Molecular states of atoms. I. Orbital energy parameters

Atomic valence state energies are analyzed to obtain values of orbital energy parameters that may be used in semiempirical molecular orbital calculations. Difficulty in defining the interaction between orbitals with non-integer electron populations is systematically avoided by distinguishing between a valence state and a molecular state of an atom, only the latter state having non-integer spin paired orbital occupancy. Application of the virial theorem to the molecular state enables a value for the orbital kinetic energy to be obtained from the valence state orbital energy parameters once an arbitrary configuration is defined as reference. The orbitals then are eigenfunctions of the atomic Fock operator for that reference molecular state and, with their energy parameters, may be employed as a fixed basis set for molecular orbital calculations.     

Geometrical properties of some Euler and circular cubics. Part 2

This paper is a continuation of Part 1, previously published under the same title. The reader is asked to refer back to Part 1 for the Glossary and references.     

The classification of topological Markov chains adapted shift equivalence

This paper is motivated by Williams’s problem: to show that shift equivalence of non-negative irreducible matrices implies topological equivalence of their associated topological Markov chains. Instead we prove thatadapted shift equivalence implies (and is implied by) topological equivalence. Supported by the Deutsche Forschungsgemeinschaft.     

Rotational Symmetries of Crystals with Defects

I use the theory of Lie groups/algebras to discuss the symmetries of crystals with uniform distributions of defects.      

3D short-range wetting and nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.     

A novel method for the determination of migration of contaminants from food contact materials

A neutron activation method has been developed for the analysis of high density polyethylene, low density polyethylene, polypropylene, polyethylene terephthalate and polystyrene food contact plastics. The method provides determination of over 50 elements at concentrations below 1 mg kg^–1. This technique has now been extended to study migration from food contact materials into standard food simulants (olive oil, acetic acid, ethanol and water). Samples of plastic are irradiated in a thermal neutron flux to produce radionuclides of the elements present in the plastic. Over a period of time the radionuclides of these elements may travel from the plastic into the food simulants, and hence the migration can be determined. Gamma ray spectrometry is performed on the simulants at the end of the test to quantify the migration. Any activity present must be due only to the migration of radionuclides of elements in the plastic and nothing else. This eliminates the need for a blank determination, which is required with existing migration methods. Preliminary studies have shown that detection limits of around 0.002 mg kg^–1 can be achieved for Sb in a retail polyethylene terephthalate (PET) bottle. This can be compared to levels of 0.005     

On a conjecture of Brandler

Quadratic residuacity properties of real quadratic units are studied.