Incremental collapse of thick-walled circular cylinders under steady axial tension and torsion loads and cyclic transient heating

The accumulation of plastic strain over a number of cycles of heating and cooling of the outer surface of a loaded thick-walled circular cylinder is computed. Two types of loadings are considered, viz. pure axial torsion and a combination of torsion and tension. The cylinder material is taken to be isotropic and linear strain-hardening; its yield stress reduces with temperature and with the number of thermal cycles completed. This cyclic softening is shown to produce an incremental collapse or ratcheting behaviour in contrast to the alternating plasticity which occurs when the yield stress on first loading is maintained.     

On singular perturbation in non well posed problems

Summary Let L_εu and L ₀ v be the elliptic and “backward” heat operators defined by(1.1) and(1.2), respectively. The following question is considered for a pair of “non-well posed” initial-boundary value problems for L_ε and L ₀ : if u and v are the respective solutions, under what restrictions on the classes of admissible solutions and in what sense, if any, does u converge to v as ɛ →0? This research was supported in part by the National Science Foundation Grant No. GP 5882 with Cornell University.     

Some superadditivity results in the torsion problem for multiply connected cross sections

In this note we prove strong superadditivity properties of the stress function in the elastic torsion problem for multiply connected regions. The results are extended to associated Green's functions and other domain functions.     

Absolute rate constants for the reaction of bromine atoms with ozone from 234 to 360 K

The rate constant for the reaction of Br + O₃ → BrO + O₂ has been measured at four temperatures from 234 to 360 K by the technique of discharge flow coupled with resonance-fluorescence detection of bromine atoms. The measured rate constants obey the Arrhenius expression k = (9.45 ± 2.48) × 10^?12 exp(-659 ± 64/T) cm³/molec·sec (one standard deviation). The results are compared with two previous studies, one of which utilized the flash-photolysis–resonance-fluorescence technique and the other utilized the discharge-flow–mass-spectrometric technique. The result is also discussed from a theoretical point of view.     

Dynamic properties of materials

Summary Bentonite and stockalite clay-water systems were strained sinusoidally in shear over a wide strain range. The hysteresis loops were shown to vary from an almost straight line (elastic system) to a ferromagnetic type loop (plastic system) as the energy of oscillation was increased. The normalised dynamic modulus-strainwork plots were shown to be very similar to those observed in carbon black-elastomer and carbon black-paraffin systems.

---

Zusammenfassung Über einen weiten Dehnbereich werden Bentonit- und Stockalit-Wasser-Systeme einer sinusförmigen Dehnbeanspruchung ausgesetzt. Die Hystereseschleifen variieren mit wachsender Schwingungsenergie von einer geraden Linie (elastisches System) bis zu einer Art ferromagnetischer Schleife (plastisches System). Die normierten dynamischen Modul-Dehnungsarbeit-Diagramme sind bei den Ruß-Elastomer- und Ruß-Paraffin-System beobachteten sehr ähnlich.

---

---

Paper presented at the British Society of Rheology Conference. held at Shrivenham, from 9th–12th September, 1968.     

Configuration space Faddeev calculations

The triton ground-state wave function calculated using the Reid soft-core potential is displayed in configuration space. Both the S-state and D-state Schrödinger wave function components and the Faddeev amplitudes from which they are constructed are plotted. Specific features resulting from the tensor nature of the two-body force and from the strong short-range repulsion of the potential are discussed. Comparisons with corresponding functions generated by the Malfliet-Tjon s-wave potential model are made. Several intuitive features of the Schrödinger wave function are discussed.     

Application of solution techniques for rapid growth of organic crystals

Single crystals of a pure hydrocarbon, 1,3,5-triphenylbenzene, with properties suitable for high-energy neutron detection were grown from toluene solutions using slow evaporation and temperature reduction methods with growth rates up to 10 mm/day. Application of the rapid growth technique developed earlier for growth of large water-soluble crystals shows that crystals of aromatic compounds can be successfully grown from solutions in large volumes required for their use as scintillator materials for radiation detection.     

Stable base loci, movable curves, and small modifications, for toric varieties

We show that the dual of the cone of divisors on a complete -factorial toric variety X whose stable base loci have dimension less than k is generated by curves on small modifications of X that move in families sweeping out the birational transforms of k-dimensional subvarieties of X. We give an example showing that it does not suffice to consider curves on X itself. Supported by a Graduate Research Fellowship from the NSF