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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Number of terms required in the Fourier expansion of the reflection function for optically thick atmospheres

Computational results are presented for the separate terms in the Fourier expansion of the phase function and the reflection function of a semiinfinite, conservatively scattering atmosphere composed of cloud particles. The calculations involve successive applications of invariant imbedding, doubling, and asymptotic fitting methods to cover the range from very thin to very thick atmospheres. From the results, the ratio of the total reflection function to the first-order reflection function is determined as well as the number of terms required to describe the reflection function to an accuracy of 0.1 percent. The number of terms required depends strongly on the zenith angles of incidence and reflection as well as on details of the phase function. These results are compared with similar results obtained for a Henyey-Greenstein phase function having the same asymmetry factor as in the cloud model.

King, M. D.↗
DOE OSTI2022

New quantum physics, solving puzzles of Wheeler’s delayed choice and a particle’s passing N slits simultaneously and quantum oscillator in experiments

Abstract This paper discovers new quantum physics, and gives solutions to puzzles of Wheeler’s delayed choice and a particle’s passing many slits simultaneously by exact quantum physics expressions. We further show new quantum control, new quantum oscillation, new quantum control experiments and new quantum oscillator being able to be installed in quantum communication network etc. We discover that the ability of a photon to hit electrons out in photoelectric effect is complementarily equivalent to the ability of wave of a photon to simultaneously pass through many slits in wave-particle duality. Objective criterion for distinguishing classical and quantum particles is found, and this paper gives applicable realm of quantum theories and new quantum physics expressions of wave-particle duality. All these studies above should be classified as classical and quantum particles, then classical particle and quantum particle wave cannot and can pass many slits, respectively. This paper discovers wave-particle duality’s origin of displaying both wave property from plane wave part of the general Fourier expansion and particle property from the general Fourier expansion coefficients with the particle’s global property and spins etc. We give the superposition state representation of wave-particle duality, further find the collapse of the duality superposition state to wave or particle state. The collapsed wave or particle state is related to the measure of wave or particle property. Then, we explain why sometimes it's a wave or a particle. Our achieved results are truly tested, and we discover new measured attractive state and quantum wave collapse velocity expression.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1977

A note of expansions of functions of velocity in the two-body problem

Fourier expansions based on both the true anomaly and the mean anomaly are obtained for the functions of velocity in the two-body problem; the series of coefficients is written from classical formulae involving associated Legendre polynomials, Gegenbauer polynomials, or Bessel functions. The Fourier expansions are compared with the expansions in powers of eccentricity developed by Broucke (1974) through use of computerized Poisson series manipulation.

Kinoshita, H.↗
NASA NTRSDate not supplied

Development of An Improved BRDF Hotspot Model and its Use in VLIDORT to Study the Impact of Atmospheric Scattering on Hotspot Directional Signatures in the Atmosphere

The term “hotspot” refers to the sharp increase of reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick-LiSparse-Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan- Bréon but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately. To improve its use in atmospheric radiative transfer (RT) model simulations, in this paper we have developed a modified version based on the Maignan-Bréon’s hotspot BRDF model that converge much faster numerically, making it more practical for use in RT models that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures. Using the vector linearized discrete ordinate radiative transfer model (VLIDORT), we found that reasonable TOA hotspot accuracy can be obtained with just 23 Fourier terms for clear atmospheres, and 63 Fourier terms for atmospheres with aerosol scattering. One advantage of this modified model is that the new hotspot model agrees very well with the original RossThick model away the hotspot region, making it is very convenient to use in the condition with and without hotspot in applications. This model can calculate the amplitude of hot spot accurately, and has been added in the most recent version of VLIDORT. However, there are some difference of this modified model with the original model for scattering angle close the hot spot, and it may not be appropriate for those who need an exact representation of the hot spot angular signature close to hot spot.

Xiaozhen (Shawn) Xiong↗
NASA NTRSDate not supplied

A New BRDF Hotspot Model and its Use in Improving Radiative Transfer Model Efficiency and Application to VLIDORT-based PCRTM Model

The term “hotspot” refers to the sharp increase of reflectance occurring when incident (solar) and reflected (viewing) directions almost coincide in the backscatter direction. The accurate simulation of hotspot directional signatures is important for many remote sensing applications. The RossThick-LiSparse-Reciprocal (RTLSR) Bidirectional Reflectance Distribution Function (BRDF) model is widely used in radiative transfer simulations, and the hotspot model mostly used is from Maignan- Bréon but it typically requires large values of numerical quadrature and Fourier expansion terms in order to represent the hotspot accurately. To improve its use in atmospheric radiative transfer (RT) model simulations, we have developed a modified version based on the Maignan-Bréon’s hotspot BRDF model that converge much faster numerically, making it more practical for use in RT models that require Fourier expansion of BRDF to simulate the top-of-atmosphere (TOA) hotspot signatures. On basis of the vector linearized discrete ordinate radiative transfer model (VLIDORT), we have built a line-by-line based simulation system that can simulate the TOA radiance for atmospheres with 26 gases, different aerosols, dust and clouds, and surface with different BRDF. Using simulated results under diverse atmospheric conditions, we have developed VLIDORT-PCRTM model.

Xiaozhen Xiong↗
DOE OSTI2022

FLOW Estimation and Rose Superposition (FLOWERS): an integral approach to engineering wake models

Abstract. Annual energy production (AEP) is often the objective function in wind plant layout optimization studies. The conventional method to compute AEP for a wind farm is to first evaluate power production for each discrete wind direction and speed using either computational fluid dynamics simulations or engineering wake models. The AEP is then calculated by weighted-averaging (based on the wind rose at the wind farm site) the power produced across all wind directions and speeds. We propose a novel formulation for time-averaged wake velocity that incorporates an analytical integral of a wake deficit model across every wind direction. This approach computes the average flow field more efficiently, and layout optimization is an obvious application to exploit this benefit. The clear advantage of this new approach is that the layout optimization produces solutions with comparable AEP performance yet is completed 2 orders of magnitude faster. The analytical integral and the use of a Fourier expansion to express the wind speed and wind direction frequency create a relatively smooth solution space for the gradient-based optimizer to excel in comparison to the existing weighted-averaging power calculation.

17 WIND ENERGY↗
NASA NTRS1974

Contoured patterns from reflector systems - A spherical wave expansion solution

Any electromagnetic field - e.g., a contoured antenna pattern may be expanded into a sum of spherical waves, similar to a one-dimensional Fourier expansion. This expanded wave could then be scattered from a source reflector to determine a resulting required feed field in the vicinity of the focal region. This is of questionable value, and the more significant information to produce would be the required feed pattern itself. Hence the required contour pattern is instead scattered from the back of the reflector, and the result is the required feed pattern with origin at the focus of the chosen reflector.

Williams, W. F.↗
NASA NTRS1992

Resolution properties of the Fourier method for discontinuous waves

In this paper we discuss the wave-resolution properties of the Fourier approximations of a wave function with discontinuities. It is well known that a minimum of two points per wave is needed to resolve a periodic wave function using Fourier expansions. For Chebyshev approximations of a wave function, a minimum of pi points per wave is needed. Here we obtain an estimate for the minimum number of points per wave to resolve a discontinuous wave based on its Fourier coefficients. In our recent work on overcoming the Gibbs phenomenon, we have shown that the Fourier coefficients of a discontinuous function contain enough information to reconstruct with exponential accuracy the coefficient of a rapidly converging Gegenbauer expansion. We therefore study the resolution properties of a Gegenbauer expansion where both the number of terms and the order increase.

Gottlieb, David↗
NASA NTRS1990

Task reports on developing techniques for scattering by 3D composite structures and to generate new solutions in diffraction theory using higher order boundary conditions

There are two tasks described in this report. First, an extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. Second, the diffraction by a material discontinuity in a thick dielectric/ferrite layer is considered by modeling the layer as a distributed current sheet obeying generalized sheet transition conditions (GSTC's).

Volakis, John L.↗
NASA NTRS1990

A finite element conjugate gradient FFT method for scattering

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Collins, Jeffery D.↗
DOE OSTI2023

Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications of the PCA-SVD to event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that the sine and cosine functions chosen a priori in the traditional Fourier analysis are naturally the most optimal basis for azimuthal flow studies according to the data itself. We perform PCA-SVD analyses of mid-central Au+Au collisions at $E$ $beam$ / $A$ =1.23 GeV simulated using an isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model to address the following two questions: (1) if the principal components of the covariance matrix of nucleon azimuthal angle distributions in heavy-ion reactions around 1 GeV/nucleon are naturally sine and/or cosine functions and (2) what if any advantages the PCA-SVD may have over the traditional flow analysis using the Fourier expansion for studying the EOS of dense nuclear matter. In conclusion, we find that (1) in none of our analyses the principal components come out naturally as sine and/or cosine functions, (2) while both the eigenvectors and eigenvalues of the covariance matrix are appreciably EOS dependent, the PCA-SVD has no apparent advantage over the traditional Fourier analysis for studying the EOS of dense nuclear matter using the azimuthal collective flow in heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Azimuthal anisotropy of dijet events in PbPb collisions at $$ \sqrt{s_{\textrm{NN}}} $$ = 5.02 TeV

A bstract The path-length dependent parton energy loss within the dense partonic medium created in lead-lead collisions at a nucleon-nucleon center-of-mass energy of $$ \sqrt{s_{\textrm{NN}}} $$ s NN = 5 . 02 TeV is studied by determining the azimuthal anisotropies for dijets with high transverse momentum. The data were collected by the CMS experiment in 2018 and correspond to an integrated luminosity of 1.69 nb − 1 . For events containing back-to-back jets, correlations in relative azimuthal angle and pseudorapidity ( η ) between jets and hadrons, and between two hadrons, are constructed. The anisotropies are expressed as the Fourier expansion coefficients v n , n = 2–4 of these azimuthal distributions. The dijet v n values are extracted from long-range (1 . 5 < |∆ η | < 2 . 5) components of these correlations, which suppresses the background contributions from jet fragmentation processes. Positive dijet v 2 values are observed which increase from central to more peripheral events, while the v 3 and v 4 values are consistent with zero within experimental uncertainties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Adiabatic approximation and Aharonov-Casher bands in twisted homobilayer transition metal dichalcogenides

Topological flat moiré bands with nearly ideal quantum geometry have been identified in homobilayer transition metal dichalcogenide moiré superlattices, and are thought to be crucial for understanding the fractional Chern insulating states recently observed therein. Previous study proposed viewing the system using an adiabatic approximation that replaces the position dependence of the layer spinor with a nonuniform periodic effective magnetic field. When the local zero-point kinetic energy of this magnetic field cancels identically against that of an effective Zeeman energy, a Bloch-band version of Aharonov-Casher zero-energy modes, which we refer to as Aharonov-Casher band, emerges leading to ideal quantum geometry. Here, we critically examine the validity of the adiabatic approximation and identify the parameter regimes under which Aharonov-Casher bands emerge. We show that the adiabatic approximation is accurate for a wide range of parameters including those realized in experiments. Furthermore, we show that while the cancellation leading to the emergence of Aharonov-Casher bands is generally not possible beyond the leading Fourier harmonic, the leading harmonic is the dominant term in the Fourier expansions of the zero-point kinetic energy and Zeeman energy. Finally, the leading harmonic expansion accurately captures the trend of the bandwidth and quantum geometry, although it may fail to quantitatively reproduce more detailed information about the bands such as the Berry curvature distribution.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Fourier coefficients of noninterdependent collective motions in heavy-ion collisions

Here, we present a scenario in heavy-ion collisions where different modes of collective motions are noninterdependent, driven by factorized actions in the created nuclear medium. Such physics mechanisms could each dominate at a distinct evolution stage, or coexist simultaneously. If the probability of particle emission is modulated by each nondependent collective motion with a single-harmonic Fourier expansion, the particle azimuthal distribution should be the product of all these expansions. Consequently, nonleading cross terms between collectivity modes appear, and their contributions to experimental observables could be significant. In particular, we argue that the chiral magnetic effect (CME) and elliptic flow can develop separately, with their convolution affecting the observable that is sensitive to the shear-induced CME. We will use the event-by-event anomalous-viscous fluid dynamics model to illustrate the effects of this scenario. Besides giving insights into searches for the CME, we also propose feasible experimental tests based on conventional flow harmonics, and demonstrate the emergence of nonleading cross terms with a multiphase transport model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

POLCA8 - modelling of cross section variations inside hexagonal assemblies

This paper presents the POLCA8 approach for modelling non-constant cross section distributions inside hexagonal fuel assemblies. The multigroup diffusion equation is modified to account for intranodal cross section variations. The obtained equation is solved in a node-wise manner based on the Fourier expansion method. As a result of varying cross sections, the solution includes a particular part additionally to the homogeneous one. A method for obtaining the particular solution is derived. Numerical tests on a VVER-1000 core are presented showing the impact of cross-section variations to some key parameters for reactor operation. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Stability and Conservation properties of Hermite-based approximations of the Vlasov-Poisson System

Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided by adding high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Zwicky Transient Facility and Globular Clusters: the Period–Luminosity and Period–Luminosity–Color Relations for Late-type Contact Binaries

In this work, we aimed to derive the gri-band period–luminosity (PL) and period–luminosity–color (PLC) relations for late-type contact binaries, for the first time, located in globular clusters, using the homogeneous light curves collected by the Zwicky Transient Factory (ZTF). We started with 79 contact binaries in 15 globular clusters, and retained 30 contact binaries in 10 globular clusters that have adequate numbers of data points in the ZTF light curves and are unaffected by blending. Magnitudes at mean and maximum light of these contact binaries were determined using a fourth-order Fourier expansion, while extinction corrections were done using the Bayerstar2019 3D reddening map together with adopting the homogeneous distances to their host globular clusters. After removing early-type and “anomaly” contact binaries, our derived gri-band PL and period–Wesenheit (PW) relations exhibited a much larger dispersion with large errors on the fitted coefficients. Nevertheless, the gr-band PL and PW relations based on this small sample of contact binaries in globular clusters were consistent with those based on a larger sample of nearby contact binaries. Good agreements of the PL and PW relations suggested both samples of contact binaries in the local Solar neighborhood and in the distant globular clusters can be combined and used to derive and calibrate the PL, PW, and PLC relations. The final derived gr-band PL, PW, and PLC relations were much improved over those based on the limited sample of contact binaries in the globular clusters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗