Rydberg states of diatomic and polyatomic molecules using model potentials

A simple model potential is used to calculate Rydberg series for the molecules: nitrogen, oxygen, nitric oxide, carbon monoxide, carbon dioxide, nitrogen dioxide, nitrous oxide, acetylene, formaldehyde, formic acid, diazomethane, ketene, ethylene, allene, acetaldehyde, propyne, acrolein, dimethyl ether, 1, 3-butadiene, 2-butene, and benzene. The model potential for a molecule is taken as the sum of atomic potentials, which are calibrated to atomic data and contain no further parameters. Our results agree with experimentally measured values to within 5-10% in all cases. The results of these calculations are applied to many unresolved problems connected with the above molecules. Some of the more notable of these problems are the reassignment of states in carbon monoxide, the first ionization potential of nitrogen dioxide, the interpretation of the V state in ethylene, and the mystery bands in substituted ethylenes, the identification of the R and R’ series in benzene and the determination of the orbital scheme in benzene from electron impact data.

Applications of plasticity theory to selected problems in soil mechanics

Two topics in plane strain perfect plasticity are studied using the method of characteristics. The first is the steady-state indentation of an infinite medium by either a rigid wedge having a triangular cross section or a smooth plate inclined to the direction of motion. Solutions are exact and results include deformation patterns and forces of resistance; the latter are also applicable for the case of incipient failure. Experiments on sharp wedges in clay, where forces and deformations are recorded, showed a good agreement with the mechanism of cutting assumed by the theory; on the other hand the indentation process for blunt wedges transforms into that of compression with a rigid part of clay moving with the wedge. Finite element solutions, for a bilinear material model, were obtained to establish a correspondence between the response of the plane strain wedge and its axi-symmetric counterpart, the cone. Results of the study afford a better understanding of the process of indentation of soils by penetrometers and piles as well as the mechanism of failure of deep foundations (piles and anchor plates).

The second topic concerns the plane strain steady-state free rolling of a rigid roller on clays. The problem is solved approximately for small loads by getting the exact solution of two problems that encompass the one of interest; the first is a steady-state with a geometry that approximates the one of the roller and the second is an instantaneous solution of the rolling process but is not a steady-state. Deformations and rolling resistance are derived. When compared with existing empirical formulae the latter was found to agree closely.