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An improved radiation metric is obtained in which light rays make a small nonzero angle with the radius, thus representing a source of finite size. Kaufmann's previous solution is criticized. The stabilization of a scatterer near a source of gravitational field and radiation is slightly enhanced for sources of finite size.
In order to account for some special features of lunar seismograms, namely, the gradual build-up of the signal, the extremely prolonged tail, and the lack of apparent coherence among three orthogonal components of ground motion, a statistical approach is proposed for describing transmission of seismic energy through a medium in which strong scattering takes place. A seismic diffusion theory is presented for a medium with randomly distributed scatterers of a given size distribution. A solution of the resulting diffusion equation for an impulsive energy source gives a curve which fairly closely reproduces the envelope of typical lunar impact seismograms. Since the model is based on constant diffusivity, long-range transmission will require a combination of diffusion and wave propagation treatments for accurate description.
Existing two-stream approximations to radiative transfer theory for particulate media are shown to be represented by identical forms of coupled differential equations if the intensity is replaced by integrals of the intensity over hemispheres. One set of solutions thus suffices for all methods and provides convenient analytical comparisons. The equations also suggest modifications of the standard techniques so as to duplicate exact solutions for thin atmospheres and thus permit accurate determinations of the effects of typical aerosol layers. Numerical results for the plane albedos of plane-parallel atmospheres are given for conventional and modified Eddington approximations, conventional and modified two-point quadrature schemes, the hemispheric-constant method and the delta-function method, all for comparison with accurate discrete-ordinate solutions. A new two-stream approximation is introduced that reduces to the modified Eddington approximation in the limit of isotropic phase functions and to the exact solution in the limit of extreme anisotropic scattering. Comparisons of plane albedos and transmittances show the new method to be generally superior over a wide range of atmospheric conditions (including cloud and aerosol layers), especially in the case of nonconservative scattering.
The effects of a given nonthermal low-frequency density-fluctuation spectrum on the amplification of Langmuir waves by a 'bump-on-tail' beam of electrons are studied. The density-fluctuation spectrum is assumed to contain a uniform distribution of wavelengths ranging from much shorter than the beam mode wavelength to of the same order. This permits multiple large-angle (back) scattering to occur. One-dimensional numerical solutions of the kinetic equations are found which yield criteria for linear saturation of the beam instability of a cascade of backscattering to high wavenumber. The relevant time scales and spectral shapes are also determined in both the stable and unstable regions. Linear damping and Cerenkov emission by a possible nonthermal tail of electrons is taken into account. An application is made to the beam modes observed simultaneously with density fluctuations off the Jovian bow shock. It is shown that the observed level of density fluctuations is sufficient to saturate the unstable Langmuir waves, although nonthermal Landau damping may prevent a cascade to very high wavenumbers.
In order to predict the thermal efficiency of a solar pond it is necessary to know total average solar energy reaching the storage layer. One method for determining this energy for water containing dissolved colored species is based upon spectral transmission measurements using a laboratory spectrophotometer. This method is examined and some of the theoretical ground work needed to discuss the measurement of transmission of light water. Results of in situ irradiance measurements from oceanography research are presented and the difficulties inherent in extrapolating laboratory data obtained with ten centimeter cells to real three dimensional pond situations is discussed. Particular emphasis is put on the need to account for molecular and particulate scattering in measurements done on low absorbing solutions. Despite these considerations it is expected that attenuation calculations based upon careful measurements using a dual beam spectrophotometer technique combined with known attenuation coefficients will be useful in solar pond modeling and monitoring for color buildup. Preliminary results using the CSM method are presented.
A technique is described for extracting cloud cover parameters from multispectral satellite radiometric measurements. Utilizing three channels from the AVHRR (Advanced Very High Resolution Radiometer) on NOAA polar orbiting satellites, it is shown that one can retrieve four parameters for each pixel: cloud fraction within the FOV, optical thickness, cloud-top temperature and a microphysical model parameter. The last parameter is an index representing the properties of the cloud particle and is determined primarily by the radiance at 3.7 microns. The other three parameters are extracted from the visible and 11 micron infrared radiances, utilizing the information contained in the two-dimensional scatter plot of the measured radiances. The solution is essentially one in which the distributions of optical thickness and cloud-top temperature are maximally clustered for each region, with cloud fraction for each pixel adjusted to achieve maximal clustering.
The quest for the highest resolution microwaves imaging and the principle of time-domain imaging is the primary motivation for recent developments in time-domain techniques. With the present technology fast time varying signals can now be measured and recorded both in magnitude and in phase. It has also enhanced the ability to extract relevant details concerning the scattering object. In the past, the inference of object geometry or shape from scattered signals has received substantial attention in radar technology. Various inverse scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequenty swept holography, and the synthetic radar imaging, all of which have two things in common: the physical optic far-field approximation and the utilization of the channels as an extra physical dimension, were also advanced significantly. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The use of time-domain imaging for space robotic vision applications was proposed. A multisensor approach to vision was shown to have several advantages over the video-only approach.
The quest for the highest resolution microwave imaging and principle of time-domain imaging has been the primary motivation for recent developments in time-domain techniques. With the present technology, fast time varying signals can now be measured and recorded both in magnitude and in-phase. It has also enhanced our ability to extract relevant details concerning the scattering object. In the past, the interface of object geometry or shape for scattered signals has received substantial attention in radar technology. Various scattering theories were proposed to develop analytical solutions to this problem. Furthermore, the random inversion, frequency swept holography, and the synthetic radar imaging, have two things in common: (1) the physical optic far-field approximation, and (2) the utilization of channels as an extra physical dimension, were also advanced. Despite the inherent vectorial nature of electromagnetic waves, these scalar treatments have brought forth some promising results in practice with notable examples in subsurface and structure sounding. The development of time-domain techniques are studied through the theoretical aspects as well as experimental verification. The use of time-domain imaging for space robotic vision applications has been suggested.
A finite element solution and computer code for the electromagnetic scattering of inhomogeneous penetrable bodies is presented. The application for the code is for the analysis and design of leading and trailing edge terminations when conducting and nonconducting materials are used. Examples of simple triangular shaped terminations are also presented.
The modal ring method for electromagnetic scattering from perfectly electric conducting (PEC) symmetrical bodies is presented. The scattering body is represented by a line of finite elements (triangular) on its outer surface. The infinite computational region surrounding the body is represented analytically by an eigenfunction expansion. The modal ring method effectively reduces the two dimensional scattering problem to a one-dimensional problem similar to the method of moments. The modal element method is capable of handling very high frequency scattering because it has a highly banded solution matrix.
In the first two papers in this series, we developed a method for studying electron-hydrogen scattering that does not use partial wave analysis. We constructed an ansatz for the wave function in both the static and static exchange approximations and calculated the full scattering amplitude. Here we go beyond the static exchange approximation, and include correlation in the wave function via a modified polarized orbital. This correlation function provides a significant improvement over the static exchange approximation: the resultant elastic scattering amplitudes are in very good agreement with fully converged partial wave calculations for electron-hydrogen scattering. A fully variational modification of this approach is discussed in the conclusion of the article Popular summary of Direct calculation of the scattering amplitude without partial wave expansion. III ....." by J. Shertzer and A. Temkin. In this paper we continue the development of In this paper we continue the development of a new approach to the way in which researchers have traditionally used to calculate the scattering cross section of (low-energy) electrons from atoms. The basic mathematical problem is to solve the Schroedinger Equation (SE) corresponding the above physical process. Traditionally it was always the case that the SE was reduced to a sequence of one-dimensional (ordinary) differential equations - called partial waves which were solved and from the solutions "phase shifts" were extracted, from which the scattering cross section was calculated.
In this paper we consider the effects of the isotopic composition of the primary galactic cosmic rays (GCR), nuclear fragmentation cross-sections, and isotopic-grid on the solution to transport models used for shielding studies. Satellite measurements are used to describe the isotopic composition of the GCR. For the nuclear interaction data-base and transport solution, we use the quantum multiple-scattering theory of nuclear fragmentation (QMSFRG) and high-charge and energy (HZETRN) transport code, respectively. The QMSFRG model is shown to accurately describe existing fragmentation data including proper description of the odd-even effects as function of the iso-spin dependence on the projectile nucleus. The principle finding of this study is that large errors (+/-100%) will occur in the mass-fluence spectra when comparing transport models that use a complete isotopic-grid (approx.170 ions) to ones that use a reduced isotopic-grid, for example the 59 ion-grid used in the HZETRN code in the past, however less significant errors (<+/-20%) occur in the elemental-fluence spectra. Because a complete isotopic-grid is readily handled on small computer workstations and is needed for several applications studying GCR propagation and scattering, it is recommended that they be used for future GCR studies.
Brightness temperatures (TB) from GMI and related sensors contain information about the types and amounts of precipitation particles in a column. Approaches like GPROF or machine learning are good for providing precipitation estimates and other quantified information, but it can be difficult to understand why / how a given set of TBs traces to a given retrieval solution. Outlier TBs that are not well-represented in a training sample can lead to dubious solutions. Our goal is to use the scattering signatures at multiple frequencies to determine whether hail is present, or otherwise graupel, or otherwise snow, or otherwise liquid rain without a substantial precipitation ice component. (A hierarchical approach is employed, so a prediction of hail can include the presence of all other categories, but a prediction of snow implies a lack of graupel or hail, and a prediction of liquid rain implies a lack of any detectable precipitation ice.)
The multiple scattering of electromagnetic waves in forests is studied using a two-step hybrid method. First, the T-matrix of a single tree is calculated based on its far-field computed with the full-wave simulations of the FEKO software. The T-matrix captures the multiple scattering caused by the tree structure. Second, the the interactions among different trees are considered using the T-matrices of the individual trees and the Foldy-Lax equations. The result of the two-step hybrid method is validated with FEKO by solving scattering from two trees directly. The multiple scattering effects are illustrated by the field solutions.
Brightness temperatures (TB) from GMI and related sensors contain information about the types and amounts of precipitation particles in a column. Approaches like GPROF or machine learning are good for providing precipitation estimates and other quantified information, but it can be difficult to understand why / how a given set of TBs traces to a given retrieval solution. Outlier TBs that are not well-represented in a training sample can lead to dubious solutions. Our goal is to use the scattering signatures at multiple frequencies to determine whether hail is present, or otherwise graupel, or otherwise snow, or otherwise liquid rain without a substantial precipitation ice component. (A hierarchical approach is employed, so a prediction of hail can include the presence of all other categories, but a prediction of snow implies a lack of graupel or hail, and a prediction of liquid rain implies a lack of any detectable precipitation ice.)
Solutions are presented for the dispersion relation of waves propagating parallel to the ambient magnetic field, in a plasma having an arbitrary ratio of thermal to magnetic pressure, beta. Previous results applicable only to wave frequencies much lower than the ion cyclotron frequency are extended to include all frequencies lower than the electron cyclotron frequency. The cyclotron turnovers are found to occur at significantly lower frequencies in finite beta plasmas. Cyclotron damping is significant for small wavelength waves. These results show that in energetic particle scattering by electromagnetic turbulence in a plasma with beta value greater than 40, scattering by waves with wave frequencies greater than the ion cyclotron frequency can be neglected. This condition is satisfied in many astrophysical plasmas.
The direct method for the solution of the spherical harmonics approximation to the equation of transfer of radiation is applied to the cases of (1) scattering of the solar radiation in the atmosphere with the Lambertian boundary and (2) thermal radiation transfer.
Metallic tape is commonly used to cover the interpanel gaps which occur in paneled compact-range reflectors. It is therefore of interest to study the effect of the scattering by the tape on the field in the target zone of the range. An analytical solution is presented for the target zone fields scattered by 2D metallic tapes. It is formulated by the generalized scattering matrix technique in conjunction with the Wiener-Hopf procedure. An extension to treat 3D tapes can be accomplished using the 2D solution via the equivalent current concept. The analytical solution is compared with a reference moment method solution to confirm the accuracy of the former.