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An approximation to a classification algorithm incorporating spatial context information in a general, statistical manner is presented which is computationally less intensive. Classifications that are nearly as accurate are produced.
A comprehensive overview of the state of the art of well-posedness and stability analysis of difference approximations for initial boundary value problems of the hyperbolic type is presented. The applicability of recent theoretical development to practical calculations for nonlinear gas dynamics is examined. The one dimensional inviscid gas dynamics equations in conservation law form are selected for numerical experiments. The class of implicit schemes developed from linear multistep methods in ordinary differential equations is chosen and the use of linear extrapolation as an explicit or implicit boundary scheme is emphasized. Specification of boundary data in the primitive variables and computation in terms of the conservative variables in the interior is discussed. Some numerical examples for the quasi-one-dimensional nozzle are given.
The computational efficiency of the impedance type loads prediction method was studied. Three goals were addressed: devise a method to make the impedance method operate more efficiently in the computer; assess the accuracy and convenience of the method for determining the effect of design changes; and investigate the use of the method to identify design changes for reduction of payload loads. The method is suitable for calculation of dynamic response in either the frequency or time domain. It is concluded that: the choice of an orthogonal coordinate system will allow the impedance method to operate more efficiently in the computer; the approximate mode impedance technique is adequate for determining the effect of design changes, and is applicable for both statically determinate and statically indeterminate payload attachments; and beneficial design changes to reduce payload loads can be identified by the combined application of impedance techniques and energy distribution review techniques.
For computational solution of the incompressible Navier-Stokes equations, the approximate factorization (AF) algorithm is used to solve the vectorized momentum equation in delta form based on the pressure calculated in the previous time step. The newly calculated velocities are substituted into the pressure equation (obtained from a linear combination of the continuity and momentum equation), which is then solved by means of line SOR. Computational results are presented for the NACA 66 sub 3 018 airfoil at Reynolds numbers of 1000 and 40,000 and attack angles of 0 and 6 degrees. Comparison with wind tunnel data for Re = 40,000 indicates good qualitative agreement between measured and calculated pressure distributions. Quantitative agreement is only fair, however, with the calculations somewhat displaced from the measurements. Furthermore, the computed velocity profiles are unrealistically thick around the airfoil, due to the excessive amount of artificial viscosity needed for stability. Based on the performance of the algorithm with regard to stability, it is concluded that AF/SOR is suitable for calculations at Reynolds numbers less than 10,000. Speedwise, the method is faster than point SOR by at least a factor of two.
The stability of finite difference approximations to initial boundary hyperbolic systems is studied. As is well known, a proper specification of boundary conditions for such systems is essential for their solutions to be well defined. A discrete analogue of the above is proved - if the numerical boundary conditions are consistent with an inflow part of the problem, they render the overall computation unstable. An example of the inviscid gasdynamics equations is considered.
A method for determining highly accurate approximations to families of strongly nonlinear solutions which are either continuous or discontinuous, and which represent variations in some arbitrary parameters, is developed and evaluated. The procedure consists of defining a unit perturbation by employing two or more nonlinear solutions which differ from one another by a nominal change in some geometric or flow parameter, and then using that unit perturbation to predict a family of related nonlinear solutions over a range of parameter variation. Coordinate straining is used in determining the unit perturbation to account for the movement of discontinuities and maxima of high-gradient regions due to the perturbation. Although the procedure is generally applicable, results are presented here for nonlinear aerodynamic applications. Attention is focused in particular on transonic flows which are strongly supercritical and exhibit large surface shock movement over the parametric range studied; and on subsonic flows which display large pressure variations in the stagnation and peak suction pressure regions. Flows past both isolated airfoils and compressor cascades involving a variety of flow and geometry parameter changes are considered. Comparisons with the corresponding 'exact' nonlinear solutions indicate a remarkable accuracy and range of validity of such a procedure. Computational time is trivial.
An argument is presented to determine the accuracy with which a solution of Einstein's field equations of gravitation must be approximated in order to describe the dominant effects of gravitational radiation emission from weak-field systems. Several previous calculations are compared in the light of this argument, and some apparent discrepancies among them are resolved. The majority of these calculations support the 'quadrupole formulae' for gravitational radiation energy loss and radiation reaction.
A method of fluid-structure coupling which provides symmetrical matrix equations of standard form solved by existing finite element computer programs is presented. The method postulates that the uncoupled vibration modes of the fluid or the structure be calculated before the coupled analysis. A numerical solution of vibration modes in an axisymmetric container demonstrated that a static approximation to higher order fluid modes can improve the accuracy of dynamic response computations using modal methods.
The time-consuming nature of limb relaxation-type inversion algorithms is due primarily to the numerous integrations over an absorption band to obtain forward radiance values with which to compare measured values. A new method has been devised for the quick and accurate (0.5% error) calculation of single gas broadband (approximately 100 per cm) limb radiance. The method uses a precalculated data base consisting of homogeneous path emissivity vs mass path data for a wide range of temperature and pressure. A 50-km altitude range, 1-km resolution, constituent inversion employing this method requires under 1 sec of computational time when run on modern computer hardware. The method does not rely upon a priori statistical knowledge.
A modification of an implicit approximate-factorization finite-difference algorithm applied to partial differential equations is presented. This algorithm is applied to the two- and three-dimensional Euler equations in general curvilinear coordinates. The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work. For steady-state applications, the resulting diagonal algorithm retains the stability and accuracy characteristics of the original algorithm. The diagonal algorithm reduces the storage requirement of the implicit solution process and therefore has an important effect on the application of implicit finite-difference schemes to vector processors. Results are presented for realistic two-dimensional transonic flow fields about airfoils. Computation costs are reduced to 24-34%.
The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations for initial-boundary-value problems of the hyperbolic type. For the numerical experiments, select the one-dimensional inviscid gas-dynamic equations in conservation-law form is selected. A class of implicit schemes based on linear multistep methods for ordinary differential equations is chosen and the use of space or space-time extrapolations as implicit or explicit boundary schemes is emphasized. Some numerical examples with various inflow-outflow conditions highlight the commonly discussed issues: explicit versus implicit boundary schemes, unconditionally stable schemes, and underspecification or overspecification of boundary conditions.
Two beamlike particle events (30 keV/charge to 160 keV/charge) upstream of the earth's bow shock have been investigated with the Max-Planck-Institut/University of Maryland ultralow energy and charge analyzer on ISEE 1. These beams consist of protons as well as of alpha particles, and the spectra are generally steep and are decreasing with increasing energy. During one event the spectra of both protons and alpha particles have a maximum at approximately 65 keV/charge. During these events, the interplanetary magnetic field through the satellite position was almost tangent to the bow shock, and application of the theory of acceleration predicts acceleration of a solar wind particle up to 60 keV/nucleon in a single reflection. The observation of reflected protons as well as alpha particles has implications for the physical reflection process usually not discussed in acceleration theories.
Data from lunar materials which may be interpreted as suggesting an increase in solar cosmic ray activity approximately 20,000 years ago is examined. The evidence includes the iron track within pit data of Hartung and Storzer (1974), the lunar whole rock pit and track data, lunar C-14 radioactivity data, lunar Ni-59 radioactivity data, the impact pit and iron track data of Morrison and Zinner (1975, 1977) and the lunar thermoluminescence data. While numerous explanations are possible for each set of data, it is shown that the first four data sets may be explained by a past increase in solar cosmic ray activity, and the remaining data sets are not necessarily incompatible with solar activity a factor of 20 to 40 times higher than at present for several thousand years prior to about 20,000 years ago.
A simplified approximate analytical method for predicting vortex lift and center of pressure on slender wings is presented. Two empirical corrections are proposed. The method is compared with experimental data and gives accurate estimates.
An approximation method is presented for reducing a nonlinear differential equation (for the 'weather vaning' motion of a wind turbine) to an equivalent constant moment of inertia problem. The integrated average of the moment of inertia is determined. Cycle time was found to be the equivalent cycle time if the rotating speed is 4 times greater than the system's minimum natural frequency.
The eikonal approach developed previously for calculating electron-capture cross sections for bare projectiles colliding with hydrogenic targets is extended here to allow for multielectron targets. Both the impact and wave pictures are employed and their equivalence is discussed. As a first approximation, each atomic orbital is specified by the three hydrogenic quantum numbers, an effective nuclear charge Z sub t, and an energy eigenvalue in the impact picture, or ionization potential in the wave picture. The Z sub t prime appearing in the eikonal phase factor is left undetermined because of incomplete information on the many-body target. However, analytic expressions are derived for the theoretical cross sections, and numerical values are calculated for simple choices of Z sub t prime. Those results are compared with existing experimental data for C, Ne, Ar, N2, O2, and He targets.
The propagation of photons in a medium with strongly anisotropic scattering is a problem with a considerable history. Like the propagation of electrons in metal foils, it may be solved in the small-angle scattering approximation by the use of Fourier-transform techniques. In certain limiting cases, one may even obtain analytic expressions. This paper presents some of these results in a model-independent form and also illustrates them by the use of four different phase-function models. Sample calculations are provided for comparison purposes
A complete sample of elliptical galaxies in the core of the Virgo cluster is used to derive a relation between stellar velocity dispersion and luminosity. L is found to approximately equal sigma to the nth power, where n = 3.2 + or - 0.2 over two decades of luminosity, with a scatter of 0.38 mag. The possibility of curvature in the relation or rotational support of the galaxies is examined, and a derivation of a law of slope 3 is presented and compared with the derivation for a slope of 4. It is concluded that the lack of increased scatter as the points deviate from a slope of 4 implies that rotation is not important.