Travelling wave profiles in some models with nonlinear diffusion

We study some properties of the monotone solutions of the boundary value problem (p(u'))' - cu' + f(u) = 0, u(-infinity) = 0, u(+infinity) = 1, where f is a continuous function, positive in (0, 1) and taking the value zero at 0 and 1, and P may be an increasing homeomorphism of (0, 1) or (0, +infinity) onto [0, +infinity). This problem arises when we look for travelling waves for the reaction diffusion equation partial derivative u/partial derivative t = partial derivative/partial derivative x [p(partial derivative u/partial derivative x)] + f(u) with the parameter c representing the wave speed. A possible model for the nonlinear diffusion is the relativistic curvature operator p(nu)= nu/root 1-nu(2). The same ideas apply when P is given by the one- dimensional p- Laplacian P(v) = |v|(p-2)v. In this case, an advection term is also considered. We show that, as for the classical Fisher- Kolmogorov- Petrovski- Piskounov equations, there is an interval of admissible speeds c and we give characterisations of the critical speed c. We also present some examples of exact solutions. (C) 2014 Elsevier Inc. All rights reserved.

Solid-state sensory properties of Calix-Poly(Phenylene Ethynylene)s toward nitroaromatic explosives

This study is primarily focused in establishing the solid-state sensory abilities of several luminescent polymeric calix[4]arene-based materials toward selected nitroaromatic compounds (NACs), creating the foundations for their future application as high performance materials for detection of high explosives. The phenylene ethynylene-type polymers possessing bis-calix[4]arene scaffolds in their core were designed to take advantage of the known recognition abilities of calixarene compounds toward neutral guests, particularly in solid-state, therefore providing enhanced sensitivity and selectivity in the sensing of a given analyte. It was found that all the calix[4]arene-poly(para-phenylene ethynylene)s here reported displayed high sensitivities toward the detection of nitrobenzene, 2,4-dinitrotoluene and 2,4,6-trinitrotoluene (TNT). Particularly effective and significant was the response of the films (25-60 nm of thickness) upon exposure to TNT vapor (10 ppb): over 50% of fluorescence quenching was achieved in only 10 s. In contrast, a model polymer lacking the calixarene units showed only reduced quenching activity for the same set of analytes, clearly highlighting the relevance of the macrocyclics in promoting the signaling of the transduction event. The films exhibited high photostability (less than 0.5% loss of fluorescence intensity up to 15 min of continuous irradiation) and the fluorescence quenching sensitivity could be fully recovered after exposure of the quenched films to saturated vapors of hydrazine (the initial fluorescence intensities were usually recovered within 2-5 min of exposure to hydrazine).

Comparing wind generation profiles: A circular data approach

The importance of wind power energy for energy and environmental policies has been growing in past recent years. However, because of its random nature over time, the wind generation cannot be reliable dispatched and perfectly forecasted, becoming a challenge when integrating this production in power systems. In addition the wind energy has to cope with the diversity of production resulting from alternative wind power profiles located in different regions. In 2012, Portugal presented a cumulative installed capacity distributed over 223 wind farms [1]. In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour (s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.In this work the circular data statistical methods are used to analyze and compare alternative spatial wind generation profiles. Variables indicating extreme situations are analyzed. The hour (s) of the day where the farm production attains its maximum daily production is considered. This variable was converted into circular variable, and the use of circular statistics enables to identify the daily hour distribution for different wind production profiles. This methodology was applied to a real case, considering data from the Portuguese power system regarding the year 2012 with a 15-minutes interval. Six geographical locations were considered, representing different wind generation profiles in the Portuguese system.