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Their work, as is the work of most atomic theorists, is concerned with solving the Schroedinger equation accurately for wave function in cases where there is no exact analytical solution. In particular, Temkin is associated with electron scattering from atoms and ions. When he started there already were a number of methods to study the scattering of electrons from atoms.
The exact solutions are obtained for a one dimensional model of a scattering and absorbing medium. The results are given for both the reflected and transmitted radiance for any arbitrary surface albedo as well as for the interior radiance. These same quantities are calculated by the matrix operator method. The relative error of the solutions is obtained by comparison with the exact solutions as well as by an error analysis of the equations. The importance of an accurate starting value for the reflection and transmission operators is shown. A fourth order Runge-Kutta method can be used to solve the differential equations satisfied by these operators in order to obtain such accurate starting values.
Contraction theory is applied to an iterative formulation of electromagnetic scattering from periodic structures and a computational method for insuring convergence is developed. A short history of spectral (or k-space) formulation is presented with an emphasis on application to periodic surfaces. The mathematical background for formulating an iterative equation is covered using straightforward single variable examples including an extension to vector spaces. To insure a convergent solution of the iterative equation, a process called the contraction corrector method is developed. Convergence properties of previously presented iterative solutions to one-dimensional problems are examined utilizing contraction theory and the general conditions for achieving a convergent solution are explored. The contraction corrector method is then applied to several scattering problems including an infinite grating of thin wires with the solution data compared to previous works.
The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the transverse magnetic (TM) or the transverse electric (TE) wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3x2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.
Scattered electromagnetic waves from material bodies of different forms contain, in an intricate way, precise information on the intrinsic, geometrical and physical properties of the objects. Scattering theories, ever deepening, aim to provide dependable interpretation and prediction to the complicated interaction of electromagnetic radiation with matter. There are well-established multiple-scattering formulations based on classical electromagnetic theories. An example is the Generalized Multi-particle Mie-solution (GMM), which has recently been extended to a special version ̶ the GMM-PA approach, applicable to finite periodic arrays consisting of a huge number (e.g., >>106) of identical scattering centers [1]. The framework of the GMM-PA is nearly complete. When the size of the constituent unit scatterers becomes considerably small in comparison with incident wavelength, an appropriate array of such small element volumes may well be a satisfactory representation of a material entity having an arbitrary structure. X-ray diffraction is a powerful characterization tool used in a variety of scientific and technical fields, including material science. A diffraction pattern is nothing more than the spatial distribution of scattered intensity, determined by the distribution of scattering matter by way of its Fourier transform [1]. Since all linear dimensions entered into Maxwell's equations are normalized by wavelength, an analogy exists between optical and X-ray diffraction patterns. A large set of optical diffraction patterns experimentally obtained can be found in the literature [e.g., 2,3]. Theoretical results from the GMM-PA have been scrutinized using a large collection of publically accessible, experimentally obtained Fraunhofer diffraction patterns. As far as characteristic structures of the patterns are concerned, theoretical and experimental results are in uniform agreement; no exception has been found so far. Closely connected with the spatial distribution of scattered intensities are cross sections, such as for extinction, scattering, absorption, and radiation pressure, as a critical type of key quantity addressed in most theoretical and experimental studies of radiative scattering. Cross sections predicted from different scattering theories are supposed to be in general agreement. For objects of irregular shape, the GMM-PA solutions can be compared with the highly flexible Discrete Dipole Approximation (DDA) [4,5] when dividing a target to no more than ~106 unit cells. Also, there are different ways to calculate the cross sections in the GMM-PA, providing an additional means to examine the accuracy of the numerical solutions and to unveil potential issues concerning the theoretical formulations and numerical aspects. To solve multiple scattering by an assembly of material volumes through classical theories such as the GMM-PA, the radiative properties of the component scatterers, the complex refractive index in particular, must be provided as input parameters. When using a PA to characterize a material body, this involves the use of an adequate theoretical tool, an effective medium theory, to connect Maxwell's phenomenogical theory with the atomistic theory of matter. In the atomic theory, one regards matter as composed of interacting particles (atoms and molecules) embedded in the vacuum [6]. However, the radiative properties of atomic-scaled particles are known to be substantially different from bulk materials. Intensive research efforts in the fields of cluster science and nanoscience attempt to bridge the gap between bulk and atom and to understand the transition from classical to quantum physics. The GMM-PA calculations, which place virtually no restriction on the component-particle size, might help to gain certain insight into the transition.
Two simple scattering mechanisms are fitted to polarimetric synthetic aperture radar (SAR) observations of forests. The mechanisms are canopy scatter from a reciprocal medium with azimuthal symmetry and a ground scatter term that can represent double-bounce scatter from a pair of orthogonal surfaces with different dielectric constants or Bragg scatter from a moderately rough surface, which is seen through a layer of vertically oriented scatterers. The model is shown to represent the behavior of polarimetric backscatter from a tropical forest and two temperate forest sites by applying it to data from the National Aeronautic and Space Agency/Jet Propulsion Laboratory's Airborne SAR (AIRSAR) system. Scattering contributions from the two basic scattering mechanisms are estimated for clusters of pixels in polarimetric SAR images. The solution involves the estimation of four parameters from four separate equations. This model fit approach is justified as a simplification of more complicated scattering models, which require many inputs to solve the forward scattering problem. The model is used to develop an understanding of the ground-trunk double-bounce scattering that is present in the data, which is seen to vary considerably as a function of incidence angle. Two parameters in the model fit appear to exhibit sensitivity to vegetation canopy structure, which is worth further exploration. Results from the model fit for the ground scattering term are compared with estimates from a forward model and shown to be in good agreement. The behavior of the scattering from the ground-trunk interaction is consistent with the presence of a pseudo-Brewster angle effect for the air-trunk scattering interface. If the Brewster angle is known, it is possible to directly estimate the real part of the dielectric constant of the trunks, a key variable in forward modeling of backscatter from forests. It is also shown how, with a priori knowledge of the forest height, an estimate for the attenuation coefficient of the canopy can be obtained directly from the multi-incidence-angle polarimetric observations. This attenuation coefficient is another key variable in forward models and is generally related to the canopy density.
Atomic model potentials for spectroscopic and scattering data, using perturbation theory
A general analytic solution is obtained for the interaction of the moon and its downstream cavity with a linearly polarized plane electromagnetic wave propagating parallel to the cavity axis. The solution is formulated in terms of a spherical moon model with arbitrary radially dependent electromagnetic parameters and a nonconducting cylindrical downstream cavity. Use is made of a number of approximations that are consistent with the physical nature of the interaction between the moon and the solar wind.
The four-year grant began May 1, 1996 (5-1-96 to 4-30-00, $100,000/year). We have finished 4 major research projects and published 10 papers during this grant period. An important aspect of this research has been the education of students at graduate and undergraduate levels. They have been fully involved in the research described below: 1. Polymer-induced depletion interaction in colloid-polymer mixtures. 2. Colloidal sedimentation in polymer solutions. 3. Velocity fluctuations in particle sedimentation. New laser light scattering techniques for velocity difference measurements.
A new method is described for generating and predicting the power scattered at multiple frequencies from a periodic array excited by a monochromatic incident plane wave. The scattered power is predicted by developing an equivalent circuit representation from the exact method of moment solution of the unloaded periodic problem and then employing a modified method of moments approach to predict the scattered fields due to time-varying loads. An advantage of this method is that the generality of the equivalent circuit can be exploited to study the effects of different loads on the power scattered in the harmonic frequencies with a minimal amount of effort. The method can also be applied to multiple incident frequencies.
The Stokes scattering operator is noted to be the most useful characterization of incoherent scattering in radar imaging; the polarization that would yield an optimum amount of power received from the scatterer is obtained by assuming a knowledge of the Stokes scattering operator instead of the 2x2 scattering matrix with complex elements. It is thereby possible to find the optimum polarizations for the case in which the scatterers can only be fully characterized by their Stokes scattering operator, and the case in which the scatterer can be fully characterized by the complex 2x2 scattering matrix. It is shown that the optimum polarizations reported in the literature form the solution for a subset of a more general class of problems, so that six optimum polarizations can exist for incoherent scattering.
The spring 2008 Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) experiment was one of major intensive field campaigns of the International Polar Year aimed at detailed characterization of atmospheric physical and chemical processes in the Arctic region. A part of this campaign was a unique snow bidirectional reflectance experiment on the NASA P-3B aircraft conducted on 7 and 15 April by the Cloud Absorption Radiometer (CAR) jointly with airborne Ames Airborne Tracking Sunphotometer (AATS) and ground-based Aerosol Robotic Network (AERONET) sunphotometers. The CAR data were atmospherically corrected to derive snow bidirectional reflectance at high 1 degree angular resolution in view zenith and azimuthal angles along with surface albedo. The derived albedo was generally in good agreement with ground albedo measurements collected on 15 April. The CAR snow bidirectional reflectance factor (BRF) was used to study the accuracy of analytical Ross-Thick Li-Sparse (RTLS), Modified Rahman-Pinty-Verstraete (MRPV) and Asymptotic Analytical Radiative Transfer (AART) BRF models. Except for the glint region (azimuthal angles phi less than 40 degrees), the best fit MRPV and RTLS models fit snow BRF to within 0.05. The plane-parallel radiative transfer (PPRT) solution was also analyzed with the models of spheres, spheroids, randomly oriented fractal crystals, and with a synthetic phase function. The latter merged the model of spheroids for the forward scattering angles with the fractal model in the backscattering direction. The PPRT solution with synthetic phase function provided the best fit to measured BRF in the full range of angles. Regardless of the snow grain shape, the PPRT model significantly over-/underestimated snow BRF in the glint/backscattering regions, respectively, which agrees with other studies. To improve agreement with experiment, we introduced a model of macroscopic snow surface roughness by averaging the PPRT solution over the slope distribution function and by adding a simple model of shadows. With macroscopic roughness described by two parameters, the AART model achieved an accuracy of about plus or minus 0.05 with a possible bias of plus or minus 0.03 in the spectral range 0.4-2.2 micrometers. This high accuracy holds at view zenith angles below 55-60 degrees covering the practically important range for remote sensing applications, and includes both glint and backscattering directions.
A solution is presented for the backscatter (monostatic) radar cross section of dielectric disks of arbitrary shape, thickness, and dielectric constant. The result is obtained by employing a Kirchhoff-type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner will be shown to agree with known results in the special cases of normal incidence, thin disks, and perfect conductivity. It will also be shown that the solution can be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff-type approximation without additional assumptions.
The present solutions to the linear transport equation pertain to monoenergetic particles' interaction with a multiple scattering/absorbing layered medium with a general anisotropic internal source term. Attention is given to a novel exponential-linear approximation to the internal source, as a function of scattering depth, which furnishes an at-once efficient and accurate solution to the linear transport equation through its reduction of the spatial mesh size. The great superiority of the proposed method is demonstrated by the numerical results obtained in the illustrative cases of (1) an embedded thermal source and (2) a rapidly varying beam pseudosource.
This thesis develops a method to model the acoustic field generated by a monopole source placed in a moving rectangular duct. The walls of the duct are assumed to be infinitesimally thin and the source is placed at the center of the duct. The total acoustic pressure is written in terms of the free-space pressure, or incident pressure, and the scattered pressure. The scattered pressure is the augmentation to the incident pressure due to the presence of the duct. It satisfies a homogeneous wave equation and is discontinuous across the duct walls. Utilizing an integral representation of the scattered pressure, a set of singular boundary integral equations governing the unknown jump in scattered pressure is derived. This equation is solved by the method of collocation after representing the jump in pressure as a double series of shape functions. The solution obtained is then substituted back into the integral representation to determine the scattered pressure, and the total acoustic pressure at any point in the field. A few examples are included to illustrate the influence of various geometric and kinematic parameters on the radiated sound field.
The normal mode expansion technique is applied to the transformed monoenergetic integral transport equation to develop a solution for the rotationally invariant and axially infinite, critical, two-region cylinder with a finite outer reflector boundary. Isotropic scattering and identical neutron mean free paths in the core and reflector regions are assumed. The solution in terms of singular integral equations is obtained by applying a completeness theorem found for the singular eigenfunctions. Numerical results for a variety of core and reflector multiplying properties and reflector thickness are presented and compared with the results of other method. An example of this type of application is given in a study of approximations inherent in the neutronic design analysis of a small, fast-neutron-spectrum reactor concept proposed as a space power source.
A solution is presented for the backscatter (nonstatic) radar cross section of dielectric disks of arbitrary shape, thickness and dielectric constant. The result is obtained by employing a Kirchhoff type approximation to obtain the fields inside the disk. The internal fields induce polarization and conduction currents from which the scattered fields and the radar cross section can be computed. The solution for the radar cross section obtained in this manner is shown to agree with known results in the special cases of normal incidence, thin disks and perfect conductivity. The solution can also be written as a product of the reflection coefficient of an identically oriented slab times the physical optics solution for the backscatter cross section of a perfectly conducting disk of the same shape. This result follows directly from the Kirchhoff type approximation without additional assumptions.
Results from the Fifth AIAA CFD Drag Prediction Workshop (DPW-V) are presented. As with past workshops, numerical calculations are performed using industry-relevant geometry, methodology, and test cases. This workshop focused on force/moment predictions for the NASA Common Research Model wing-body configuration, including a grid refinement study and an optional buffet study. The grid refinement study used a common grid sequence derived from a multiblock topology structured grid. Six levels of refinement were created resulting in grids ranging from 0.64x10(exp 6) to 138x10(exp 6) hexahedra - a much larger range than is typically seen. The grids were then transformed into structured overset and hexahedral, prismatic, tetrahedral, and hybrid unstructured formats all using the same basic cloud of points. This unique collection of grids was designed to isolate the effects of grid type and solution algorithm by using identical point distributions. This study showed reduced scatter and standard deviation from previous workshops. The second test case studied buffet onset at M=0.85 using the Medium grid (5.1x106 nodes) from the above described sequence. The prescribed alpha sweep used finely spaced intervals through the zone where wing separation was expected to begin. Some solutions exhibited a large side of body separation bubble that was not observed in the wind tunnel results. An optional third case used three sets of geometry, grids, and conditions from the Turbulence Model Resource website prepared by the Turbulence Model Benchmarking Working Group. These simple cases were intended to help identify potential differences in turbulence model implementation. Although a few outliers and issues affecting consistency were identified, the majority of participants produced consistent results.