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At least 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

A theoretical and numerical study of polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum

In this paper, theoretical and numerical results of the polarimetric scattering and emission from random rough surfaces with anisotropic directional spectrum are presented for the remote sensing of ocean and soil surfaces. The polarimetric scattered field for rough dielectric surfaces is derived to the second order by the small perturbation method (SPM). It is found that the second-order scattered field is coherent in nature, and its coefficients for different polarizations present the lowest-order corrections to the Fresnel reflection coefficients of the surfaces. In addition, the cross-polarized (HV and VH) components of the coherent fields are reciprocal and not zero for surfaces with anisotropic directional spectrum when the azimuth angle of the incident direction is not aligned with the symmetry directions of surfaces. In order to verify the energy conservation condition of the theoretical results, which is important if the theory is to be applied to the passive polarimetry of rough surfaces, a Monte Carlo simulation is performed to numerically calculate the polarimetric reflectivities of one-dimensional random rough surfaces which are generated with a prescribed power-law spectrum in the spectral domain and transformed to the spatial domain by the FFT. The surfaces simulated by this approach are periodic with the period corresponding to the low-wavenumber cutoff. To calculate the scattering from periodic dielectric surfaces, the authors present a new numerical technique which applies the Floquet theorem to reduce the problem to one period and does not require the evaluation of one-dimensional periodic Green's function used in the conventional method of moment formulation. Once the scattering coefficients are obtained, the polarimetric Stokes vectors for the emission from the random surfaces are then calculated according to the Kirchhoff's law and are illustrated as functions of relative azimuth observation and row directions. The second-order SPM is also reduced to this one-dimensional case, and theoretical results for all four Stokes parameters are in excellent agreement with the numerical results obtained from the Monte Carlo simulation. Moreover, the second order coherent fields are found to be necessary for the theoretical evaluation of the third and fourth Stokes parameters. Without that, the reflectivities of random rough surfaces are significantly over-estimated, and the signs of the third and the fourth Stokes parameters are found to be incorrect, if calculated by using the first-order incoherent fields alone.

Yueh, S. H.↗
DOE OSTI2025

Desmearing small-angle scattering data by central moment expansions of instrument resolution

This study introduces an enhanced numerical technique tailored specifically for refining 1D small-angle scattering (SAS) intensity profiles affected by smearing. Our primary objective is to address the resolution blurring commonly encountered in SAS data, particularly in systems with clearly defined correlation peaks whose spread aligns with the width of the resolution function at corresponding Q positions. Unlike previous approaches that expanded the SAS intensity using central moment expansion, the new method focuses on expanding the resolution function itself, thus eliminating artificial oscillations observed in smeared spectra due to limitations inherent in our earlier algorithm. This method is straightforward to implement, computationally efficient and consistently performs well in numerical benchmarking. To illustrate its effectiveness, we present a case study of a lamellar phase characterized by distinct peaks in its small-angle neutron scattering intensities.

central moment expansions↗
DOE OSTI2022

Synthesis and structural properties of a 2D Zn( II ) dodecahydroxy- closo -dodecaborate coordination polymer

Here, in this work, we discuss the synthesis and characterization of a 2D coordination polymer composed of a dianionic perhydroxylated boron cluster, [B 12 (OH) 12 2– ], coordinated to Zn( II )—the first example of a transition metal-coordinated [B 12 (OH) 12 ] 2– compound. This material was synthesized via cation exchange from the starting cesium salt and then subjected to rigorous characterization prior to and after thermal activation. Numerous techniques, including XRD, FTIR, SEM, TGA, and solid-state NMR revealed a 2D coordination polymer composed of sheets of Zn( II ) ions intercalated between planes of boron clusters. The as-synthesized material was then evacuated of solvent via thermal treatment, and atomic-level changes from this transformation were elucidated through a combination of 1D and 2D solid-state NMR analyses of 11 B and 1 H nuclei, suggesting the full removal of coordinated solvent molecules. Evidence also suggested that [B 12 (OH) 12 2– ] can adjust its coordination to Zn( II ) in the solid-state through hemilability of its numerous –OH ligands.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1982

The dependence of the shape and stability of captive rotating drops on multiple parameters

Asymptotic and numerical techniques in bifurcation theory are applied to the Young-Laplace equation governing meniscus shape in order to analyze the dependence of the shape and stability of rigidly rotating drops held captive between corotating solid faces on multiple parameters. Asymptotic analysis of the evolution of drop shape from the cylindrical as a function of distance between the solid faces, drop volume, rotational Bond number and gravitational Bond number shows that some shape bifurcations from cylinders to wavy, axisymmetric menisci are ruptured by small changes in drop volume or gravity. Computer calculations of axisymmetric drop shapes based on a finite element representation of the interface and numerical algorithms for tracking shape families and singular points are then used to map drop stability for the four-dimensional parameter space. The results of the asymptotic and numerical analyses are shown to agree well within the limited range of parameters where the asymptotic analysis is valid.

Ungar, L. H.↗
NASA NTRS1984

Interactive computer modeling of combustion chemistry and coalescence-dispersion modeling of turbulent combustion

An interactive computer code for simulation of a high-intensity turbulent combustor as a single point inhomogeneous stirred reactor was developed from an existing batch processing computer code CDPSR. The interactive CDPSR code was used as a guide for interpretation and direction of DOE-sponsored companion experiments utilizing Xenon tracer with optical laser diagnostic techniques to experimentally determine the appropriate mixing frequency, and for validation of CDPSR as a mixing-chemistry model for a laboratory jet-stirred reactor. The coalescence-dispersion model for finite rate mixing was incorporated into an existing interactive code AVCO-MARK I, to enable simulation of a combustor as a modular array of stirred flow and plug flow elements, each having a prescribed finite mixing frequency, or axial distribution of mixing frequency, as appropriate. Further increase the speed and reliability of the batch kinetics integrator code CREKID was increased by rewriting in vectorized form for execution on a vector or parallel processor, and by incorporating numerical techniques which enhance execution speed by permitting specification of a very low accuracy tolerance.

Pratt, D. T.↗
NASA NTRS1994

An application of a two-equation model of turbulence to three-dimensional chemically reacting flows

A numerical study of three dimensional chemically reacting and non-reacting flowfields is conducted using a two-equation model of turbulence. A generalized flow solver using an implicit Lower-Upper (LU) diagonal decomposition numerical technique and finite-rate chemistry has been coupled with a low-Reynolds number two-equation model of turbulence. This flow solver is then used to study chemically reacting turbulent supersonic flows inside combustors with synergetic fuel injectors. The reacting and non-reacting turbulent combustor solutions obtained are compared with zero-equation turbulence model solutions and with available experimental data. The hydrogen-air chemistry is modeled using a nine-species/eighteen reaction model. A low-Reynolds number k-epsilon model was used to model the effect of turbulence because, in general, the low-Reynolds number k-epsilon models are easier to implement numerically and are far more general than algebraic models. However, low-Reynolds number k-epsilon models require a much finer near-wall grid resolution than high-Reynolds number models to resolve accurately the near-wall physics. This is especially true in complex flowfields, where the stiff nature of the near-wall turbulence must be resolved. Therefore, the limitations imposed by the near-wall characteristics and compressible model corrections need to be evaluated further. The gradient-diffusion hypothesis is used to model the effects of turbulence on the mass diffusion process. The influence of this low-Reynolds number turbulence model on the reacting flowfield predictions was studied parametrically.

Lee, J.↗
NASA NTRS1988

Development of an integrated BEM for hot fluid-structure interaction

One of the most difficult problems in engine structural component durability analysis is the determination of the temperatures and fluxes in the structural components directly in contact with the hot gas flow path. Currently there exists no rational analytical or numerical technique which can effectively deal with this problem. Since the temperature distribution in the structural components are strongly influenced by both the fluid flow and the deformation as well as the cooling system in the structure, the only effective way to deal with this problem is to develop an integrated solid mechanics, fluid mechanics and heat transfer analysis for this problem. Herein, the Boundary Element Method (BEM) is chosen as the basic analysis tool principally because the definition of quantities like fluxes, temperatures, displacements, and velocities are very precise on a boundary based discretization scheme. One fundamental difficulty is that a BEM analysis requires a considerable amount of analytical work which is not present in other numerical methods. During the past year, all of this analytical work was completed and a two dimensional, general purpose code was written. A portion of the work is summarized.

Dargush, G. F.↗
DOE OSTI2023

Particle-in-cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms

Abstract Relativistic magnetic reconnection is a nonideal plasma process that is a source of nonthermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a nonstandard finite-difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that, for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than that of Yee, resulting in a ∼40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss’s law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4–3 times over the standard Yee step still yields accurate results, but it only translates to modest performance improvements over CKC, due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1991

A theoretical analysis of the electromagnetic environment of the AS330 super Puma helicopter external and internal coupling

Numerical techniques such as Finite Difference Time Domain (FDTD) computer programs, which were first developed to analyze the external electromagnetic environment of an aircraft during a wave illumination, a lightning event, or any kind of current injection, are now very powerful investigative tools. The program called GORFF-VE, was extended to compute the inner electromagnetic fields that are generated by the penetration of the outer fields through large apertures made in the all metallic body. Then, the internal fields can drive the electrical response of a cable network. The coupling between the inside and the outside of the helicopter is implemented using Huygen's principle. Moreover, the spectacular increase of computer resources, as calculations speed and memory capacity, allows the modellization structures as complex as these of helicopters with accuracy. This numerical model was exploited, first, to analyze the electromagnetic environment of an in-flight helicopter for several injection configurations, and second, to design a coaxial return path to simulate the lightning aircraft interaction with a strong current injection. The E field and current mappings are the result of these calculations.

Flourens, F.↗
NASA NTRS1972

Fracture Behavior in Nylon 6 Fibers

Electron paramagnetic resonance (EPR) techniques are used to determine the number of free radicals produced during deformation leading to fracture of nylon 6 fibers. A reaction rate molecular model is proposed to explain some of the deformation and bond rupture behavior leading to fracture. High-strength polymer fibers are assumed to consist of a sandwich structure of disordered and ordered regions along the fiber axis. In the disordered or critical flaw regions, tie chains connecting the ordered or crystalline block regions are assumed to have a statistical distribution in length. These chains are, therefore, subjected to different stresses. The effective length distribution was determined by EPR. The probability of bond rupture was assumed to be controlled by reaction-rate theory with a stress-aided activation energy and behavior of various loadings determined by numerical techniques. The model is successfully correlated with experimental stress, strain, and bond rupture results for creep, constant rate loadings, cyclic stress, stress relaxation and step strain tests at room temperature.

Lloyd, B. A.↗
DOE OSTI2024

Distributionally Robust Variational Quantum Algorithms With Shifted Noise

Given their potential to demonstrate near-term quantum advantage, variational quantum algorithms (VQAs) have been extensively studied. Although numerous techniques have been developed for VQA parameter optimization, it remains a significant challenge. A practical issue is the high sensitivity of quantum noise to environmental changes, and its propensity to shift in real time. This presents a critical problem as an optimized VQA ansatz may not perform effectively under a different noise environment. For the first time, we explore how to optimize VQA parameters to be robust against unknown shifted noise. We model the noise level as a random variable with an unknown probability density function (PDF), and we assume that the PDF may shift within an uncertainty set. This assumption guides us to formulate a distributionally robust optimization problem, with the goal of finding parameters that maintain effectiveness under shifted noise. We utilize a distributionally robust Bayesian optimization solver for our proposed formulation. This provides numerical evidence in both the Quantum Approximate Optimization Algorithm (QAOA) and the Variational Quantum Eigensolver (VQE) with hardware-efficient ansatz, indicating that we can identify parameters that perform more robustly under shifted noise. We regard this work as the first step towards improving the reliability of VQAs influenced by real-time noise.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Ising meson spectroscopy on a noisy digital quantum simulator

Abstract Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Science & Technology - Other Topics↗
NASA NTRS1990

Efficient solution of parabolic equations by Krylov approximation methods

Numerical techniques for solving parabolic equations by the method of lines is addressed. The main motivation for the proposed approach is the possibility of exploiting a high degree of parallelism in a simple manner. The basic idea of the method is to approximate the action of the evolution operator on a given state vector by means of a projection process onto a Krylov subspace. Thus, the resulting approximation consists of applying an evolution operator of a very small dimension to a known vector which is, in turn, computed accurately by exploiting well-known rational approximations to the exponential. Because the rational approximation is only applied to a small matrix, the only operations required with the original large matrix are matrix-by-vector multiplications, and as a result the algorithm can easily be parallelized and vectorized. Some relevant approximation and stability issues are discussed. We present some numerical experiments with the method and compare its performance with a few explicit and implicit algorithms.

Gallopoulos, E.↗
DOE OSTI2022

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order phase-field fracture models have gained wide adoption given their ability to capture the formation of complex fracture patterns, e.g. via crack merging and branching, and their suitability for implementation within the context of the conventional finite element method. Higher-order phase-field models have also been proposed to increase the regularity of the exact solution and thus increase the spatial convergence rate of its numerical approximation. However, they require special numerical techniques to enforce the necessary continuity of the phase field solution. In this paper, we derive a fourth-order phase-field model of fracture in two independent ways; namely, from Hamilton’s principle and from a higher-order micromechanics-based approach. The latter approach is novel, and provides a physical interpretation of the higher-order terms in the model. In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution. This method employs Lagrange polynomial shape functions to guarantee -continuity of the solution at inter-element boundaries, and enforces the required regularity with the aid of additional variational and interior penalty terms in the weak form. Finally, the phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials. Two benchmark problems are presented to compare the numerical behavior of the C/DG method with mixed finite element methods.

42 ENGINEERING↗
NASA NTRS1995

Thermocapillary convection in a rectangular cavity with a deformable interface

A finite-volume method and a boundary element technique are used to compute two-dimensional (2D) thermocapillary convection in a rectangular cavity. The free surface is deformable and the deviations from a flat interface, h, are assumed small in the finite-volume calculations as appropriate for small Capillary (Ca). Two asymptotic approaches are employed; the first is an expansion valid as Ca tends towards 0 and the second assumes h tends towards 0, retaining Ca explicitly as a parameter. On the other hand, the boundary elements approach can be used with O(1) surface deformations. These three different formulations are used to calculate thermocapillary motions in fluids with small Prandtl numbers of about 0.01, Ca less than 0.05, aspect ratios (width/height) 1, 2 and 4, and various values of the Maragoni number (Ma). The same solutions are calculated with these different approaches and are found in good agreement for values of Ca up to 0.05. All solutions calculated are steady, which is both in agreement and disagreement with recently published results by different authors employing different numerical techniques.

Mundrane, M.↗
NASA NTRS1992

Analytic and numerical models of wave-CISK with conditional heating

Wave-CISK with conditional heating is investigated in the equatorial zonal-height plane by analytic and numerical techniques. For two- and three-level models, previous results are extended to give additional evidence that the most unstable mode has a single wet region of infinitesimal width. A three-level model has qualitatively similar behavior as the two-level model except that propagating solutions are possible due to coalescence of internal vertical modes. Phase speeds with conditional heating are found to be slightly greater than those for unconditional heating. The structure has one circulation cell in the vertical and is asymmetric in longitude with stronger motion on the leading edge. Growth rate is inversely proportional to the width of the single wet region. That width can be limited by second-order diffusion. A general integral relationship between growth rate, viscosity, phase speed, and heating is derived. The main conclusion is that the linear wave-CISK catastrophe is modified by conditional heating but not eliminated. The preferred mode of instability has one wet region, but it occurs on the smallest possible scale. It is likely that numerical models that use conditional heating are sensitive to resolution, especially for the commonly used spectral truncations, unless there is sufficiently strong damping at the smallest scales.

Crum, Francis X.↗
DOE OSTI2023

Sensitivity analysis of a layered piezoelectric system using ZFEM

The complex variable finite element method (ZFEM) is a numerical technique which aims to find the partial derivatives of the independent variables with respect to variation in dependent parameters declared in the physics. This is done by combining the complex Taylor series expansion within the weak formulation of the governing equation in a coupled system of linear equations forming a complex valued block matrix given by the Cauchy–Riemann matrix representation. In this work, two-dimensional linear first-order elements have been implemented in ZFEM to predict the design derivatives of the mechanical displacement field and the voltage potential field for a layered piezoelectric system in a steady-state study with Dirichlet boundary condition applied at the top and bottom edges of the geometry. This approach allows the standard FEM solution to quantify the sensitivity of the mechanical displacement and voltage potential fields with respect to small variations in the material properties through the information obtained from the computation of the derivatives. The domain is formed by a layered body with PZT-4 and PZT-5 stacked together. For result verification, the numerical solution obtained with ZFEM was compared to results from a commercial FEM package and the solution from the imaginary part was compared to the exact solution of a well-known benchmark problem. In conclusion, comparison of the results showed good agreement for both the real and imaginary parts of the solution and the largest sensitivities were found in PZT-5 specifically in C 13 , C 33 , and ε 33 .

42 ENGINEERING↗
DOE OSTI2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The O ( N ) model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. Further, we work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗