A study of the composition of the solar corona and solar wind
Solar corona and wind composition, accounting for He flux and heavy elements from diffusion equations solution
Nakada, M. P.↗
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Two-dimensional inert accumulation in space hydrogen-oxygen fuel cells
Dead ended compartments concentration and current distributions calculation in space hydrogen-oxygen fuel cells, using mathematical model with convective diffusion equation
Gidaspow, D.↗
Variable boundary II heat conduction
Computer program for solving both transient and steady-state heat transfer problems is presented. Specific applications of computer program are described. Formulation for individual nodes of solid medium for heat balance is presented. Diffusion equation is solved for all nodes simultaneously at finite increments of time.
Gramer, J.↗
Behavior of nitric oxide formed by the space shuttle in the mesosphere
A numerical model of eddy diffusive transport of emitted gases from the space shuttle wake, including chemical reactions between the emitted constituents and the ambient atmosphere, has been constructed for 75 km altitude. The numerical methods involve explicit solution of the diffusion equation and Runge-Kutta method for the chemical reactions. The time required to reach background levels of nitric oxide concentration of 7 x 10 to the 7th power molecules/cc has been calculated. This relaxation time depends strongly on atmospheric conditions.
Eberstein, I. J.↗
Diffusion in a unidirectional filament reinforced metal composite.
A theoretical analysis has been developed to describe composition changes resulting from exposure of a unidirectional filament reinforced metal composite to an elevated temperature environment. The analysis was based on a simple superposition of finite-difference solutions of the diffusion equation, and was applicable to the case for which the filament and matrix metals comprised an isomorphous binary alloy system. The possibility of chemical reaction between filaments and matrix was excluded. Excellent agreement was obtained between calculated concentration profiles and results of quantitative electron microprobe analyses of nickel filament reinforced copper samples.
Herring, H. W.↗
Thermalization and transport of photoelectrons - A comparison of theoretical approaches.
Three methods of studying ionospheric photoelectron thermalization, in which transport effects are evaluated in different ways, are outlined and compared. One method uses a diffusion equation formulation, the second proceeds from a two-stream approximation to the general particle transfer equation, and the third employs a Monte Carlo technique to simulate electron paths. The methods are compared by applying them to identically prepared models. The methods are in close agreement for altitudes in the region of local energy loss, but higher altitudes reveal a discrepancy of as much as a factor of 2 in the net flux of photoelectrons. The discrepancy is removed by appropriately modifying the computational techniques.
Cicerone, R. J.↗
A study of the diffusional behavior of a two-phase metal matrix composite exposed to a high temperature environment
The progress of diffusion-controlled filament-matrix interaction in a metal matrix composite where the filaments and matrix comprise a two-phase binary alloy system was studied by mathematically modeling compositional changes resulting from prolonged elevated temperature exposure. The analysis treats a finite, diffusion-controlled, two-phase moving-interface problem by means of a variable-grid finite-difference technique. The Ni-W system was selected as an example system. Modeling was carried out for the 1000 to 1200 C temperature range for unidirectional composites containing from 6 to 40 volume percent tungsten filaments in a Ni matrix. The results are displayed to show both the change in filament diameter and matrix composition as a function of exposure time. Compositional profiles produced between first and second nearest neighbor filaments were calculated by superposition of finite-difference solutions of the diffusion equations.
Tenney, D. R.↗
Rigid format alter packets for the analysis of electromagnetic field problems
The computer program NASTRAN is used to solve electromagnetic field problems. The diffusion equation and the boundary conditions valid for problems of these kinds together with a replacing potential energy function are given. The extent to which an analogy with finite element displacement and temperature approaches holds is indicated. The outputting of complex quantities is made possible after adjustment of standard rigid format 1 input data blocks to module SDR2. The applications made involve the study of the proximity effect in a system of three parallel conductors and the analysis of the magnetic field in the vicinity of the points of contact in circuit breakers.
Spreeuw, E.↗
Monte Carlo analysis of uncertainty propagation in a stratospheric model. 1: Development of a concise stratospheric model
A concise model has been developed to analyze uncertainties in stratospheric perturbations, yet uses a minimum of computer time and is complete enough to represent the results of more complex models. The steady state model applies iteration to achieve coupling between interacting species. The species are determined from diffusion equations with appropriate sources and sinks. Diurnal effects due to chlorine nitrate formation are accounted for by analytic approximation. The model has been used to evaluate steady state perturbations due to injections of chlorine and NO(X).
Rundel, R. D.↗
Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges
Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.
Farley, G. L.↗
Microscopic Lagrangian description of warm plasmas. III - Nonlinear wave-particle interaction
The averaged-Lagrangian method is applied to nonlinear wave-particle interactions in an infinite, homogeneous, magnetic-field-free plasma. The specific example of Langmuir waves is considered, and the combined effects of four-wave interactions and wave-particle interactions are treated. It is demonstrated how the latter lead to diffusion in velocity space, and the quasilinear diffusion equation is derived. The analysis is generalized to the random phase approximation. The paper concludes with a summary of the method as applied in Parts 1-3 of the paper.
Galloway, J. J.↗
Optically thick X-ray transfer - The shell game
This paper investigates the radiative transfer of X-rays through a shell that is optically thick to Compton scattering, surrounding a point source of continuum X-rays. The emission and absorption of X-rays due to K-shell transitions of iron are included. The calculations are done in two entirely independent ways: by Monte Carlo simulation and by solving a Fokker-Planck diffusion equation. The emergent spectra agree very well for Thomson depths of at least about 2. The validity is confirmed of the modification to the Fokker-Planck equation of Kompaneets (1957) that is required when the photon energy is large compared with the average thermal energy of the electrons. A procedure is also developed for treating models of compact X-ray sources consisting of incomplete shells.
Langer, S. H.↗
Uncertainty propagation in a stratospheric model. I - Development of a concise stratospheric model. II - Monte Carlo analysis of imprecisions due to reaction rates
The paper discusses the development of a concise stratospheric model which uses iteration to obtain coupling between interacting species. The one-dimensional, steady-state, diurnally-averaged model generates diffusion equations with appropriate sources and sinks for species odd oxygen, H2O, H2, CO, N2O, odd nitrogen, CH4, CH3Cl, CCl4, CF2Cl2, CFCl3, and odd chlorine. The model evaluates steady-state perturbations caused by injections of chlorine and NO(x) and may be used to predict ozone depletion. The model is used in a Monte Carlo study of the propagation of reaction-rate imprecisions by calculating an ozone perturbation caused by the addition of chlorine. Since the model is sensitive to only 10 of the more than 50 reaction rates considered, only about 1000 Monte Carlo cases are required to span the space of possible results.
Rundel, R. D.↗
Silicon solar cell fabrication technology
The laser cell scanner was used to characterize a number of solar cells made in various materials. An electron beam-induced current (EBIC) study was performed using a stereoscan scanning electron microscope. Planar p-n junctions were analyzed. A theory for the EBIC based on the analytical solution of the ambipolar diffusion equation under the influence of electron beam excitation parameter z (which is related to beam penetration), the junction depth Z sub j, the beam current and the surface recombination, was formulated and tested. The effect of a grain boundary was studied.
Stafsudd, O. M.↗
Variational description of the positive column with two-stem ionization
The ionization balance in diffusion dominated discharges which depends on both one and two step ionization processes is considered. The Spenke diffusion equation (D sq delta n + neutrino n + sq kn =0) describing such conditions is solved by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between neutrino,k,D and the discharge dimensions, are derived for planar and cylindrical geometry, and compared with exact computations for certain limiting cases.
Crawford, F. W.↗
Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges
Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite-element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite-difference solution of the diffusion equation. It is shown that hygroscopic-induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.
Farley, G. L.↗
Variational description of the positive column with two-step ionization
The ionization balance in diffusion-dominated discharges may depend on both one- and two-step ionization processes. The Spenke diffusion equation describing such conditions is solved in this paper by the Rayleigh-Ritz variational method. Simple analytic approximations to the density profile, and the similarity relation between the equation parameter, and the discharge dimensions, are derived for planar and cylindrical geometry and compared with exact computations for certain limiting cases.
Crawford, F. W.↗
Pseudospectral method for problems with nonperiodic boundary conditions
The capability of the pseudospectral technique and the time integration scheme for the time dependent nonperiodic problem is demonstrated. Significant improvements are shown in the accuracy for calculation of the two dimensional time dependent advection diffusion equation. The pseudospectral method is a viable alternative to the finite difference methods for the equation of the spatial deriviations.
Lee, H. N.↗