Continuity of Dynamical Structures for Nonautonomous Evolution Equations Under Singular Perturbations

In this paper we study the continuity of invariant sets for nonautonomous infinite-dimensional dynamical systems under singular perturbations. We extend the existing results on lower-semicontinuity of attractors of autonomous and nonautonomous dynamical systems. This is accomplished through a detailed analysis of the structure of the invariant sets and its behavior under perturbation. We prove that a bounded hyperbolic global solutions persists under singular perturbations and that their nonlinear unstable manifold behave continuously. To accomplish this, we need to establish results on roughness of exponential dichotomies under these singular perturbations. Our results imply that, if the limiting pullback attractor of a nonautonomous dynamical system is the closure of a countable union of unstable manifolds of global bounded hyperbolic solutions, then it behaves continuously (upper and lower) under singular perturbations.

Delay nonlinear boundary conditions as limit of reactions concentrating in the boundary

In this work, we are interested in the dynamic behavior of a parabolic problem with nonlinear boundary conditions and delay in the boundary. We construct a reaction-diffusion problem with delay in the interior, where the reaction term is concentrated in a neighborhood of the boundary and this neighborhood shrinks to boundary, as a parameter epsilon goes to zero. We analyze the limit of the solutions of this concentrated problem and prove that these solutions converge in certain continuous function spaces to the unique solution of the parabolic problem with delay in the boundary. This convergence result allows us to approximate the solution of equations with delay acting on the boundary by solutions of equations with delay acting in the interior and it may contribute to analyze the dynamic behavior of delay equations when the delay is at the boundary. (C) 2012 Elsevier Inc. All rights reserved.

Turing patterns in the chlorine dioxide-iodine-malonic acid reaction with square spatial periodic forcing

We use the photosensitive chlorine dioxide-iodine-malonic acid reaction-diffusion system to study wavenumber locking of Turing patterns to two-dimensional "square" spatial forcing, implemented as orthogonal sets of bright bands projected onto the reaction medium. Various resonant structures emerge in a broad range of forcing wavelengths and amplitudes, including square lattices and superlattices, one-dimensional stripe patterns and oblique rectangular patterns. Numerical simulations using a model that incorporates additive two-dimensional spatially periodic forcing reproduce well the experimental observations.

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.

SUFFICIENT CONDITIONS ON DIFFUSIVITY FOR THE EXISTENCE AND NONEXISTENCE OF STABLE EQUILIBRIA WITH NONLINEAR FLUX ON THE BOUNDARY

A reaction-diffusion equation with variable diffusivity and non-linear flux boundary condition is considered. The goal is to give sufficient conditions on the diffusivity function for nonexistence and also for existence of nonconstant stable stationary solutions. Applications are given for the main result of nonexistence.

On the Reaction of Lupulones, Hops beta-Acids, with 1-Hydroxyethyl Radical

Lupulones, hops beta-acids, are one of the main constituents of the hops resin and have an important contribution to the overall bacteriostatic activity of hops during beer brewing. The use of lupulones as natural alternatives to antibiotics is increasing in the food industry and also in bioethanol production. However, lupulones are easy oxidizable and have been shown to be very reactive toward 1-hydroxyethyl radical with apparent bimolecular rate constants close to diffusion control k = 2.9 x 10(8) and 2.6 x 10(8) L mol(-1) s(-1) at 25.0 +/- 0.2 degrees C in ethanol water solution (10% of ethanol (v/v)) as probed by EPR and ESI-IT-MS/MS spin-trapping competitive kinetics, respectively. The free energy change for an electron-transfer mechanism is Delta G degrees = 106 kJ/mol as calculated from the oxidation peak potential experimentally determined for lupulones (1.1 V vs NHE) by cyclic voltammetry and the reported reduction potential for 1-hydroxyethyl radical. The major reaction products identified by LC-ESI-IT-MS/MS and ultrahigh-resolution accurate mass spectrometry (orbitrap FT-MS) are hydroxylated lupulone derivatives and 1-hydroxyethyl radical adducts. The lack of pH dependence for the reaction rate constant, the calculated free energy change for electron transfer, and the main reaction products strongly suggest the prenyl side chains at the hops beta-acids as the reaction centers rather than the beta,beta'-triketone moiety.

Exact correlation functions in particle-reaction models with immobile particles

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball-Deker-Haake dynamics. In this way, both in finite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

New Approaches for the Ethanol Oxidation Reaction of Pt/C on Carbon Cloth Using ATR-FTIR

This work describes the study of the ethanol oxidation reaction of a Pt/C Etek electrocatalyst that was supported on different substrates, such as gold, glassy carbon and carbon cloth treated with PTFE. In the ethanol oxidation reaction, the activity varies with the substrate, as well as the pathways for ethanol oxidation, as studied by an ATR-FTIR in situ setup using the carbon cloth as the electrocatalyst support. The electrocatalyst Pt/C supported on gold starts acetaldehyde production from ethanol oxidation at an onset potential of 0.1 V less than that observed for the same process on Teflon-treated carbon cloth. The Pt/C supported on the carbon cloth starts its CO2 production for the same oxidation process at 0.2 V less than on the Pt/C supported on gold substrate. The differences in catalytic activity for the ethanol oxidation reaction depend not only on the electrocatalyst but also on various electrode factors, such as the substrate, the roughness of the electrode and the charge transfer resistance.