Some aspects of numerical solution of boundary value problems.
Numerical solution of boundary value problems, discussing spectral domain and scattering matrix formalisms
Lee, S. W.↗
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Transfer of resonance-line radiation in differentially expanding atmospheres. II - Analytic solution for the case of coherence in the frame of the fluid.
Derivation of an exact solution for the problem of line transfer by resonant scattering (assumed coherent in the fluid frame) in a differentially expanding atmosphere. The probabilistic method developed is a generalization of the method of addition of layers plus a decomposition of the radiation field into partial radiation fields due to those photons that scatter exactly n times before escaping (n = 0, 1, 2, 3,
Noerdlinger, P. D.↗
A technique for interpretation of multispectral remote sensor data
The author has identified the following significant results. The U.S. Army Engineer Waterways Experiment Station is engaged in a study to detect from ERTS-1 satellite data alterations to the absorption and scattering properties caused by movement of suspended particles and solutes in selected areas of the Chesapeake Bay and to correlate the data to determine the feasibility of delineating flow patterns, flushing action of the estuary, and sediment and pollutant dispersion. As a part of this study, ADP techniques have been developed that permit automatic interpretation of data from any multispectral remote sensor with computer systems which have limited memory capacity and computing speed. The multispectral remote sensor is considered as a reflectance spectrophotometer. The data which define the spectral reflectance characteristics of a scene are scanned pixel by pixel. Each pixel whose spectral reflectance matches a reference spectrum is identified, and the results are shown in a map that identifies the locations where spectrum matches were detected and spectrum that was matched. The interpretation technique is described and an example of interpreted data from ERTS-1 is presented.
Williamson, A. N.↗
TM surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface
The diffraction of a TM sub o surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation, the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained by a combination of the generalized scattering matrix technique and function theoretic methods.
Pathak, P. H.↗
A coupled radiative-convective-photochemical model of the stratosphere
A one-dimensional atmospheric model is described. The neutral photochemical processes of the troposphere and stratosphere are presented by a reaction set of 87 kinetic processes and 28 photolytic reactions, with vertical transport being taken into account by an eddy diffusion parameter. The vertical temperature profiles are coupled with the chemical calculations by means of a radiative-convective code. The model has the capability of including effects of multiple scattering and diurnal variations in species concentrations. The numerical solution methodology is described in detail, and current input data are given along with results obtained in a sample calculation.
Boughner, R. E.↗
Surface wave diffraction by a truncated dielectric slab recessed in a perfectly conducting surface
The diffraction of a TM sub 0 surface wave by a terminated dielectric slab which is flush mounted in a perfectly conducting surface is studied. The incident surface wave gives rise to waves reflected and diffracted by the termination; these reflected and diffracted fields may be expressed in terms of the geometrical theory of diffraction by introducing surface wave reflection and diffraction coefficients which are associated with the termination. In this investigation the surface wave reflection and diffraction coefficients have been deduced from a formally exact solution to this canonical problem. The solution is obtained via a combination of the generalized scattering matrix technique and the Wiener-Hopf procedure. Expressions for the reflection and diffraction coefficients contain integrals which can be evaluated numerically.
Pathak, P. H.↗
Propagation of propeller tone noise through a fuselage boundary layer
In earlier experimental and analytical studies, it was found that the boundary layer on an aircraft could provide significant shielding from propeller noise at typical transport airplane cruise Mach numbers. In this paper a new three-dimensional theory is described that treats the combined effects of refraction and scattering by the fuselage and boundary layer. The complete wave field is solved by matching analytical expressions for the incident and scattered waves in the outer flow to a numerical solution in the boundary layer flow. The model for the incident waves is a near-field frequency-domain propeller source theory developed previously for free field studies. Calculations for an advanced turboprop (Prop-Fan) model flight test at 0.8 Mach number show a much smaller than expected pressure amplification at the noise directivity peak, strong boundary layer shielding in the forward quadrant, and shadowing around the fuselage. Results are presented showing the difference between fuselage surface and free-space noise predictions as a function of frequency and Mach number. Comparison of calculated and measured effects obtained in a Prop-Fan model flight test show good agreement, particularly near and aft of the plane of rotation at high cruise Mach number.
Hanson, D. B.↗
Characterization of a thermally imidized soluble polyimide film
A soluble aromatic poly(amic acid) film was converted to a soluble polyimide by staging at 25 deg intervals to 325 C and characterized at each interval by several analytical methods. The behavior observed was consistent with an interpretation that a reduction occurred in molecular weight of the poly(amic acid) during the initial stages of cure before the ultimate molecular weight was achieved as a polyimide. This interpretation was supported by the results of solution viscosity, gel permeation chromatography, low angle laser light scattering photometry and infrared spectroscopy analysis. The results serve to increase the fundamental understanding of how polyimides are thermally formed from poly(amic acids).
Young, Philip R.↗
Characterization of a thermally imidized soluble polyimide film
A soluble aromatic poly(amic acid) film was converted to a soluble polyimide by staging at 25 deg intervals to 325 C and characterized at each interval by several analytical methods. The behavior observed was consistent with an interpretation that a reduction occurred in molecular weight of the poly(amic acid) during the initial stages of cure before the ultimate molecular weight was achieved as a polyimide. This interpretation was supported by the results of solution viscosity, gel permeation chromatography, low angle laser light scattering photometry and infrared spectroscopy analysis. The results serve to increase the fundamental understanding of how polyimides are thermally formed from poly(amic acids).
Young, Philip R.↗
Geometrically thin, hot accretion disks - Topology of the thermal equilibrium curves
All the possible thermal equilibrium states of geometrically thin alpha-disks around stellar-mass black holes are presented. A (vertically) one-zone disk model is employed and it is assumed that a main energy source is viscous heating of protons and that cooling is due to bremsstrahlung and Compton scattering. There exist various branches of the thermal equilibrium solution, depending on whether disks are effectively optically thick or thin, radiation pressure-dominated or gas pressure-dominated, composed of one-temperature plasmas or of two-temperature plasmas, and with high concentration of e(+)e(-) pairs or without pairs. The thermal equilibrium curves at high temperatures (greater than or approximately equal to 10 exp 8 K) are substantially modified by the presence of e(+)e(-) pairs. The thermal stability of these branches are examined.
Kusunose, Masaaki↗
Two-Flux Method for Transient Radiative Transfer in a Semitransparent Layer
The two-flux method was used to obtain transient solutions for a plane layer including internal reflections and scattering. The layer was initially at uniform temperature, and was heated or cooled by external radiation and convection. The two-flux equations were examined as a means for evaluating the radiative flux gradient in the transient energy equation. Comparisons of transient temperature distributions using the two-flux method were made with results where the radiative flux gradient was evaluated from the exact radiative transfer equations. Good agreement was obtained for optical thicknesses from 0.5 to 5 and for refractive indices of 1 and 2. Illustrative results obtained with the two-flux method demonstrate the effect of isotropic scattering coupled with changing the refractive index. For small absorption with large scattering the maximum layer temperature is increased when the refractive index is increased. For larger absorption the effect is opposite, and the maximum temperature decreases with increased refractive index .
Siegel, Robert↗
Obliquity Driven Climate Change in Mars' Recent Past
We use the NASA/Ames grid Mars general circulation model with an updated radiation code and cloud nlicrophysics scheme. To speed up the simulations, we run the model at fairly coarse resolution (7.5" latitude x 22.5" longitude). Radiation Code Fluxes and heating rates are calculated from a radiation code based on the two-stream solution to radiative transfer that fully accounts for multiple scattering in the presence of gaseous absorp- tion. The model has 12 spectral intervals. Dust and water ice scattering properties are included. For dust, we use the Ockert-Bell [9] values in the visible, and Forget [IO] values in the infrared. For ice, we can either compute them online as the cloud evolves, or we can specify them. Gaseous opacities for water vapor and CO2 are calculated from correlated k-distributions taken from full line-by-line models. Cloud Microphysics Our cloud scheme is based on momentlorder scheme in which the mass mixing ratio and number density of the cloud ensemble are the advected species. From these we obtain a mean particle size and an estimate or the particle size distribution assuming a variance) which we then divide into 8 bins. Cloud microphysics is performed in each of these bins and includes nucleation, condensation, and gravitational settling. Dust is treated as a tracer and serves as condensation nuclei. The altered size distribution is then converted back into a mean size, a mixing ratio, and a particle number density.
Haberle, R. M.↗
In-SITU Raman Spectroscopy of Single Microparticle Li-Intercalation Electrodes
Modifications in the vibrational properties of a single microparticle of LiMn2O4 induced by extraction and subsequent injection of Li(+) into the lattice have been monitored in situ via simultaneous acquisition of Raman scattering spectra and cyclic voltammetry data in 1M LiC1O4 solutions in ethylene carbonate (EC):diethyl carbonate (DEC) mixtures (1:1 by volume). Statistical analyses of the spectra in the range 15 < SOD < 45%, where SOD represents the state of discharge (in percent) of the nominally fully charged material, i.e. lambda-MnO2, were found to be consistent with the coexistence of two distinct phases of lithiated metal oxide in agreement with information derived from in situ X-ray diffraction (XRD) measurements involving more conventional battery-type electrodes.
Dokko, Kaoru↗
Applications of the conjugate gradient FFT method in scattering and radiation including simulations with impedance boundary conditions
The theoretical and computational aspects related to the application of the Conjugate Gradient FFT (CGFFT) method in computational electromagnetics are examined. The advantages of applying the CGFFT method to a class of large scale scattering and radiation problems are outlined. The main advantages of the method stem from its iterative nature which eliminates a need to form the system matrix (thus reducing the computer memory allocation requirements) and guarantees convergence to the true solution in a finite number of steps. Results are presented for various radiators and scatterers including thin cylindrical dipole antennas, thin conductive and resistive strips and plates, as well as dielectric cylinders. Solutions of integral equations derived on the basis of generalized impedance boundary conditions (GIBC) are also examined. The boundary conditions can be used to replace the profile of a material coating by an impedance sheet or insert, thus, eliminating the need to introduce unknown polarization currents within the volume of the layer. A general full wave analysis of 2-D and 3-D rectangular grooves and cavities is presented which will also serve as a reference for future work.
Barkeshli, Kasra↗
Analysis of all-frequency variational behavior of the Kirchhoff approximation for a classic surface-scattering model
In testing a stochastic variational principle at high frequencies by using a Kirchhoffean trial function in an idealized model for surface scattering - a randomly embossed plane - we have found not only the predicted high-frequency improvement but also an unexpected low-frequency improvement in the calculated scattering amplitudes. To investigate systematically the all-frequency variational behavior, we consider here the deterministic one-boss case - Rayleigh's classic model whose exact solution is available for comparison - over all wavelengths, polarizations, and configurations of incidence and scattering. We examine analytically in particular the long-wave limit of the variational-Kirchhoff amplitudes; the results demonstrate improvements in both wavelength and angle depedence for horizontal (TM) polarization and some variational improvements for vertical (TE) polarization. This low-frequency behavior in tandem with the foreseen high-frequency improvement leads to good variational-Kirchhoff results through the intermediate resonance-frequency regime for this model.
Bird, J. F.↗
Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency-doubled Alexandrite laser wavelength in cesium vapor
The solutions for the imaginary susceptibility of the Raman field transition with arbitrary relaxation rates and field strengths are examined for three different sets of relaxation rates. These rates correspond to: (1) Far Infrared (FIR) Raman lasers in the diabatic collision regime without consideration of coupled population decay in a closed system, (2) Raman FIR lasers in the diabatic collision regime with coupled population conserving decay, and (3) IR Raman gain in cesium vapor. The model is further expanded to include Doppler broadening and used to predict the peak gain as a function of detuning for a frequency doubled Alexandrite laser-pumped cesium vapor gain cell.
Lawandy, Nabil M.↗
Solution of Aeroacoustic Problems by a Nonlinear, Hybrid Method
Category 1, problem 3 (scattering of sound by a sphere) and category 2, problem 1 (spherical source in a cylindrical duct subject to uniform flow) are solved in generalized coordinates using the nonlinear Euler equations together with nonreflecting boundary conditions. A temporally and spatially fourth-order accurate finite-difference, Runge-Kutta time-marching technique is employed for the near-field calculations and a Kirchhoff method is employed for the prediction of far-field sound. Computations are all performed on parallel processors using the data-parallel paradigm.
Oezyoeruek, Yusuf↗
The inverse scattering problem for transmission lines
A number of exact and approximate methods for solving the inverse scattering problem for transmission lines are reviewed. In particular, the application to transmission lines of Marcenko's version of the Gelfand-Levitan exact method for the quantum mechanical problem is compared with a more direct approach based on a different version of the Gelfand-Levitan method. In addition, some aspects of the lack of uniqueness of solutions are discussed, and some open questions related to the inverse scattering problem are suggested.
Kay, I.↗