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.

Pt/Carbon materials as Bi-Functional catalysts for N-decane hydroisomerization

The activity and selectivity of bi-functional carbon-supported platinum catalysts for the hydroisomerization of n-alkanes have been studied. The influence of the properties of the carbon support on the performance of the catalysts were investigated by incorporating the metallic function on a series of carbons with varied porosity (microporous: GL-50 from Norit, and mesoporous: CMK-3) and surface chemistry (modified by wet oxidation). The characterization results achieved with H-2 chemisorption and TEM showed differences in surface metal concentrations and metal-support interactions depending on the support composition. The highest metal dispersion was achieved after oxidation of the carbon matrix in concentrated nitric acid, suggesting that the presence of surface functional sites distributed in inner and outer surface favors a homogeneous metal distribution. On the other hand, the higher hydrogenating activity of the catalysts prepared with the mesoporous carbon pointed out that a fast molecular traffic inside the pores plays an important role in the catalysts performance. For n-decane hydroisomerization of long chain n-alkanes, higher activities were obtained for the catalysts with an optimized acidity and metal dispersion along with adequate porosity, pointing out the importance of the support properties in the performance of the catalysts.

Properties of patchy colloidal particles close to a surface: a Monte Carlo and density functional study

We investigate the behavior of a patchy particle model close to a hard-wall via Monte Carlo simulation and density functional theory (DFT). Two DFT approaches, based on the homogeneous and inhomogeneous versions of Wertheim's first order perturbation theory for the association free energy are used. We evaluate, by simulation and theory, the equilibrium bulk phase diagram of the fluid and analyze the surface properties for two isochores, one of which is close to the liquid side of the gas-liquid coexistence curve. We find that the density profile near the wall crosses over from a typical high-temperature adsorption profile to a low-temperature desorption one, for the isochore close to coexistence. We relate this behavior to the properties of the bulk network liquid and find that the theoretical descriptions are reasonably accurate in this regime. At very low temperatures, however, an almost fully bonded network is formed, and the simulations reveal a second adsorption regime which is not captured by DFT. We trace this failure to the neglect of orientational correlations of the particles, which are found to exhibit surface induced orientational order in this regime.

Liquid-vapor interfaces of patchy colloids

We investigate the liquid-vapor interface of a model of patchy colloids. This model consists of hard spheres decorated with short-ranged attractive sites ("patches") of different types on their surfaces. We focus on a one-component fluid with two patches of type A and nine patches of type B (2A9B colloids), which has been found to exhibit reentrant liquid-vapor coexistence curves and very low-density liquid phases. We have used the density-functional theory form of Wertheim's first-order perturbation theory of association, as implemented by Yu and Wu [J. Chem. Phys. 116, 7094 (2002)], to calculate the surface tension, and the density and degree of association profiles, at the liquid-vapor interface of our model. In reentrant systems, where AB bonds dominate, an unusual thickening of the interface is observed at low temperatures. Furthermore, the surface tension versus temperature curve reaches a maximum, in agreement with Bernardino and Telo da Gama's mesoscopic Landau-Safran theory [Phys. Rev. Lett. 109, 116103 (2012)]. If BB attractions are also present, competition between AB and BB bonds gradually restores the monotonic temperature dependence of the surface tension. Lastly, the interface is "hairy," i.e., it contains a region where the average chain length is close to that in the bulk liquid, but where the density is that of the vapor. Sufficiently strong BB attractions remove these features, and the system reverts to the behavior seen in atomic fluids.

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.