The direct calculation of the H-function for completely noncoherent scattering
H-function integrals for noncoherent isotropic scattering for two level atom, tabulating numerical values for Lorentz scattering profile
Warming, R. F.↗
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Results for “SCATTERING FUNCTION”
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Supporting studies for the coronagraph contamination experiment
Calculations of Mie scattering functions involved individual as well as mixed scattering of particles. In particular, computations were completed for a 15A particle and for particles subjected to incident light of ultraviolet wavelengths. Calculations of contaminant atmospheres for Gemini, Apollo, and Skylab considered leakage rates for the respective vehicles and the mass column density of the atmospheres surrounding them. Atmospheres for these vehicles have been computed for a uniform particle size distribution, and for a particle size distribution in which size varied.
Kovar, N. S.↗
On obtaining the forward phase functions of Saturn ring features from radio occultation observations
It is noted that the near-forward scattering functions of particles in Saturn ring features are related to 3.6 cm radio occultation power spectra by a Fredholm integral equation of the first kind. The equation reduces to an algebraic system of equation whose solution by usual inversion techniques (that is, least mean squares) is ruled out by the near singularity of the forward transformation matrix. A combination of constrained linear inversion and a filtering algorithm based on eigenvector decomposition of the matrix reduces the instabilities; this yields derived phase functions valid over the range of zero to about 12 mrad. It is noted that these functions represent the collective forward diffraction lobe of particles greater than about 1 m in radius. Since multiple scattering of the signal is a significant effect, the measured phase functions must be adjusted to obtain the singly scattered component. This single-scattering correction is examined for two physical models, namely the monolayer and the classical discrete random slab; in addition, the fraction of opacity in submeter particles for each model for particular ring features is estimated.
Zebker, H. A.↗
Femtosecond x-ray photon correlation spectroscopy enables direct observations of atomic-scale relaxations of glass forming liquids
Glass-forming liquids exhibit structural relaxation behaviors, reflecting underlying atomic rearrangements on a wide range of timescales and playing a crucial role in determining material properties. However, the relaxation processes on the atomic scale are not well-understood due to the experimental difficulties in directly characterizing the evolving correlations of atomic-scale order in disordered systems. Here, in this study, we harness the coherence and ultrashort pulse characteristics of an x-ray free electron laser to directly probe atomic-scale ultrafast relaxation dynamics in the model system Ge 15 Te 85 . We demonstrate an analysis strategy for determining the intermediate scattering function by extracting the contrast decay of summed scattering patterns from two rapidly successive, nearly identical femtosecond x-ray pulses generated by a split-delay system. The result indicates a full decorrelation of atomic-scale order on the sub-picosecond timescale, supporting the argument for a high-fluidity fragile state of liquid Ge 15 Te 85 above its dynamic crossover temperature. The demonstrated strategy opens an avenue for experimental studies of relaxation dynamics in liquids, glasses, and other highly disordered systems.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Brillouin scattering and the dispersion of hypersonic waves.
Dispersion and absorption of hypersonic waves analyzed by examining Brillouin scattering as function of scattering angle
ULTRASONIC WAVE↗
Surface Textural Properties of Icy Satellites: A Comparison between Europa and Rhea
Solar phase curves for Rhea are presented using new telescopic opposition data along with Voyager imaging observations. Two viable solutions were found to Hapke's model which was used to describe this phase curve. The porosity derived from the model's opposition parameters show that the optically active portion of Rhea's regolith has a porosity between 80 and 95 percent, which is slightly lower than the porosity seen on Europa and higher than the porosity measured for the Moon using similar methods. The macroscopic roughness is comparable to that measured by Vebiscer and Veverka for Rhea. The single particle scattering functions found in this study are predominantly forward scattering, which contradicts the results of Vebiscer and Veverka.
Domingue, D. L.↗
Alpha-relaxation by scattering and medium-range atomic correlation in simple liquids
The relaxation dynamics of liquid and glass can be studied by inelastic x-ray or neutron scattering through the intermediate scattering function F(Q, t), where Q is the momentum transfer of scattering. Because of the time-consuming nature of these measurements, F(Q, t) is usually measured only at the first peak of the structure function S(Q), and its principal decay time is referred to as the α-relaxation time τ α . τ α is generally considered to describe the relaxation time of the bulk, which is related to viscosity and is controlled by the atomic cage around an atom. Here, through simulations on metallic liquids, we show that the α-relaxation time determined by scattering experiments does not purely reflect viscosity but is influenced by changes in spatial cooperativity. We also demonstrate that atomic caging is not exerted by the nearest neighbors but involves more cooperative atomic dynamics of the atomic medium-range order.
Glass transitions↗
Tables of auxiliary functions for the nonconservative Rayleigh phase matrix in semi-infinite atmospheres
Tables of scattering functions and albedo for semiinfinite atmospheres according to nonconservative Rayleigh phase matrix for diffuse radiation computation
Abhyankar, K. D.↗
Scattered light in the echelle modes of the Goddard high-resolution spectrograph aboard the Hubble Space Telescope. I - Analysis of prelaunch calibration data
A study of scattered light in the echelle mode of the Goddard high-resolution spectrograph (GHRS), one of the first-generation science instruments aboard the Hubble Space Telescope, is reported. The data analyzed are from the GHRS ground-based test program and include observations with the 500 channel Digicon detectors through the small science aperture of UV emission-line sources, continuum sources, and continuum sources viewed through molecular absorption cells. The two largest contributors to scattered light are the echelle and cross-disperser, the effects of which have been quantified. A computer simulation using the derived scattering functions demonstrates that the combined effects of these sources of scattered light adequately explain the observed level of interorder light when viewing UV continuum sources. Observing strategies and data reduction algorithms for measuring and removing the effects of the scattered light are discussed.
Cardelli, Jason A.↗
Electron Impact Excitation of Forbidden and Allowed Transitions in O(II)
The B-spline R-matrix method is used to investigate the electron impact excitation of forbidden and allowed transitions in singly ionized oxygen. The relativistic effects have been incorporated in the Breit-Pauli Hamiltonian. Flexible non-orthogonal sets of radial functions are used to obtain accurate target description and to represent the scattering functions. The 47 fine-structure levels of the 2s(sup 2)2p(sup 3), 2s2p(sup 4), 2s(sup 2)2p(sup 2)3s, 2s(sup 2)2p(sup 2)3p and 2s(sup 2)2p(sup 2)3d configurations have been included in the scattering calculation. A calculation with 62 levels in the close-coupling expansion using the Breit-Pauli R-matrix (BPRM) method with orthogonal radial functions has also been carried out to check electron correlation, relativistic and channel coupling effects. The present results are in good agreement with the previous 16-level BPRM calculation by Montenegro et a1 (2006 J. Phys. B: At. Mol. Opt. Phys. 39 1863-77) for the forbidden transitions, but differ from the 21-level BPRM calculation by McLaughlin and Bell (1998 J. Phys. B: At. Mol. Opt. Phys. 31 4317-29). Our cross sections for the first forbidden (sup 4)S(sup o)-(sup 2)D(sup o)and resonance (sup 4)S(sup o)-2s(sup 2)p(sup 4) (sup 4)P transitions are in reasonably good agreement with the electron energy-loss and merged-beams experiment.
Tayal, S. S.↗
Fractal dimension in nonhyperbolic chaotic scattering
In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.
Lau, Yun-Tung↗
Radiative transfer theory for scattering by layered media
Remote sensing of brightness temperatures of a scattering medium composed of spherical scatterers beneath a homogeneous surface layer is studied by using Mie scattering functions. We illustrate the effects of a surface layer by plotting the brightness temperatures as functions of frequency and viewing angle for different layer thicknesses, dielectric constants, and fractional scattering volumes. It is found that the brightness temperature increases when the loss tangent of the surface layer is increased and when the fractional volume occupied by the scatterers is decreased. In the absence of a surface layer the brightness temperature is usually decreasing as a function of frequency. The presence of a homogeneous layer may cause the brightness temperature to increase with frequency. At all viewing angles the vertical polarization is brighter than the horizontal polarization.
Tsang, L.↗
Radiative transfer theory for polarimetric remote sensing of pine forest
The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. To take into account the clustered structures with the radiative transfer theory, the scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. Subsequently, the resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including the multi-scale structures, namely, trunks, primary and secondary branches, as well as needles, we interpret and simulate the polarimetric radar responses from pine forest for different frequencies and looking angles. The preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.
Hsu, C. C.↗
Radiative transfer theory for polarimetric remote sensing of pine forest
The radiative transfer theory is applied to interpret polarimetric radar backscatter from pine forest with clustered vegetation structures. The scattering function of each cluster is calculated by incorporating the phase interference of scattered fields from each component. The resulting phase matrix is used in the radiative transfer equations to evaluate the polarimetric backscattering coefficients from random medium layers embedded with vegetation clusters. Upon including multiscale structures (trunks, primary and secondary branches, and needles), polarimetric radar responses from pine forest for different frequencies and looking angles are interpreted and simulated. Preliminary results are shown to be in good agreement with the measured backscattering coefficients at the Landes maritime pine forest during the MAESTRO-1 experiment.
Hsu, C. C.↗
Physical characteristics of cometary dust from optical studies
Observations of the sunlight scattered and thermal emission from cometary dust, which may be used to infer the physical properties of the dust grains, are reviewed. Consideration is given to the observed wavelength dependence of the scattered light from cometary coma and tails, the average scattering function of the dust grains, the average grain Bond albedo, the polarization of the scattered light, and grain temperatures deduced from thermal infrared emission. The thermal properties of dust grains are illustrated for models based on magnetite or olivine grain materials, with consideration given to the variation of thermal properties with particle radius and heliocentric distance. Comparison of the models with observations indicates that a disordered or amorphous olivine composition can give a reasonable fit to the data for appropriate grain sizes and temperatures. The observations acquired are noted to indicate an optically important particle size of 1 micron, with silicate particles not larger than a few microns usually present although pure silicate grains can not be responsible for the thermal emission, and the cometary dust grains are most likely not spherical. Further observations needed in the infrared are indicated.
Hanner, M. S.↗
Scattering properties of the Venusian surface - Preliminary results from Magellan
Extraction of the scattering function over incidence angles between 0 and 4-10 deg from Magellan altimetry radar data is discussed. The scattering model includes a surface which is statistically homogeneous and isotropic in its scattering behavior. The results indicate that the model is useful in a global context, but further improvements to the analysis procedure are required if the best results are to be obtained locally. The procedures used here are still under development and include several steps which have not been fully optimized but which are expected to be effective over a wide range of Venusian conditions.
Tyler, G. L.↗
Problem footprints in Magellan altimetry data
The intensity, time-delay, and frequency content of radar echoes from the Magellan altimetry system are reduced to several parameters that are of great use in addressing many geological issues of the surface of Venus. These parameters include planetary radius, power reflection coefficient (reflectivity, both uncorrected and corrected for diffuse scattering), rms slope, and scattering functions (the behavior of backscatter as a function of incidence angle). Because the surface of Venus often reflects radio energy in unpredictable ways, models of radar scattering and their associated algorithms occasionally fail to accurately solve for the above surface parameters. Methods for identifying possible 'problem' altimetry data footprints, and techniques for resolving some key ambiguities are presented.
Plaut, Jeffrey J.↗
Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using X-ray Photon Correlation Spectroscopy
Supercritical fluids exhibit distinct thermodynamic and transport properties, making them of particular interest for a wide range of scientific and engineering applications. These anomalous properties emerge from structural heterogeneities due to the formation of molecular clusters at conditions above the critical point. While the static behavior of these clusters and their effects on the thermodynamic response functions have been recognized, the relation between the ultrafast cluster dynamics and transport properties remains elusive. By measuring the intermediate scattering function in carbon dioxide at conditions near the critical point with X-ray photon correlation spectroscopy, we directly capture the cross-over dynamics between 4 and 13 picoseconds, revealing the transition between ballistic and diffusive motion. Complementary analysis using large-scale molecular dynamics simulations reveals that this behavior arises from collisions between unbound molecules and clusters. This study provides direct evidence of the ultrafast momentum exchange between clusters, which has significant impact on transport properties, solvation processes, and reaction kinetics in supercritical fluids.
carbon capture and storage↗