Application of the Inverse Scattering Transform to the Solar Wind Magnetic Field Data
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Inverse Scattering↗
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SAR Polarimetry
Radar Scattering includes: Surface Characteristics, Geometric Properties, Dielectric Properties, Rough Surface Scattering, Geometrical Optics and Small Perturbation Method Solutions, Integral Equation Method, Magellan Image of Pancake Domes on Venus, Dickinson Impact Crater on Venus (Magellan), Lakes on Titan (Cassini Radar, Longitudinal Dunes on Titan (Cassini Radar), Rough Surface Scattering: Effect of Dielectric Constant, Vegetation Scattering, Effect of Soil Moisture. Polarimetric Radar includes: Principles of Polarimetry: Field Descriptions, Wave Polarizations: Geometrical Representations, Definition of Ellipse Orientation Angles, Scatter as Polarization Transformer, Scattering Matrix, Coordinate Systems, Scattering Matrix, Covariance Matrix, Pauli Basis and Coherency Matrix, Polarization Synthesis, Polarimeter Implementation.
radar scattering↗
The Toda lattice as a forced integrable system
The analytic properties of the Jost functions for the inverse scattering transform associated with the forced Toda lattice are shown to determine the time evolution of this particular boundary value problem. It is suggested that inverse scattering methods may be used generally to analyze forced integrable systems. Thus an extension of the applicability of the inverse scattering transform is indicated.
Hansen, P. J.↗
The soliton transform and a possible application to nonlinear Alfven waves in space
The inverse scattering transform (IST) based on the derivative nonlinear Schroedinger (DNLS) equation is applied to a complex time series of nonlinear Alfven wave data generated by numerical simulation. The IST describes the long-time evolution of quasi-parallel Alfven waves more efficiently than the Fourier transform, which is adapted to linear rather than nonlinear problems. When dissipation is added, so the conditions for the validity of the DNLS are not strictly satisfied, the IST continues to provide a compact description of the wavefield in terms of a small number of decaying envelope solitons.
Hada, T.↗
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.↗
Formation of quasiparallel Alfven solitons
The formation of quasi-parallel Alfven solitons is investigated through the inverse scattering transformation (IST) for the derivative nonlinear Schroedinger (DNLS) equation. The DNLS has a rich complement of soliton solutions consisting of a two-parameter soliton family and a one-parameter bright/dark soliton family. In this paper, the physical roles and origins of these soliton families are inferred through an analytic study of the scattering data generated by the IST for a set of initial profiles. The DNLS equation has as limiting forms the nonlinear Schroedinger (NLS), Korteweg-de-Vries (KdV) and modified Korteweg-de-Vries (MKdV) equations. Each of these limits is briefly reviewed in the physical context of quasi-parallel Alfven waves. The existence of these limiting forms serves as a natural framework for discussing the formation of Alfven solitons.
Hamilton, R. L.↗
Initial conditions and Korteweg-de Vries solitons
The effects of rectangular initial data on the evolution of solitons governed by the Korteweg-de Vries equation is studied. Both isolated and separated disturbances are considered, providing some general insight into how the nature of the initial condition influences the appearance of solitons in the asymptotic state. The analytic approach is based on the inverse scattering transform which relates the initial condition to Schroedinger's equation. The results are used to model the initial shallow-water disturbances, and the results can be summarized by stating that the number of evolved solitons depends on the strength of each rectangular disturbance, the relative amplitudes of the rectangular disturbances, and the relative proximity of the disturbances.
Weidman, P. D.↗
Transform approach to electromagnetic scattering
In this paper, a comprehensive review of the Fourier transform technique as applied to the problem of high-frequency scattering is presented and the concepts of the spectral theory of diffraction (STD) are introduced. In contrast to the more commonly employed ray-optical method for high-frequency scattering, the STD approach interprets the scattered field as the spectrum, or the Fourier transform of the induced current on the scatterer. Such an interpretation offers several important advantages: uniform nature of representation, capacity to improve and extend the ray-optical formulas in a systematic manner, and convenient accuracy tests for the results. Methods for combining integral equation methods with the Galerkin procedure and asymptotic techniques in the transform domain are described, and representative examples illustrating the application of the spectral approach are included.
Mittra, R.↗
Relations between the elements of the phase matrix for scattering
Element relations of phase transformation matrix for scattering, relating radiation field vector to scattered field vector
Abhyankar, K. D.↗
Transverse electric scattering widths for strips-Fourier transform technique
A technique which is based on Fourier transformations is introduced for predicting scattering widths. For a strip it is shown that explicit determination of the linear current density is not necessary for bistatic or monostatic scattering width calculations. Comparisons of the predictions of the technique are made with the integral equation technique predictions, which do not require explicit evaluations of linear current densities.
Cockrell, C. R.↗
A transform-pair relationship between incident and scattered fields from an arbitrary reflector
It is shown that a transform-pair relationship exists between incident and scattered fields from an infinite, perfectly conducting reflector of arbitrary shape, when the physical optics approximation is applied. As an example of potential applications, this relationship is used to synthesize a reflector feed pattern required to produce a desired far-field pattern from a given paraboloidal reflector.
Ludwig, A. C.↗
The effect of a hot, spherical scattering cloud on quasi-periodic oscillation behavior
A Monte Carlo technique is used to investigate the effects of a hot electron scattering cloud surrounding a time-dependent X-ray source. Results are presented for the time-averaged emergent energy spectra and the mean residence time in the cloud as a function of energy. Moreover, after Fourier transforming the scattering Green's function, it is shown how the cloud affects both the observed power spectrum of a time-dependent source and the cross spectrum (Fourier transform of a cross correlation between energy bands). It is found that the power spectra intrinsic to the source are related to those observed by a relatively simple frequency-dependent multiplicative factor (a transmission function). The cloud can severely attenuate high frequencies in the power spectra, depending on optical depth, and, at lower frequencies, the transmission function has roughly a Lorentzian shape. It is also found that if the intrinsic energy spectrum is constant in time, the phase of the cross spectrum is determined entirely by scattering. Finally, the implications of the results for studies of the X-ray quasi-periodic oscillators are discussed.
Bussard, R. W.↗
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.↗
Regional Distribution of Forest Height and Biomass from Multisensor Data Fusion
Elevation data acquired from radar interferometry at C-band from SRTM are used in data fusion techniques to estimate regional scale forest height and aboveground live biomass (AGLB) over the state of Maine. Two fusion techniques have been developed to perform post-processing and parameter estimations from four data sets: 1 arc sec National Elevation Data (NED), SRTM derived elevation (30 m), Landsat Enhanced Thematic Mapper (ETM) bands (30 m), derived vegetation index (VI) and NLCD2001 land cover map. The first fusion algorithm corrects for missing or erroneous NED data using an iterative interpolation approach and produces distribution of scattering phase centers from SRTM-NED in three dominant forest types of evergreen conifers, deciduous, and mixed stands. The second fusion technique integrates the USDA Forest Service, Forest Inventory and Analysis (FIA) ground-based plot data to develop an algorithm to transform the scattering phase centers into mean forest height and aboveground biomass. Height estimates over evergreen (R2 = 0.86, P < 0.001; RMSE = 1.1 m) and mixed forests (R2 = 0.93, P < 0.001, RMSE = 0.8 m) produced the best results. Estimates over deciduous forests were less accurate because of the winter acquisition of SRTM data and loss of scattering phase center from tree ]surface interaction. We used two methods to estimate AGLB; algorithms based on direct estimation from the scattering phase center produced higher precision (R2 = 0.79, RMSE = 25 Mg/ha) than those estimated from forest height (R2 = 0.25, RMSE = 66 Mg/ha). We discuss sources of uncertainty and implications of the results in the context of mapping regional and continental scale forest biomass distribution.
Yu, Yifan↗
A new system model for radar polarimeters
The validity of the 2 x 2 receive R and transmit T model for radar polarimeter systems, first proposed by Zebker et al. (1987), is questioned. The model is found to be invalid for many practical realizations of radar polarimeters, which can lead to significant errors in the calibration of polarimetric radar images. A more general model is put forward, which addresses the system defects which cause the 2 x 2 model to break down. By measuring one simple parameter from a polarimetric active radar calibration (PARC), it is possible to transform the scattering matrix measurements made by a radar polarimeter to a format compatible with a 2 x 2 R and T matrix model. Alternatively, the PARC can be used to verify the validity of the 2 x 2 model for any polarimetric radar system. Recommendations for the use of PARCs in polarimetric calibration and to measure the orientation angle of the horizontal (H) and vertical (V) coordinate system are also presented.
Freeman, Anthony↗
Analytical optical scattering in clouds
An analytical optical model for scattering of light due to lightning by clouds of different geometry is being developed. The self-consistent approach and the equivalent medium concept of Twersky was used to treat the case corresponding to outside illumination. Thus, the resulting multiple scattering problem is transformed with the knowledge of the bulk parameters, into scattering by a single obstacle in isolation. Based on the size parameter of a typical water droplet as compared to the incident wave length, the problem for the single scatterer equivalent to the distribution of cloud particles can be solved either by Mie or Rayleigh scattering theory. The super computing code of Wiscombe can be used immediately to produce results that can be compared to the Monte Carlo computer simulation for outside incidence. A fairly reasonable inverse approach using the solution of the outside illumination case was proposed to model analytically the situation for point sources located inside the thick optical cloud. Its mathematical details are still being investigated. When finished, it will provide scientists an enhanced capability to study more realistic clouds. For testing purposes, the direct approach to the inside illumination of clouds by lightning is under consideration. Presently, an analytical solution for the cubic cloud will soon be obtained. For cylindrical or spherical clouds, preliminary results are needed for scattering by bounded obstacles above or below a penetrable surface interface.
Phanord, Dieudonne D.↗
Low-energy electron scattering from CO. 2: Ab-initio study using the frame-transformation theory
The Wigner-Eisenbud R matrix method has been combined with the frame transformation theory to study electron scattering from molecular systems. The R matrix, calculated at the boundary point of the molecular core radius, has been transformed to the space frame in order to continue the solution of the scattering equations in the outer region where rotational motion of the nuclei is taken into account. This procedure has been applied to a model calculation of thermal energy electron scattering from CO.
Chandra, N.↗
Interrelations for the elements of the scattering matrix
Light scattered by molecules and particulate matter in planetary atmospheres was analyzed. The 4x4 scattering matrix that transforms the Stokes parameters of the incident beam into those of the scattered beam is discussed. Elementary methods are described to obtain interrelations for the 16 elements of the scattering matrix, when light is scattered by a particle of arbitrary size, shape and composition or by a collection of such particles. The implications of the results for the interpretation of polarimetric data of planets with an atmosphere are outlined.
Hovenier, J. W.↗