Results for “Greens function” — Page 7

NASA NTRS2013

The Prediction of Jet Noise Ground Effects Using an Acoustic Analogy and a Tailored Green's Function

An assessment of an acoustic analogy for the mixing noise component of jet noise in the presence of an infinite surface is presented. The reflection of jet noise by the ground changes the distribution of acoustic energy and is characterized by constructive and destructive interference patterns. The equivalent sources are modeled based on the two-point cross- correlation of the turbulent velocity fluctuations and a steady Reynolds-Averaged Navier-Stokes (RANS) solution. Propagation effects, due to reflection by the surface and refaction by the jet shear layer, are taken into account by calculating the vector Green's function of the linearized Euler equations (LEE). The vector Green's function of the LEE is written in relation to Lilley's equation; that is, approximated with matched asymptotic solutions and the Green's function of the convective Helmholtz equation. The Green's function of the convective Helmholtz equation for an infinite flat plane with impedance is the Weyl-van der Pol equation. Predictions are compared with an unheated Mach 0.95 jet produced by a nozzle with an exit diameter of 0.3302 meters. Microphones are placed at various heights and distances from the nozzle exit in the peak jet noise direction above an acoustically hard and an asphalt surface. The predictions are shown to accurately capture jet noise ground effects that are characterized by constructive and destructive interference patterns in the mid- and far-field and capture overall trends in the near-field.

Miller, Steven A. E.↗

DOE OSTI2019

Green’s Function of the Schrödinger Equation in the Potential Quantization Method

The problem for determining Green’s function G(r, r') for the time-independent Schrödinger equation is considered using the potential quantization method. The expression for G(r, r') is obtained in terms of the eigenfunctions and eigenvalues of this method. The equivalence of the used and traditional methods for solving the given problem has been proven.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Electronic Excitations in Complex Molecular Environments: Many-Body Green’s Functions Theory in VOTCA-XTP

Many-body Green’s functions theory within the GW approximation and the Bethe-Salpeter Equation (BSE) is implemented in the open-source VOTCA-XTP software, aiming at the calculation of electronically excited states in complex molecular environments. Based on Gaussian-type atomic orbitals and making use of resolution of identity techniques, the code is designed specifically for nonperiodic systems. Application to a small molecule reference set successfully validates the methodology and its implementation for a variety of excitation types covering an energy range from 2 to 8 eV in single molecules. Further, embedding each GW-BSE calculation into an atomistically resolved surrounding, typically obtained from Molecular Dynamics, accounts for effects originating from local fields and polarization. Using aqueous DNA as a prototypical system, different levels of electrostatic coupling between the regions in this GW-BSE/MM setup are demonstrated. Particular attention is paid to charge-transfer (CT) excitations in adenine base pairs. It is found that their energy is extremely sensitive to the specific environment and to polarization effects. The calculated redshift of the CT excitation energy compared to a nucelobase dimer treated in vacuum is of the order of 1 eV, which matches expectations from experimental data. Predicted lowest CT energies are below that of a single nucleobase excitation, indicating the possibility of an initial (fast) decay of such an UV excited state into a binucleobase CT exciton. Furthermore, the results show that VOTCA-XTP’s GW-BSE/MM is a powerful tool to study a wide range of types of electronic excitations in complex molecular environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1985

A first-order Green's function approach to supersonic oscillatory flow: A mixed analytic and numeric treatment

A frequency domain Green's Function Method for unsteady supersonic potential flow around complex aircraft configurations is presented. The focus is on the supersonic range wherein the linear potential flow assumption is valid. In this range the effects of the nonlinear terms in the unsteady supersonic compressible velocity potential equation are negligible and therefore these terms will be omitted. The Green's function method is employed in order to convert the potential flow differential equation into an integral one. This integral equation is then discretized, through standard finite element technique, to yield a linear algebraic system of equations relating the unknown potential to its prescribed co-normalwash (boundary condition) on the surface of the aircraft. The arbitrary complex aircraft configuration (e.g., finite-thickness wing, wing-body-tail) is discretized into hyperboloidal (twisted quadrilateral) panels. The potential and co-normalwash are assumed to vary linearly within each panel. The long range goal is to develop a comprehensive theory for unsteady supersonic potential aerodynamic which is capable of yielding accurate results even in the low supersonic (i.e., high transonic) range.

Freedman, M. I.↗

DOE OSTI2020

The discrete Green's function paradigm for two-way coupled Euler-Lagrange simulation

We outline a methodology for the simulation of particle-laden flows whereby the dispersed and fluid phases are two-way coupled. The drag force which couples fluid and particle momentum depends on the undisturbed fluid velocity at the particle location, and this latter quantity requires modelling. We demonstrate that the undisturbed fluid velocity, in the low particle Reynolds number limit, can be related exactly to the discrete Green's function of the discrete Stokes equations. The method is general in that it can be extended to other partial differential equations which may be associated with particle-laden flows, such as the thermal energy equation or Maxwell's equations. In this work, we demonstrate the method of discrete Green's functions by obtaining these functions for the Navier-Stokes equations at low particle Reynolds number in a two-plane channel geometry. We perform verification at low and finite particle Reynolds number for the case of a point-particle settling under gravity parallel to a plane wall, for different wall normal separations. In comparing to other point-particle schemes the discrete Green's function approach is the most robust at low particle Reynolds number, accurate at all wall-normal separations and is the most accurate in the near wall region at finite Reynolds number. We discuss how the accuracy away from the wall at finite Reynolds number could be improved by appealing to Oseen-like discrete Green's functions. Finally we demonstrate that the discrete Green's function approach can have important implications on statistics of particle-laden turbulent channel flow.

42 ENGINEERING↗

DOE OSTI2025

A Green’s function fast multipole method for computation of micromechanical fields in heterogeneous materials

Computation of micromechanical fields in heterogeneous materials is usually performed using either the finite element method or the Green’s function method based on FFTs. The finite element method allows for accurate discretization and for non-periodic boundary conditions but is computationally expensive. On the other hand, the FFT-based method is computationally efficient but requires discretization on a regular grid of hexahedral voxels. In this paper, a Green’s function method allowing for accurate discretization using tetrahedral elements and for non-periodic boundary conditions is proposed. The convolution is computed using the fast multipole method, which provides good accuracy even for low-order expansion due to the fast decay of interactions between elements. The proposed Green’s function fast multipole method is verified by comparison with analytical and FFT-based solutions. Furthermore, the computational time is analyzed and compared to the FFT-based method for non-periodic convolution. Finally, effective properties of an elastic polycrystalline microstructure containing thin intergranular cracks are computed and analyzed.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Green's function fast multipole method for continuum mechanics (SM-FMM)

Solid Mechanics Fast Multipole Method based on elastic Green's function and accelerated using FFTs The code calculates the mechanical fields (stress and strain) for a heterogeneous elasto-plastic material unit cell under quasi-static conditions (no dynamic effects). The fields are calculated using a Green's function method, where the strain field is given by a discrete convolution of Green's operator with an auxiliary stress field. The convolution is calculated using the fast multipole method.

Zecevic, Miroslav↗

NASA NTRS1993

Green's function methods in heavy ion shielding

An analytic solution to the heavy ion transport in terms of Green's function is used to generate a highly efficient computer code for space applications. The efficiency of the computer code is accomplished by a nonperturbative technique extending Green's function over the solution domain. The computer code can also be applied to accelerator boundary conditions to allow code validation in laboratory experiments.

Wilson, John W.↗

NASA NTRS1995

Two-Flux and Green's Function Method for Transient Radiative Transfer in a Semi-Transparent Layer

A method using a Green's function is developed for computing transient temperatures in a semitransparent layer by using the two-flux method coupled with the transient energy equation. Each boundary of the layer is exposed to a hot or cold radiative environment, and is heated or cooled by convection. The layer refractive index is larger than one, and the effect of internal reflections is included with the boundaries assumed diffuse. The analysis accounts for internal emission, absorption, heat conduction, and isotropic scattering. Spectrally dependent radiative properties are included, and transient results are given to illustrate two-band spectral behavior with optically thin and thick bands. Transient results using the present Green's function method are verified for a gray layer by comparison with a finite difference solution of the exact radiative transfer equations; excellent agreement is obtained. The present method requires only moderate computing times and incorporates isotropic scattering without additional complexity. Typical temperature distributions are given to illustrate application of the method by examining the effect of strong radiative heating on one side of a layer with convective cooling on the other side, and the interaction of strong convective heating with radiative cooling from the layer interior.

Siegel, Robert↗

NASA NTRSDate not supplied

Reconstruction of Thermal Protection System Aeroheating using a Green’s Function Approach

Inverse heat transfer (IHT) techniques are often used to reconstruct the surface heating conditions on spacecraft thermal protection systems (TPS) during atmospheric entry. Current IHT techniques for entry spacecraft applications, however, demand substantial computational resources, and are impractical for analyses such as uncertainty quantification and real-time health monitoring. In this paper, a Green’s function sensor fusion approach is used to reconstruct the TPS surface aeroheating conditions on experimental spaceflight and ground test systems from collocated temperature and heat flux sensors embedded in the TPS. The algorithm leverages Green’s functions to model the heat conduction within the spacecraft TPS and stabilizes the recovery of the surface heating condition using the direct heat flux sensor measurement. The algorithm is validated using arc-jet ground test data and applied to the reconstruction of the Mars 2020 backshell heating during Martian atmospheric entry. The performance of the algorithm is benchmarked against a current state-of-the-art IHT framework, FIAT_Opt. The Green’s function-based reconstruction algorithm recovers the net hot-wall heat flux absorbed by the TPS and the incident heat flux from the atmospheric entry environment in close agreement with FIAT_Opt. Notably, computation of the surface heating condition is completed in three orders of magnitude less time with the Green’s function sensor fusion approach using a consumer-grade PC, versus with FIAT_Opt running on a high performance computer cluster. The efficiency of the algorithm is leveraged to compute the uncertainty contributions of input parameters to the total uncertainty in reconstructed Mars 2020 backshell heating for the full atmospheric entry heat pulse. The sensitivity analysis uncovers that, at different times throughout the entry heat pulse, uncertainties in the TPS specific heat, thermal conductivity, and emissivity are all dominant drivers of the reconstruction uncertainty. These results demonstrate Green’s functions and sensor-fusion techniques as promising IHT approaches to reconstruct atmospheric entry environments from TPS-embedded measurements, and highlight how these techniques may give access to post-flight analyses previously hindered by the prohibitive cost of current methods.

Kenneth McAfee↗

NASA NTRSDate not supplied

Reconstruction of Thermal Protection System Aeroheating using a Green’s Function Approach

Inverse heat transfer (IHT) techniques are often used to reconstruct the surface heating conditions on spacecraft thermal protection systems (TPS) during atmospheric entry. Current IHT techniques for entry spacecraft applications, however, demand substantial computational resources, and are impractical for analyses such as uncertainty quantification and real-time health monitoring. In this paper, a Green’s function sensor fusion approach is used to reconstruct the TPS surface aeroheating conditions on experimental spaceflight and ground test systems from collocated temperature and heat flux sensors embedded in the TPS. The algorithm leverages Green’s functions to model the heat conduction within the spacecraft TPS and stabilizes the recovery of the surface heating condition using the direct heat flux sensor measurement. The algorithm is validated using arc-jet ground test data and applied to the reconstruction of the Mars 2020 backshell heating during Martian atmospheric entry. The performance of the algorithm is benchmarked against a current state-of-the-art IHT framework, FIAT_Opt. The Green’s function-based reconstruction algorithm recovers the net hot-wall heat flux absorbed by the TPS and the incident heat flux from the atmospheric entry environment in close agreement with FIAT_Opt. Notably, computation of the surface heating condition is completed in three orders of magnitude less time with the Green’s function sensor fusion approach using a consumer-grade PC, versus with FIAT_Opt running on a high performance computer cluster. The efficiency of the algorithm is leveraged to compute the uncertainty contributions of input parameters to the total uncertainty in reconstructed Mars 2020 backshell heating for the full atmospheric entry heat pulse. The sensitivity analysis uncovers that, at different times throughout the entry heat pulse, uncertainties in the TPS specific heat, thermal conductivity, and emissivity are all dominant drivers of the reconstruction uncertainty. These results demonstrate Green’s functions and sensor-fusion techniques as promising IHT approaches to reconstruct atmospheric entry environments from TPS-embedded measurements, and highlight how these techniques may give access to post-flight analyses previously hindered by the prohibitive cost of current methods.

Kenneth McAfee↗

DOE OSTI2015

Excitons and Davydov splitting in sexithiophene from first-principles many-body Green’s function theory

Organic semiconductors have promising and broad applications in optoelectronics. Understanding their electronic excited states is important to help us control their spectroscopic properties and performance of devices. There have been a large amount of experimental investigations on spectroscopies of organic semiconductors, but theoretical calculation from first principles on this respect is still limited. Here, we use density functional theory (DFT) and many-body Green’s function theory, which includes the GW method and Bethe-Salpeter equation, to study the electronic excited-state properties and spectroscopies of one prototypical organic semiconductor, sexithiophene. The exciton energies of sexithiophene in both the gas and bulk crystalline phases are very sensitive to the exchange-correlation functionals used in DFT for ground-state structure relaxation. We investigated the influence of dynamical screening in the electron-hole interaction on exciton energies, which is found to be very pronounced for triplet excitons and has to be taken into account in first principles calculations. In the sexithiophene single crystal, the energy of the lowest triplet exciton is close to half the energy of the lowest singlet one. While lower-energy singlet and triplet excitons are intramolecular Frenkel excitons, higher-energy excitons are of intermolecular charge-transfer type. The calculated optical absorption spectra and Davydov splitting are in good agreement with experiments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1981

Mean dyadic Green's function for a two layer random medium

The mean dyadic Green's function for a two-layer random medium with arbitrary three-dimensional correlation functions has been obtained with the zeroth-order solution to the Dyson equation by applying the nonlinear approximation. The propagation of the coherent wave in the random medium is similar to that in an anisotropic medium with different propagation constants for the characteristic transverse electric and transverse magnetic polarizations. In the limit of a laminar structure, two propagation constants for each polarization are found to exist.

Zuniga, M. A.↗

NASA NTRS1990

Green's functions for dislocations in bonded strips and related crack problems

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Ballarini, R.↗

NASA NTRS1991

Green's functions for dislocations in bonded strips and related crack problems

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Ballarini, R.↗

NASA NTRS1995

A Green's function method for heavy ion beam transport

The use of Green's function has played a fundamental role in transport calculations for high-charge high-energy (HZE) ions. Two recent developments have greatly advanced the practical aspects of implementation of these methods. The first was the formulation of a closed-form solution as a multiple fragmentation perturbation series. The second was the effective summation of the closed-form solution through nonperturbative techniques. The nonperturbative methods have been recently extended to an inhomogeneous, two-layer transport media to simulate the lead scattering foil present in the Lawrence Berkeley Laboratories (LBL) biomedical beam line used for cancer therapy. Such inhomogeneous codes are necessary for astronaut shielding in space. The transport codes utilize the Langley Research Center atomic and nuclear database. Transport code and database evaluation are performed by comparison with experiments performed at the LBL Bevalac facility using 670 A MeV 20Ne and 600 A MeV 56Fe ion beams. The comparison with a time-of-flight and delta E detector measurement for the 20Ne beam and the plastic nuclear track detectors for 56Fe show agreement up to 35%-40% in water and aluminium targets, respectively.

NASA Discipline Radiation Health↗

DOE OSTI2021

Numerically exact generalized Green's function cluster expansions for electron-phonon problems

We generalize the family of approximate momentum average methods to formulate a numerically exact, convergent hierarchy of equations whose solution provides an efficient algorithm to compute the Green's function of a particle dressed by bosons suitable in the entire parameter regime. We use this approach to extract ground-state properties and spectral functions. Our approximation-free framework, dubbed the generalized Green's function cluster expansion (GGCE), allows access to exact numerical results in the extreme adiabatic limit, where many standard methods struggle or completely fail. We showcase the performance of the method, specializing three important models of charge-boson coupling in solids and molecular complexes: the molecular Holstein model, which describes coupling between charge density and local distortions, the Peierls model, which describes modulation of charge hopping due to intersite distortions, and a more complex Holstein + Peierls system with couplings to two different phonon modes, paradigmatic of charge-lattice interactions in organic crystals. Furthermore, the GGCE serves as an efficient approach that can be systematically extended to different physical scenarios, thus providing a tool to model the frequency dependence of dressed particles in realistic settings.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS2014

Transient Thermoelectric Solution Employing Green's Functions

The study works to formulate convenient solutions to the problem of a thermoelectric couple operating under a time varying condition. Transient operation of a thermoelectric will become increasingly common as thermoelectric technology permits applications in an increasing number of uses. A number of terrestrial applications, in contrast to steady-state space applications, can subject devices to time varying conditions. For instance thermoelectrics can be exposed to transient conditions in the automotive industry depending on engine system dynamics along with factors like driving style. In an effort to generalize the thermoelectric solution a Greens function method is used, so that arbitrary time varying boundary and initial conditions may be applied to the system without reformulation. The solution demonstrates that in thermoelectric applications of a transient nature additional factors must be taken into account and optimized. For instance, the materials specific heat and density become critical parameters in addition to the thermal mass of a heat sink or the details of the thermal profile, such as oscillating frequency. The calculations can yield the optimum operating conditions to maximize power output andor efficiency for a given type of device.

thermoelectric power generation↗