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Investigations on problems of the type which arise in the control of switched electrical networks are reported. The main results concern the algebraic structure and stochastic aspects of these systems. Future reports will contain more detailed applications of these results to engineering studies.
A physical model for a thruster discharge was developed, consisting of a spatially diverging plasma sustained electrically between a small ring cathode and a larger ring anode in a cylindrical chamber with an axial magnetic field. The associated boundary-value problem for the coupled partial differential equations with mixed boundary conditions, which describe the electric potential and the plasma velocity fields, was solved in closed form. By means of quantum-mechanical perturbation theory, a formula for the number S(E) of atoms sputtered on the average by an ion of energy E was derived from first principles. The boundary-value problem describing the diffusion of the sputtered atoms through the surrounding rarefied electron-ion plasma to the system surfaces of ion propulsion systems was formulated and treated analytically. It is shown that outer boundary-value problems of this type lead to a complex integral equation, which requires numerical resolution.
The spatial density of impact craters larger than 100 m on the four great volcanic shields in the Tharsis region is analyzed, assuming that each observed crater population represents the total formed since the local surface was last renewed. Previous investigations of this type are reviewed, problems encountered in those studies are discussed, and an attempt is made to overcome these problems by applying explicit criteria for the separation of craters smaller than approximately 1 km in diameter according to their origin and by ignoring larger craters. Relative ages are determined by comparing crater populations at a common diameter, and such comparisons are carried out for six populations on Arsia Mons, one population on Pavonis Mons, several craters on Ascraeus Mons, and two populations on Olympus Mons. The results, presented in terms of 'crater ages', indicate that most dated surfaces on the great shields range in age from 0.5 to 1.2 billion years, that the eruption patterns of the volcanoes are similar to those of the Hawaiian basaltic shields, and that the most frequently renewed surfaces are on the middle-to-lower flanks as well as within the summit calderas. The youngest surfaces are estimated to date from the period between 0.5 billion years ago and the present; the oldest dated surfaces are shown to suggest that the volcanoes had attained essentially their present sizes over 1 billion years ago.
Reports describing various types of communication problems are presented along with summaries dealing with judgment and decision making. Concerns relating to the ground proximity warning system are summarized and several examples of true terrain proximity warnings are provided. An analytic study of reports relating to profile descents was performed. Problems were found to be associated with charting and graphic presentation of the descents, with lack of uniformity of the descent procedures among facilities using them, and with the flight crew workload engendered by profile descents, particularly when additional requirements are interposed by air traffic control during the execution of the profiles. A selection of alert bulletins and responses to them were reviewed.
DBAS 1 computer program provides analyst with simple algorithms for exact rapid solutions of systems with planar, cylindrical, or spherical interfaces. Conventional solutions are complex and present convergence problems. Two algorithm types are figured for each geometry; one converges rapidly for short and the other for long diffusion times. DBAS 1 is written in FORTRAN IV for batch execution.
A cryogenic wind tunnel is based on the twofold idea of lowering drive power and increasing Reynolds number by operating with nitrogen near its boiling point. There are two possible types of condensation problems involved in this mode of wind tunnel operation. They concern the expansion from the nozzle supply to the test section at relatively low cooling rates, and secondly the expansion around models in the test section. This secondary expansion involves higher cooling rates and shorter time scales. In addition to these two condensation problems it is not certain what purity of nitrogen can be achieved in a large facility. Therefore, one cannot rule out condensation processes other than those of homogeneous nucleation.
Bonded and bolted designs are presented for each of four major attachment types. Prepreg processing problems are discussed and quality control data are given for lots 2W4604, 2W4632 and 2W4643. Preliminary design allowables test results for tension tests and compression tests of laminates are included. The final small specimen test matrix is defined and the configuration of symmetric step-lap joint specimens are shown. Finite element modeling studies of a double lap joint were performed to evaluate the number of elements required through the adhesive thickness to assess effects of various joint parameters on stress distributions. Results of finite element analyses assessing the effect of an adhesive fillet on the stress distribution in a double lap joint are examined.
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
A computational technique is developed that is suitable for performing preliminary design aeroelastic and structural dynamic analyses of large aspect ratio lifting surfaces. The method proves to be quite general and can be adapted to solving various two point boundary value problems. The solution method, which is applicable to both fixed and rotating wing configurations, is based upon a formulation of the structural equilibrium equations in terms of a hybrid state vector containing generalized force and displacement variables. A mixed variational formulation is presented that conveniently yields a useful form for these state vector differential equations. Solutions to these equations are obtained by employing an integrating matrix method. The application of an integrating matrix provides a discretization of the differential equations that only requires solutions of standard linear matrix systems. It is demonstrated that matrix partitioning can be used to reduce the order of the required solutions. Results are presented for several example problems in structural dynamics and aeroelasticity to verify the technique and to demonstrate its use. These problems examine various types of loading and boundary conditions and include aeroelastic analyses of lifting surfaces constructed from anisotropic composite materials.
It is noted that for the years 1970-1972 global ozone may be calculated by using extrapolated values for polar night regions and then deriving direct daily averages. After 1972, regions larger than the polar night often lack data, increasing the error of extrapolation. It is shown that problems of this type can be overcome by using zonal averages, calculating the annual wave through harmonic analysis, and subtracting the annual wave so derived. Linear fits can then be employed to obtain long-term zonal changes and yearly zonal averages. Global results can be derived in the form of an area-weighted average of the zonal results. It is pointed out that no values need be assumed for ozone when data are lacking. The uncertainty from this procedure is estimated at + or - 0.4% of the yearly average. However, other uncertainties in the backscatter ultraviolet experiment may be larger.
The use of infrared spectroscopy in astronomy has increased dramatically in the past ten years. The broad design considerations are discussed in terms of wavelength coverage and resolution. Three rough resolution ranges, lambda/Delta lambda of approximately 100, 1000 and 10,000, are identified in which various types of astronomical problems can be studied. Numerous existing systems are briefly discussed and references are given to more complete descriptions.
Laser holographic interferometry is being applied to many different types of aerodynamics problems. These include two and three dimensional flows in wind tunnels, ballistic ranges, rotor test chambers and turbine facilities. Density over a large field is measured and velocity, pressure, and mach number can be deduced.
The thermoelectric properties alloys of the nickel-base, iron-base, and cobalt-base groups containing from 1% to 25% 106 chromium were compared and correlated with the following material characteristics: atomic percent of the principle alloy constituent; ratio of concentration of two constituents; alloy physical property (electrical resistivity); alloy phase structure (percent precipitate or percent hardener content); alloy electronic structure (electron concentration). For solid-solution-type alloys the most consistent correlation was obtained with electron concentration, for precipitation-hardenable alloys of the nickel-base superalloy group, the thermoelectric potential correlated with hardener content in the alloy structure. For solid-solution-type alloys, no problems were found with thermoelectric stability to 1000; for precipitation-hardenable alloys, thermoelectric stability was dependent on phase stability. The effects of the compositional range of alloy constituents on temperature measurement uncertainty are discussed.
The 20-W S-band power amplifiers aboard the GOES E and F spacecraft exemplify the problems that type-IIa diamond heat sinks have been developed to solve, including the requirement for junction temperatures to be kept below 125 C. Diamond heat sinks allow high power S-band semiconductors to operate at a flange temperature of 70 C without exceeding the stipulated maximum junction temperature. Type-IIA diamond, which is an excellent electrical insulator, possesses a thermal conductivity four times better than pure copper at 100 C, and outperforms BeO by an even greater margin. Higher costs are offset by high reliability. Attention is presently given to the results of tests conducted by the NASA Goddard Space Flight Center.
The threshold energy problem of exotic type interactions is discussed on the basis of available information from the Chacaltaya emulsion chamber experiment. The genetic hypothesis is proposed as a working hypothesis to explain the discrepancy seen in cosmic ray study and CERN p bar -p collider experiments.
A computer program designed to simulate and improve multilevel optimization techniques is described. By using simple analytic functions to represent complex engineering analyses, the simulator can generate and test a large variety of multilevel decomposition strategies in a relatively short time. This type of research is an essential step toward routine optimization of large aerospace systems. The paper discusses the types of optimization problems handled by the simulator and gives input and output listings and plots for a sample problem. It also describes multilevel implementation techniques which have value beyond the present computer program. Thus, this document serves as a user's manual for the simulator and as a guide for building future multilevel optimization applications.
A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.
A diffusion-reaction model with time-dependent reactivity is formulated and applied to unimolecular reactions. The model is solved exactly numerically and approximately analytically for the unreacted fraction as a function of time. It is shown that the approximate analytical solution is valid even when the system is far from equilibrium, and when the reactivity probability is more complicated than a square-wave function of time. A discussion is also given of an approach to problems of this type using a stochastically fluctuating reactivity, and the first-passage time for a particular example is derived.