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Results for “invariant imbeddings”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1998

Massively Parallel Solution of Poisson Equation on Coarse Grain MIMD Architectures

In this paper a new algorithm, designated as Fast Invariant Imbedding algorithm, for solution of Poisson equation on vector and massively parallel MIMD architectures is presented. This algorithm achieves the same optimal computational efficiency as other Fast Poisson solvers while offering a much better structure for vector and parallel implementation. Our implementation on the Intel Delta and Paragon shows that a speedup of over two orders of magnitude can be achieved even for moderate size problems.

parallel algorithms MIMD parallel architectures↗
NASA NTRS1968

A new approach to stochastic control.

Optimizing stochastic control problem by addition of estimation-penalty functions to performance index, using invariant imbedding procedure

Melsa, J. L.↗
NASA NTRS1971

On the relationship between aerosol content and errors in telephotometer experiments.

This paper presents an invariant imbedding theory of multiple scattering phenomena contributing to errors in telephotometer experiments. The theory indicates that there is a simple relationship between the magnitudes of the errors introduced by successive orders of scattering and it is shown that for all optical thicknesses each order can be represented by a coefficient which depends on the field of view of the telescope and the properties of the scattering medium. The verification of the theory and the derivation of the coefficients have been accomplished by a Monte Carlo program. Both monodisperse and polydisperse systems of Mie scatterers have been treated. The results demonstrate that for a given optical thickness the coefficients increase strongly with the mean particle size particularly for the smaller fields of view.

Thomas, R. W. L.↗
NASA NTRS1971

Reduction of the Dirichlet problem to an initial value problem.

Although the derivation is concerned with solutions for plane regions with prescribed boundary values, the approach presented could by easily generalized to higher dimensions. The initial-value method is derived by a combination of invariant imbedding techniques and the Fredholm integral equation method of representation of the potential as a function of a dilayer distribution on the boundary of the region in question.

Kalaba, R.↗
NASA NTRS1972

Nonlinear filtering for random signals in statistically unknown noise.

Natural and effective formulation of the filtering problem involved in satellite orbit determination, aircraft navigation, and missile tracking. The problem arises because the environment of the sensor keeps changing from time to time, and it is quite impractical and sometimes impossible to collect the statistical data of the noise incurred in the observation. Computable filtering equations are deduced. The idea of invariant imbedding along with stochastic differential calculus is used to derive differential equations for the optimal estimate.

Loo, J. T.↗
NASA NTRS1972

Random deflections of a string on an elastic foundation.

The paper is concerned with the problem of a taut string on a random elastic foundation subjected to random loads. The boundary value problem is transformed into an initial value problem by the method of invariant imbedding. Fokker-Planck equations for the random initial value problem are formulated and solved in some special cases. The analysis leads to a complete characterization of the random deflection function.

Sanders, J. L., Jr.↗
NASA NTRS1973

Mathematical models for the reflection coefficients of dielectric half-spaces

The reflection coefficients at normal incidence are found for a large class of one-dimensionally inhomogeneous or stratified half-spaces, which contain a homogeneous half-space. The formulation of the problem involves a combination of the classical boundary value technique, and the nonclassical principle of invariant imbedding. Solutions are in closed form and expressible in terms of Bessel functions. All results are given in terms of the ratio of the distance between free space and the homogeneous half-space to the wavelength in vacuo. One special case is that of an arbitrary number of layers lying on a homogeneous half-space where the dielectric constant of each layer has a constant gradient. A number of other special cases, limiting cases, and generalizations are developed including one in which the thickness of the top layer obeys a probability distribution.

Evans, D. D.↗
NASA NTRS1975

Chandrasekhar-type algorithms for fast recursive estimation in linear systems with constant parameters

In this recursive method proposed, the gain matrix for the Kalman filter and the convariance of the state vector are computed not via the Riccati equation, but from certain other equations. These differential equations are of Chandrasekhar-type. The 'invariant imbedding' idea resulted in the reduction of the basic boundary value problem of transport theory to an equivalent initial value system, a significant computational advance. Initial value experience showed that there is some computational savings in the method and the loss of positive definiteness of the covariance matrix is less vulnerable.

Choudhury, A. K.↗
NASA NTRS1976

Theory of thermal microwave emission from a two-layer medium

Thermal microwave emission from a scattering layer overlying a homogeneous half space is studied with the radiative transfer approach. Scattering models of random medium and discrete spherical scatterers are used. The radiative transfer equations are solved by both the classical method and the invariant imbedding method. The brightness temperatures of the two-layer model exhibit distinguishing features important to microwave passive remote sensing.

Tsang, L.↗
NASA NTRS1978

Microwave emission from polar firn

The microwave emission from a half-space medium, characterized by coordinate dependent scattering and absorbing centers, was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. Rayleigh scattering phase functions and scattering induced polarization of the radiation were included in the calculation. Using the scattering and extinction data of polar firn the brightness temperature was calculated for the 1.55 cm wavelength. This study was the first quantitative comparison of the results of numerical calculation using the actual measured information of crystal size with the observed data.

Chang, A. T. C.↗
NASA NTRS1978

Minimum energy control of a class of electrically driven vehicles

Theoretical and experimental results are obtained in the investigation of a minimum energy control problem associated with a class of electrically driven vehicles. Analytical results are obtained by making several justifiable approximations in the dynamical equations of the plant, the performance index of which is related to the minimization of system energy consumption for any required control action. The control problem of interest is simplified and solved by using Bellman's invariant imbedding technique. The optimality of the resulting control law is compared with those of the bang-bang control law, which is the exact solution for the case of speed-setting control action, and the classical control laws under identical conditions. A stochastic optimization problem is then formulated and solved by using Bellman's dynamic programming technique. The resulting control law is mechanized for a particular vehicle configuration which is simulated in the laboratory.

Sahinkaya, Y. E.↗
NASA NTRS1978

Microwave brightness of polar firn as measured by Nimbus 5 and 6 ESMR

The microwave emission from a half-space medium characterized by coordinate dependent scattering and absorbing centers was calculated by numerically solving the radiative transfer equation by the method of invariant imbedding. A Mie scattering phase function and surface polarization was included in the calculation. Also included are the physical temperature profile and the temperature variation of the index of refraction for ice. Using published values of grain size and temperature profile data of polar firn, the brightness temperature was calculated for the 1.55 cm and 0.8 cm wavelengths. For selected regions in Greenland and Antarctica, the results are in reasonable agreement with the observed Nimbus-5 and Nimbus-6 ESMR data.

Chang, A. T. C.↗
NASA NTRS1979

Numerical results for the thermal scattering functions

A recent formulation in radiative transfer defined the thermal scattering functions that characterize radiative transfer from a general plane-parallel finite medium driven solely by an internal distribution of thermal sources. Exiting diffuse intensities are expressed as space convolutions of the thermal scattering functions with any thermal source distribution. A parametric study is presented to obtain the basic structure of these scattering functions. The independent variables of these azimuthally independent functions are the direction cosine and source location, while the parameters are the single-scattering albedo, total optical depth, and the asymmetry factor in the Henyey-Greenstein phase function. The basic functional trends are discussed by using various parametric plots, and selected results are given to allow numerical checks. The computational method is invariant imbedding.

Cogley, A. C.↗
NASA NTRS1979

Scattering of emitted radiation from inhomogeneous and nonisothermal layers

A parametric study is performed for the exiting monochromatic intensities scattered from finite plane-parallel inhomogeneous layers that are driven solely by a distribution of thermal sources. Intensities are obtained by invariantly imbedding the standard and thermal scattering functions. The single-scattering albedo and the Henyey-Greenstein phase-function parameter are varied independently, and both linear and exponential profiles are considered. Linear temperature profiles are used, including temperature inversions. The resulting intensities, as a function of the direction cosine of propagation, are discussed from a remote-sensing point of view. For an isothermal and homogeneous medium, the gross characteristics of the exiting intensity, represented by its overall slope, mean value (magnitude), and an interior maximum value, can be related to the total optical depth, single-scattering albedo, and phase function, respectively. For a homogeneous medium, linearly decreasing (in the line of sight) temperature profiles tend to obscure the phase-function information and decrease the apparent optical depth. On the other hand, linearly increasing temperature profiles tend to retain phase-function information and increase the apparent optical depth. Temperature inversion profiles give intensities very similar to those for purely linear profiles.

Bergstrom, R. W.↗
NASA NTRS1980

Investigation of numerical properties of Hovenier's exit function equation for multiple scattering of light

A technique of deriving Hovenier's exit function equation (1978) for multiple scattering, starting with a set of invariant imbedding equations, is presented. The feasibility of the exit function equation as a means to obtain reflection and transmission functions is investigated for isotropic, Rayleigh, and Henyey-Greenstein phase functions with emphasis on the numerical stability, accuracy and timing. It is possible to compute the reflection function rather accurately with an efficiency comparable to that of the standard doubling technique for the same phase functions with moderate anisotropy. The resulting transmission is slightly less accurate than the reflection function, but it may be acceptable for practical purposes.

Kawabata, K.↗
NASA NTRS1980

Numerical grid generation techniques

The state of the art in topology and flow geometry is presented. Solution techniques for partial differential equations are reviewed and included developments in coordinate transformations, conformal mapping, and invariant imbeddings. Applications of these techniques in fluid mechanics, flow geometry, boundary value problems, and fluidics are presented.

Source record↗
NASA NTRS1982

Solidification of a binary mixture

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Antar, B. N.↗
NASA NTRS1981

Spectral albedos of midlatitude snowpacks

Spectral albedos of impure-nonhomogeneous snowpacks, typical of midlatitudes, from 400 to 2200 nm were modeled through a numerical solution of the radiative transfer equation in the two-stream approximation. Discrete depth-dependent values of density, grain size and impurity concentration were used to characterize the snowpacks. The model is for diffuse incident radiation, and the numerical method is based on doubling and invariant imbedding. The effect of soot impurities on snowpack albedos is illustrated when a snowpack is several centimeters deep and soot reduces the albedos at visible wavelengths, however, when a snowpack is only a few centimeters deep, soot may increase the albedos at visible wavelengths. By adjusting soot content and snow grain size, good quantitative agreement with some observations at the Cascade Mountains (Washington) and at Point Barrow (Alaska) are obtained; however, the model grain sizes are found to be fifty to four hundred percent larger than the measured values. For satellite snowcover observations, a model for effective albedo of partially snow-covered areas was developed and compared with some NOAA-2 observations of the southeastern United States.

Choudhury, B.↗