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All sourcesNASA NTRSDOE OSTI
NASA NTRS2011

Multidimensional Generalized Functions in Aeroacoustics and Fluid Mechanics: Basic Concepts and Operations - Part 1

This paper is the first part of a three part tutorial on multidimensional generalized functions (GFs) and their applications in aeroacoustics and fluid mechanics. The subject is highly fascinating and essential in many areas of science and, in particular, wave propagation problems. In this tutorial, we strive to present rigorously and clearly the basic concepts and the tools that are needed to use GFs in applications effectively and with ease. We give many examples to help the readers in understanding the mathematical ideas presented here. The first part of the tutorial is on the basic concepts of GFs. Here we define GFs, their properties and some common operations on them. We define the important concept of generalized differentiation and then give some interesting elementary and advanced examples on Green's functions and wave propagation problems. Here, the analytic power of GFs in applications is demonstrated with ease and elegance. Part 2 of this tutorial is on the diverse applications of generalized derivatives (GDs). Part 3 is on generalized Fourier transformations and some more advanced topics. One goal of writing this tutorial is to convince readers that, because of their powerful operational properties, GFs are absolutely essential and useful in engineering and physics, particularly in aeroacoustics and fluid mechanics.

Farassat, Fereidoun↗
DOE OSTI2023

Variational Monte Carlo calculations of n + H 3 scattering

A paramount goal in nuclear physics is to unify ab initio treatments of bound and unbound states. The position-space quantum Monte Carlo (QMC) methods have a long history of successful bound-state calculations in light systems but have seen minimal implementation in unbound systems. Here, we introduce a numerical method to improve the efficiency and accuracy of unbound-state calculations in QMC. As an initial application, we compute scattering observables for the smallest system available to probe three-body forces, the neutron-triton system, using variational Monte Carlo (VMC) wave functions. The method involves inferring long-range amplitudes in the wave function from integrals over the short-range region where all the particles interact. This approach using integral relations is well established in the literature; here, we develop it for the QMC framework. We validate our approach with a consistency check between short-range spectroscopic overlap functions computed from direct evaluation and from the integral relations; scattering amplitudes are long-range asymptotics of those overlaps. Comparison against published benchmark calculations using the same potential demonstrates that when applied to the current VMC wave functions, the integral method produces more accurate scattering observables than direct evaluation from the same variational wave function. However, it still differs noticeably from the exact results. Using additional interactions, we then present phase shifts and mixing parameters for the n + 3 H system. In particular, we present one of the first applications of the Norfolk family of local coordinate-space chiral potentials in unbound systems of A > 2. The Norfolk results accurately describe s-wave scattering but predict p-wave cross sections too large. Compared with previous QMC scattering calculations, the integral method avoids difficulties associated with the precise computation of energy differences and with convergence outside the interaction region, which is particularly severe in the variational calculation. Application of the integral method here paves the way for its use in Green's function Monte Carlo (GFMC) calculations. In GFMC, the wave functions are more accurate, but the high-precision convergence of their tails is slow, and there are additional difficulties in reading out amplitudes. Here, the integral methods will address both of those remaining problems.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Single-Molecule Electron Transport in Peptoids

Peptoids are structural analogs of peptides in which side chains are appended to the backbone nitrogen rather than the α-carbon. The sequence-defined modularity of peptoids enables precise control over structure−function relationships, enabling applications in energy storage and biomedical materials. Despite recent progress, the role of sequence and conformation on electron transport in peptoid molecules is not fully understood. Here, we synthesize a library of peptoid oligomers and characterize their molecular electronic properties using the scanning tunneling microscope-break junction (STM-BJ) technique. Our results show well-defined electron transport behavior for peptoid sequences containing aromatic side groups lacking hydrogen bonds (H-bonds) and without chemical substitutions at the N−C α position. This behavior fundamentally differs from electron transport in peptides, where H-bond interactions give rise to higher conductance states. All-atom molecular dynamics (MD) simulations are used to understand the conformational heterogeneity of peptoids, and molecular conformations obtained from MD simulations are used in quantum mechanical calculations based on the nonequilibrium Green’s function−density functional theory (NEGF-DFT) formalism. In all cases, computational results are in reasonable qualitative agreement with experiments. Our work demonstrates that the conductance behavior of peptoids depends on monomer identity, including side-chain aromaticity and substitution at the N−C α position. Overall, this work provides new insights into the structure−function relationships governing electron transport in peptoid-based materials and establishes design rules for peptoid-based molecular junctions.

Charge transport↗
DOE OSTI2022

Ab initio estimation of E 2 strengths in Li 8 and its neighbors by normalization to the measured quadrupole moment

For electric quadrupole (E2) observables, which depend on the large-distance tails of the nuclear wave function, ab initio no-core configuration interaction (NCCI) calculations converge slowly, making meaningful predictions challenging to obtain. Nonetheless, the calculated values for different E2 matrix elements, particularly those involving levels with closely-related structure (e.g., within the same rotational band) are found to be robustly proportional. This observation suggests that a known value for one observable may be used to determine the overall scale of E2 strengths, and thereby provide predictions for others. In particular, we demonstrate that meaningful predictions for E2 transitions may be obtained by calibration to the ground-state quadrupole moment. Here, we test this approach for well-measured low-lying E2 transitions in 7 Li and 9 Be, then provide predictions for transitions in 8 Li and 9 Li. In particular, we address the 2 + → 1 + transition in 8 Li, for which the reported measured strength exceeds ab initio Green's function Monte Carlo (GFMC) predictions by over an order of magnitude.

6 ≤ A ≤ 19↗
DOE OSTI2024

Journey to Time-Variable Moment Tensors through Inversion of Acoustic and Seismoacoustic Data

We explore the capability of acoustic and seismoacoustic datasets to directly resolve a complex, time-variable source consisting of a buried mechanism, represented as a moment tensor, and a spall mechanism, represented as a vertical force at the surface. Traditionally, each component of a resolved moment tensor assumes one underlying source time function, which likely fails to capture the full evolution of a dynamic source, such as an explosion followed by slip on near-source joints or development of spallation. Specifically, we expand previous work to resolve a time-variable moment tensor using single-modality and joint-modality inversion frameworks through analysis of infrasound and seismoacoustic data recorded as part of the Source Physics Experiment Phase II: Dry Alluvium Geology (DAG). We investigate the impact of including signals from seismic-to-air coupling that are local to each infrasound sensor in comparison to mainly atmosphere-propagating acoustic signals, which occur from coupling of the wavefield from the subsurface to the atmosphere directly above the source. Additionally, we assess the ability of our inversion algorithm to fit observed infrasound data using a variety of time-variable source mechanisms. First, we consider the buried moment tensor source alone, which assumes that the determined Green’s functions incorporate effects from spallation or that the impact from spallation is minimal. Second, we examine the estimated buried moment tensor and vertical surface spallation as terms that must both be resolved in the inversion. Third, we assess the ability for an estimated vertical surface spallation source to fit the acoustic data on its own. Finally, we compare results from the joint inversion of both seismic geophone and infrasound acoustic data for the buried-only source compared to buried and spallation sources. Our results are a preliminary investigation into the applications of the inversion technique to recorded datasets and show the technique has limited capabilities using acoustic data alone. Instead, this method shows promise for seismic and seismoacoustic datasets to resolve the time-variable mechanisms of a buried source.

47 OTHER INSTRUMENTATION↗
NASA NTRS1987

Radar scene generation for tactical decision aids

The Mueller matrix and polarization covariance matrix for polarimetric radar systems was studied. The clutter is modeled by a layer of random permittivity, described by a three-dimensional correlation function, with variance, and horizontal and vertical correlation lengths. A general mixing formula was derived for discrete scatters immersed in a host medium. The results are applicable to general multiphase mixtures. The strong fluctuation theory was used to derive the backscattering cross sections, and was further extended to include higher order co-polarized and cross-polarized moments. A two-layer anisotropic random medium model was developed for the active and passive remote sensing of ice fields. A three-layer random medium model was adopted to study the volume scattering effects for the active and passive microwave remote sensing of snow-covered ice fields. The snow layer was simulated by an isotropic random medium and the ice layer by an anisotropic random medium. The vegetation canopy and snow-covered ice field were studied with a three-layer model, an isotropic random medium layer overlying an anisotropic random medium. The dyadic Green's function of the three-layer medium and the scattered electromagnetic intensities with Born approximation were calculated.

Kong, J. A.↗
DOE OSTI2016

Phases of new physics in the CMB

Fluctuations in the cosmic neutrino background are known to produce a phase shift in the acoustic peaks of the cosmic microwave background. It is through the sensitivity to this effect that the recent CMB data has provided a robust detection of free-streaming neutrinos. In this paper, we revisit the phase shift of the CMB anisotropy spectrum as a probe of new physics. The phase shift is particularly interesting because its physical origin is strongly constrained by the analytic properties of the Green's function of the gravitational potential. For adiabatic fluctuations, a phase shift requires modes that propagate faster than the speed of fluctuations in the photon-baryon plasma. This possibility is realized by free-streaming relativistic particles, such as neutrinos or other forms of dark radiation. Alternatively, a phase shift can arise from isocurvature fluctuations. We present simple models to illustrate each of these effects. We then provide observational constraints from the Planck temperature and polarization data on additional forms of radiation. We also forecast the capabilities of future CMB Stage IV experiments. Whenever possible, we give analytic interpretations of our results.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Metastable antiphase boundary ordering in CaFe 2 O 4

CaFe 2 O 4 is an $\textit{S}$ = 5/2 antiferromagnet exhibiting two magnetic orders that shows regions of coexistence at some temperatures. Using a Green’s function formalism, we model neutron scattering data of the spin wave excitations in this material, elucidating the microscopic spin Hamiltonian. In doing so, we suggest that the low-temperature A phase order (↑↑↓↓) finds its origins in the freezing of antiphase boundaries created by thermal fluctuations in a parent B phase order (↑↓↑↓). In this work, the low-temperature magnetic order observed in CaFe 2 O 4 is thus the result of a competition between the exchange coupling along $\textit{c}$, which favors the B phase, and the single-ion anisotropy, which stabilizes thermally generated antiphase boundaries, leading to static metastable A phase order at low temperatures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2019

Quantum dynamics of a molecular emitter strongly coupled with surface plasmon polaritons: A macroscopic quantum electrodynamics approach

In this work, we study a molecular emitter above a silver surface in the framework of macroscopic quantum electrodynamics and explore the population dynamics including non-Markovian effects. The theory we present is general for molecular fluorescence in the presence of dielectrics with any space-dependent, frequency-dependent, or complex dielectric functions. Furthermore, the proposed theory allows us to calculate the memory kernel of polaritons using computational electrodynamics packages. In the limit of a high vibration frequency, the different strengths of exciton-polariton couplings lead to distinct characteristics in the population dynamics, e.g., Franck-Condon-Rabi oscillation. (The frequency of Rabi oscillation is dependent on the Franck-Condon factor.) Additionally, in a specific condition, we derive a parameter-free formula that can be used to estimate the exciton-polariton coupling between a molecular emitter and a nanocavity, and the coupling estimated by our theory is in good agreement with the reported experimental results.

Surface plasmon polaritons↗
DOE OSTI2015

Designing field-controllable graphene-dot-graphene single molecule switches: A quantum-theoretical proof-of-concept under realistic operating conditions

A theoretical proof of the concept that a particularly designed graphene-based moletronics device, constituted by two semi-infinite graphene subunits, acting as source and drain electrodes, and a central benzenoid ring rotator (a “quantum dot”), could act as a field-controllable molecular switch is outlined and analyzed with the density functional theory approach. Besides the ideal (0 K) case, we also consider the operation of such a device under realistic operating (i.e., finite-temperature) conditions. An in-depth insight into the physics behind device controllability by an external field was gained by thorough analyses of the torsional potential of the dot under various conditions (absence or presence of an external gating field with varying strength), computing the torsional correlation time and transition probabilities within the Bloembergen-Purcell-Pound formalism. Both classical and quantum mechanical tunneling contributions to the intramolecular rotation were considered in the model. The main idea that we put forward in the present study is that intramolecular rotors can be controlled by the gating field even in cases when these groups do not possess a permanent dipole moment (as in cases considered previously by us [I. Petreska et al., J. Chem. Phys. 134, 014708-1–014708-12 (2011)] and also by other groups [P. E. Kornilovitch et al., Phys. Rev. B 66, 245413-1–245413-7 (2002)]). Consequently, one can control the molecular switching properties by an external electrostatic field utilizing even nonpolar intramolecular rotors (i.e., in a more general case than those considered so far). Molecular admittance of the currently considered graphene-based molecular switch under various conditions is analyzed employing non-equilibrium Green’s function formalism, as well as by analysis of frontier molecular orbitals’ behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Josephson current in Fe-based superconducting junctions: Theory and experiment

Here we present a theory of the dc Josephson effect in contacts between Fe-based and spin-singlet s -wave superconductors. The method is based on the calculation of temperature Green's function in the junction within the tight-binding model. We calculate the phase dependencies of the Josephson current for different orientations of the junction relative to the crystallographic axes of Fe-based superconductor. Further, we consider the dependence of the Josephson current on the thickness of an insulating layer and on temperature. Experimental data for PbIn / Ba 1 – x K x ( FeAs ) 2 point-contact Josephson junctions are consistent with theoretical predictions for s ± symmetry of an order parameter in this material. The proposed method can be further applied to calculations of the dc Josephson current in contacts with other new unconventional multiorbital superconductors, such as Sr 2 RuO 4 and the superconducting topological insulator Cu x Bi 2 Se 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

α decay of the T = 1 , 2 + state in B 10 and isospin symmetry breaking in the A = 10 triplet

Here, the rate of the T =1, 2+ to T =1, 0 + transition in 10 B ( T =1, T z =0) is compared to the analog transitions in 10 Be ( T =1, T z =–1) and 10 C ( T =1, T z =+1) to provide constraints on ab initio calculations using realistic nuclear forces. The relevant state in 10 B, at E x =5.164 MeV, is particle unbound. Therefore, a determination of the B ( E 2) electromagnetic transition rate requires a precise and accurate determination of the width of the state, as well as the α-particle and γ-ray branching ratios. Previous measurements of the α-particle branching ratio are just barely in agreement. We report on a new study of the α-particle branch by studying the 10 B(p,p') 10 B* reaction in inverse kinematics with the HELIOS spectrometer. The α-particle branching ratio that we observe, 0.144±0.027, is in good agreement with the evaluated value and improves the associated uncertainty. The resulting experimental B ( E 2) value is 7.0±2.2 e 2 fm 4 and is more consistent with a flat trend across the A=10 triplet than previously reported. This is inconsistent with Green's function Monte Carlo predictions using realistic three-nucleon Hamiltonians, which overpredict the B ( E 2) value in 10 C and 10 B.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Breakdown of the drift-diffusion model for transverse spin transport in a disordered Pt film

Spin-accumulation and spin-current profiles are calculated for a disordered Pt film subjected to an in-plane electric current within the nonequilibrium Green's function approach. In the bulklike region of the sample, this approach captures the intrinsic spin Hall effect found in other calculations. Near the surfaces, the results reveal qualitative differences with the results of the widely used spin-diffusion model, even when the boundary conditions are modified to try to account for them. One difference is that the effective spin-diffusion length for transverse spin transport is significantly different from its longitudinal counterpart and is instead similar to the mean-free path. Furthermore, this feature may be generic for spin currents generated via the intrinsic spin Hall mechanism because of the differences in transport mechanisms compared to longitudinal spin transport. Orbital accumulation in the Pt film is only significant in the immediate vicinity of the surfaces and has a small component penetrating into the bulk only in the presence of spin-orbit coupling, as a secondary effect induced by the spin accumulation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Nucleophilic C—H functionalization of arenes: a contribution to green chemistry

The review is focused on premises, features and scope of the reactions leading to the direct functionalization of the C—H bond in arenes by the action of nucleophiles. Practical importance and a contribution of synthetic approaches with minimal steps, the so called PASE- (pot-, atom-, and step-economic) processes, to green chemistry are also discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Waveform inversion of acoustic waves for explosion yield estimation

We present a new waveform inversion technique to estimate the energy of near-surface explosions using atmospheric acoustic waves. Conventional methods often employ air blast models based on a homogeneous atmosphere, where the acoustic wave propagation effects (e.g., refraction and diffraction) are not taken into account, and therefore, their accuracy decreases with increasing source-receiver distance. In this study, three-dimensional acoustic simulations are performed with a finite difference method in realistic atmospheres and topography, and the modeled acoustic Green's functions are incorporated into the waveform inversion for the acoustic source time functions. The strength of the acoustic source is related to explosion yield based on a standard air blast model. The technique was applied to local explosions (<10 km) and provided reasonable yield estimates (<~30% error) in the presence of realistic topography and atmospheric structure. In conclusion, the presented method can be extended to explosions recorded at far distance provided proper meteorological specifications.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2016

An analytical thermohydraulic model for discretely fractured geothermal reservoirs

In discretely fractured reservoirs such as those found in Enhanced/Engineered Geothermal Systems (EGS), knowledge of the fracture network is important in understanding the thermal hydraulics, i.e., how the fluid flows and the resulting temporal evolution of the subsurface temperature. Here, the purpose of this study was to develop an analytical model of the fluid flow and heat transport in a discretely fractured network that can be used for a wide range of modeling applications and serve as an alternative analysis tool to more computationally intensive numerical codes. Given the connectivity and structure of a fracture network, the flow in the system was solved using a linear system of algebraic equations for the pressure at the nodes of the network. With the flow determined, the temperature in the fracture was solved by coupling convective heat transport in the fracture with one-dimensional heat conduction perpendicular to the fracture, employing the Green’s function derived solution for a single discrete fracture. The predicted temperatures along the fracture surfaces from the analytical solution were compared to numerical simulations using the TOUGH2 reservoir code. Through two case studies, we showed the capabilities of the analytical model and explored the effect of uncertainty in the fracture apertures and network structure on thermal performance. While both sources of uncertainty independently produce large variations in production temperature, uncertainty in the network structure, whenever present, had a predominant influence on thermal performance.

58 GEOSCIENCES↗
DOE OSTI2015

A class of exact solutions for population balances with arbitrary internal coordinates

We develop a novel transformation that maps the linear, nonhomogeneous, multidimensional population balance equation (PBE) into an advection equation that is readily solved using the method of characteristics. The PBEs targeted by this transformation exclude aggregation, breakage, and time dependent birth and death rates. In addition, internal coordinates are assumed to grow independently of each other. The ensuing general formulation is then used to recover closed‐form analytical solutions for problems with monosurface and bulk‐diffusion growth‐rates as well as Gaussian‐type nucleation. For completeness, we derive the multidimensional Green's functions for our approach. This is followed by a brief discussion on how the proposed framework may be used for code verification of moment methods such as the quadrature method of moments and the direct quadrature method of moments. Finally, a sample Mathematica code is provided to derive analytical solutions for the single‐internal‐coordinate case given user‐specified growth, birth, and death rates. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1691–1698, 2015

Saad, Tony↗
DOE OSTI2026

Machine Learning Approach to Modeling of Neutral Particles Transport in Plasma

A propagator‐based approach is investigated for Monte‐Carlo (MC) modeling of neutral particle transport in fusion boundary plasmas. The propagator is based on a Green's function for the neutral kinetic equation, which depends on the plasma profiles. A neural network (NN)‐based model for the propagator provides a fast and accurate solution for the neutral distribution function in plasma. Preliminary results from a small 1D test problem look encouraging. The proposed approach, a propagator‐based NN model for neutral transport in plasma, has potential for generalization to higher dimensions and efficient coupling with plasma models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗