The finite element method is applied to the spatial variables of multi-group neutrontransport equation in the two-dimensional cylindrical (r, z) geometry. The equation is discretized using regular rectangular subregions in the (r, z) plane. The discontinuous method with bilinear or biquadratic Lagrange's interpolating polynomials as basis func-tions is incorporated into a computer code FEMRZ. Here, the angular fluxes are allowed to be discontinuous across the subregion boundaries.
Some numerical calculations have been performed and the results indicated that, inthe case of biquadratic approximation, the solutions are sufficiently accurate and numer-ically stable even for coarse meshes. The results are also compared with those obtained by a diamond difference S_n code TWOTRAN-II. The merits of the discontinuous method are demonstrated through the numerical studies.

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Revised December 13, 1976To examine the stability of the natural mode. the followinv method is develooed. Atfirst, the characteristic equation is derived by applying the finite element method to the basic equation for the natural mode. Then, the Nyquist stability criterion is applied to this equation for the present purpose.
Using this method, the lowest threshold values of the moderator temperature coeffi-cient are evaluated by trial and error for the azimuthal modes : 1, cos θ, cos 29, cos 3θ. Thereupon these results are compared with those of the previous method, which used the flux shape mode as a basis of modal expansion. Both agreed well. Based on these results, we may conclude that the previous analysis gives a good approximation for the lowest threshold value of an azimuthal mode, although a more extensive study is needed for a reactor of different composition.
We can examine the stability of the natural mode by this method without evaluatingthe actual shape of radial modes, but we cannot thereby distinguish their relative stabil-ities

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Characteristics of acoustic signal produced by sodium-water reaction due to steaminjection and by Ar gas injection into sodium were experimentally investigated. Acoustic signal was measured by using Kistler 808A and 815A5 accelerometers. Root mean square (RMS) measurements and frequency analysis of the signal were conducted.
The RMS measurements could detect a small water leakage into sodium, as small as0.07 g/sec, in the present loop. The peaks in a frequency spectrum were caused by the natural vibration of a rod on which the acoustic transducer was mounted.
The RMS was approximately proportional to the one-third power of the steam leakrate and increased to some extent with the ambient sodium temperature. RMS values, both for sodium-water reaction and Ar gas injection, were about the same order of magnitude, when the data were plotted against the volumetric flow rates of steam and Ar gas.

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A separative power of a separating process δU is an increase of a value of an isotopemixture which passes through the process, and is calculated by use of a value function V(R) (R: abundance ratio). The separative power, however, involves various inconsisten-cies especially for an asymmetric process. To remove these inconsistencies, concepts of a "separative power with respect to desired material δU_b" and that δU_a with respect to undesired material are introduced. Two functional forms, having been considered to be the separative power (with respect to mixture) per unit flow rate δU/(G_a+G)_b, corre-spond to separative powers per unit flow of desired and undesired material δUb/Co, δUb/Ga, respectively :
δU_b/G_b={α(β-1)In α-(α-1)In β}/(αβ-1)=ψ_b(α, β),
δU_a/G_a={β(α-1)In β-(β-1)In α}/(αβ-1)=ψ_a(α, β),
where a and β are heads and tails separation factors. Value functions which give δU_b or δU_a la are independent of separation factors : V_b(R) =1n R, V_a(R) = -ln R, so inconsisten-cies encountered by δU never occur. δU_b or δU_a of a single element and of a cascade are obtained by the same functional form, and an additivity of separative power holds both for the desired and undesired material, respectively.
Moreover, the separative power δU with respect to mixture is interpreted with δU_b, and δU_a to elucidate the origines of inconsistencies.

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A fundamental equation for chromatography is derived starting from a very simpleconcept that the chromatographic movement of species can be expressed as the sum of the movement caused by the external force and the movement caused by the internal concentration gradient and its transformations into appropriate forms are discussed in the cases of ion exchange (or gas) chromatography and ionic migration, without or with a counterflow.
By solving the fundamental equation, making appropriate assumptions, a comprehen-sive expression which describes the concentration profile is derived for two-isotope systems in any kind of chromatography.

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The pressure recovery of supersonic flow at very low density was studied in a vane-island type diffuser for gas centrifuge.
A tester of diffuser with a rapidly rotating cylinder was used in experiments. Wallstatic pressures were measured at many points in the diffuser to observe the static pressure distribution. The change of pressure distribution with back pressure and the effect of flow rate were investigated. Pressure distribution showed that the pressure recovery occurred in the converging section. The pressure ratio increased linearly with the back pressure in this experimental range and the effect of flow rate was not observed.
A numerical analysis of the pressure recovery in the channel section of the diffuserwas made by applying the finite difference method to the slender-channel equations. The pressure distribution obtained in experiments could be explained as a result of supersonic compression with reverse flow.

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A separation cell embodying two kinds of membrane-porous and nonporous, i.e.differing in gas permeability-has a separation factor higher than possible with a con-ventional separation cell with a single kind of membrane. The performance of such separation cells and of cascades constituted thereof are analyzed theoretically and meas-ured experimentally for different conditions of operation, to determine the applicability of the concept to the separation of rare gases from gaseous waste out of nuclear plants.
Theoretical considerations indicate that, in a cascade composed of symmetricseparation cells, the separation performance can be improved by recycling part of the effluent from a cell back through the same cell (recycling cascade). It is shown that its performance is better than with the arrangement of diverting another effluent several stages upstream. With the recycling cascade, the symmetric separation recycling rate is determined by the depletion separation and enrichment separation factors relevant to the respective membranes.
The separation performance of a 9-stage recycling cascade composed of separationcells with silicone rubber tubular membranes and cellulose acetate tubular membranes is derived for a case of Kr separation from N2-Kr mixture. The experimental data coincide well with the analytical results.
From both the experimental and the analytical results, it is found that the attainable separation coefficient per stage of the cascade comes to average approximately 0.97.

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As a practical variance reduction technique applicable to Monte Carlo shielding cal-culations, the present article shows a new simple biased sampling technique on particle flight directions. Scattered particles not directed towards the detector positions are killed if they are not so important, that is, if the particle weights are sufficiently small compared to the source weight. In this way, we can reduce the sample size required for obtaining an accurate estimate for the detector response.
The present technique was incorporated into the multigroup neutron and r-raytransport code MORSE, and sample calculations were performed on spherical fast neutron systems. The results have shown that this biased technique is effective for dealing with neutron multiplication as well as neutron transmission problems. The neutron flux or the effective multiplication factor of a nuclear reactor is estimated more accurately than from the method of path-length stretching with about the same computation time. In addition, it is shown that the flight-direction biasing can further effectively be used by combining it with other variance reduction techniques.

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