The following report is part of a series of quarterly reports discussing investigations on the development of zirconium-base alloys having corrosion resistance and strength superior to Zircaloy-2 and/or development of materials of equivalent corrosion resistance by exhibiting enhanced strength. This report covers the period between May 29 and June 18 of 1958, made by the United States and the European Atomic Energy Community (EURATOM).

Abstract. The Equivalence Theorem of P. Lax is extended to difference schemes for initial-value problems for linear inhomogeneous PDE with linear inhomogeneous boundary values and for boundary-value problems.

A method for monitoring radiation damage irradiations using the change of the electrical conductivity of graphite is described. Results of monitoring operations in a number of locations are given. An attempt is made to explain the damage rate found in the converter at CP-3. An estimate of the flux spectrum in VT-4 and the converter of CP-3 is made and the damage rate is computed according to theories of Seitz and James. It is found that the experimental results are more in accord with the predictions of Seitz. A number of corrections to James' report, ORNL-307, are noted in an appendix. It is shown that some information about the fast flux spectrum can be inferred from the radiation damage rate.

High heat flux electrical cartridge heaters were tested with direct air cooling under simulated ORR Loop conditions. The cartridges and the heater design were found to be satisfactory. A gas cooled of concentric pipe design utilizing air, water, and air-water mixtures as the coolant was also evaluated and found to be satisfactory.

Paths of trip points of Mach reflections produced by 0.5-oz pentolite detonations have been observed for various burst heights. The slopes, Y, at points on the curved path are found to vary from values of Y predicted from plane shock wave data. This discrepancy is attributed to the shock strength conditions at the early inception of the Mach reflection, which later influence the triple point equilibrium, and in lesser degree to radius of curvature effects.