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."

"The energy method is applied to study the stability of two types of difference approximations to parabolic partial differential equations, the alternating direction methods Douglas, Peaceman, and Rachford, and a new semi- explicit method. Each difference scheme is proved to be unconditionally stable. These results apply to parabolic equations with variable coefficients, defined in cylindrical domains with an essentially arbitrary bounded base."

"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 program objective has been to investigate the possible similarity between a bond interface and a grain boundary. The criterion for establishing the similarity of a bond interface and a grain boundary was the migration characteristics of the boundary under the influence of controlled orientation, strain level, temperature and time. In addition, the orientation dependency of the "threshold", or minimum deformation, for bonding would have to be determined. The initial bonding studies were to be made by a "cold welding" technique; subsequently, elevated temperatures bonding would have been attempted. Migration of boundaries was to be observed by high temperature metallographic techniques.

"Short-range order coefficients were measured at 300 and 400°C for iron-aluminum alloys containing 14.8, 18.2, and 20.0 atomic per cent aluminum. These alloys exhibited a strong preference for unlike near neighbors. The short-range order was greater at the lower temperature and increased as the Fe 3Al composition was approached."

"Uranium and zirconium were bonded by melting the two metals in contact with one another in a bimetallic casting process. Tensile tests of specimens containing the original zone of interface between the two metals showed that all failures were at locations other than the interface. The coefficients obtained for diffusion between molten uranium and molten zirconium varied from 2.13 cm squared per day at 3,380 degrees F. to 9.17 cm squared per day at 3,510 degrees F. the activation energy for the diffusion process was calculated to be 182,000 calories per gram mole."

"The purposes of the program being conducted under the present contract are: 1) To determine the feasibility of cladding zirconium on uranium by a direct casting process. 2) To investigate the diffusion of liquid metals in the fusion zone."

"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.

"A broad range nuclear spectrograph of the Buechner-Bainbridge type, which characteristic radius R-50 cm. has been constructed and installed for use in conjunction with the Rochester 27" variable energy cyclotron. For a given magnetic field, particles are focused over an energy range 0.63o‹E‹1.3Eo, where Eo is the energy of particles focused with orbit radius Q-R-50 cm. The resolution of the spectrograph ∆E/E is less than 0.2%. Particles may be recorded either in nuclear emulsions or in an array of solid state counters. Results of calibration measurements and typical nuclear data taken with the spectrograph are presented."

"The projection operator technique is used to generate electronic wave functions which are eigenfunctions of both spin and orbital angular momentum. All the functions which arise in the L-S coupling of any allowed system of electrons in a single s, p, d, or f shell are computed as well as some functions for a few electrons in the g-shell. In addition, functions arising in the coupling of electrons in different shells are obtained, and these eigenfunctions are of particular interest in configuration interaction studies of atomic structure. A few representative eigenfunctions are listed."

"The canonical theory of motion of a charged particle in a slowly varying, static electromagnetic field is formulated. The Hamiltonian is written down explicitly in terms of the coordinates of the gyration and the drift. The method of approach is analogous to that of the canonical formalism with subsidiary condition as used in theories of collective motion in many-body systems, such as the motion of the center of gravity. In the lowest order of the perturbation, it is shown that the Hamiltonian for the drift motion averaged over the gyration phase is given by adding to the original Hamiltonian a potential term equal to the product of the magnetic moment and the magnetic field strength."

"The electrical conductance of CoCl2 and CoBr2 from 10−4 to 10−1 mol/l over the temperature range 0–35°C is reported. The effects of water as trace impurity, and the halide common ion effect on conductance are examined. The properties of these solutes are also examined using spectrophotometry and transport numbers. Crystalline “solvated” compounds, of empirical formulae [CoX2(CH3CN)3]x can be separated from the saturated solutions. The magnetic susceptibilities of the crystalline substrates are in accord octahedral and tetrahedral symmetry for the cationic and anionic species in these “solvates”, the bonding in both being the spin-free type for divalent cobalt. From the optical properties of the solutions it is apparent that the “anomalous” properties of these electrolytes can be understood in a series of simultaneous processes under Mass-Law control, in which CoX2, CoX42−, Co(CH3CN)62+ and [Co(CH3CN) 62+CoX42−]° are predominant."

"A comparison of the grafting of a 2:1 molar mixture of methacrylic acid and styrene to both polypropylene film and fabric using CO60 source and electron accelerator as sources of ionizing radiation is made on the basis of mutual or simultaneous grafting and post-irradiation grafting.

"A comparison of grafting to two thicknesses of polypropylene film is made using isotope and electron accelerator initiation. The results indicate that the grafting of methacrylic acid: styrene to polypropylene is mainly a surface reaction."

"Graft polymers were made by Co60 mutual irradiation of mixtures of styrene and methyl acrylate in contact Teflon. These graft copolymers were analyzed by infra-red absorption and their composition determined. The composition of the graft copolymer formed from styrene and methyl acrylate was different from that which is predicted by the copolymer composition equation."

"A brief examination of the post irradiation grafting of machine irradiated polyethylene film with acrylic acid monomer was made. Evidence of postgrafting was detected in samples that had been irradiated to a total dose of 10 Mrads at a dose rate of 0.01 Mrad/sec. and then exposed to a 25% purified acrylic acid solution in benzene for periods of 1 to 4 days."

"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."

The APPR-1 is a pressurized water reactor having a low specific heat fuel and a water primary coolant. The primary coolant loop delivers heat from the reactor to the steam generator. The secondary water in the steam generator is converted to steam and then taken to the turbine to drive an electrical generator. The simulation of this system is broken down into three primary areas: the neutron kinetics in the reactor which are necessary to generate the primary power function, the heat transfer in the reactor, and the heat transfer in the steam generator.

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.

"A survey of the current theoretical picture of plasma containment in cusped magnetic configurations is presented together with a mention of the points of contact which exist or might soon be made to exist with experiment. A theory of containment was developed which is applicable to the whole range of plasma densities from a tenuous plasma in an essentially vacuum magnetic field to a fully developed plasma which completely excludes the magnetic field from its interior. Also presented are cursory accounts of the situation with regard to stability, cyclotron radiation, and methods of creating this type of plasma configuration."

"The correction to photon-photon scattering processes due to the existence of the particles other than electrons is reported. The correction is of the same order in the electric charge as the lowest order term in the perturbation expansion in quantum electrodynamics, although the relevant corrections to the electron-photon and electron-electron scattering are all of higher order."

"It is shown that in a class of models of quantum field theory, the perturbation expansion of the resolvent operator, (H - z)-1, converges for all complex z. The class of models consists of all theories with Yukawa coupling in which the vacuum polarization is neglected. The method used is that of comparison with the exactly solvable neutral solar model."