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NASA NTRS1989

Radiative transfer theory for inhomogeneous media with random extinction and scattering coefficients

The small-angle scattering approximation of the scalar radiative transfer equation (RTE) is examined for the case where the extinction and scattering coefficients have a component that is a deterministic function of position along the propagation path and a component that is a random function of position transverse to the propagation direction. It is found that the resulting stochastic RTE can be reduced to a system of two stochastic integrodifferential equations for the average and fluctuating components of the radiant intensity. Two transfer equations are obtained describing the average radiant intensity and the spatial correlation function of the intensity fluctuations. The average intensity equation is then solved and applied to a simple propagation scenario. An approximate solution is also derived for the equation giving the correlation function. The developed equations can be applied to problems involving short wavelength electromagnetic wave propagation through media possessing the variable characteristics of turbulence and turbidity, such as plasmas, the atmosphere, and the ocean.

Manning, Robert M.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-851O network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS1995

Optimal Signal Processing of Frequency-Stepped CW Radar Data

An optimal signal processing algorithm is derived for estimating the time delay and amplitude of each scatterer reflection using a frequency-stepped CW system. The channel is assumed to be composed of abrupt changes in the reflection coefficient profile. The optimization technique is intended to maximize the target range resolution achievable from any set of frequency-stepped CW radar measurements made in such an environment. The algorithm is composed of an iterative two-step procedure. First, the amplitudes of the echoes are optimized by solving an overdetermined least squares set of equations. Then, a nonlinear objective function is scanned in an organized fashion to find its global minimum. The result is a set of echo strengths and time delay estimates. Although this paper addresses the specific problem of resolving the time delay between the first two echoes, the derivation is general in the number of echoes. Performance of the optimization approach is illustrated using measured data obtained from an HP-X510 network analyzer. It is demonstrated that the optimization approach offers a significant resolution enhancement over the standard processing approach that employs an IFFT. Degradation in the performance of the algorithm due to suboptimal model order selection and the effects of additive white Gaussion noise are addressed.

Ybarra, Gary A.↗

NASA NTRS2004

Frequency Domain Calculations Of Acoustic Propagation

Two complex geometry problems are solved using the linearized Euler equations. The impedance mismatch method1 is used to impose the solid surfaces without the need to use a body-fitted grid. The problem is solved in the frequency domain to avoid long run times. Although the harmonic assumption eliminates all time dependence, a pseudo-time term is added to allow conventional iterative methods to be employed. A Jameson type, Runge-Kutta scheme is used to advance the solution in pseudo time. The spatial operator is based on a seven-point, sixth-order finite difference. Constant coefficient, sixth-derivative artificial dissipation is used throughout the domain. A buffer zone technique employing a complex frequency to damp all waves near the boundaries is used to minimize reflections. The results show that the method is capable of capturing the salient features of the scattering, but an excessive number of grid points are required to resolve the phenomena in the vicinity of the solid bodies because the wavelength of the acoustics is relatively short compared with the size of the bodies. Smoothly transitioning into the immersed boundary condition alleviates the difficulties, but a fine mesh is still required.

Lockard, David P.↗

NASA NTRS1993

Green vegetation, nonphotosynthetic vegetation, and soils in AVIRIS data

The problem of distinguishing between green vegetation, nonphotosynthetic vegetation (NPV, such as dry grass, leaf litter, and woody material), and soils in imaging-spectrometer data is addressed by analyzing an image taken by the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) over the Jasper Ridge Biological Preserve (California) on September 20, 1989, using spectral mixture analysis. Over 98 percent of the spectral variation could be explained by linear mixtures of three endmembers, green vegetation, shade, and soil. NPV, which could not be distinguished from soil when included as an endmember, was discriminated by residual spectra that contained cellulose and lignin absorptions. Distinct communities of green vegetation were distinguished by (1) nonlinear mixing effect caused by transmission and scattering by green leaves, (2) variations in a derived canopy-shade spectrum, and (3) the fraction of NPV.

Roberts, D. A.↗

NASA NTRS2004

Optical Levitation of Micro-Scale Particles in Air

Success has been achieved using a radiation pressure gradient to levitate microscale particles in air for as long as four hours. This work is performed as a precursor to the development of a vacuum based optical tweezers interrogation tool for nanotechnology research. It was decided to first proceed with solving the problem of achieving optical levitation of a micro-scale particle in air before trying the same in a vacuum environment. This successful optical levitation in air confirms the work of Ashkin and Dziedzic. Levitation of 10 and 13.8 microns diameter polystyrene spheres was achieved, as well as the levitation of 10 and 100 microns diameter glass spheres. Particles were raised and lowered. A modicum of success was achieved translating particles horizontally. Trapping of multiple particles in one laser beam has been photographed. Also, it has been observed that particles, that may be conglomerates or irregular in shape, can also be trapped by a focused laser beam. Levitated glass beads were photographed using laser light scattered from the beads. The fact that there is evidence of optical traps in air containing irregular and conglomerate particles provides hope that future tool particles need not be perfect spheres.

Wrbanek, Susan Y.↗

DOE OSTI2024

Adaptable SEC‐SAXS data collection for higher quality structure analysis in solution

Abstract The two major challenges in synchrotron size‐exclusion chromatography coupled in‐line with small‐angle x‐ray scattering (SEC‐SAXS) experiments are the overlapping peaks in the elution profile and the fouling of radiation‐damaged materials on the walls of the sample cell. In recent years, many post‐experimental analyses techniques have been developed and applied to extract scattering profiles from these problematic SEC‐SAXS data. Here, we present three modes of data collection at the BioSAXS Beamline 4–2 of the Stanford Synchrotron Radiation Lightsource (SSRL BL4‐2). The first mode, the High‐Resolution mode, enables SEC‐SAXS data collection with excellent sample separation and virtually no additional peak broadening from the UHPLC UV detector to the x‐ray position by taking advantage of the low system dispersion of the UHPLC. The small bed volume of the analytical SEC column minimizes sample dilution in the column and facilitates data collection at higher sample concentrations with excellent sample economy equal to or even less than that of the conventional equilibrium SAXS method. Radiation damage problems during SEC‐SAXS data collection are evaded by additional cleaning of the sample cell after buffer data collection and avoidance of unnecessary exposures through the use of the x‐ray shutter control options, allowing sample data collection with a clean sample cell. Therefore, accurate background subtraction can be performed at a level equivalent to the conventional equilibrium SAXS method without requiring baseline correction, thereby leading to more reliable downstream structural analysis and quicker access to new science. The two other data collection modes, the High‐Throughput mode and the Co‐Flow mode, add agility to the planning and execution of experiments to efficiently achieve the user's scientific objectives at the SSRL BL4‐2.

Matsui, Tsutomu↗

DOE OSTI2019

Properties of a potential energy matrix in oscillator basis

Matrix elements of potential energy are examined in detail. We consider a model problem — a particle in a central potential. The most popular forms of central potential are taken up, namely, square-well potential, Gaussian, Yukawa and exponential potentials. We study eigenvalues and eigenfunctions of the potential energy matrix constructed with oscillator functions. It is demonstrated that eigenvalues coincide with the potential energy in coordinate space at some specific discrete points. We establish approximate values for these points. It is also shown that the eigenfunctions of the potential energy matrix are the expansion coefficients of the spherical Bessel functions in a harmonic oscillator basis. We also demonstrate a close relation between the separable approximation and L{sup 2} basis (J-matrix) method for the quantum theory of scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Disentangling multiple scattering with deep learning: application to strain mapping from electron diffraction patterns

Abstract A fast, robust pipeline for strain mapping of crystalline materials is important for many technological applications. Scanning electron nanodiffraction allows us to calculate strain maps with high accuracy and spatial resolutions, but this technique is limited when the electron beam undergoes multiple scattering. Deep-learning methods have the potential to invert these complex signals, but require a large number of training examples. We implement a Fourier space, complex-valued deep-neural network, FCU-Net, to invert highly nonlinear electron diffraction patterns into the corresponding quantitative structure factor images. FCU-Net was trained using over 200,000 unique simulated dynamical diffraction patterns from different combinations of crystal structures, orientations, thicknesses, and microscope parameters, which are augmented with experimental artifacts. We evaluated FCU-Net against simulated and experimental datasets, where it substantially outperforms conventional analysis methods. Our code, models, and training library are open-source and may be adapted to different diffraction measurement problems.

36 MATERIALS SCIENCE↗

NASA NTRS1984

Finite Element Prediction of Acoustic Scattering and Radiation from Submerged Elastic Structures

A finite element formulation is derived for the scattering and radiation of acoustic waves from submerged elastic structures. The formulation uses as fundamental unknowns the displacement in the structure and a velocity potential in the field. Symmetric coefficient matrices result. The outer boundary of the fluid region is terminated with an approximate local wave-absorbing boundary condition which assumes that outgoing waves are locally planar. The finite element model is capable of predicting only the near-field acoustic pressures. Far-field sound pressure levels may be determined by integrating the surface pressures and velocities over the wet boundary of the structure using the Helmholtz integral. Comparison of finite element results with analytic results show excellent agreement. The coupled fluid-structure problem may be solved with general purpose finite element codes by using an analogy between the equations of elasticity and the wave equation of linear acoustics.

Everstine, G. C.↗

NASA NTRS1989

A statistical study of radio-source structure effects on astrometric very long baseline interferometry observations

Errors from a number of sources in astrometric very long baseline interferometry (VLBI) have been reduced in recent years through a variety of methods of calibration and modeling. Such reductions have led to a situation in which the extended structure of the natural radio sources used in VLBI is a significant error source in the effort to improve the accuracy of the radio reference frame. In the past, work has been done on individual radio sources to establish the magnitude of the errors caused by their particular structures. The results of calculations on 26 radio sources are reported in which an effort is made to determine the typical delay and delay-rate errors for a number of sources having different types of structure. It is found that for single observations of the types of radio sources present in astrometric catalogs, group-delay and phase-delay scatter in the 50 to 100 psec range due to source structure can be expected at 8.4 GHz on the intercontinental baselines available in the Deep Space Network (DSN). Delay-rate scatter of approx. 5 x 10(exp -15) sec sec(exp -1) (or approx. 0.002 mm sec (exp -1) is also expected. If such errors mapped directly into source position errors, they would correspond to position uncertainties of approx. 2 to 5 nrad, similar to the best position determinations in the current JPL VLBI catalog. With the advent of wider bandwidth VLBI systems on the large DSN antennas, the system noise will be low enough so that the structure-induced errors will be a significant part of the error budget. Several possibilities for reducing the structure errors are discussed briefly, although it is likely that considerable effort will have to be devoted to the structure problem in order to reduce the typical error by a factor of two or more.

Ulvestad, J. S.↗

NASA NTRS1999

Fatigue Failure Criteria for Single Crystal Nickel Superalloys

High Cycle Fatigue (HCF) induced failures in aircraft gas-turbine and rocket engine turbopump blades is a pervasive problem. Single crystal turbine blades are being utilized in rocket engine turbopumps and jet engines throughout industry and NASA because of their superior creep, stress rupture, melt resistance and thermomechanical fatigue capabilities over polycrystalline alloys. Single-crystal materials have highly orthotropic properties making the position of the crystal lattice relative to the pan geometry a significant factor in the overall analysis. The failure modes of single crystal turbine blades is complicated to predict due to the material orthotropy and variations in crystal orientations. A fatigue failure criteria based on the maximum shear stress amplitude [delta t max] on the 30 slip systems, is presented for single crystal nickel superalloys (FCC crystal). This criteria reduces the scatter in uniaxial LCF test data, for four different specimen orientations, for PWA 1484 at 1200 F in air, quite well. A power law curve fit of the failure parameter, delta t max, vs. cycles to failure is presented.

Arakere, Nagaraj K.↗

NASA NTRS2004

Passive Acoustic Tomography Tested for Measuring Gas Temperatures

The requirements of higher performance, better fuel economy, and lower emissions place an increasing premium on knowing the internal operating parameters of jet engines. One of the most important is the gas temperature in the post combustor section of the engine. Typically the gas temperature is measured with a thermocouple probe or by some optical technique such as Rayleigh scattering. Probes, while providing valuable information, have several limitations. The probe signal must be corrected for radiation and conduction losses, probes provide only a point measurement, and probes must be constructed of materials whose melting points are lower than the temperature of the environment into which they are inserted. Some of the disadvantages of probes are overcome by various optical techniques. Nothing needs to be inserted into the flow, and the temperature can be directly related to the signal by known physical laws. However, optical techniques require optical access (i.e., a window) and a light source (such as a laser), and they are very sensitive to the presence of particles in the flow. To overcome these problems, researchers from the NASA Glenn Research Center and The University of Nevada are developing a technique that uses sound instead of light to measure gas temperature. Like optical techniques, it is nonintrusive--no probe need be exposed to the combustion environment--and the temperature is directly related to a measured quantity--the speed of sound, which is proportional to the square root of the absolute temperature. The temperature profile inside the engine is constructed from the differences in arrival time between correlated signals from an array of microphones placed around the circumference of the engine. In much the same way as a complete picture of the inside of your body can be constructed from an array of x-ray photographs taken at different angles, the temperature profile in the engine is constructed from the angular array of microphones. It is tomography by sound waves. Active acoustic tomography, in which a sound pulse is injected into the flow and the time delays between members of an array of microphones are used to construct the temperature field has been used successfully in the stacks of power plants. However, the flow field inside a jet engine is much too noisy for it to be possible to detect an externally injected sound pulse. Instead we are developing passive acoustic tomography, which uses the sound already present in the flow.

Fralick, Gustave C.↗

NASA NTRS1997

Cirrus Cloud Radiative and Microphysical Properties from Ground Observations and In Situ Measurements During FIRE 1991 and Their Application to Exhibit Problems in Cirrus Solar Radiative Transfer Modeling

Measurements from the FIRE 1991 cirrus cloud field experiment in the central United States are presented and analyzed. The first part focuses on cirrus microphysical properties. Aircraft 2D-probe in situ data at different cloud altitudes were evaluated for cirrus cases on four different days. Also presented are simultaneous data samples from balloonborne videosondes. Only these balloonsondes could detect the smaller crystals. Their data suggest (at least for midlatitude altitudes below 10 km) that ice crystals smaller than 15 microns in size are rare and that small ice crystals not detected by 2D-probe measurements are radiatively of minor importance, as overlooked 2D-probe crystals account for about 10% of the total extinction. The second part focuses on the link between cirrus cloud properties and radiation. With cloud macrophysical properties from surface remote sensing added to the microphysical data and additional radiation measurements at the surface, testbeds for radiative transfer models were created. To focus on scattering processes, model evaluations were limited to the solar radiative transfer by comparing calculated and measured transmissions of sunlight at the surface. Comparisons under cloud-free conditions already reveal a model bias of about +45 W/sq m for the hemispheric solar downward broadband flux. This discrepancy, which is (at least in part) difficult to explain, has to be accounted for in comparisons involving clouds. Comparisons under cirrus cloud conditions identify as the major obstacle in cirrus solar radiative transfer modeling the inability of one-dimensional radiative transfer models to account for horizontal inhomogeneities. The successful incorporation of multidimensional radiative transfer effects will depend not only on better models but critically on the ability to measure and to define characteristic inhomogeneity scales of cloud fields. The relative minor error related to the microphysical treatment is in part a reflection of the improved understanding on solar scattering on ice crystals over the last decade and of the available wealth on ice-crystal size and shape data for this study. In absence of this information, uncertainties from microphysical cirrus model assumptions will remain high.

Kinne, Stefan↗

NASA NTRS2006

Aerosol Direct Radiative Effect at the Top of the Atmosphere Over Cloud Free Ocean Derived from Four Years of MODIS Data

A four year record of MODIS spaceborne data provides a new measurement tool to assess the aerosol direct radiative effect at the top of the atmosphere. MODIS derives the aerosol optical thickness and microphysical properties from the scattered sunlight at 0.55-2.1 microns. The monthly MODIS data used here are accumulated measurements across a wide range of view and scattering angles and represent the aerosol s spectrally resolved angular properties. We use these data consistently to compute with estimated accuracy of +/-0.6W/sq m the reflected sunlight by the aerosol over global oceans in cloud free conditions. The MODIS high spatial resolution (0.5 km) allows observation of the aerosol impact between clouds that can be missed by other sensors with larger footprints. We found that over the clear-sky global ocean the aerosol reflected 5.3+/-0.6W/sq m with an average radiative efficiency of 49+/-2W/sq m per unit optical thickness. The seasonal and regional distribution of the aerosol radiative effects are discussed. The analysis adds a new measurement perspective to a climate change problem dominated so far by models.

Remer, L. A.↗

DOE OSTI2018

Theoretical Analysis of the Entrainment–Mixing Process at Cloud Boundaries. Part I: Droplet Size Distributions and Humidity within the Interface Zone

Abstract The problem of a complex entrainment–mixing process is analyzed by solving a diffusion–evaporation equation for an open region in the vicinity of the cloud–dry air interface. Upon normalization the problem is reduced to a one-parametric one, the governing parameter being the potential evaporation parameter R proportional to the ratio of saturation deficit in the dry air to the available liquid water content in the cloud air. As distinct from previous multiple studies analyzing mixing within closed adiabatic volumes, we consider a principally nonstationary problem that never leads to a homogeneous equilibrium state. It is shown that at R < −1 the cloud edge shifts toward the cloud; that is, the cloud dissipates due to mixing with dry air, and the cloud volume decreases. If R > −1, the cloud edge shifts outside; that is, the mixing leads to an increase in the cloud volume. The time evolution of droplet size distribution and its moments, as well as the relative humidity within the expanding cloud–dry air interface, are calculated and analyzed. It is shown that the values of the mean volume radii rapidly decrease within the interface zone in the direction away from the cloud, indicating significant changes in the cloud edge microstructure. Scattering diagrams plotted for the cloud edge agree well with high-frequency in situ measurements, corroborating the reliability of the proposed approach. It is shown that the humidity front moves toward dry air faster than the front of liquid water content. As a result, the mixing leads to formation of a humid air shell around the cloud. The widths of the interface zone and humid shell are evaluated.

Pinsky, Mark↗

DOE OSTI2019

Weak separation, positivity and extremal Yangian invariants

We classify all positive $n$-particle N k MHV Yangian invariants in $N =$ 4 YangMills theory with $n = 5k$, which we call extremal because none exist for $n > 5k$. We show that this problem is equivalent to that of enumerating plane cactus graphs with k pentagons. We use the known solution of that problem to provide an exact expression for the number of cyclic classes of such invariants for any $k$, and a simple rule for writing them down explicitly. We provide an alternative (but equivalent) classification by showing that a product of $k$ five-brackets with disjoint sets of indices is a positive Yangian invariant if and only if the sets are all weakly separated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

A Proof of the Asymptotic Variance of Path Length Estimators for Single-Collision Monte Carlo Source Iteration in the Thick Diffusion Limit

Here, we prove a theorem relating the variance of path length estimators for single-collision Monte Carlo source iteration to a parameter that becomes infinitesimally small in an important physical regime arising in radiative transfer. In our usage, “single-collision Monte Carlo source iteration” refers to Monte Carlo Boltzmann transport methods in which each Monte Carlo particle history includes no more than a single collision, and the physics of multiple scattering is modeled by lagging the scattering source term and iterating until this term converges. Our theorem can be used to construct variance reduction techniques which improve the order of the estimator variance. This enables calculations that would otherwise require impractically large sample sizes to achieve practical estimator uncertainties. We believe this is the first postulation of a theorem relating estimator variance to a limiting case parameter for single-collision Monte Carlo source iteration, and the first proof of such a theorem. We illustrate the theorem’s value with an example in which the authors of a transport method used the theorem to design a variance reduction technique that improved the uncertainty of their solution by a factor of about 500 for a proxy problem from radiative transfer that contains both optically-thick and optically-thin material.

Mathematics and Computing↗