization error estimates for finite element spaces in this norm and optimal algebraic convergence estimates for multiplicative and additive multigrid methods applied to the resulting discrete systems. Both estimates are uniform in the Reynolds number. Moreover, our pressure-perturbed form of the generalized Stokes equations allows us to develop an analogous result for the Dirichlet problem for linear elasticity with estimates that are uniform in the Lame constants.

Cai, Z.↗

LVQ and backpropagation neural networks applied to NASA SSME data

Feedfoward neural networks with backpropagation learning have been used as function approximators for modeling the space shuttle main engine (SSME) sensor signals. The modeling of these sensor signals is aimed at the development of a sensor fault detection system that can be used during ground test firings. The generalization capability of a neural network based function approximator depends on the training vectors which in this application may be derived from a number of SSME ground test-firings. This yields a large number of training vectors. Large training sets can cause the time required to train the network to be very large. Also, the network may not be able to generalize for large training sets. To reduce the size of the training sets, the SSME test-firing data is reduced using the learning vector quantization (LVQ) based technique. Different compression ratios were used to obtain compressed data in training the neural network model. The performance of the neural model trained using reduced sets of training patterns is presented and compared with the performance of the model trained using complete data. The LVQ can also be used as a function approximator. The performance of the LVQ as a function approximator using reduced training sets is presented and compared with the performance of the backpropagation network.

Doniere, Timothy F.↗

Software Simulates Sight: Flat Panel Mura Detection

In the increasingly sophisticated world of high-definition flat screen monitors and television screens, image clarity and the elimination of distortion are paramount concerns. As the devices that reproduce images become more and more sophisticated, so do the technologies that verify their accuracy. By simulating the manner in which a human eye perceives and interprets a visual stimulus, NASA scientists have found ways to automatically and accurately test new monitors and displays. The Spatial Standard Observer (SSO) software metric, developed by Dr. Andrew B. Watson at Ames Research Center, measures visibility and defects in screens, displays, and interfaces. In the design of such a software tool, a central challenge is determining which aspects of visual function to include while accuracy and generality are important, relative simplicity of the software module is also a key virtue. Based on data collected in ModelFest, a large cooperative multi-lab project hosted by the Optical Society of America, the SSO simulates a simplified model of human spatial vision, operating on a pair of images that are viewed at a specific viewing distance with pixels having a known relation to luminance. The SSO measures the visibility of foveal spatial patterns, or the discriminability of two patterns, by incorporating only a few essential components of vision. These components include local contrast transformation, a contrast sensitivity function, local masking, and local pooling. By this construction, the SSO provides output in units of "just noticeable differences" (JND) a unit of measure based on the assumed smallest difference of sensory input detectable by a human being. Herein is the truly amazing ability of the SSO, while conventional methods can manipulate images, the SSO models human perception. This set of equations actually defines a mathematical way of working with an image that accurately reflects the way in which the human eye and mind behold a stimulus. The SSO is intended for a wide variety of applications, such as evaluating vision from unmanned aerial vehicles, measuring visibility of damage to aircraft and to the space shuttles, predicting outcomes of corrective laser eye surgery, inspecting displays during the manufacturing process, estimating the quality of compressed digital video, evaluating legibility of text, and predicting discriminability of icons or symbols in a graphical user interface.

Source record↗

Generalized invariance principles and the theory of stability.

Description of some recent extensions of the invariance principle to more generalized dynamical systems where the state space is not locally compact and the flow is unique only in the forward direction of time. A sufficient condition for asymptotic stability of an invariant set is obtained which does not require that the Liapunov function be positive-definite. A recently developed generalized invariance principle is described which is applicable to functional differential equations, partial differential equations, and, in particular, to certain stability problems arising in thermoelasticity, viscoelasticity, and distributed nonlinear networks.

Lasalle, J. P.↗

Foundations of variational discrete action theory

Variational wave functions and Green's functions are two important paradigms for solving quantum Hamiltonians, each having their own advantages. Here we detail the variational discrete action theory (VDAT), which exploits the advantages of both paradigms in order to approximately solve the ground state of quantum Hamiltonians. VDAT consists of two central components: the sequential product density matrix (SPD) ansatz and a discrete action associated with the SPD. The SPD is a variational ansatz inspired by the Trotter decomposition and characterized by an integer $\mathscr{N}$, recovering many well-known variational wave functions, in addition to the exact solution for $\mathscr{N}$ = ∞. The discrete action describes all dynamical information of an effective integer time evolution with respect to the SPD. We generalize the path integral to our integer time formalism, which converts a dynamic correlation function in integer time to a static correlation function in a compound space. We also generalize the usual many-body Green's function formalism to integer time, which results in analogous but distinct mathematical structures, yielding integer time versions of the generating functional, Dyson equation, and Bethe-Salpeter equation. We prove that the SPD can be exactly evaluated in the multiband Anderson impurity model (AIM) by summing a finite number of diagrams. For the multiband Hubbard model, we prove that the self-consistent canonical discrete action approximation (SCDA), which is the integer time analog of the dynamical mean-field theory, exactly evaluates the SPD for d = ∞. VDAT within the SCDA provides an efficient yet reliable method for capturing the local physics of quantum lattice models, which will have broad applications for strongly correlated electron materials. More generally, VDAT should find applications in various many-body problems in physics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Nonrad: Computing nonradiative capture coefficients from first principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. (2014) [8] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Finally, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Extrinsic n-type doping of Cd 3 As 2 thin films

Cd 3 As 2 provides an excellent platform for studying the physics of three-dimensional Dirac semimetals due to its stability as well as its compatibility with thin film growth. Crystals made using both bulk and thin film synthesis are unintentionally doped n-type, and other than introducing Zn to reduce the carrier concentration, no efforts have been reported to alter this intrinsic doping without major changes to the band structure. Here, group VI elements Te and Se are introduced during epitaxy to increase the electron concentration of the films. Starting from an unintentionally doped electron concentration of 1–2 × 10 17 cm -3 , concentrations of up to 3 × 10 18 cm -3 are achieved. Analysis of Shubnikov–de Haas oscillations reveals good agreement in calculated effective mass and Fermi velocity of highly doped films with unintentionally doped single crystals with similar electron concentrations. The density functional theory is also performed to study the effects of group VI substitutions and confirms no strong perturbations in the electronic structure. This work ultimately demonstrates tunability in the carrier concentration using extrinsic dopants without substantial changes in the band structure, allowing for intentional design of Fermi-level position for device applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NLTE model stellar atmospheres with line blanketing near the series limits

In this paper we study the influence of line-merging regions at the intermediate long-wavelength side of a continuum threshold on the computed model atmosphere structure and predicted spectrum. In order to model these regions sufficiently accurately, we have developed two concepts. First, we have extended the occupation probability formalism of Hummer and Mihalas to non-local thermodynamic equilibrium (non-LTE) plasmas. Second, in order to treat the very complicated opacity in the line merging region, we have generalized the concept of opacity distribution functions to treat non-LTE situations. All Rydberg states are consistently included within this framework, so that no arbitrary cutoff of high (LTE) levels is made. We have calculated several pure hydrogen models atmospheres for two effective temperatures, T(sub eff) = 20000 and 35000 K, and discussed the differences between models calculated with various treatments of the line merging. In particular, we have shown that the error in the predicted profiles of Balmer lines resulting from the neglect of line merging is typically of the order of 3-4%, while the errors in the far-UV portion of the Balmer continuum reaches 15-35%. The errors generally decrease with increasing effective temperature. At the same time, the internal accuracy of the models is shown to be about or below 0.5% for all predicted spectral features. We conclude that for interpreting current high-accuracy spectrophotometric observations models including the line merging are necessary, and that the formalism developed in this paper is capable of providing a sufficiently accurate and robust modeling technique.

Hubeny, I.↗

Generalized Bayesian MARS: Tools for Stochastic Computer Model Emulation

The multivariate adaptive regression spline (MARS) approach of Friedman and its Bayesian counterpart are effective approaches for the emulation of computer models. The traditional assumption of Gaussian errors limits the usefulness of MARS, and many popular alternatives, when dealing with stochastic computer models. Here, we propose a generalized Bayesian MARS (GBMARS) framework which admits the broad class of generalized hyperbolic distributions as the induced likelihood function. This allows us to develop tools for the emulation of stochastic simulators which are parsimonious, scalable, and interpretable and require minimal tuning, while providing powerful predictive and uncertainty quantification capabilities. GBMARS is capable of robust regression with t distributions, quantile regression with asymmetric Laplace distributions, and a general form of “Normal-Wald” regression in which the shape of the error distribution and the structure of the mean function are learned simultaneously. We demonstrate the effectiveness of GBMARS on various stochastic computer models, and we show that it compares favorably to several popular alternatives.

97 MATHEMATICS AND COMPUTING↗

The complexity of { 11 2 ¯ 1 } twin interface structure and energetics in HCP materials

Here, the quest for a deeper understanding of the mechanical properties of HCP alloys has been an ongoing effort. Due to the lack of a sufficient number of slip systems, twin nucleation and migration originate as a substantial plastic deformation mechanism in HCP metals. The paper uncovers the energetics and atomistic mechanism of the {$11\overline{2}1$} < $11\overline{2}6$ > which is one of the most prominent twin modes in HCP materials that has not been fully understood. In view of corrugated {$11\overline{2}1$} interfaces, the positioning of lattice/motif atoms needs to be clarified. First, we establish the initial twin boundary (TB) structure unambiguously via the lattice offsets resulting in volume invariancy and correct relative positioning of the twin variants. Secondly, the TB migration mechanism is determined from a crystallographic (zero net shuffle, $Σ\vec{s}$ = 0) and energetic standpoints (minimum energy path). The Generalized Planar Fault Energy (GPFE) curves are calculated for Ti, Hf, Mg, and Zr. Such GPFE curves for this twin mode are calculated for the first time, and point to unusually high unstable energies (300-850 mJ/m 2 ), and low migration barriers (<60 mJ/m 2 ) for twinning accompanied with large shuffle magnitudes, |$\vec{s}$|, comparable to the Burger’s vector (|$\vec{s}$| ≅ $b_e$ > 0.44Å)

36 MATERIALS SCIENCE↗

Exchange-correlation functional challenges in modeling quaternary chalcogenides

The development of next-generation quaternary chalcogenides, such as Cu2ZnSnS4 (CZTS) and Cu2ZnGeS4 (CZGS), for solar energy and thermoelectric applications hinges upon both careful experimentation and accurate quantum mechanical modeling. To address the latter, many have turned to density functional theory (DFT), which offers several choices for the approximate treatment of electron exchange and correlation (XC). Popular XC functionals include the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) and the recently developed strongly constrained and appropriately normed (SCAN) meta-GGA. Extensions of DFT functionals, such as adding a Hubbard U correction and introducing a fraction of the Fock exchange (hybrid functionals), have been used widely to model systems containing 3d metal ions. However, no studies yet have compared comprehensively PBE(+U) and SCAN(+U) in the quality of their predictions of the bulk and defect thermodynamics of quaternary chalcogenides, which play a critical role in device fabrication and performance. Hence, here we calculate the (i) 0 K formation energies of bulk Ge compounds and (ii) neutral defect formation energies including charge-balanced (e.g., CuZn + ZnCu) and charge-imbalanced (e.g., CuSn) combinations of antisites and vacancies in CZTS and CZGS using the PBE, PBE +U, SCAN, SCAN +U, and the hybrid Heyd-Scuseria-Ernzerhof XC frameworks. We find that the formation energies of charge-imbalanced defects are more sensitive to the choice of the XC functional than those of charge-balanced defects, which can be explained by the differences in the extent of penalization of defect-generated delocalized electrons/holes by PBE, PBE +U, SCAN, and SCAN +U. Additionally, our results show that SCAN systematically underbinds Ge-containing compounds, thus highlighting the need for even further improvement of XC functionals. Based on our findings, we recommend the use of SCAN for modeling quaternary chalcogenides because its errors are systematic, and it has the firmest theoretical underpinning. Our work provides guidance for future modeling of quaternary chalcogenides.

14 SOLAR ENERGY↗

Structure prediction of epitaxial inorganic interfaces by lattice and surface matching with Ogre

We present a new version of the Ogre open source Python package with the capability to perform structure prediction of epitaxial inorganic interfaces by lattice and surface matching. In the lattice matching step, a scan over combinations of substrate and film Miller indices is performed to identify the domain-matched interfaces with the lowest mismatch. Subsequently, surface matching is conducted by Bayesian optimization to find the optimal interfacial distance and in-plane registry between the substrate and the film. For the objective function, a geometric score function is proposed based on the overlap and empty space between atomic spheres at the interface. The score function reproduces the results of density functional theory (DFT) at a fraction of the computational cost. The optimized interfaces are pre-ranked using a score function based on the similarity of the atomic environment at the interface to the bulk environment. Final ranking of the top candidate structures is performed with DFT. Ogre streamlines DFT calculations of interface energies and electronic properties by automating the construction of interface models. The application of Ogre is demonstrated for two interfaces of interest for quantum computing and spintronics, Al/InAs and Fe/InSb.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

A new approach to the design of time-varying control systems with application to the Space Shuttle Boost

A general approach to the analysis and design of closed-loop control for slowly time-varying linear systems is presented. The approach uses the method of generalized multiple scales in which slow and fast dynamics are systematically separated by employing different 'clocks' which measure time at varying rates. The clocks, which are necessarily nonlinear functions of time, are chosen in such a manner that the system dynamics are asymptotically invariant with respect to the new time scale. A transfer function relating the output to the input for general linear slowly time-varying systems is developed and represents the actual system under certain conditions. The clock function is shown to satisfy an algebraic characteristic equation and can be determined in terms of the coefficients. The approach can be viewed as an extension of time-invariant linear feedback control theory.

Ramanth, R. V.↗

The role of surfaces in flexoelectricity

We develop the relationship between the strain derivative of the mean-inner potential and surface contributions to flexoelectricity, identifying the true surface-specific component of the flexoelectric response of finite samples. Density functional theory calculations on a range of experimentally observed, low energy SrTiO 3 , MgO, and Si surfaces demonstrate that the mean-inner potential and its contributions to flexoelectricity are sensitive to small differences in surface structure, chemistry, and adsorbates. We also introduce a method to estimate mean-inner potential contributions to flexoelectricity using electron scattering factors and use this approximation to predict total flexoelectric responses for a variety of insulators. Strategies to experimentally disentangle bulk and surface flexoelectric terms are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Spatial autocorrelation of radiation measured by the Earth Radiation Budget Experiment: Scene inhomogeneity and reciprocity violation

The spatial autocorrelation functions of broad-band longwave and shortwave radiances measured by the Earth Radiation Budget Experiment (ERBE) are analyzed as a function of view angle in an investigation of the general effects of scene inhomogeneity on radiation. For nadir views, the correlation distance of the autocorrelation function is about 900 km for longwave radiance and about 500 km for shortwave radiance, consistent with higher degrees of freedom in shortwave reflection. Both functions rise monotonically with view angle, but there is a substantial difference in the relative angular dependence of the shortwave and longwave functions, especially for view angles less than 50 deg. In this range, the increase with angle of the longwave functions is found to depend only on the expansion of pixel area with angle, whereas the shortwave functions show an additional dependence on angle that is attributed to the occlusion of inhomogeneities by cloud height variations. Beyond a view angle of about 50 deg, both longwave and shortwave functions appear to be affected by cloud sides. The shortwave autocorrelation functions do not satisfy the principle of directional reciprocity, thereby proving that the average scene is horizontally inhomogeneous over the scale of an ERBE pixel (1500 sq km). Coarse stratification of the measurements by cloud amount, however, indicates that the average cloud-free scene does satisfy directional reciprocity on this scale.

Davies, Roger↗

Hybrid magnon-phonon localization enhances function near ferroic glassy states

Ferroic materials on the verge of forming ferroic glasses exhibit heightened functionality that is often attributed to competing long- and short-range correlations. However, the physics underlying these enhancements is not well understood. The Ni 45 Co 5 Mn 36.6 In 13.4 Heusler alloy is on the edge of forming both spin and strain glasses and exhibits magnetic field–induced shape memory and large magnetocaloric effects, making it a candidate for multicaloric cooling applications. We show using neutron scattering that localized magnon-phonon hybrid modes, which are inherently spread across reciprocal space, act as a bridge between phonons and magnons and result in substantial magnetic field–induced shifts in the phonons, triple the caloric response, and alter phase stability. We attribute these modes to the localization of phonons and magnons by antiphase boundaries coupled to magnetic domains. Because the interplay between short- and long-range correlations is common near ferroic glassy states, our work provides general insights on how glassiness enhances function.

36 MATERIALS SCIENCE↗

Heat Transfer in a Liquid Metal Flowing Turbulently through a Channel with a Step Function Boundary Temperature

An analytical heat transfer solution is derived and evaluated for the general case of a turbulently flowing liquid metal which suddenly encounters a step-function boundary temperature in a channel system. Local Nusselt moduli, dimensionless mixed-mean fluid temperatures, and arithmetic-mean Nusselt moduli are given as functions of Reynolds and Prandtl moduli and a dimensionless axial-distance modulus. These solutions are compared with known solutions of more specific systems as well as with a set of experimental liquid-metal heat transfer data for a thermal entrance region.

Poppendiek, H. F.↗