Use of reciprocity considerations for the two-dimensional BEM analysis of wave propagation in an elastic half-space with applications to acoustic emission

A simple numerical treatment of the infinite boundary in the BEM analysis of two-dimensional wave propagation problems in elastic half-spaces is proposed to avoid the spurious reflections of non-decaying Rayleigh waves introduced by the truncation of the boundary. The proposed method exploits the knowledge of the far-field asymptotic behavior of the solution to adequately correct the BEM displacement system matrix for the truncated problem to account for the contribution of the omitted part of the boundary. The reciprocal theorem of elastodynamics is used for a convenient computation of this contribution exclusively in terms of the boundary integrals of the original BEM system. The method is applied to the study of the acoustic emission from nucleating and propagating surface-breaking and buried cracks in a two-dimensional elastic half-space. It is shown to be particularly advantageous since it allows for an accurate calculation of the generated signal even when the observation point is located far from the acoustic emission source.     

On the Meromorphic Functions in the Punctured Plane Without Multiple Values

The study of meromorphic functions without multiple values in the plane started by F. Nevanlinna is extended to meromorphic functions in the punctured plane \({\mathbb {C}}^{{*}}.\) It is a classical result that a meromorphic function \(f\left( z\right) \) can be obtained as quotient of solutions of the second order differential equation \(u^{{\prime \prime }}+\left\{ f\left( z\right) ,z\right\} u=0,\) where \(\left\{ f\left( z\right) ,z\right\} \) is the Schwarzian derivative of \(f\left( z\right) \). In our hypothesis of meromorphic functions of finite order without multiple values in the puntured plane, the Schwarzian derivative \(\left\{ f\left( z\right) , z\right\} \) turns out to be a rational function with only possible poles at 0 and \(\infty \). In these conditions the asymptotic behaviour of \(f\left( z\right) \) can be described by a result of Hille (Lectures on Ordinary Differential Equations in the complex plane, Addison Wesley, Boston, 1969) on ordinary differential equations in the complex plane. The results obtained are framed in the value distribution theory of meromorphic functions, in particular in the punctured plane we shall consider the work of Khrystiyanin and Kondratyuk (Mat Stud 23(1):19–30, 2005; Mat Stud 23(1):57–68, 2005) and Korhonen (Nevanlinna theory on an annulus. Value distribution theory and related topics. Adv. Complex analysis and applications, Kluwer Academic Publishers, Dordrecht, 2004).     

A first-principles study of the influence of helium atoms on the optical response of small silver clusters

Optical excitation spectra of Ag(n) and Ag(n)@He(60) (n = 2, 8) clusters are investigated in the framework of the time-dependent density functional theory (TDDFT) within the linear response regime. We have performed the ab initio calculations for two different exact exchange functionals (GGA-exact and LDA-exact). The computed spectra of Ag(n)@He(60) clusters with the GGA-exact functional accounting for exchange-correlation effects are found to be generally in a relatively good agreement with the experiment. A strategy is proposed to obtain the ground-state structures of the Ag(n)@He(60) clusters and in the initial process of the geometry optimization, the He environment is simulated with buckyballs. A redshift of the silver clusters spectra is observed in the He environment with respect to the ones of bare silver clusters. This observation is discussed and explained in terms of a contraction of the Ag-He bonding length and a consequent confinement of the s valence electrons in silver clusters. Likewise, the Mie-Gans predictions combined with our TDDFT calculations also show that the dielectric effect produced by the He matrix is considerably less important in explaining the redshifting observed in the optical spectra of Ag(n)@He(60) clusters.     

Simultaneous spectrofluorimetric determination of europium, dysprosium, gadolinium and terbium using chemometric methods

A spectrofluorimetric method for the simultaneous determination of dysprosium, europium, gadolinium and terbium in ternary and quaternary mixtures by the use of pyridine-2,6-dicarboxylic acid as a chelating agent was developed. The influence of chemical variables affecting the analytical reaction was evaluated. A partial least-squares procedure and PC Quant software were used to assess data obtained from a variable number of calibration solutions and wavelengths. The ensuing method was validated by applying it to the analysis of synthetic ternary (Eu-Dy-Tb) and quaternary mixtures (Eu-Dy-Gd-Tb) over the concentration ranges 60-550 mug Eu l(-1), 30-400 mug Dy l(-1) and 30-400 mug Tb l(-1) in the former, and 20-220 mug Eu l(-1), 20-235 mug Dy l(-1), 25-230 mug Gd l(-1) and 75-230 mug Tb l(-1) in the latter. The results obtained by using the two quantitation procedures are compared. The relative errors in the determinations were less than 8% in most cases.     

Entropies and IPR as Markers for a Phase Transition in a Two-Level Model for Atom–Diatomic Molecule Coexistence

A quantum phase transition (QPT) in a simple model that describes the coexistence of atoms and diatomic molecules is studied. The model, which is briefly discussed, presents a second-order ground state phase transition in the thermodynamic (or large particle number) limit, changing from a molecular condensate in one phase to an equilibrium of diatomic molecules–atoms in coexistence in the other one. The usual markers for this phase transition are the ground state energy and the expected value of the number of atoms (alternatively, the number of molecules) in the ground state. In this work, other markers for the QPT, such as the inverse participation ratio (IPR), and particularly, the Rényi entropy, are analyzed and proposed as QPT markers. Both magnitudes present abrupt changes at the critical point of the QPT.     

A one side superlinear Ambrosetti-Prodi problem for the Dirichlet p-laplacian

We study the solvability of the quasilinear elliptic problem of parameter s