The role of Ce(III) in BZ oscillating reactions

Herein we present results on the oscillatory dynamics in the bromate-oxalic acid-acetone-Ce(III)/Ce(IV) system in batch and also in a CSTR. We show that Ce(III) is the necessary reactant to allow the emergence of oscillations. In batch, oscillations occur with Ce(III) and also with Ce(IV), but no induction period is observed with Ce(III). In a CSTR, no oscillations were found using a freshly prepared Ce(IV), but only when the cerium-containing solution was aged, allowing partial conversion of Ce(IV) to Ce(III) by reaction with acetone. (C) 2012 Elsevier B. V. All rights reserved.

Coupling collective modes in a trapped superfluid

We consider a superfluid cloud composed of a Bose-Einstein condensate oscillating within a magnetic trap (dipole mode) where, due to the existence of a Feshbach resonance, an effective periodic time-dependent modulation in the scattering length is introduced. Under this condition, collective excitations such as the quadrupole mode can take place. We approach this problem by employing both the Gaussian and the Thomas-Fermi variational Ansatze. The resulting dynamic equations are analyzed by considering both linear approximations and numerical solutions, where we observe coupling between dipole and quadrupole modes. Aspects of this coupling related to the variation of the dipole oscillation amplitude are analyzed. This may be a relevant effect in situations where oscillation in a magnetic field in the presence of a bias field B takes place, and should be considered in the interpretation of experimental results.

A nonlinear elliptic problem with terms concentrating in the boundary

In this paper, we investigate the behavior of a family of steady-state solutions of a nonlinear reaction diffusion equation when some reaction and potential terms are concentrated in a e-neighborhood of a portion G of the boundary. We assume that this e-neighborhood shrinks to G as the small parameter e goes to zero. Also, we suppose the upper boundary of this e-strip presents a highly oscillatory behavior. Our main goal here was to show that this family of solutions converges to the solutions of a limit problem, a nonlinear elliptic equation that captures the oscillatory behavior. Indeed, the reaction term and concentrating potential are transformed into a flux condition and a potential on G, which depends on the oscillating neighborhood. Copyright (C) 2012 John Wiley & Sons, Ltd.