The critical problem is considered for finite cylindrical reactors. By applying the concept embodied in the asymptotic solution of the mono-energetic transport equation, it is possible to reduce the two-dimensional transport equation to an axially and radi-ally reduced one-dimensional form. In essence, the idea is to approximate one of the two space dimensions by the assumption of the asymptotic distribution, and to extend the reactor medium and the asymptotic distribution toward infinity. The resulting reduced equation is solved by making use of the singular eigenfunction expansion method introduced by Case. It is found that the two-dimensional flux distribution can be obtained with high accuracy from the reduced equation, excluding exceptional cases of extremely poor conditions.
Numerical results are presented for a wide range of reactor multiplication factor, and are compared with the results obtained by the variational method. It is found that there is only a small contribution of the boundary transient term brought to the axially and radially reduced problem. The error introduced in reducing the space dimension can be evaluated by the perturbation theory. Numerical results for various sizes of reactor show that the perturbation is not very large, and that it does not bring marked changes to the eigenvalues of the transport operators.

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An experimental study has been undertaken on the frequency of presented by the undulations occurring on the surface of a falling liquid film. The configuration of the film surface was observed by measuring the changes in the film thickness by means of a capacitometer. The flow regime was in the range of turbulent flow region, in which the undulations occur prominently and travel down along with the fluid film. The undulations proceed downward in an almost fixed pattern. The frequency of the passage of crests observed from a fixed point was evaluated from power spectral analysis to be about 20--30 Hz, and this value changed very little with the Reynolds number and with heat flux applied to the falling liquid film. It is shown that this constancy of observed frequency is related to the fact that the large undulations move at the same velocity as the bulk of the fluid film, and that the speed of propagation is corresponding to a group velocity for ripples on the film surface.

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A theoretical study was carried out on the time-dependent neutron spectrum in a small graphite assembly into which the neutron pulses were injected through a premoderator layer of polyethylene. Numerical analyses were performed by means of the usual time-step method, as well as by the spatial mode expansion time-step and two-region difference equation methods.
It was verified that addition of the pre-moderator does not substantially affect the space-time-dependent spectral behavior of neutrons in a graphite system of dimensions adopted in current experimental arrangements.
A strong space dependence of the time-dependent spectra was observed in the form of spectral hardening in increasing distance from source, which was termed "propagation hardening". The space-time-dependence and neutron trapping at Bragg peak energies appearing on the measured spectra were well reproduced by both the spatial mode expansion time-step and two-region calculations.

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The U-Mo-C system has been studied to supplement the hitherto available phase-diagram data and to deduce therefrom the thermodynamic property of UMoC_1.7 and UMoC₂. It is shown that a peritectic four-phase reaction takes place : UC+Mo⇔UMoC_1.7+liquid, at 1, 830°±30°C. The phase relations between orthorhombic UMoC₂ and mono-clinic UMoC_1.7 may be defined by UMoC_1.7⇔UMoC₂+liquid, which will occur at some temperature between 2, 200° and 2, 350°C, the reported melting point of UMoC₂. Liquidus projection for the U-Mo-C system is presented on the basis of these results and from data found in literature. The free energy equations for the formation of UMoC_1.7 and UMoC₂ are respectively estimated to be ΔG°_f(UMoC_1.7)=-40, 350-0.69T cal/mol and ΔG°_f(UMoC₂)= -46, 360-0.69T cal/mol, both in the temperature range 2982, 100 K.

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The rates of absorption of iodine vapor contained in air by aqueous sodium hydroxide solutions were measured at 298 K using a liquid jet column that established a contacting time between 0.006 and 0.025 sec.
The overall mass transfer coefficient varies in a complex manner depending on the concentrations of both iodine in the feed gas and sodium hydroxide in the absorbent solution. This results from the variation of the rate controlling step in the chemical reactions taking place in the liquid film. It was concluded from the present experimental work that the mechanism of iodine vapor absorption is as follows : Iodine in air dissolves into the aqueous phase through the gas liquid interface in conformity with Henry's law. This iodine in the aqueous phase forms hypoiodous acid and iodide ions through base catalytic hydrolysis, and then the resulting iodide ions react with the iodine to generate tri-iodide ions. The instantaneous dissociation reactions of water and of sodium hydroxide have to be taken into account. Iodate slowly forms from the hypoiodous acid, but this reaction has no influence upon the overall absorption rate under the conditions prevailing in the present instance.

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With the object of gaining information on the behavior of radioactive corrosion products such as ⁵⁴Mn, ⁶⁵Zn and ¹²⁴Sb in relation with oxygen concentration in liquid sodium-stainless steel systems, deposition experiments were undertaken with use made of stainless steel capsules, each containing 20 g of sodium and a trace amount of one of these radioisotopes.
Each capsule was set vertically and subjected to a steep temperature gradient, descending toward the bottom, for 700 hr of run to let the sodium oxide diffuse through the liquid sodium and settle on the bottom. The oxygen concentration in the sodium was controlled by varying the bottom temperature. The concentrations of the radioisotope at different radial positions on various cross sections along the capsule axis were determined on sodium samples dissected from the capsule after quick solidification of the sodium by chilling.The values of the activation energy of deposition were determined for each radioisotope from partition coefficients, defined as the ratio of specific radioactivity between that of the stainless steel surfaces and that in the liquid sodium. Manganese deposition involves precipitation in the lower temperature region, and adsorption-associated loosely with oxygen in the sodium-in the higher temperatures. Zinc adsorption was observed on the wall surface only when it had been previously treated with sodium before dissolution of the radioisotope in the sodium. Antimony deposition is attributable to coprecipitation with sodium oxide.

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