Wiener's theory of least square optimization with quadratic constraint has been applied to reactor control systems design. Stochastic and deterministic cases are treated here, taking white disturbance of reactivity and step reference input as examples. The mean square and integral square errors have been minimized subject to the constraint on the reactivity rate controlled externally for white noise and step input respectively. The reactor transfer function is based on linear approximation for single-group delayed neutrons with no feedback of reactivity.
Numerical calculations have been performed for effective neutron lifetimes in the range from 10^-3 to 10^-5 sec, and the resulting optimized controllers are physically realizable. Analytical results with an analog computer indicate - in the case of l*=10^-4 sec - that the transient responses of the optimized control systems are excellent for step inputs and that a considerable reduction in the output fluctuation is obtainable for white noise, granted a large peak of reactivity rate with a small value of reactivity.

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Thermal neutron flux perturbation due to two or three adjacent detectors in water has been experimentally investigated. The detectors employed were gold foils and pins. The results have been compared with theoretical values calculated on the basis of Dalton's theory. The comparison gives fairly good agreement.

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More than 400 pieces of test sections - flat plates made of various metals and alloys - were placed in saturated water under atmospheric pressure and heated to physical destruction by passing electric current directly through them.
Several non-hydrodynamic parameters have marked effect upon the critical beat flux, which indicates that purely hydrodynamic theories are not directly applicable to general prediction of the critical heat flux.
The critical heat flux data was found to be well correlated with the heat capacity per unit surface area of the test section: the critical heat flux is reduced with decrease of this parameter, while with increasing parameter it approaches a certain asymptotic value.
The fluctuation of surface temperature due to alternate contact with vapor and liquid was calculated by the proposed model, and the trend of dryout duration was estimated from the critical heat flux data.

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A basic study was performed on the mass spectrometric determination of burnup for a UO₂ specimen irradiated in the HFR. It has been found that:
(1) By isotopic analysis of uranium, the contribution to burnup provided by the specimen through fissioning of ²³⁵U was determined to be 4, 370 MWD/T. The loss of ²³⁵U through neutron capture was distinguished by the production of ²³⁶U.
(2) The contribution to burnup of the specimen by fissioning of ²³⁹Pu was determined to be 3, 610 MWD/T from the excess formation of fission products such as ⁹³Zr, based on the known number of ²³⁵U fissions.
(3) The total burnup of the UO₂ specimen was taken to be 7, 980 MWD/T, since no other isotopes of plutonium were identified.

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The electron microscope has been used to observe the behavior of He gas bubbles in cold-worked Al-Li alloys upon post-irradiation heating. The bubbles appeared occasionally along the grain boundary in the A1-2.7w/0 Li specimen irradiated to 4.1×10¹⁹n/cm2 and then heated to about 300°C. Upon beating to higher temperatures, up to 450°C, the bubbles in the specimen grew along with the gradual growth of the recrystallized grains. When the bubbles reached sizes of 0.3-0.6μ, upon beating to 500°C, the grain boundaries migrated, leaving the bubbles detached from them. In the Al-0.4w/0 Li specimen, the bubbles migrated out of the specimen surface, along with the grain boundary, upon heating to the temperatures above 450°C. The grain sizes of the irradiated Al-2.7w/0Li specimen heated for 1 hr to 450°C were smaller than in unirradiated specimen heated for 1 hr to 400°C.
In the displacement of grain boundary caused by grain growth, the gas bubbles are swept together to form larger bubbles until they reach a certain critical size. And as the bubbles become larger, they detach from the moving boundary. The bubbles impede the grain boundary movement, but do not suppress it completely. The bubbles found on the grain boundaries differed in shape from the bubbles that had grown in the grain interior.

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Sintered UO₂ pellets irradiated at high temperature to a burnup of 2, 700 MWD/T-UO₂ were studied by replica electron microscopy. The as-irradiated pellet surfaces were covered by a thin layer easily soluble in dilute acid. This layer apparently was deposited as a sublimate during irradiation. The etched surfaces of the irradiated specimens were uniformly dispersed with flat circular domes about 1μ in diameter, constituted of precipitates resistant to etching solution, apparently a mixture of fission products and UO₂. On the surface of each dome were several "sprout" precipitates 0.1 to 0.3μ in diameter, and almost immune to chemical etchant.

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The maximum numerical values of the Doppler coefficient of a single Breit Wigner resonance and the dilutions for which the stationary values occur have been found as a function of temperature. The results are tabulated in terms of parameters which are independent of the particular resonance and model.

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