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At least 523 records · Page 29

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NASA NTRS2014

Modeling Sound Propagation Through Non-Axisymmetric Jets

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Leib, Stewart J.↗

DOE OSTI2019

Magnetized orbifolds and localized flux

Magnetized orbifolds play an important role in compactifications of string theories and higher-dimensional field theories to four dimensions. Magnetic flux leads to chiral fermions, it can be a source of supersymmetry breaking and it is an important ingredient of moduli stabilization. Flux quantization on orbifolds is subtle due to the orbifold singularities. Generically, Wilson line integrals around these singularities are non-trivial, which can be interpreted as localized flux. As a consequence, flux densities on orbifolds can take the same values as on tori. We determine the transition functions for the flux vector bundle on the orbifold T 2 /Z 2 and the related twisted boundary conditions of zero-mode wave functions. We also construct “untwisted” zero-mode functions that are obtained for singular vector fields related to the Green’s function on a torus, and we discuss the connection between zeros of the wave functions and localized flux. Twisted and untwisted zero-mode functions are related by a singular gauge transformation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Numerical integration for ab initio many-electron self energy calculations within the GW approximation

We present a numerical integration scheme for evaluating the convolution of a Green's function with a screened Coulomb potential on the real axis in the GW approximation of the self energy. Our scheme takes the zero broadening limit in Green's function first, replaces the numerator of the integrand with a piecewise polynomial approximation, and performs principal value integration on subintervals analytically. We give the error bound of our numerical integration scheme and show by numerical examples that it is more reliable and accurate than the standard quadrature rules such as the composite trapezoidal rule. We also discuss the benefit of using different self energy expressions to perform the numerical convolution at different frequencies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Demonstration of resonant inelastic x-ray scattering as a probe of exciton-phonon coupling

Resonant inelastic x-ray scattering (RIXS) is a promising technique for obtaining electron-phonon coupling constants. However, the ability to extract these coupling constants throughout the Brillouin zone for crystalline materials remains limited. To address this need, we developed a Green's function formalism to capture electron-phonon contributions to core-level spectroscopies without explicitly solving the full vibronic problem. Our approach is based on the cumulant expansion of the Green's function combined with many-body theory calculated vibrational coupling constants. The methodology is applied to x-ray photoemission spectroscopy, x-ray absorption spectroscopy (XAS), and RIXS. In the case of the XAS and RIXS, we use a two-particle exciton Green's function, which accounts implicitly for particle-hole interference effects that have previously proved difficult. To demonstrate the methodology and gain a deeper understanding of the experimental technique, we apply our formalism to small molecules, for which unambiguous experimental data exist. This comparison reveals that the vibronic coupling constant probed by RIXS is in fact related to exciton-phonon coupling rather than electron-phonon coupling, challenging the conventional interpretation of the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2019

Sparse low rank approximation of potential energy surfaces with applications in estimation of anharmonic zero point energies and frequencies

We introduce a method that exploits sparse representation of potential energy surfaces (PES) on a polynomial basis set selected by compressed sensing . The method is useful for studies involving large numbers of PES evaluations, such as the search for local minima, transition states, or integration. We apply this method for estimating zero point energies and frequencies of molecules using a three step approach. In the first step, we interpret the PES as a sparse tensor on polynomial basis and determine its entries by a compressed sensing based algorithm using only a few PES evaluations. Then, we establish a rank reduction strategy to compress this tensor in a suitable low-rank canonical tensor format using standard tensor compression tools. This allows representing a high dimensional PES as a small sum of products of one dimensional functions. Finally, a low dimensional Gauss–Hermite quadrature rule is used to integrate the product of sparse canonical low-rank representation of PES and Green’s function in the second-order diagrammatic vibrational many-body Green’s function theory (XVH2) for estimation of zero-point energies and frequencies. Numerical tests on molecules considered in this work indicate a more efficient scaling of computational cost with molecular size as compared to other methods.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1995

An extension of the Lighthill theory of jet noise to encompass refraction and shielding

A formalism for jet noise prediction is derived that includes the refractive 'cone of silence' and other effects; outside the cone it approximates the simple Lighthill format. A key step is deferral of the simplifying assumption of uniform density in the dominant 'source' term. The result is conversion to a convected wave equation retaining the basic Lighthill source term. The main effect is to amend the Lighthill solution to allow for refraction by mean flow gradients, achieved via a frequency-dependent directional factor. A general formula for power spectral density emitted from unit volume is developed as the Lighthill-based value multiplied by a squared 'normalized' Green's function (the directional factor), referred to a stationary point source. The convective motion of the sources, with its powerful amplifying effect, also directional, is already accounted for in the Lighthill format: wave convection and source convection are decoupled. The normalized Green's function appears to be near unity outside the refraction dominated 'cone of silence', this validates our long term practice of using Lighthill-based approaches outside the cone, with extension inside via the Green's function. The function is obtained either experimentally (injected 'point' source) or numerically (computational aeroacoustics). Approximation by unity seems adequate except near the cone and except when there are shrouding jets: in that case the difference from unity quantifies the shielding effect. Further extension yields dipole and monopole source terms (cf. Morfey, Mani, and others) when the mean flow possesses density gradients (e.g., hot jets).

Ribner, Herbert S.↗

NASA NTRS2014

Acoustics of Jet Surface Interaction - Scrubbing Noise

Concepts envisioned for the future of civil air transport consist of unconventional propulsion systems in the close proximity to the structure or embedded in the airframe. While such integrated systems are intended to shield noise from the community, they also introduce new sources of sound. Sound generation due to interaction of a jet flow past a nearby solid surface is investigated here using the generalized acoustic analogy theory. The analysis applies to the boundary layer noise generated at and near a wall, and excludes the scattered noise component that is produced at the leading or the trailing edge. While compressibility effects are relatively unimportant at very low Mach numbers, frictional heat generation and thermal gradient normal to the surface could play important roles in generation and propagation of sound in high speed jets of practical interest. A general expression is given for the spectral density of the far field sound as governed by the variable density Pridmore-Brown equation. The propagation Green's function is solved numerically for a high aspect-ratio rectangular jet starting with the boundary conditions on the surface and subject to specified mean velocity and temperature profiles between the surface and the observer. It is shown the magnitude of the Green's function decreases with increasing source frequency and/or jet temperature. The phase remains constant for a rigid surface, but varies with source location when subject to an impedance type boundary condition. The Green's function in the absence of the surface, and flight effects are also investigated

Jet Noise↗

DOE OSTI2015

Calculation of the spectrum of quasiparticle electron excitations in organic molecular semiconductors

A quasiparticle electronic spectrum belongs to the characteristics of nanoobjects that are most important for applications. The following methods of calculating the electronic spectrum are analyzed: the Kohn-Sham equations of the density functional theory (DFT), the hybrid functional method, the GW approximation, and the Lehmann approximation used in the spectral representation of one-electron Green’s function. The results of these approaches are compared with the data of photoemission measurements of benzene, PTCDA, and phthalocyanine (CuPc, H{sub 2}Pc, FePc, PtPc) molecules, which are typical representatives of organic molecular semiconductors (OMS). This comparison demonstrates that the Kohn-Sham equations of DFT incorrectly reproduce the electronic spectrum of OMS. The hybrid functional method correctly describes the spectrum of the valence and conduction bands; however, the HOMO-LUMO gap width is significantly underestimated. The correct gap width is obtained in both the GW approximation and the Lehmann approach, and the total energy in this approach can be calculated in the local density approximation of DFT.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Quantum solver for single-impurity Anderson models with particle-hole symmetry

Quantum embedding methods, such as dynamical mean-field theory (DMFT), provide a powerful framework for investigating strongly correlated materials. A central computational bottleneck in DMFT is in solving the Anderson impurity model (AIM), whose exact solution is classically intractable for large bath sizes. In this work, we benchmark a quantum-classical hybrid solver tailored for particle-hole symmetric AIMs, using the variational quantum eigensolver to prepare the ground state of the model with shallow quantum circuits. The solver uses shallow quantum ansätze and one set of variational parameters to prepare the ground state and its particle and hole excitations, enabling the construction of the impurity Green’s function through a continued-fraction expansion. We evaluate the performance of this approach across a few bath sizes and interaction strengths under noisy, shot-limited conditions. We compare three optimization routines (COBYLA, Adam, and L-BFGS-B) in terms of convergence and fidelity, assess the benefits of estimating a quantum-computed moment correction to the variational energies, and benchmark the approach by comparing the density of states computed from the impurity Green’s function against that obtained using a classical pipeline. Our results demonstrate the feasibility of Green’s function construction on near-term devices and establish practical benchmarks for quantum impurity solvers embedded within self-consistent DMFT loops.

Karabin, Mariia [ORNL]↗

DOE OSTI2017

ShiftNMFk 1.2

The ShiftNMFk1.2 code, or as we call it, GreenNMFk, represents a hybrid algorithm combining unsupervised adaptive machine learning and Green's function inverse method. GreenNMFk allows an efficient and high performance de-mixing and feature extraction of a multitude of nonnegative signals that change their shape propagating through the medium. The signals are mixed and recorded by a network of uncorrelated sensors. The code couples Non-negative Matrix Factorization (NMF) and inverse-analysis Green's functions method. GreenNMF synergistically performs decomposition of the recorded mixtures, finds the number of the unknown sources and uses the Green's function of the governing partial differential equation to identify the unknown sources and their charecteristics. GreenNMF can be applied directly to any problem controlled by a known partial-differential parabolic equation where mixtures of an unknown number of sources are measured at multiple locations. Full GreenNMFk method is a subject LANL U.S. Patent application S133364.000 August, 2017. The ShiftNMFk 1.2 version here is a toy version of this method that can work with a limited number of unknown sources (4 or less).

Alexandrov, BoianS.↗

NASA NTRS1999

Coupling of Low Speed Fan Stator Vane Unsteady Pressures to Duct Modes: Measured versus Predicted

Uniform-flow annular-duct Green's functions are the essential elements of the classical acoustic analogy approach to the problem of computing the noise generated by rotor-stator interaction inside the fan duct. This paper investigates the accuracy of this class of Green's functions for predicting the duct noise levels when measured stator vane unsteady surface pressures are used as input to the theoretical formulation. The accuracy of the method is evaluated by comparing the predicted and measured acoustic power levels for the NASA 48 inch low speed Active Noise Control Fan. The unsteady surface pressures are measured,by an array of microphones imbedded in the suction and pressure sides of a single vane, while the duct mode levels are measured using a rotating rake system installed in the inlet and exhaust sections of the fan duct. The predicted levels are computed using properly weighted integrals of measured surface pressure distribution. The data-theory comparisons are generally quite good particularly when the mode cut-off criterion is carefully interpreted. This suggests that, at least for low speed fans, the uniform-flow annular-duct Green's function theory can be reliably used for prediction of duct mode levels if the cascade surface pressure distribution is accurately known.

Sutliff, Daniel L.↗

DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

First-principles calculations of solute transport in zirconium: Vacancy-mediated diffusion with metastable states and interstitial diffusion

Zirconium alloys are the most widely used nuclear fuel cladding materials for light water power reactors where irradiation damage causes solute redistribution, leading to degradation of alloy properties such as corrosion resistance. Designing radiation-tolerant zirconium alloys requires a thorough understanding of the atomic-scale transport behavior of the alloying elements in Zr. In this work, we perform density function theory calculations to investigate the diffusion of Sn, Cr, Fe, Be, Al, and Ni in the hexagonal close-packed (HCP) Zr matrix. We develop a methodology to accurately model the metastable vacancy states along the basal migration path, known to occur in group IV metals. We compute the vacancy-mediated solute diffusion coefficients and drag ratios using the kinetic Monte Carlo method and an analytic Green's function method—the agreement between the two validates our methodology. The computed diffusion coefficients of Sn and Al show good agreement with the experimental data and we expect these solutes to diffuse via the vacancy-mediated mechanism. We use a Green's function approach, parameterized with data from density functional theory calculations, to compute the interstitial diffusion coefficients of Cr, Fe, Be, and Ni in the HCP Zr lattice. The computed diffusion coefficients of Cr, Ni, and Be agree with the experimental measurements within one order of magnitude, while those of Fe are within two orders of magnitude of the experimental measurements. The drag ratios for Cr, Fe, Be, and Ni are positive up to 1235 K, which suggests that nonequilibrium vacancy fluxes could drag these solutes toward sinks such as dislocation loops and grain boundaries. We also compute the transport coefficients without including the metastable states, and using the eight- and thirteen-frequency model. Our results show significant differences in drag ratio for the eight- and thirteen-frequency model predictions compared with the Green's function methodology, but smaller errors in the solute diffusivity. Combining interstitial and vacancy-mediated diffusivities, we predict the unusual result that increased vacancy concentration slows down solute diffusivity, while a sufficiently high vacancy concentration can change the dominant mechanism to an accelerated vacancy-mediated diffusion.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Iterative subspace algorithms for finite-temperature solution of Dyson equation

One-particle Green’s functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green’s function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles. In this paper, we study acceleration techniques to target the self-consistent solution of the Dyson equation directly. We use the direct inversion in the iterative subspace (DIIS), the least-squared commutator in the iterative subspace (LCIIS), and the Krylov space accelerated inexact Newton method (KAIN). We observe that the definition of the residual has a significant impact on the convergence of the iterative procedure. Based on the Dyson equation, we generalize the concept of the commutator residual used in DIIS and LCIIS and compare it with the difference residual used in DIIS and KAIN. The commutator residuals outperform the difference residuals for all considered molecular and solid systems within both GW and GF2. For a number of bond-breaking problems, we found that an easily obtained high-temperature solution with effectively suppressed correlations is a very effective starting point for reaching convergence of the problematic low-temperature solutions through a sequential reduction of temperature during calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

The effect of Coulomb interactions on nonlinear thermovoltage and thermocurrent in quantum dots

In the present work, we theoretically study the nonlinear regime of charge transport through a quantum dot coupled to the source and drain reservoirs. The investigation is carried out using a nonequilibrium Green’s function formalism beyond the Hartree-Fock approximation. Employed approximations for the relevant Green’s functions allow to trace a transition from Coulomb blockade regime to Kondo regime in the thermoelectric transport. Effects arising when electrons move in response to thermal gradient applied across the system are discussed, including experimentally observed thermovoltage zeros.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

spec-org/gfcc

Green's Function Coupled Cluster Library SPEC GFCC library enables calculations for spectral functions and binding energies of molecular systems using highly scalable implementation of the Green's function coupled cluster (GFCC) approach

Panyala, Ajay↗

DOE OSTI2015

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Inter-layer coupling induced valence band edge shift in mono- to few-layer MoS 2

In this study, recent progress in the synthesis of monolayer MoS 2 , a two-dimensional direct band-gap semiconductor, is paving new pathways toward atomically thin electronics. Despite the large amount of literature, fundamental gaps remain in understanding electronic properties at the nanoscale. Here,we report a study of highly crystalline islands of MoS 2 grown via a refined chemical vapor deposition synthesis technique. Using high resolution scanning tunneling microscopy and spectroscopy (STM/STS), photoemission electron microscopy/spectroscopy (PEEM) and μ-ARPES we investigate the electronic properties of MoS 2 as a function of the number of layers at the nanoscale and show in-depth how the band gap is affected by a shift of the valence band edge as a function of the layer number. Green’s function based electronic structure calculations were carried out in order to shed light on the mechanism underlying the observed bandgap reduction with increasing thickness, and the role of the interfacial Sulphur atoms is clarified. Our study, which gives new insight into the variation of electronic properties of MoS 2 films with thickness bears directly on junction properties of MoS2, and thus impacts electronics application of MoS 2 .

36 MATERIALS SCIENCE↗