Conditions for equality of decomposable symmetric tensors. II.

We derive consequences of a condition for the equality of two star products given by the second author. We also study another method for the same problem which consists of comparing the components, in an appropriate basis, of the star products involved.     

Localized states in polymeric molecules III The electronic structure of polyacetylene

The Transfer Matrix approach is used to treat the relaxed defect problem in trans-polyacetylene. We use a particular choice of parametrization for the hopping integrals, which is related to the existence of solitons in this material, to discuss its electronic structure. We obtain closed expressions for the density of states and for the wavefunctions associated to the localized state at any site of the chain.     

Column separation and preconcentration of copper(II), lead(II) and zinc(II) from seawater

Summary The sample of seawater (51) is freed from solid particles, buffered at pH 5.6 and percolated through a column filled with ED₃A. After sample passage 15 ml 1 M hydrochloric acid solution are pumped through the column to dissolve the concentrated ions. The final measurement using flame atomic absorption is carried out in the hydrochloric acid solution. The total labour time is less than 15 min. The standard deviations (4 analyses) for the determination of Cu, Pb and Zn (in the normal concentration range of 2–6 g · l^–1) were 2–5%, 5% and 1–10%, the recoveries 100%, 102% and 104%, respectively. A concentration coefficient of 300–500 was obtained.On leave from Lisbon University, Portugal     

Single-ion approach to the susceptibility of an intermediate valence compound paramagnetic Imse

The magnetic properties of an intermediate valence compound are discussed within a single-ion framework. The effects of configuration mixing, crystalline electric fields, and external magnetic fields are included in the hamiltonian. The method incorporates in one single consistent approach both coherent (quantum) and incoherent (thermal) fluctuations. Numerical evaluation of the susceptibility and field dependent magnetization with parameters appropriate for TmSe yields results in good agreement with experiment.     

Photon channelling in foams

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 65, 414 (2004)) demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of ɛ.     

Magnetic nanoscale aggregates of cobalt and nickel in MgO single crystals

The magnetic properties of Co and Ni nanosized aggregates formed after implantation of nickel and cobalt ions in magnesium oxide single crystals were investigated. The influence of the implantation energy and annealing treatments was characterized. The particle size distribution was determined from the combined analysis of the magnetic moment dependence on both magnetic field and temperature, and used to determine the magnetic anisotropy constant of the aggregates. The results for nickel aggregates indicate the presence of an antiferromagnetic layer after the annealing treatments.