Final report for a grant contract documenting information about the scope of the project and results.

"An algorithm for the generation of feasible schedules and the computation of the completion times of the job operations of feasible schedule is presented. Using this algorithm, the distribution of schedule times over the set of feasible schedule—or a subset of feasible schedules—was determined for technological orderings that could occur in a general machine shop. These distributions are found to be approximately normal. Biasing techniques corresponding to “first come first serve,” random choice of jobs ready at each machine and combinations of these two extremes were used to compute distributions of schedule times."

"Acoustic energy generated by mechanical or electrical signals and its effect on pool boiling of isopropanol were studied. Daring the course of the investigation, a method was devised to determine the amount of heat-transfer surface wetted by the boiling isopropanol. Plots of heat flux versus temperature difference for each frequency showed that the acoustic energy did not significantly affect the heat flux at burnout, but slightly increased the critical temperature difference. No general effect of frequency variation was found even at the frequencies of the "boiling songs" of isopropanol. The over- all effect of the acoustic energy was to disturb the vapor tending te coat the heat transfer surface. This was most evident from the absence of film boiling even at temperature differences far above the critical temperature difference. The application of alternating current to the boiling system gives promise of a self-regulating method to increase boiling heat transfer when required, and is the most significant new finding of this investigation. Two pertinent Russian papers were translated and are appended."

"The problem of a steady boundary layer or sheath between a plasma and a magnetic field is considered. A self-consistent transition layer is found which joins a uniform magnetic field at plus infinity with a collisionless field-free plasma region with arbitrary velocity distribution at minus infinity, i.e., a magnetic field profile is found such that the exact particle orbits in this field produce a current which gives rise to this field. An interesting feature of the solution is that, with any nonsingular velocity distribution at minus infinity, the magnetic field the plasma extends to infinity, exponentially attenuated, into the magnetic field region. The scale of length is the Larmor radius. Electric fields arising from charge separation in the case of particles of different mass are ignored."

The differential cross-section for bremestrahlung in p-p collisions at an energy of 140 Mev is calculated at the upper end of the photon spectrum. the only transition which is considered is the E2 transition between 1D2 and the 1S0 state. The Siegart theorem is used and influence of the Coulomb force between the two protons is neglected.

"The grafting of methacrylic acid, styrene (2: 1 mole ratio) co-monomer mixture on polypropylene film and fabric, was studied to compare electron accelerators and isotopes as sources of radiation. An aluminum block that contalns i/8-in.-deep pockets covered with Mylar film for holding sample and monomer during mutual irradiatlon was developed. A preliminary comparison was made in post grafting polypropylene film and fabric preirradiated with Cow and with an electron accelerator source. It was found that post grafting was rapid at 80 ts C but slow at room temperature. Monomer equilibration before irradiation increased the grafting rate. Higher grafts were obtained when samples were irradiated in sparged and sealed containers. The grafting rate increased as dose rate decreased."

When light propagates with the wave normal in the direction of an optic axis of a biaxial crystal, the usual ray theory breaks down. This phenomenon can be analyzed by means of an asymptotic solution of Maxwell's equations. The intensity is governed by a partial differential equation within the phase surfaces, instead of ordinary differential equations along rays. This example slows that light does not always propagate along rays. A similar phenomenon occurs in hydromagnetics.

"This is the second quarterly report under Contract AT(30-1)-2528 for the decontamination and recovery of precious metals from contaminated scrap. the emphasis on the analytical chemical techniques and methods was continued during this report period."

"In this paper we solve for the diffracted wave which results when a weak hydromegnetic shock impinges on a rigid perfectly conducting half plans."

A program has begun embodying a study of the diffusion rates of krypton and xenon into unirradiated UO2 and UC at temperatures between 1000°C and 2500°C.The experimental technique is described in some detail, involving exposure of UO2 and UC samples to a Kr85 atmosphere at various temperatures, removal of surface-adsorbed krypton, dissolution of the sample, collection and ion chamber measurement of the diffused Kr, and calculation of diffusion coefficients from these data.

"In 1935, Yukawa proposed that a field must exist, analogous to the electromagnetic field but different in nature, which is responsible for the attraction between a proton and a neutron in a nucleus. He was led to the prediction of the existence of particles, quanta of this field, with mass intermediate between that of the electron and proton. In 1947, using photographic plates, the Bristol group led by Powell confirmed the existence of these particles, meons."

"We compute the equilibrium configuration of a collision-free plasma contained in an axially symmetric magnetic field. The plasma is characterized by a non-scalar pressure tensor which is obtained from a microscopic distribution function in a form suggested b the guiding center approximation. The solution is calculated in the limit where the ratio of the width to the length of the plasma region and the ratio of the gas to the magnetic pressure are both small. Boundary values at the midplane as well as the shape of the plasma appear as arbitrary parameters in the solution. We give the solution to a corresponding scalar pressure problem for comparison."

"This report describes two experiments performed in an effort to supply evidence for the universality of the V-A theory in weak interactions and for the law of conservation of leptons. In this first part the production rate of B to the 12th by the absorption of negative mu mesons in carbon was measured. From the amplitudes of the muon decay curve and the boron decay curve the rate was calculated to be (5.8 plus or minus 1.3) x 10 to the 3rd sec -1, in agreement with the hypothesis of a universal V_A theory. In the second part an attempt was made to measure the helicity of negative mu mesons by stopping longitudinally polarized muons in a carbon target and observing the electron asymmetry in the β-decay of the spin-1 B to the 12th. The results of this part were inconclusive, a consequence attributed to a short boron thermal relaxation time."

The objective of the study which is being carried out under contract AT(30-1)-2477 is the exploration of all aspects of research in water resources and supply to determine the potential for using radioisotope technology in this research. Problem areas in the application of tracers in this research are being investigated through the evaluation of past experimentation with radioisotopic techniques and through discussions with those who are active in this work. A series of suggestions relating to these techniques will de drawn up to indicate which techniques should be developed further in order that more extensive applications may be found for them.

...Development during this quarter have caused a shift in emphasis of the Pebble Bed Reactor Fuel Element Development Program from coatings on the sphere surface to coatings on individual fuel particles as the major deterrent to fission product leakage. In a high level irradiation test, cracks developed in the coatings of specimens coated with pyrolytic carbon and siliconized silicon carbide. In another high level irradiation test, a graphite sphere fueled with Al2O3 coated with UO2 particles is showing excellent fission product retention. The leakage factors (i.e. rate of release/rate of production) for long lived volatile fission products such as Kr85m, Kr87, Kr88, Xe133, Xe135 are ranging from 10 to the negative 9th to 10 to the negative 6th. If this degree of fission product retention is maintained in a large power reactor, it would result in essentially a "clean" primary loop.

"One of the fundamental concepts of macroscopic physics is that of a homogeneous system. The state of such a system is completely described by a set of intensive parameters which make no reference at all to the size or shape of the system, and by the total number of particles, N (unless otherwise specified we deal with one-component fluid). In actual systems, there are always inhomogeneities due to boundaries and to gravitational body forces."

Conclusions from the study: "Radioactive dusts are carcinogenic, and can cause cancer of the lung. complete dose response curves have not yet been determined. All the parameters that render this demonstrably toxic material (radioactive dust) have not yet been evaluated. It is strongly suggested by the experimental data that duration of radiological insult to the lung is an important factor in eliciting lung cancer. The atmospheric tolerance concentrations now in use seem to afford little margin of safety."

"We want to point out that there is a possible method for determining the anomalous magnetic moment of the Λ from the observation of metastable states of hyperframents. There are two possible sources for the apparent difference of binding energies of a hyperfragment. One of these comes from the difference of Q values due to the decay into an excited and ground states of the residual nucleus. The other possibility will arise if there exists a metastable state of the decaying hyperfragment."

"A new phenomenon which can, under certain circumstances, account for anomalous magnetic and spectral behavior of planar nickel(II) complexes has been discovered. This is a molecular association of the solute molecules in solvents of low coordinating power. It is shown that the magnetic moment and spectrum of bis(2.6-dimethyl1-3,5-heptanediono)nickel(II), Ni(DIBM)z, dissolved in toluene, are dependent upon both temperature and concentration.

"The design of the nuclear track intensifier was further analyzed to compare performance with design objectives. A preliminary analysis of the electron optics showed that the tube design suffers a small degree of astigmatism, which is increased in actual tabes by misalignment of parts, One tube was successfully completed and tested. Transit time of electrons from cathode to screen was determined to be 2.5 x 10/sup -8/ sec, 0.5 x 10/sup -8/ sec. Decay characteristics of several standard phosphors were measured. In the phosphor development phase, a latin square test was designed to evaluate combinations of thallium-activated rubidium iodide and cesium iodide phosphors under various evaporating conditions. Data were taken on various tests and analyzed statistically. On target samples submitted for tube evaluation, a reaction, which reduced light output, occurred between the aluminum and phosphor during vacuum bake. Oue image tube prepared with an alkali iodide mixture showed 10 to 25% improvement in screen resolution as compared to a P-11 screen."

"Development of a nuclear track image intensifier which is to have a cathode dia. of 83 in. and an output screen dia. of 1 in. is reported. Spherical faceplates for the intensifier which were etched to a thickness of 0.025 in. over a dia. of 80 in. withstood a pressure differential of 2 atm. Techniques were developed to measure spectral energy distribution, phosphor burn characteristics, phosphor efficiency, and phosphor persistence. Thallium- activated RbI and CsI were evaluated for use in the first stage of the image intensifier system. A color shift toward the yellow was accomplished in rubidium iodide phosphor by increasing the mole % of Th activator. Burn varied widely in different samples."

"A finite difference approximation to a non-linear set of parabolic differential equations arising in shallow water theory is given. These difference equations were used to determine the shape and rate of propagation of a hum of fluid down a channel of constant depth. The hump of fluid was found to spread instead of steepen, as is the case in the usual shallow water theory."

"As an extension of an earlier paper the Green's function is evaluated for the Lundquist equation linearized about uniform magnetic field, constant matter density, and zero flow velocity. It is assumed that all quantities are functions of two space variables and time only. In the general magnetic field configuration considered here a pure Alfvén disturbance no longer exists; there is instead a wave with properties of both the Alfvén and fast‐slow disturbance."

An approximate Boltzmann equation, known as the single relaxation model is studied here. This equation is linearized and the fundamental solution is considered. Following N. Grad, the solution, asymptotic in small values of the ratio of mean-free-path to distance from the origin, is sought. It can be shown that the fundamental solution itself gives the asymptotic description of the flow field past an object. This solution gives the asymptotic description when the distance from the origin is much greater than either the mean-free-path or the body size. This is true independently of the Knudsen number.