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A class of finite-state, finite-memory stochastic control problems is considered. A minimum principle is derived. Signaling strategies are defined and related to the necessary conditions of the minimum principle. Min-H algorithms for the problem are described.
Hearn's (1975) models of the energy balance and mass loss of stellar coronae, based on a 'minimum flux corona' concept, are critically examined. First, it is shown that the neglect of the relevant length scales for coronal temperature variation leads to an inconsistent computation of the total energy flux F. The stability arguments upon which the minimum flux concept is based are shown to be fallacious. Errors in the computation of the stellar wind contribution to the energy budget are identified. Finally we criticize Hearn's (1977) suggestion that the model, with a value of the thermal conductivity modified by the magnetic field, can explain the difference between solar coronal holes and quiet coronal regions.
A theoretical method was developed for determining the optimum span load distribution for minimum induced drag for subsonic nonplanar configurations. The undistorted wing wake is assumed to have piecewise linear variation of shed vortex sheet strength, resulting in a quadratic variation of bound circulation and span load. The optimum loading is obtained either through a direct technique, whereby derivatives of the drag expression are calculated analytically in terms of the unknown wake vortex sheet strengths. Both techniques agree well with each other and with available exact solutions for minimum induced drag.
The effect of the external wind on the quality of the flow in the test section was studied. The flow quality achievable with the complex treatment as well as that with the planned minimum treatment system is discussed. A scale model coupled with on site wind measurements demonstrated that the minimum treatment selected can provide adequate testing capabilities in the presence of the prevailing local winds, and that test programs will not be significantly affected by adverse wind effects on the test section flow quality.
The framework in which minimum-commitment analyses of creep-rupture data can be implemented is outlined. The approach is termed the focal point convergence method (FPCM) because the basic parameter A, also known as stability factor, is geometrically the (imaginary) focal point of convergence of all isothermals when extended to the very long or very short times necessary for such convergence to occur. The method can be implemented either by manual-graphical analysis or by computer code. The method is illustrated in detail for the nickel-base alloy Astroloy, as well as for steels, other nickel-base alloys, and aluminum alloys. The minimum-commitment concept is extended to the analysis of creep-rupture data where each isothermal is generated by an oblique translation of the 'master curve' when plotted on log rupture time and log stress axes. The oblique translation method uses the same types of functions in the FPCM. Approaches for treating multiheats on the basis of the FPCM are discussed in detail.
Families of zero-mass-loss coronal models based on the minimum-flux prescription of Hearn (1975), in which bound-bound, bound-free, and free-free radiative processes with their differing emissivity vs. temperature laws are included, have been computed. These models are applied to the case of white-dwarf envelopes of pure hydrogen or helium, and the results are expressed as relationships between the required total energy flux, the coronal base pressure, and its temperature. The soft X-ray detection of Sirius by the ANS group is discussed. If all the X-ray flux is ascribed to a minimum-flux hydrogen corona surrounding the white dwarf Sirius B, it must have a temperature of 1.6 + or -0.3 million K and a base pressure of 110,000 + or - 40,000 dyne/sq cm. The surface energy flux needed to heat such a corona is (9 + or - 5) x 10 to the 10th erg/sq cm per sec.
An analysis and computer program which optimizes laser turret geometry to obtain minimum phase distortion is described. Phase distortion due to compressible, inviscid flow over small perturbation laser turrets in subsonic or supersonic flow is calculated. The turret shape is determined by a two dimensional Fourier series; in a similar manner, the flow properties are given by a Fourier series. Phase distortion is calcualted for propagation at serveral combinations of elevation and azimuth angles. A sum is formed from the set of values, and this sum becomes the objective function for an optimization computer program. The shape of the turret is varied to provide minimum phase distortion.
Kaula's minimum energy approach was extended to include the nonhydrostatic gravitational potential energy and the density perturbation field was obtained to degree and order eight. The depth profiles for the density perturbation show a stratification with density excesses and deficiencies alternating with depth. The addition of the gravitational potential energy in the minimization process does not change significantly the conclusions based on results for the minimum shear strain energy case, concerning the inability of the mantle to withstand the lateral loading elastically.
The reply to the criticisms of the minimum flux theory is discussed. These criticisms are correct in substance, as well as in detail. Counter arguments that the minimum flux corona theory is untenable, because of errors in its formulation, are presented.
Condensation effects are responsible for the minimum operating temperatures of cryogenic wind tunnels at total pressures up to about 9 atmospheres. The two primary modes of condensation homogeneous nucleation and heterogeneous nucleation and the conditions with which either may limit minimum operating temperatures are reveiwed. Previous hypersonic and supersonic condensation data are reviewed as are data taken in the nitrogen gas, Langley 0.3 Meter Transonic Cryogenic Tunnel. Analysis of data in the 0.3 m tunnel suggests that the onset of homogenous nucleation may be approximated by an analysis by sivier and that the onset of heterogeneous nucleation is only apparent just below free stream saturation. Extension of the results from the 0.3 m tunnel to other nitrogen gas cryogenic tunnels is discussed and is shown to depend on length scales, purity of the liquid nitrogen injected for cooling, number of particulates in the flow, and the extent to which the injected liquid nitrogen is evaporated.
The problem of minimum fuel airplane trajectories from arbitrary initial states to be fixed final state is considered. There are four state variables (two position coordinates, heading, and constrained velocity) and two constrained controls (thrust and bank angle). The fuel optimality of circular and straight line flightpaths is examined. Representative extremals (trajectories satisfying the necessary conditions of the minimum principle) of various types are computed and used to evaluate trajectories generated by an on line algorithm. Attention is paid to the existence of Darboux points (beyond which an extremal ceases to be globally optimal). One fuel flow rate model includes a term quadratic in thrust; hence, the optimal thrust is continuous and nonsingular. The other fuel flow rate model is linear in thrust, and consequently the optimal thrust is discontinuous and singular.
Fifty-seven measurements of the minimum lubricant film separating the elastohydrodynamically lubricated point contact of a steel crowned roller and a flat sapphire disk were made by an optical interferometry technique. The data collected were used to evaluate the Hamrock and Dowson minimum EHD film thickness model over a practical range of contact ellipticity ratio where the major axis of the contact ellipse is aligned both parallel and perpendicular to the direction of motion. A statistical analysis of the measured film thickness data showed that on the average the experimental data averaged 30 percent greater film thickness than the Hamrock and Dowson model predicts.
Spectrophotometric observations of AM Her during its 1980 minimum are reported. The M dwarf in the system is revealed by its TiO bands and domination of the spectrum longward of 6000 A. The blue region of the spectrum reveals a hot, magnetic white dwarf with Zeeman-split hydrogen absorption lines, and emission lines of H, He I, and Fe II. The inferred surface magnetic field of roughly 10 to the 7th gauss permits the presence of an accretion disk in the system. Velocities and intensities of the H emission lines indicate an origin in the X-ray-heated atmosphere of the M dwarf. The continuum light variation in the red appears to result from the heating of the secondary, while the blue light variation probably results from the rotation of the bright spot at the white dwarf's magnetic pole. A self-consistent geometrical model is proposed, in which the minimum state is interpreted as a lull in the rate of accretion onto the white dwarf.
Five sounding rocket experiments conducted between December 1972 and March 1977, a period spanning solar minimum between cycles 20 and 21, provide full disc solar irradiance data in the spectral range 120-190 nm. The five measurements have been combined to give a solar minimum reference table. This spectrum is compared with other measurements obtained during the same time period. A table of intensities for the strong emission lines at wavelengths between 120 and 190 nm is presented.
The possibility that the strong heating produced at temperature-minimum levels during solar flares is due to resistive dissipation of Alfven waves generated by the primary energy release process in the corona is studied. It is shown how, for suitable parameters, these waves can carry their energy essentially undamped into the temperature-minimum layers and can then produce a degree of heating consistent with observations.
A new design was developed for the Space Shuttle Transition Phase Digital Autopilot to reduce the impact of large measurement uncertainties in the rate signal during attitude control. The signal source, which was dictated by early computer constraints, is characterized by large quantization, noise, bias, and transport lag which produce a measurement uncertainty larger than the minimum impulse rate change. To ensure convergence to a minimum impulse limit cycle, the design employed bias and transport lag compensation and a switching logic with hysteresis, rate deadzone, and 'walking' switching line. The design background, the rate measurement uncertainties, and the design solution are documented.
A new series of high resolution pictures of the sun has been obtained during the second flight of the Transition Region Camera which occurred on September 23, 1980. The qualitative analysis of the results indicates that a substantial portion of the solar surface at the temperature minimum radiates in non-magnetic regions and from features below 1 arcsec in size. Wave patterns are observed on the 160 nm temperature minimum pictures. They are absent on the Lyman alpha pictures. Their physical characteristics are compatible with those of gravitational and acoustic waves generated by exploding granules.
Closed-form analytical solutions for the design equations of a minimum-mass reactor for a two-winding voltage-or-current step-up converter are derived. A quantitative relationship between the three parameters - minimum total reactor mass, maximum output power, and switching frequency - is extracted from these analytical solutions. The validity of the closed-form solution is verified by a numerical minimization procedure. A computer-aided design procedure using commercially available toroidal cores and magnet wires is also used to examine how the results from practical designs follow the predictions of the analytical solutions.