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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

A simple analytical function for bidirectional reflectance

A simple bidirectional reflectance model based on physical scattering laws is developed to calculate the bidirectional reflectance of a wide variety of surfaces. Chandrasekhar's radiative transfer solution, obtained for the anisotropically scattering semi-infinite medium, is used to compute the multiple-scattered radiances. However, since the radiative transfer solution does not take architectural effects into consideration, we adopt Hapke's (1986) approach and add an empirical term to explain the hot-spot phenomenon and use Cox and Munk's (1954) formulation to take into account the specular reflection. The physical parameters of the model are retrieved from bidirectional reflectance measurements. For each surface, only one set of model parameters is needed for application to all illumination and viewing geometries. The validity of the model is established by comparing the computed and measured reflectances for sets of viewing and illumination angles that were not included in the inversion algorithm. Good agreement is shown between the model-computed and the observed reflectances for dense prairie vegetation canopies, a sparse desert scrub community, a plowed agricultural field, and an alkali flat.

Ahmad, Suraiya P.↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
NASA NTRS1974

A three parameter analytic phase function for multiple scattering calculations

A simple procedure was developed to fit the first three moments of an actual phase function with a three parameter analytic phase function. The exact Legendre Polynomial decomposition of this function is, suitable for multiple scattering calculations. The use of this function is expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo omega sub 0 is greater than or equal to 0.9.

Kattawar, G. W.↗
NASA NTRS1975

A three-parameter analytic phase function for multiple scattering calculations

A very simple procedure has been developed to fit the first three moments of an actual phase function with a three-parameter analytic phase function. The exact Legendre polynomial decomposition of this function is known which makes it quite suitable for multiple scattering calculations. The use of this function can be expected to yield excellent flux values at all depths within a medium. Since it is capable of reproducing the glory, it can be used in synthetic spectra computations from planetary atmospheres. Accurate asymptotic radiance values can also be achieved as long as the single scattering albedo is not less than 0.9.

Kattawar, G. W.↗
DOE OSTI2019

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

A second order interface anchoring method has been developed and used with fast sweeping algorithm for reinitialization of a level set function. The algebraic anchoring formulation ensures that the location of the actual interface is preserved, leading to better mass conservation property. It also provides high order accurate algebraic constraint for solving the Eikonal equation on a finite difference grid. Geometric properties of the interface such as surface normal and curvature are subsequently computed from the reinitialized distance function. Various analytical functions for modeling distortion in level set field are considered and accuracy of reinitialization is evaluated using first and second order anchoring schemes. It is also shown that accurate computation of interface curvature requires a high order anchor in addition to a high order fast sweeping method. Mass conservation property of reinitialization is also analyzed by considering test problems from literature including the classic Rider–Kothe single vortex problem. The formulation is suitable for efficient parallelization for both distributed memory and on-node shared memory parallel systems. In conclusion, scalability and performance of the reinitialization scheme on multiple architectures are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Generalized Bessel–Struve Operator and Its Properties

We define the generalized Bessel–Struve operator in the space of functions analytic in an arbitrary domain. The conditions of equivalence of the generalized Bessel–Struve operator to the operator of second derivative are investigated. We also describe the commutant of the generalized Bessel–Struve operator and establish its hypercyclicity and chaotic nature.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Approximating accelerator impedances with resonator networks

It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a general manner for excitations that are not necessarily Gaussian in nature. Here, the conventional method for doing this involves taking the inverse Fourier Transform of the component impedance, obtaining the Green's Function, and then convolving it with the desired excitation distribution. This method can prove numerically cumbersome, for a convolution integral must be evaluated for each individual point in time when the wake function is desired. An alternative to this method would be to compute the wake function analytically, which would sidestep the need for repetitive integration. Only a handful of cases, however, are simple enough for this method to be tenable. One of these cases is the case where the component in question is an RLC resonator, which has a closed-form analytical wake function solution. This means that a component which can be represented in terms of resonators can leverage this solution. As it happens, common network synthesis techniques may be used to map arbitrary impedance profiles to RLC resonator networks in a manner the accelerator community has yet to take advantage of. In this work, we will use Foster Canonical Resonator Networks and partial derivative descent optimization to develop a technique for synthesizing resonator networks that well approximate the impedances of real-world accelerator components. We will link this synthesis to the closed-form resonator wake function solution, giving rise to a powerful workflow that may be used to streamline beam dynamics simulations.

43 PARTICLE ACCELERATORS↗
DOE OSTI2018

Inverse Thermal Analysis of Ti-6Al-4V Friction Stir Welds Using Numerical-Analytical Basis Functions with Pseudo-Advection

Inverse thermal analysis of Ti-6Al-4V friction stir welds is presented that demonstrates application of a methodology using numerical-analytical basis functions and temperature-field constraint conditions. This analysis provides parametric representation of friction-stir-weld temperature histories that can be adopted as input data to computational procedures for prediction of solid-state phase transformations and mechanical response. These parameterized temperature histories can be used for inverse thermal analysis of friction stir welds having process conditions similar those considered here. Case studies are presented for inverse thermal analysis of friction stir welds that use three-dimensional constraint conditions on calculated temperature fields, which are associated with experimentally measured transformation boundaries and weld-stir-zone cross sections.

36 MATERIALS SCIENCE↗
NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

Park, Michael A.↗
NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment.

Park, Michael A.↗
DOE OSTI2017

Analytical trial functions for modelling a two-dimensional Bose condensate

Approximate analytical solutions to the time-independent two-dimensional Gross–Pitaevsky equation are obtained by a variational method. The solutions found are compared with the results of direct numerical calculations. The accuracy of analytical solutions is determined under various conditions of the problem, primarily the degree of nonlinear interaction of atoms in a Bose condensate. (paper)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Solutions of Boundary-Value Problems for the Helmholtz Equation in Simply Connected Domains of the Complex Plane

The bases in the spaces of functions analytic in simply connected domains are constructed with the help of conformal mappings of these domains onto a circle. The obtained basis functions are biorthogonal to the Faber polynomials. By using the expansions of analytic functions in series in systems of basis functions, we determine the solutions of boundary-value problems for the Helmholtz equation whose boundary values coincide with the boundary values of these functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A high precision semi-analytic mass function

In this paper, extending past works of Del Popolo, we show how a high precision mass function (MF) can be obtained using the excursion set approach and an improved barrier taking implicitly into account a non-zero cosmological constant, the angular momentum acquired by tidal interaction of proto-structures and dynamical friction. In the case of the ΛCDM paradigm, we find that our MF is in agreement at the 3% level to Klypin's Bolshoi simulation, in the mass range M {sub vir} = 5 × 10{sup 9} h {sup −1} M {sub ⊙}–−5 × 10{sup 14} h {sup −1} M {sub ⊙} and redshift range 0 ∼< z ∼< 10. For z = 0 we also compared our MF to several fitting formulae, and found in particular agreement with Bhattacharya's within 3% in the mass range 10{sup 12}–10{sup 16} h {sup −1} M {sub ⊙}. Moreover, we discuss our MF validity for different cosmologies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Hemisphere partition function and analytic continuation to the conifold point

We show that the hemisphere partition function for certain U(1) gauged linear sigma models (GLSMs) with D-branes is related to a particular set of Mellin-Barnes integrals which can be used for analytic continuation to the singular point in the Kähler moduli space of an $h^{1,1}=1$ Calabi-Yau (CY) projective hypersurface. We directly compute the analytic continuation of the full quantum corrected central charge of a basis of geometric D-branes from the large volume to the singular point. In the mirror language this amounts to compute the analytic continuation of a basis of periods on the mirror CY to the conifold point. However, all calculations are done in the GLSM and we do not have to refer to the mirror CY. We apply our methods explicitly to the cubic, quartic and quintic CY hypersurfaces.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Conformal truncation of chern-simons theory at large $N$ f

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to N f fermions in the limit of large Nf using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff Δ max . In both the Chern-Simons theory, and in the O(N) model at infinite N, we compute the current spectral functions analytically as a function of Δ max and reproduce previous results in the limit that the truncation Δ max is taken to ∞. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.

1/N expansion, Chern-Simons Theories↗