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At least 199 records · Page 11

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NASA NTRS1973

Program for solution of ordinary differential equations

A program for the solution of linear and nonlinear first order ordinary differential equations is described and user instructions are included. The program contains a new integration algorithm for the solution of initial value problems which is particularly efficient for the solution of differential equations with a wide range of eigenvalues. The program in its present form handles up to ten state variables, but expansion to handle up to fifty state variables is being investigated.

Sloate, H.↗

NASA NTRS2000

Distribution of expansins in graviresponding maize roots

To test if expansins, wall loosening proteins that disrupt binding between microfibrils and cell wall matrix, participate in the differential elongation of graviresponding roots, Zea mays L. cv. Merit roots were gravistimulated and used for immunolocalization with anti-expansin. Western blots showed cross-reaction with two proteins of maize, one of the same mass as cucumber expansin (29 kDa), the second slightly larger (32 kDa). Maize roots contained mainly the larger protein, but both were found in coleoptiles. The expansin distribution in cucumber roots and hypocotyls was similar to the distribution in maize. Roots showed stronger expansin signals on the expanding convex side than the concave flank as early as 30 min after gravistimulation. Treatment with brefeldin A, a vesicle transport inhibitor, or the auxin transport inhibitor, naphthylphthalamic acid, showed delayed graviresponse and the appearance of differential staining. Our results indicate that expansins may be transported and secreted to cell walls via vesicles and function in wall expansion.

Non-NASA Center↗

NASA NTRS1992

Model of a rotating magnetic cloud

The possibility that magnetic clouds rotate while they propagate antisunward was investigated. Magnetic clouds are modeled as magnetic flux ropes which rotate rigidly about the axis of symmetry. An ideal magnetohydrodynamic model, in which the evolution of the magnetic structure is related to the time evolution of the angular frequency, is developed. A class of 'separable' magnetic fields is employed to reduce the problem to a nonlinear ordinary differential equation for the evolution function, and it is solved numerically. The corresponding effective potential gives rise to two modes of evolution--expansion and oscillation--depending on the energy and on the value of a dimensionless parameter, k. Parameter k depends on the gas pressure, the ratio of the magnetic field components, and the frequency of rotation. There is a critical value of k, k(sub c), above which the oscillatory regime disappears and the flux rope invariably expands, regardless of the energy. Below k(sub c) the energy determines whether the configuration is confined or unbounded. Rotation always helps expansion by lowering the potential barrier. A data example was studied and features which are interpreted as signatures of rotation are presented. The angular speed is comparable to the Alfven speed, and the core of the rotating cloud completes on average one full revolution every three days at 1 AU. The parameter k is calculated from observations, and it is found to be close to, but below, critical. Only three out of the nine clouds examined showed signatures of rotation. Theoretical analysis suggests that close to the Sun rotation effects may play a more important role in the evolution of magnetic clouds than 1 AU.

Farrugia, C. J.↗

NASA NTRS1995

Extensional flow convecting a reactant undergoing a first order homogeneous reaction and diffusional mass transfer from a sphere at low to intermediate Peclet and Damkohler numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 less than or equal to Pe less than or equal to 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 less than or equal to Da less than or equal to 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r, Theta) = Sum of c(n)(r)P(n)(cos Theta) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions Pn(cos Theta), the variable coefficient PDE can be reduced to a system of N + 1 second order ODEs for the radial functions c(sub n)(r), n = 0, 1, 2,..., N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N + 1) first order differential equations as a two-point boundary value problem on 1 less than or equal to r less than or equal to r(sub infinity). Convergence of the expansion for a specific value of N can thus be established and provides 'spectral' behavior as well as the full concentration field c(r, Theta).

Shah, N. Y.↗

NASA NTRS1994

Modeling jets in cross flow

Various approaches to the modeling of jets in cross flow are reviewed. These are grouped into four classes, namely: empirical models, integral models, perturbation models, and numerical models. Empirical models depend largely on the correlation of experimental data and are mostly useful for first-order estimates of global properties such as jet trajectory and velocity and temperature decay rates. Integral models are based on some ordinary-differential form of the conservation laws, but require substantial empirical calibration. They allow more details of the flow field to be obtained; simpler versions have to assume similarity of velocity and temperature profiles, but more sophisticated ones can actually calculate these profiles. Perturbation models require little empirical input, but the need for small parameters to ensure convergent expansions limits their application to either the near-field or the far-field. Therefore, they are mostly useful for the study of flow physics. Numerical models are based on conservation laws in partial-differential form. They require little empirical input and have the widest range of applicability. They also require the most computational resources. Although many qualitative and quantitative features of jets in cross flow have been predicted with numerical models, many issues affecting accuracy such as grid resolution and turbulence model are not completely resolved.

Demuren, A. O.↗

NASA NTRS1994

Effects of non-unity Lewis numbers in diffusion flames

The purpose of this work is to carry out direct numerical simulations of diffusion controlled combustion with non-unity Lewis numbers for the reactants and products, thus accounting for the differential diffusion effects of the temperature and concentration fields. We use a formulation based on combining the conservation equations in a way to eliminate the reaction terms similar to the method used by Burke and Schumann (1928) for unity Lewis numbers. We present calculations for an axisymmetric fuel jet and for a planar, time evolving mixing layer, leaving out the effects of thermal expansion and variations of the transport coefficients due to the heat release. Our results show that the front of the flame shifts toward the fuel or oxygen sides owing to the effect of the differential diffusion and that the location of maximum temperature may not coincide with the flame. The dependence of the distribution of the reaction products on their Lewis number has been investigated.

Linan, A.↗

NASA NTRS1990

A hybrid perturbation-Galerkin technique for partial differential equations

A two-step hybrid perturbation-Galerkin technique for improving the usefulness of perturbation solutions to partial differential equations which contain a parameter is presented and discussed. In the first step of the method, the leading terms in the asymptotic expansion(s) of the solution about one or more values of the perturbation parameter are obtained using standard perturbation methods. In the second step, the perturbation functions obtained in the first step are used as trial functions in a Bubnov-Galerkin approximation. This semi-analytical, semi-numerical hybrid technique appears to overcome some of the drawbacks of the perturbation and Galerkin methods when they are applied by themselves, while combining some of the good features of each. The technique is illustrated first by a simple example. It is then applied to the problem of determining the flow of a slightly compressible fluid past a circular cylinder and to the problem of determining the shape of a free surface due to a sink above the surface. Solutions obtained by the hybrid method are compared with other approximate solutions, and its possible application to certain problems associated with domain decomposition is discussed.

Geer, James F.↗

NASA NTRS1989

A Hierarchy of Transport Approximations for High Energy Heavy (HZE) Ions

The transport of high energy heavy (HZE) ions through bulk materials is studied neglecting energy dependence of the nuclear cross sections. A three term perturbation expansion appears to be adequate for most practical applications for which penetration depths are less than 30 g per sq cm of material. The differential energy flux is found for monoenergetic beams and for realistic ion beam spectral distributions. An approximate formalism is given to estimate higher-order terms.

Wilson, John W.↗

NASA NTRS2006

Thermodynamic Structure of Collision-Dominated Expanding Plasma: Heating of Interplanetary Coronal Mass Injections

We investigate the thermodynamic structure of interplanetary coronal mass ejections (ICMEs) using combined surveys of the ejecta between 0.3 and 20 AU. ICMEs are shown to have a moderate expansion in the solar wind compared with theoretical predictions. The expansion seems to be governed by a polytrope with gamma approx. 1.3 in this distance range. We find that Coulomb collisions are important contributors to the ion-ion equilibration process in the ICME plasma. The alpha-proton differential speed quickly drops to below 10 km/s due to strong Coulomb collisions. However, the two species of particles are far from thermal equilibrium with a temperature ratio T(sub alpha/T(sub p) = 4-6, suggestive of a preferential heating of alpha particles. The plasma heating rate as a function of heliocentric &stance required for the temperature profile is deduced by taking into account the expansion and energy transfer between protons and alphas via Coulomb collisions. The turbulence dissipation rate is also inferred from the inertial range power spectrum of magnetic fluctuations within ICMEs. Comparison of the turbulence dissipation rate with the required heating rate shows that turbulence dissipation seems sufficient to explain the ICME heating. Sources powering the turbulence are also investigated by examining the instabilities induced by temperature anisotropies and energy deposition by pickup ions.

Liu, Y.↗

NASA NTRS1984

Measurement of high temperature strain by the laser-speckle strain gauge

By using the laser-speckle strain gauge, the strain of metal at the temperature lower than 250 C is measured. The principle of the gauge is to measure the expansion or contraction of the fine structures of surface by detecting the resultant speckle displacement in an optoelectronic way, whereby the effect of rigid-body motion is automatically cancelled out with the aid of a differential detection system. A transportable apparatus was built and a comparison experiment performed with a resistance strain gauge at room temperature. It has a strain sensitivity of .00002, a gauge length smaller than 1 mm, and no upper limit in a range of strain measurement. In the measurement of high-temperature strain it is free from the need for a dummy gauge and insensitive to an electric drift effect. As examples of strain measurement at high-temperature, thermal expansion and contraction of a top of a soldering iron are measured. The interval of the measurement can be made at shortest 1.6 sec. and the change in the strain is clearly followed until the ultimate stationary temperature is reached.

Yamaguchi, I.↗

NASA NTRS1974

Theoretical predictions of latitude dependencies in the solar wind

Results are presented which were obtained with the Winge-Coleman model for theoretical predictions of latitudinal dependencies in the solar wind. A first-order expansion is described which allows analysis of first-order latitudinal variations in the coronal boundary conditions and results in a second-order partial differential equation for the perturbation stream function. Latitudinal dependencies are analytically separated out in the form of Legendre polynomials and their derivative, and are reduced to the solution of radial differential equations. This analysis is shown to supply an estimate of how large the coronal variation in latitude must be to produce an 11 km/sec/deg gradient in the radial velocity of the solar wind, assuming steady-state processes.

Winge, C. R., Jr.↗

NASA NTRS1976

Applicability of ERTS-1 to Montana geology

The author has identified the following significant results. Late autumn imagery provides the advantages of topographic shadow enhancement and low cloud cover. Mapping of rock units was done locally with good results for alluvium, basin fill, volcanics, inclined Paleozoic and Mesozoic beds, and host strata of bentonite beds. Folds, intrusive domes, and even dip directions were mapped where differential erosion was significant. However, mapping was not possible for belt strata, was difficult for granite, and was hindered by conifers compared to grass cover. Expansion of local mapping required geologic control and encountered significant areas unmappable from ERTS imagery. Annotation of lineaments provided much new geologic data. By extrapolating test site comparisons, it is inferred that 27 percent of some 1200 lineaments mapped from western Montana represent unknown faults. The remainder appear to be localized mainly by undiscovered faults and sets of minor faults or joints.

Weidman, R. M.↗

NASA NTRS1983

Physical aging and its influence on the reliability of network epoxies and epoxy-matrix composites

The matrix-dominated physical and mechanical properties of a carbon fiber reinforced epoxy composite and a neat epoxy resin were found to be affected by sub-Tg annealing in nitrogen and dark atmosphere. Postcured specimens of Thornel 300 carbon-fiber/Fiberite 934 epoxy as well as Fiberite 934 epoxy resin were quenched from above Tg and given annealing at 140 C, 110 C, or 80 C, for time up to one-hundred thousand minutes. No weight loss was observed during annealing at these temperatures. Significant variations were found in density, modulus, hardness, damping, moisture absorption ability, thermal expansivity. Moisture-epoxy interactious were also studied. The kinetics of aging as well as the molecular aggregation during this densification process were monitored by differential scanning calorimetry, dynamic mechanical analysis, density gradient column, microhardness tester, Instron, and solid-state nuclear magnetic resonance spectroscopy.

Heinemann, K.↗

NASA NTRS1989

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1993

Approximate optimal guidance for the advanced launch system

A real-time guidance scheme for the problem of maximizing the payload into orbit subject to the equations of motion for a rocket over a spherical, non-rotating earth is presented. An approximate optimal launch guidance law is developed based upon an asymptotic expansion of the Hamilton - Jacobi - Bellman or dynamic programming equation. The expansion is performed in terms of a small parameter, which is used to separate the dynamics of the problem into primary and perturbation dynamics. For the zeroth-order problem the small parameter is set to zero and a closed-form solution to the zeroth-order expansion term of Hamilton - Jacobi - Bellman equation is obtained. Higher-order terms of the expansion include the effects of the neglected perturbation dynamics. These higher-order terms are determined from the solution of first-order linear partial differential equations requiring only the evaluation of quadratures. This technique is preferred as a real-time, on-line guidance scheme to alternative numerical iterative optimization schemes because of the unreliable convergence properties of these iterative guidance schemes and because the quadratures needed for the approximate optimal guidance law can be performed rapidly and by parallel processing. Even if the approximate solution is not nearly optimal, when using this technique the zeroth-order solution always provides a path which satisfies the terminal constraints. Results for two-degree-of-freedom simulations are presented for the simplified problem of flight in the equatorial plane and compared to the guidance scheme generated by the shooting method which is an iterative second-order technique.

Feeley, T. S.↗

NASA NTRS1972

On the tidal effects in the motion of artificial satellites.

The general perturbations in the elliptic and vectorial elements of a satellite as caused by the tidal deformations of the non-spherical Earth are developed into trigonometric series in the standard ecliptical arguments of Hill-Brown lunar theory and in the equatorial elements of the satellite. The integration of the differential equations for variation of elements of the satellite in this theory is easy because all arguments are linear or nearly linear in time. The trigonometrical expansion permits a judgment about the relative significance of the amplitudes and periods of different tidal 'waves' over a long period of time. Graphs are presented of the tidal perturbations in the elliptic elements of the BE-C satellite which illustrate long term periodic behavior. The tidal effects are clearly noticeable in the observations and their comparison with the theory permits improvement of the 'global' Love numbers for the Earth.

Musen, P.↗

NASA NTRS2002

Elliptic Relaxation of a Tensor Representation of the Pressure-Strain and Dissipation Rate

A formulation to include the effects of wall-proximity in a second moment closure model is presented that utilizes a tensor representation for the redistribution term in the Reynolds stress equations. The wall-proximity effects are modeled through an elliptic relaxation process of the tensor expansion coefficients that properly accounts for both correlation length and time scales as the wall is approached. DNS data and Reynolds stress solutions using a full differential approach at channel Reynolds number of 590 are compared to the new model.

Carlson, John R.↗

NASA NTRS1981

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

Wanag, S. S.↗