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All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Scattering from nonspherical Chebyshev particles. I - Cross sections, single-scattering albedo, asymmetry factor, and backscattered fraction

Using the extended boundary condition method, scattering calculations from randomly oriented rotationally symmetric nonspherical particles were made, the size parameters (1-25) and the refractive indicies (1.5 0.02i) of which were chosen to relate to the transfer of solar and IR radiation in an aerosol atmosphere. Comparison of computations for 23 Chebyshev shapes to corresponding size-averaged spherical results revealed that nonsphericity increased absorption for size parameters larger than around 10 and decreased the asymmetry factor, and correspondingly increased the backscattered fraction, in the size ranges 8-15. The scattering efficiency was somewhat larger for nonspherical particles, while the single-scattering albedo tended to be smaller, and concavity was shown to almost always enhance spherical-nonspherical differences.

Mugnai, A.↗
NASA NTRS1986

Single scattering from nonspherical Chebyshev particles: A compendium of calculations

A large set of exact calculations of the scattering from a class of nonspherical particles known as Chebyshev particles' has been performed. Phase function and degree of polarization in random orientation, and parallel and perpendicular intensities in fixed orientations, are plotted for a variety of particles shapes and sizes. The intention is to furnish a data base against which both experimental data, and the predictions of approximate methods, can be tested. The calculations are performed with the widely-used Extended Boundary Condition Method. An extensive discussion of this method is given, including much material that is not easily available elsewhere (especially the analysis of its convergence properties). An extensive review is also given of all extant methods for nonspherical scattering calculations, as well as of the available pool of experimental data.

Wiscombe, W. J.↗
NASA NTRS1989

Scattering from nonspherical Chebyshev particles. III - Variability in angular scattering patterns

Shape-induced variability in the scattered intensity from randomly oriented nonspherical particles is studied. A comparison is made between bands of shape-induced variability for six size intervals within the size parameter range of 1 to 20 and corresponding spherical intensities. It is found that averaging spherical intensities over narrow size ranges produces effects that are qualitatively similar to a slightly distorted single sphere. The results also show that, for Chebyshev particles which are neither small nor large compared to the wavelength, shape-induced variability is often comparable to the mean.

Mugnai, Alberto↗
NASA NTRS2016

The Microwave Radiative Properties of Falling Snow Derived from Nonspherical Ice Particle Models. Part II: Initial Testing Using Radar, Radiometer and In Situ Observations

In this study, two different particle models describing the structure and electromagnetic properties of snow are developed and evaluated for potential use in satellite combined radar-radiometer precipitation estimation algorithms. In the first model, snow particles are assumed to be homogeneous ice-air spheres with single-scattering properties derived from Mie theory. In the second model, snow particles are created by simulating the self-collection of pristine ice crystals into aggregate particles of different sizes, using different numbers and habits of the collected component crystals. Single-scattering properties of the resulting nonspherical snow particles are determined using the discrete dipole approximation. The size-distribution-integrated scattering properties of the spherical and nonspherical snow particles are incorporated into a dual-wavelength radar profiling algorithm that is applied to 14- and 34-GHz observations of stratiform precipitation from the ER-2 aircraft-borne High-Altitude Imaging Wind and Rain Airborne Profiler (HIWRAP) radar. The retrieved ice precipitation profiles are then input to a forward radiative transfer calculation in an attempt to simulate coincident radiance observations from the Conical Scanning Millimeter-Wave Imaging Radiometer (CoSMIR). Much greater consistency between the simulated and observed CoSMIR radiances is obtained using estimated profiles that are based upon the nonspherical crystal/aggregate snow particle model. Despite this greater consistency, there remain some discrepancies between the higher moments of the HIWRAP-retrieved precipitation size distributions and in situ distributions derived from microphysics probe observations obtained from Citation aircraft underflights of the ER-2. These discrepancies can only be eliminated if a subset of lower-density crystal/aggregate snow particles is assumed in the radar algorithm and in the interpretation of the in situ data.

Ice particles; Radiances; Radiative transfer; Airc↗
NASA NTRS2019

On the Convergence of Numerical Computations for Both Exact and Approximate Solutions for Electromagnetic Scattering by Nonspherical Dielectric Particles

We summarize the size parameter range of the applicability of four lightscattering computational methods for nonspheric dielectric particles. These methods include two exact methods - the extended boundary condition method (EBCM) and the invariant imbedding T-matrix method (II-TM) and two approximate approaches - the physical-geometric optics method (PGOM) and the improved geometric optics method (IGOM). For spheroids, the single-scattering properties computed by EBCM and II-TM agree for size parameters up to 150, and the comparison gives us confidence in using IITM as a benchmark for size parameters up to 150 for other geometries (e.g., hexagonal columns) because the applicability of II-TM with respect to particle shape is generic, as demonstrated in our previous studies involving a complex aggregate. This study demonstrates the convergence of the exact II-TM and approximate PGOM solutions for the complete set of single-scattering properties of a nonspherical shape other than spheroids and circular cylinders with particle sizes of ~48λ, specifically a hexagonal column with a size parameter of length as kL=300, where k=2π/λ and L is the column length. IGOM is also quite accurate except near the exact 180º backscattering direction. This study demonstrates that a synergetic combination of the numerically-exact II-TM and the approximate PGOM can seamlessly cover the entire size parameter range of practical interest. To demonstrate the applicability of the approach, we compute the optical properties of dust particles with a downstream application to the retrieval of dust aerosol optical thickness and effective particle size from polarimetric observations.

Ping Yang↗
NASA NTRS1988

Scattering from nonspherical Chebyshev particles. II - Means of angular scattering patterns

The calculated angular scattering properties of over 250 randomly oriented nonspherical Chebyshev particles are examined for the effect of three factors: size; concavity vs convexity; and amount of deformation from a sphere. Both shape and size averaging are performed to reveal general features of the angular scattering not discernible for particular shapes and sizes. Comparisons with a comparably extensive experimental study published by Zerull in 1976 reveal remarkable qualitative similarities, even though Zerull used greatly different shapes from ours. This augurs well for the eventual development of a general theory of nonspherical scattering, although such a theory must account for concavity in addition to the amount of deviation from a sphere; and it cannot be entirely deterministic, as the third paper in this series will argue.

Wiscombe, Warren J.↗
DOE OSTI2026

An Approach for Simulating Transport of Nonspherical, Sublimating Particles in Rarefied Gas Flows via the Direct Simulation Monte Carlo Method

This paper extends the particle Green’s function approach of Gallis et al. [Phys. Fluids 13, 3482–3492 (2001)] to compute the force and heat transfer on nonspherical, sublimating particles in rarefied gas flows. Green’s functions are derived for rods and plates, which are representative of ice particle shapes, and a numerical procedure is developed for computing the Green’s functions for a general discretized convex shape. Additionally, a sublimation model is developed to simulate the evolution of ice particles in rarefied gas flows. These models are implemented in a direct simulation Monte Carlo code and demonstrated for the case of ice-particle-laden hypersonic flow over a ramp.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2001

Shape and Structure

The convenient availability and simplicity of the Lorenz-Mie theory has resulted in a widespread practice of treating nonspherical particles (especially those in random orientation) as if they were spheres to which Lorenz-Mie results are applicable. However, the assumption of sphericity is rarely made after first having studied the effects of nonsphericity and having concluded that they are negligible. On the contrary, overwhelming evidence suggests that scattering properties of nonspherical particles, including those in random orientation, can significantly differ from those of volume- or surface-equivalent spheres. Hence, the last few decades have demonstrated major research efforts aimed at a significantly better understanding of the effects of particle shape and morphology on electromagnetic scattering. The goal of this presentation is to provide a concise summary of these efforts. The recent availability of theoretical techniques for computing single and multiple scattering of light by realistic polydispersions of spherical and nonspherical particles and the strong dependence of the Stokes scattering matrix on particle size, shape, and refractive index make polarization and depolarization measurements a powerful particle characterization tool. This presentation will focus on recent applications of photopolarimetric and lidar depolarization measurements to remote sensing characterization of tropospheric aerosols, polar stratospheric clouds (PSCs) and contrails. The talk will include (1) a short theoretical overview of the effects of particle microphysics on particle single-scattering characteristics; (2) the use of multi-angle multi-spectral photopolarimetry to retrieve the optical thickness, size distribution, refractive index, and number concentration of tropospheric aerosols over the ocean surface; and (3) the application of the T-matrix method to constraining the PSC and contrail particle microphysics using multi-spectral measurements of lidar backscatter and depolarization

Mishchenko, Michael↗
NASA NTRS1983

Voyager 2 photopolarimeter observations of Titan

Observations of Titan's whole-disk polarization at 2460 and 7500 A are presented and analyzed in terms of model scattering atmospheres. If the Titan aerosols are spherical or nearly spherical, no single combination of refractive index and size distribution is able to fit data at both wavelengths. However, a vertically inhomogeneous distribution suggested by Tomasko and Smith (1980), characterized by a size gradient with altitude, fits the data at 2640 A moderately well but must be modified at intermediate and large optical depths to fit the 7500-A data. Results for synthetic phase functions indicate that the single-scattering polarization must be 70 percent or larger in the UV and 78 percent or larger in the near-IR at 90-deg phase angle, depending on the phase function. If the correct phase function is similar to that for 0.5-micron-radius spheres, the UV single-scattered polarization must be 84 percent and the near-IR single-scattered polarization must be over 90 percent. Such large polarizations are impossible for 0.5-micron-radius spheres but may be possible for nonspherical particles with effective radii near 0.5 micron, although the existence of nonspherical particles with the scattering properties required by these and other observations has not been demonstrated.

West, R. A.↗
NASA NTRS2001

Constraints on PSC Particle Microphysics Derived From Lidar Observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index Alpha and the depolarization color index Beta are essentially shape-independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type la PSCs is about 0.8 microns or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 microns. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 micron modeled as cylinders or prolate spheroids.

Liu, Li↗
NASA NTRS1997

Sensitivity of Multiangle Remote Sensing Observations to Aerosol Sphericity

Multiangle, multispectral remote sensing observations, such as those anticipated from the Earth Observing System (EOS) multiangle imaging spectroradiometer (MISR), can distinguish spherical from nonspherical particles over calm ocean for mineral-dust-like particles with the range of sizes and column amounts expected under natural conditions. The ability to make such distinctions is critical if remote sensing of atmospheric aerosol properties is to provide significant new contributions to our understanding of the global-scale, clear-sky solar radiation balance. According to theoretical simulations the measurements can retrieve column optical depth for nonspherical particles to an accuracy of at least 0.05 or 10%, whichever is larger. In addition, three to four distinct size groups between 0.1 and 2.0 microns effective radius can be identified at most latitudes.

Kahn, Ralph↗
NASA NTRS1980

Evidence for fragmentation of strongly nonspherical dust particles in the tail of Comet West 1976 VI

Motion of 16 striae through the dust tail of Comet West 1976 VI are observed over a time interval of more than three days. Initiation times for most of the 16 striae are found to coincide with the times of discrete violent bursts of dust, determined from the motions of streamers. It is also found that fragments are subjected to repulsive accelerations between 0.6 and 2.7 the solar attraction, indicating submicron-size absorbing particles, while repulsive accelerations imparted to parent articles are slightly lower than the average acceleration of fragments. The sizes of the fragments are estimated to be between one tenth and a few tenths of a micron. No effect of the Lorentz force on striae motion is detected. It is concluded that the theoretical assumption that striae are products of fragmentation of friable dust particles ejected from the nucleus agrees with observations.

Sekanina, Z.↗
NASA NTRS1989

Comet ejection and dynamics of nonspherical dust particles and meteoroids

This paper generalizes the formalism for calculating the ejection velocity of meteoroids and dust from comets and the forces to which such objects are subject in interplanetary space, including the dust tail of comets. It is found that spheres have the smallest cross section of any geometrical figures of the same valume averaged over random orientations, so for a fixed volume and mass, both the ejection velocity and beta reaches a minimum for bodies of spherical shapes. Flakes in random orientation are ejected near 70 percent of the highest ejection velocity for any orientation. Needles in random orientation escape a comet at nearly 90 percent of their maximum velocities. Randomly oriented cylinders of finite thickness escape at lower velocities that are slightly closer to their maximum velocities. The average beta acting on spin-aligned, perfectly absorbing needles is more than half that acting on a sphere of the same material and radius.

Gustafson, Bo A. S.↗
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 NTRS2000

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

For scattering calculations involving nonspherical particles such as ice crystals, we show that the transverse wave condition is not applicable to the refracted electromagnetic wave in the context of geometric optics when absorption is involved. Either the TM wave condition (i.e., where the magnetic field of the refracted wave is transverse with respect to the wave direction) or the TE wave condition (i.e., where the electric field is transverse with respect to the propagating direction of the wave) may be assumed for the refracted wave in an absorbing medium to locally satisfy the electromagnetic boundary condition in the ray tracing calculation. The wave mode assumed for the refracted wave affects both the reflection and refraction coefficients. As a result, a nonunique solution for these coefficients is derived from the electromagnetic boundary condition. In this study we have identified the appropriate solution for the Fresnel reflection/refraction coefficients in light scattering calculation based on the ray tracing technique. We present the 3 x 2 refraction or transmission matrix that completely accounts for the inhomogeneity of the refracted wave in an absorbing medium. Using the Fresnel coefficients for an absorbing medium, we derive an asymptotic solution in an analytical format for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations. The asymptotic theory can produce reasonable accuracy in the phase function calculations in the infrared window region (wavelengths near 10 micron) if the particle size (in diameter) is on the order of 40 micron or larger. However, since strong absorption is assumed in the computation of the single-scattering albedo in the asymptotic theory, the single scattering albedo does not change with variation of the particle size. As a result, the asymptotic theory can lead to substantial errors in the computation of single-scattering albedo for small and moderate particle sizes. However, from comparison of the asymptotic results with the FDTD solution, it is expected that a convergence between the FDTD results and the asymptotic theory results can be reached when the particle size approaches 200 micron. We show that the phase function at side-scattering and backscattering angles is insensitive to particle shape if the random orientation condition is assumed. However, if preferred orientations are assumed for particles, the phase function has a strong dependence on scattering azimuthal angle. The single-scattering albedo also shows very strong dependence on the inclination angle of incident radiation with respect to the rotating axis for the preferred particle orientations.

Yang, Ping↗
DOE OSTI2026

Energy-conserving contact dynamics of nonspherical rigid-body particles

Understanding the contact dynamics of nonspherical particles is crucial for accurately modeling colloidal and granular systems where shape anisotropy dictates structural organization and transport properties. We here introduce an energy-conserving contact dynamics framework for arbitrary convex rigid-body particles by implementing vertex–boundary interactions in 2D and vertex–surface and edge–edge detection in 3D. The established formulation enables continuous force evaluation and prevents particle overlap while conserving total energy during translational and rotational motion. We demonstrate the framework’s stability and its utility to capture packing behavior, anisotropic diffusion, and equations of state of polygonal and polyhedral particles as examples. The framework establishes a robust and extensible foundation for investigating nonequilibrium dynamics of complex nonspherical particulate systems, enabling enhanced understanding of phenomena across spatiotemporal scales in self- and directed-assembly, granular flows, and hydrodynamics, potentially coupled with interactions that represent underlying physical mechanisms.

Discrete element method↗
NASA NTRS1987

Toward automated analysis of particle holograms

A preliminary study of approaches for extracting and analyzing data from particle holograms is discussed. It concludes that: (1) for thin spherical particles, out-of-focus methods are optimum; (2) for thin nonspherical particles, out-of-focus methods are useful but must be supplemented by in-focus methods; (3) a complex method of projection and back projection can remove out-of-focus data for deep particles.

Caulfield, H. J.↗