Focusing of dispersive phonons in GaAs

The ballistic propagation of highly dispersive phonons in GaAs in analyzed with both a bond-charge model (BCM) and a shell model, and compared to imaging experiments. When scattering is neglected, both models predict dispersive focusing pattern which depend strongly on the selected group velocities. In contrast, velocity-selected phonon images obtained with a PbBi tunnel-junction detector on a 0.7-mm thick crystal, display well-defined caustic lines whose angular positions do not shift at longer delay times. When isotope scattering is considered in the calculation, however, the shell model reproduces the experimental focusing structures remarkably well.For highly dispersive phonons, the bond-charge and shell models predict markedly different phonon-focusing patterns. In particular, a concentration of heat flux along [100] is predicted by BCM forv=1.7–2.0 THz slow-transverse (ST) phonons., but this effect is absent in the shell model. Both models predict new focusing structures in the fasttransverse (FT) mode at high frequencies. Our calculations which include isotope scattering indicate that to observe these new structures considerable technical advances are required in the phonon-imaging experiments.     

Asymptotic normality of a robust kernel estimator of the regression function for functional ergodic data: Case of an unknown scale parameter

Under a nonparametric robust regression model, we consider the problem of estimating the score function ${\psi }_x$ for a fixed x in a functional space and with unknown scale parameter. The principal aim of this work is to establish the asymptotic normality of this estimator for a stationary ergodic process without any use of traditional mixing conditions.     

Evaluation of the reactivity,selectivity and lifetime of hydrotalcite-based catalysts using isopropanol as probe molecule

Hydrotalcite catalysts derived from NiAl and NiAlMg mixed oxides were successfully prepared by coprecipitation at a constant pH of 11. Physicochemical methods were investigated to determine their structural and textural properties. Using isopropanol as a probe molecule, the acid–base properties of the catalysts were investigated, and the evaluation of reactivity, selectivity and lifetime was established.

     

Asymptotic behavior of an age-structured population model with diffusion

A reaction-diffusion system with stage-structure is studied. We provide well-posedness of the model and prove that time-dependent solutions evolve either towards a positive equilibrium or to the trivial one. Under suitable conditions, a branch of positive equilibrium is shown to exist.