Reaction Between K2O and Al2O3-SiO2 Refractories as Related to Blast-Furnace Linings

An examination was conducted to determine the mechanism of peeling of fire-clay brick in the low-temperature region of a blast furnace where 3 to 10% K₂O is the principal contaminant. In laboratory tests, as-received high-duty and superduty fire-clay brick and 70% alumina brick treated with KCl-K₂CO₃ mixtures showed no peeling at a temperature of 1600°F. Cracks were found in high-duty brick that were treated with KCN at 1500°F. under partially reducing conditions. X-ray diffraction studies of mixtures of crushed brick and K₂CO₃ indicated the formation of leucite (K₂O.Al₂O₃.4SiO₂) and kaliophilite (K₂O.-Al₂O₃.2SiO₂) at temperatures below 1700°F. These latter data, confirmed by specimens from used blast-furnace linings, showed that silica is the first constituent attacked by alkali. Since the formation of leucite and kaliophilite in fire-clay brick is the probable cause of peeling, the increased reaction of silica, in a dense Al₂O₃.SiO₂ refractory of higher silica content than fire-clay brick, should confine the alkali attack to the surface of the brick in low-temperature applications.     

Stability of Inorganic Fluorine-Bearing Compounds: II, Complex Fluorides

The thermal stabilities of some alkali and alkaline-earth fluosilicates and cuspidine when heated in atmospheres of dry and moist air were investigated. IN the decomposition of K₂SiF₆ the compound K₃SiF₇ was noted. The alkali and alkaline-earth fluosilicates lose SiF₄ whereas cuspidine does not. In moist air atmospheres, α-cristobalite is found among the residual products from the fluosilicates of sodium and potassium. K₂TiF₆ hydrolyzes, first at low temperatures to an intermediate series of compounds and then at higher temperatures to fluorine-free potassium titanates. Both K₂ZrF₆ and Na₅Zr₂FI₃ hydrolyze to ZrO₂ and the alkali fluoride by way of an intermediate heptafluoride (M₃ZrF₇).     

Optimal feedback control of saturating systems

Feedback synthesis of optimal saturating controls for linear systems is considered. An integral cost is introduced, with integrand comprised of quadratic and certain non-quadratic functions of the state. The latter (non-quadratic) functions are chosen so as to regularize the problem in the sense that an explicit feedback solution, of particularly simple form, is obtained. Finite and semi-infinite time horizon formulations are treated and several examples are presented.     

Gaussian sum approximation for non-linear fixed-point prediction

Fixed-point prediction is the estimation of the state of a system at a future fixed time based on a noisy measurement with sequence length that increases with current time. A recursive algorithm for generating fixed-point prediction is given using the integrated form of the chain rule. For non-linear systems no general filter solution exists ; thus a gaussian sum approximation is developed. The method provides a numerical approximation for the time-dependant a posteriori density from which a filter can be generated.     

Entanglement of orbital angular momentum for the signal and idler beams in parametric down-conversion

We calculate the anticipated correlation between measurements of the orbital angular momentum of the signal and idler beams for parametric down-conversion. These calculations apply to the experiments where the orbital angular momentum state is measured by the use of computer-generated holograms. Displacement of these holograms with respect to the beam axis allows the measurement of superpositions of Laguerre—Gaussian modes. The correlations between such superposition modes of the signal and idler beams show their entanglement and could be used for Bell-type tests of nonlocality.     

Analysis of robot positioning error

Positioning errors of robots used for material handling and assembly can be sufficiently large to cause problems. These errors are due to imperfect repeatability of the robots, and their effects can be ameliorated or exacerbated by tolerances on the workpieces and on the jigs and fixtures. In this paper, a model for characterizing the positioning errors of robots is developed. A statistical analysis of positioning error data is performed to make inferences about the stochastic nature of the robotic system. The basic issue is whether the positioning errors of the robot are state dependent or state invariant.     

Optimal sensitivity theory for multivariate distributed plants

In this note we generalized the results of Foias and Tannenbaum (1986 a) and Foias et al. (1987) on optimal sensitivity minimization to a much broader class of distributed plants. We relate our results to certain kinds of Hankel norm approximation problems that frequently appear in control engineering applications.