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At least 145 records · Page 8

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NASA NTRS1990

Dynamical basis sets for algebraic variational calculations in quantum-mechanical scattering theory

New basis sets are proposed for linear algebraic variational calculations of transition amplitudes in quantum-mechanical scattering problems. These basis sets are hybrids of those that yield the Kohn variational principle (KVP) and those that yield the generalized Newton variational principle (GNVP) when substituted in Schlessinger's stationary expression for the T operator. Trial calculations show that efficiencies almost as great as that of the GNVP and much greater than the KVP can be obtained, even for basis sets with the majority of the members independent of energy.

Sun, Yan↗

NASA NTRS1989

Comparison of theoretical and measured brightness temperature of a soybean canopy

A model for the brightness temperature of a canopy which is based on the physical characteristics of the vegetation is being developed. This model uses the Peake model to relate the scattering coefficient of the vegetation to its radiometric brightness temperature and a discrete scattering model to computer the scattering coefficient. A distorted Born approximation is used to provide a tractable solution to the scattering problem. To verify the theory a comparison has been made with experiments. Radiometric measurements of brightness temperature were made at L- and C-bands over a crop of mature soybeans, along with ground truth measurements. All model input parameters were measured; there were no free parameters to adjust to obtain agreement with the measurements. Results showed that agreement between theory and measurements was reasonable for horizontal polarization at both L- and C-bands with dry underlying soil.

Lang, R. H.↗

NASA NTRS1991

Microwave absorption by a lossy dielectric sphere in a rectangular cavity

A new theory of absorption of microwave power by a lossy dielectric sphere in a resonant rectangular chamber is developed here. In this treatment, resonant modes of the cavity are resolved into traveling plane-wave fields, and Mie's theory of scattering and absorption of a plane electromagnetic wave by a sphere is utilized. The fields in the cavity containing the sphere are found by superposition of results for the individual scattering problem for each traveling plane wave. Absorbed power is then calculated by evaluating the time-averaged Poynting vector and integrating over the surface of the sphere. Applications of microwave power absorption are discussed, with particular emphasis on processing of materials. Numerical studies based on the newly derived formulas are presented. The results exhibit the manner in which microwave absorption is influenced by a number of different experimentally controllable parameters. The examples considered were chosen with a view toward designing experiments and apparatus for containerless processing of materials in the microgravity environment of space.

Jackson, H. W.↗

NASA NTRS1992

Stability and bifurcation of quasiparallel Alfven solitons

The inverse scattering transformation (IST) is used to study the one-parameter and two-parameter soliton families of the derivative nonlinear Schroedinger (DNLS) equation. The two-parameter soliton family is determined by the discrete complex eigenvalue spectrum of the Kaup-Newell scattering problem and the one-parameter soliton family corresponds to the discrete real eigenvalue spectrum. The structure of the IST is exploited to discuss the existence of discrete real eigenvalues and to prove their structural stability to perturbations of the initial conditions. Also, though the two-parameter soliton is structurally stable in general, it is shown that a perturbation of the initial conditions may change the two-parameter soliton into a degenerate soliton which, in turn, is structurally unstable. This degenerate, or double pole, soliton may bifurcate due to a perturbation of the initial conditions into a pair of one-parameter solitons. If the initial profile is on compact support, then this pair of one-parameter solitons must be compressive and rarefactive respectively. Finally, the Gelfand-Levitan equations appropriate for the double pole soliton are solved.

Hamilton, R. L.↗

NASA NTRS1993

On the accurate long-time solution of the wave equation in exterior domains: Asymptotic expansions and corrected boundary conditions

We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.

Hagstrom, Thomas↗

NASA NTRS1992

Complex generalized minimal residual algorithm for iterative solution of quantum-mechanical reactive scattering equations

Complex dense matrices corresponding to the D + H2 and O + HD reactions were solved using a complex generalized minimal residual (GMRes) algorithm described by Saad and Schultz (1986) and Saad (1990). To provide a test case with a different structure, the H + H2 system was also considered. It is shown that the computational effort for solutions with the GMRes algorithm depends on the dimension of the linear system, the total energy of the scattering problem, and the accuracy criterion. In several cases with dimensions in the range 1110-5632, the GMRes algorithm outperformed the LAPACK direct solver, with speedups for the linear equation solution as large as a factor of 23.

Chatfield, David C.↗

NASA NTRS1993

Massively parallel computation of RCS with finite elements

One of the promising combinations of finite element approaches for scattering problems uses Whitney edge elements, spherical vector wave-absorbing boundary conditions, and bi-conjugate gradient solution for the frequency-domain near field. Each of these approaches may be criticized. Low-order elements require high mesh density, but also result in fast, reliable iterative convergence. Spherical wave-absorbing boundary conditions require additional space to be meshed beyond the most minimal near-space region, but result in fully sparse, symmetric matrices which keep storage and solution times low. Iterative solution is somewhat unpredictable and unfriendly to multiple right-hand sides, yet we find it to be uniformly fast on large problems to date, given the other two approaches. Implementation of these approaches on a distributed memory, message passing machine yields huge dividends, as full scalability to the largest machines appears assured and iterative solution times are well-behaved for large problems. We present times and solutions for computed RCS for a conducting cube and composite permeability/conducting sphere on the Intel ipsc860 with up to 16 processors solving over 200,000 unknowns. We estimate problems of approximately 10 million unknowns, encompassing 1000 cubic wavelengths, may be attempted on a currently available 512 processor machine, but would be exceedingly tedious to prepare. The most severe bottlenecks are due to the slow rate of mesh generation on non-parallel machines and the large transfer time from such a machine to the parallel processor. One solution, in progress, is to create and then distribute a coarse mesh among the processors, followed by systematic refinement within each processor. Elimination of redundant node definitions at the mesh-partition surfaces, snap-to-surface post processing of the resulting mesh for good modelling of curved surfaces, and load-balancing redistribution of new elements after the refinement are auxiliary steps expected to result in a robust low i/o system for very large finite element problems.

Parker, Jay↗

NASA NTRS1993

Validation of a nonintrusive optical technique for the measurement of liquid mass distribution in a two-phase spray

This work is the continuation of an optical technique development program initiated as part of the 1992 Summer Faculty Fellowship Program. The 1992 work consisted of the formulation and implementation of a technique ivolving the spatial deconvolution of fluorescence data from a uniformly illuminated, seeded densed spray to obtain quantitative measurements of the liquid density profiles. This measurement approach largely overcomes substantial scattering problems associated with other optical approaches for two-phase flows. However, to apply this measurement approach with confidence to unknown flows, the technique must be validated. Consequently, technique validation using classical grid patternator techniques has been focus of the current work. This work has included the design and construction of a patternator rig and the implementation of a test program designed for the comparison of patternator data with the deconvolved optical data. The flow field used for the validation is the plume of an axisymetric swirl coaxial LOX injector being considered for use in the Space Transportation System Main Engine. The flow facility is an improved version of the test rig which was constructed in 1992 for the initial technique development. This report includes a brief description of the optical measurement technique and the patternator rig and a presentation of the data comparisons.

Hartfield, Roy, Jr.↗

NASA NTRS1998

Calculation of the Bulk Electromagnetic Properties of Thunderclouds Using a Two-Space Scattering Formalism

A two-space scatterer formalism and equivalent medium approach of Twersky are used to obtain formulae for the bulk electromagnetic parameters of a thundercloud medium that is illuminated by lightning optical emissions. A modified WKB approximation is applied to derive the two-space scattering amplitude. Optical constants of dry air, moist atmosphere, and water,.are inserted into the formulae to generate numerical values via iteration. The two-space scatterer formalism results are close to those obtained from free- or sin-le-space formalisms for the dilute case. The numerical values of the bulk parameters are required to successfully transform the scattering problem to that of an equivalent obstacle excited by an incident wave traveling in K - space but radiating in k(sub 1) -space.

Phanord, Dieudonne D.↗

NASA NTRS2001

A Linear Bicharacteristic FDTD Method

The linear bicharacteristic scheme (LBS) was originally developed to improve unsteady solutions in computational acoustics and aeroacoustics [1]-[7]. It is a classical leapfrog algorithm, but is combined with upwind bias in the spatial derivatives. This approach preserves the time-reversibility of the leapfrog algorithm, which results in no dissipation, and it permits more flexibility by the ability to adopt a characteristic based method. The use of characteristic variables allows the LBS to treat the outer computational boundaries naturally using the exact compatibility equations. The LBS offers a central storage approach with lower dispersion than the Yee algorithm, plus it generalizes much easier to nonuniform grids. It has previously been applied to two and three-dimensional freespace electromagnetic propagation and scattering problems [3], [6], [7]. This paper extends the LBS to model lossy dielectric and magnetic materials. Results are presented for several one-dimensional model problems, and the FDTD algorithm is chosen as a convenient reference for comparison.

Beggs, John H.↗

NASA NTRS2005

A Tower-based Prototype VHF/UHF Radar for Subsurface Sensing: System Description and Data Inversion Results

Knowledge of subsurface characteristics such as permittivity variations and layering structure could provide a breakthrough in many terrestrial and planetary science disciplines. For Earth science, knowledge of subsurface and subcanopy soil moisture layers can enable the estimation of vertical flow in the soil column linking surface hydrologic processes with that in the subsurface. For planetary science, determining the existence of subsurface water and ice is regarded as one of the most critical information needs for the study of the origins of the solar system. The subsurface in general can be described as several near-parallel layers with rough interfaces. Each homogenous rough layer can be defined by its average thickness, permittivity, and rms interface roughness assuming a known surface spectral distribution. As the number and depth of layers increase, the number of measurements needed to invert for the layer unknowns also increases, and deeper penetration capability would be required. To nondestructively calculate the characteristics of the rough layers, a multifrequency polarimetric radar backscattering approach can be used. One such system is that we have developed for data prototyping of the Microwave Observatory of Subcanopy and Subsurface (MOSS) mission concept. A tower-mounted radar makes backscattering measurements at VHF, UHF, and L-band frequencies. The radar is a pulsed CW system, which uses the same wideband antenna to transmit and receive the signals at all three frequencies. To focus the beam at various incidence angles within the beamwidth of the antenna, the tower is moved vertically and measurements made at each position. The signals are coherently summed to achieve focusing and image formation in the subsurface. This requires an estimate of wave velocity profiles. To solve the inverse scattering problem for subsurface velocity profile simultaneously with radar focusing, we use an iterative technique based on a forward numerical solution of the layered rough surface problem. The layers are each defined in terms of a small number of unknown distributions as given above. An a priori estimate of the solution is first assumed, based on which the forward problem is solved for the backscattered measurements. This is compared with the measured data and using iterative techniques an update to the solution for the unknowns is calculated. The process continues until convergence is achieved. Numerical results will be shown using actual radar data acquired with the MOSS tower radar system in Arizona in Fall 2003, and compared with in-situ measurements.

Moghaddam, Mahta↗

NASA NTRS2012

Efficient Implementation of the Invariant Imbedding T-Matrix Method and the Separation of Variables Method Applied to Large Nonspherical Inhomogeneous Particles

Three terms, ''Waterman's T-matrix method'', ''extended boundary condition method (EBCM)'', and ''null field method'', have been interchangeable in the literature to indicate a method based on surface integral equations to calculate the T-matrix. Unlike the previous method, the invariant imbedding method (IIM) calculates the T-matrix by the use of a volume integral equation. In addition, the standard separation of variables method (SOV) can be applied to compute the T-matrix of a sphere centered at the origin of the coordinate system and having a maximal radius such that the sphere remains inscribed within a nonspherical particle. This study explores the feasibility of a numerical combination of the IIM and the SOV, hereafter referred to as the IIMþSOV method, for computing the single-scattering properties of nonspherical dielectric particles, which are, in general, inhomogeneous. The IIMþSOV method is shown to be capable of solving light-scattering problems for large nonspherical particles where the standard EBCM fails to converge. The IIMþSOV method is flexible and applicable to inhomogeneous particles and aggregated nonspherical particles (overlapped circumscribed spheres) representing a challenge to the standard superposition T-matrix method. The IIMþSOV computational program, developed in this study, is validated against EBCM simulated spheroid and cylinder cases with excellent numerical agreement (up to four decimal places). In addition, solutions for cylinders with large aspect ratios, inhomogeneous particles, and two-particle systems are compared with results from discrete dipole approximation (DDA) computations, and comparisons with the improved geometric-optics method (IGOM) are found to be quite encouraging.

Invariant imbedding method↗

NASA NTRS2018

Simulation of Sound Absorption by Scattering Bodies Treated with Acoustic Liners Using a Time-Domain Boundary Element Method

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.

Pizzo, Michelle E.↗

NASA NTRS2020

An Overview of the Null-Field Method. I. Formulation and Basic Results

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

Null-field method↗

NASA NTRS2021

Evaluation of Higher-order Quadrature Schemes in Improving Computational Efficiency for Orientation-averaged Single-Scattering Properties of Nonspherical Ice Particles

We evaluate several high-order quadrature schemes for accuracy and efficacy in obtaining orientation-averaged single-scattering properties (SSPs). We use the highly efficient MIDAS to perform electromagnetic scattering calculations to evaluate the gain in efficiency from these schemes. MIDAS is shown to be superior to DDSCAT, a popular discrete dipole approximation (DDA) method. This study is motivated by the fact that quality physical precipitation retrievals rely on using accurate orientation-averaged SSPs derived from realistic hydrometeors as input to radiative transfer Models (RTMs). The DDA has been a popular choice for single-scattering calculations, due to its versatility with respect to target geometry. However, being iterative-solver-based (ISB), the most used DDA codes, e.g. DDSCAT and ADDA, must solve the scattering problem for each orientation of the target separately. As the size parameter and geometric anisotropy of the hydrometeor increase, the number of orientations needed to obtain accurate orientation-averages can increase drastically and so does the computation cost incurred by the ISB-DDA methods. MIDAS is a Direct-Solver-Based (DSB) code, its decomposition of the original large matrix with a high rank into multiple more manageable smaller matrices of lower ranks makes it much more computationally efficient while maintaining excellent accuracy. In addition, direct solvers consider all requested orientations at once, giving MIDAS further advantage over popular ISB-DDA methods. MIDAS, when combined with high-order quadrature for orientation averaging, can be greater than three orders of magnitude more efficient in obtaining RTM-ready SSPs of complex-shaped hydrometeors than existing ISB-DDA methods, with the native quadrature schemes they offer.

Ines Fenni↗

NASA NTRS1987

The finite-difference time-domain (FD-TD) method for electromagnetic scattering and interaction problems

The formulation and recent applications of the finite-difference time-domain (FD-TD) method for the numerical modeling of electromagnetic scattering and interaction problems are considered. It is shown that improvements in FD-TD modeling concepts and software implementation often make it a preferable choice for structures which cannot be easily treated by conventional integral equations and asymptotic approaches. Recent FD-TD modeling validations in research areas including coupling to wires and wire bundles in free space and cavities, scattering from surfaces in relativistic motion, inverse scattering, and radiation condition theory, are reviewed. Finally, the advantages and disadvantages of FD-TD, and guidelines concerning when FD-TD should and should not be used in high-frequency electromagnetic modeling problems, are summarized.

Taflove, A.↗

NASA NTRS1979

Solution of electromagnetic scattering and radiation problems using a spectral domain approach - A review

This paper presents a brief review of some recent developments on the use of the spectral-domain approach for deriving high-frequency solutions to electromagnetics scattering and radiation problems. The spectral approach is not only useful for interpreting the well-known Keller formulas based on the geometrical theory of diffraction (GTD), it can also be employed for verifying the accuracy of GTD and other asymptotic solutions and systematically improving the results when such improvements are needed. The problem of plane wave diffraction by a finite screen or a strip is presented as an example of the application of the spectral-domain approach.

Mittra, R.↗

NASA NTRS1977

A novel methodology for radiative transfer in a planetary atmosphere. I - The functions a exponent m and b exponent m of anisotropic scattering

The original problem of anisotropic scattering in an atmosphere illuminated by a unidirectional source is replaced by an analogous formulation where the incident light is omnidirectional. A radiative-transfer equation for the omnidirectional case is obtained in which the direction of illumination plays no role and the source-function analog, Sobolev's (1972) source function Phi exponent m, contains only a single integral term. For radiation incident on the top or the bottom of the atmosphere, this equation involves the functions b exponent m and h exponent m, respectively, with m corresponding to the order of the harmonic component of the scattered radiation field; these two functions are shown to be only one through some simple reciprocity relations. The transfer problem is then reformulated for the function a exponent m, in which case the source-function analog (Sobolev's function D exponent m) involves incident direction.

Fymat, A. L.↗