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NASA NTRS1988

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Nitsche, Ludwig C.↗

NASA NTRS1987

Implementation of an ADI method on parallel computers

In this paper the implementation of an ADI method for solving the diffusion equation on three parallel/vector computers is discussed. The computers were chosen so as to encompass a variety of architectures. They are the MPP, an SIMD machine with 16-Kbit serial processors; Flex/32, an MIMD machine with 20 processors; and Cray/2, an MIMD machine with four vector processors. The Gaussian elimination algorithm is used to solve a set of tridiagonal systems on the Flex/32 and Cray/2 while the cyclic elimination algorithm is used to solve these systems on the MPP. The implementation of the method is discussed in relation to these architectures and measures of the performance on each machine are given. Simple performance models are used to describe the performance. These models highlight the bottlenecks and limiting factors for this algorithm on these architectures. Finally conclusions are presented.

Fatoohi, Raad A.↗

NASA NTRS1988

Monte Carlo modeling of large-scale ion-conic generation

Cyclotron resonance with observed electric field fluctuations is demonstrated to be responsible for production of the oxygen ion conics that are observed by the Dynamics Explorer 1 satellite in the central plasma sheet region of the earth's auroral zone. The ion velocity distribution is described by a quasi-linear diffusion equation which is solved using the Monte Carlo technique. The acceleration produced by the observed wave spectrum agrees well with the ion observations, in both form and magnitude.

Retterer, J. M.↗

NASA NTRS1988

A method of boundary parameter estimation for a two-dimensional diffusion system under noisy observations

The purpose of this paper is to establish a method for identifying unknown parameters involved in the boundary state of a class of diffusion systems under noisy observations. A mathematical model of the system dynamics is given by a two-dimensional diffusion equation. Noisy observations are made by sensors allocated on the system boundary. Starting with the mathematical model mentioned above, an online parameter estimation algorithm is proposed within the framework of the maximum likelihood estimation. Existence of the optimal solution and related necessary conditions are discussed. By solving a local variation of the cost functional with respect to the perturbation of parameters, the estimation mechanism is proposed in a form of recursive computations. Finally, the feasibility of the estimator proposed here is demonstrated through results of digital simulation experiments.

Sunahara, Y.↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1989

Distribution function of continuously created newborn and pickup ions in outer cometary exospheres

The time evolution of the distribution function of newborn ions in the solar wind is investigated using a quasi-linear-type diffusion equation. The initial distribution is taken to be a ring beam, which is approximated by delta function in pitch angle and velocity, and it is assumed that the ions are created at a constant rate with a similar distribution. A long-time asymptotic form of ion distribution is obtained, which is a mixture of newborn ions and ions generated throughout the entire process. It is shown that the time asymptotic distribution function exists even in the presence of a continuous ionization process. The stability of the long-time asymptotic distribution was examined for the case of parallel propagation, and the results show that the distribution function can be unstable to low-frequency hydromagnetic waves. The results of the analysis were found to agree with recent satellite observations.

Gaffey, J. D., Jr.↗

NASA NTRS1990

Computation of the unsteady facilitated transport of oxygen in hemoglobin

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Davis, Sanford↗

NASA NTRS1990

Fourier analysis of finite element preconditioned collocation schemes

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Deville, Michel O.↗

NASA NTRS1990

Electric currents in E-like planetary ionospheres

In this paper an MHD approach is used to consider the conduction of electric current in a lightly ionized gas, taking into account the gradients of pressure in the ion and electron gases, in addition to the electric field. The coefficients of electrical conductivity are found for each driver of current. New expressions for the components of heat dissipation associated with each driver of current are developed, which are fully consistent with kinetic theory. The relationship of the results to those obtained by kinetic theory is discussed. New components of currents associated with planetary equatorial electrojets are found. A new diffusion equation for magnetic induction is found, applicable in E-like regions of planetary ionospheres, and stellar photospheres.

Cole, K. D.↗

NASA NTRS1990

Electron heating in quasi-perpendicular shocks - A Monte Carlo simulation

To study the problem of electron heating in quasi-perpendicular shocks, under the combined effects of 'reversible' motion, in the shock electric potential and magnetic field, and wave-particle interactions a diffusion equation was derived, in the drift (adiabatic) approximation and it was solved by using a Monte Carlo method. The results show that most of the observations can be explained within this framework. The simulation has also definitively shown that the electron parallel temperature is determined by the dc electromagnetic field and not by any wave particle induced heating. Wave-particle interactions are effective in smoothing out the large gradients in phase space produced by the 'reversible' motion of the electrons, thus producing a 'cooling' of the electrons. Some constraints on the wave-particle interaction process may be obtained from a detailed comparison between the simulation and observations. In particular, it appears that the adiabatic approximation must be violated in order to explain the observed evolution of the perpendicular temperature.

Veltri, Pierluigi↗

NASA NTRS1990

Pitch angle diffusion of newborn ions due to intrinsic turbulence in the solar wind

The objective of the present study is to understand the interaction of the solar wind with newborn ions in far upstream regions of a comet where the level of intrinsic turbulence is moderately low. Based on the assumption that quasi-linear theory is adequate and applicable, the pitch angle diffusion process and the time evolution of the newborn ion distribution function are investigated. Numerical solutions to the quasi-linear diffusion equation, including the effect of resonance broadening and that of continuous creation of newborn ions due to the ionization process, are obtained under several assumptions and approximations. It is found that theoretical results are consistent with the Giotto observations recently reported by Neugebauer et al. (1989).

Ziebell, L. F.↗

NASA NTRS1991

Modeling of chemical vapor infiltration for ceramic composites reinforced with layered, woven fabrics

A homogeneous model is developed for the chemical vapor infiltration by one-dimensional diffusion into a system of layered plies consisting of woven tows containing bundles of filaments. The model predictions of the amount of deposition and the porosity of the sample as a function of time are compared with the predictions of a recent nonhomogeneous model with aligned holes formed by the weave. The nonhomogeneous model allows for diffusion through the aligned holes, into the spaces between plies, and into the gaps around filaments; i.e., three diffusion equations apply. Relative to the nonhomogeneous results, the homogeneous model underestimates the amount of deposition, since the absence of holes and spaces allows earlier occlusion of gaps around filaments and restricts the vapor infiltration.

Chung, Gui-Yung↗

NASA NTRS1991

Flux-limited diffusion in a scattering medium

A diffusion equation (FDT) is presented with a coefficient that reduces to the appropriate limiting form in the streaming and near thermodynamic limits for a moving fluid in which the dominant source of opacity is Thomson scattering. The present results are compared to those obtained with the corresponding equations for an absorptive medium. It is found that FDT for a scattering medium is accurate to better than less than about 17 percent over the range of optical depths of tau in the range of about 0 to 3.

Melia, Fulvio↗

NASA NTRS1991

Layer tracking, asymptotics, and domain decomposition

A preliminary report is presented on the work on the tracking of internal layers in a singularly-perturbed convection-diffusion equation. It is shown why such tracking may be desirable, and it is also shown how to do it using domain decomposition based on asymptotic analysis.

Brown, D. L.↗

NASA NTRS1991

Characterization of directionally solidified Hg(1-x)Zn(x)Se semiconducting alloys

Hg(1-x)Zn(x)Se alloys with composition between x = 0.08 and 0.115 were synthesized from elemental constituents and were resolidified using a Bridgman-Stockbarger growth technique. By performing precision mass-density measurements on selected wafers cut perpendicular to the growth axis, it was shown that the axial compositional profiles fit a numerical solution to the 1D diffusion equation which takes into account the variation of interface velocity with time. Infrared transmission-edge measurements performed on selected transverse slices from each ingot showed that the relative radial variations in composition decreased with decreasing growth rate. Van der Pauw measurements on selected wafers showed that the 10 exp 18/cu cm electron concentration, typical of as-grown crystals, could be reduced by approximately an order of magnitude by annealing in Se vapor.

Cobb, S. D.↗

NASA NTRS1991

Discrete observability and numerical quadrature

The authors consider the problem of approximate observability of a one-dimensional diffusion equation on a finite spatial domain with spatial point measurements. The problem of the optimal selection of the measurement points is considered under three conditions: (1) no preassigned measurement nodes; (2) one preassigned node and; (3) two preassigned nodes. The main observation is that the optimal choice is related to three classical procedures in numerical analysis: (1) Gaussian quadrature; (2) Radau quadrature and; (3) Lobatto quadrature. It is shown that the existence of the Radau and Lobatto quadrature is closely related to classical root locus theory.

Martin, Clyde F.↗

NASA NTRS1992

Subsurface emissions from Mercury - VLA radio observations at 2 and 6 centimeters

Radio observations of Mercury made with the VLA; once in 1986, and on two dates in February of 1988 are presented. These observations are the first to spatially map both hot regions associated with the theoretical hot poles. These 'hot poles' are separated by 180 deg and are a result of the unusual diurnal heating from Mercury's 3/2 spin-orbit resonance and eccentric orbit. The highest resolution data maps areas of the planet as small as 330 km. Maps of total intensity, brightness temperature, polarized intensity, fractional polarization, depolarization, and spectral index are included. It is found that the subsurface thermal emissions from Mercury are characteristic of blackbody reradiation from the solar insolation over a diurnal cycle. These observations to produce full-disk thermophysical models are used. The one-dimensional, time-dependent heat-diffusion equation for all observed disk elements at each epoch in order to constrain thermophsyical parameters and properties of the subsurface material are solved. Using typical lunar values for several of the parameters, it is possible to reproduce the temperature morphology and most of the observed temperature values. It is found that the best-fit models require a substantial contribution of the heat transport in the subsurface to be radiative in nature. The primary difficulty in the models is in predicting the observed temperature differences as a function of frequency.

Ledlow, Michael J.↗

NASA NTRS1992

Estimation of unknown variable parameters in moving boundary problems

The problem of estimating unknown variable parameters appearing in moving boundary problems is considered; these are specifically nonlinear diffusion equations defined on a moving spatial domain. A spline-based approximation method that results in a sequence of computationally tractable approximate parameter estimation problems has been developed. A convergence result is proved for a certain class of these moving boundary problems. The paper is concluded with a set of representative numerical examples.

Murphy, K. A.↗