A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Influence of network effects on the diffusion of information systems: the case of open source

Doutoramento em Gestão

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.

Laser-induced diffusion decomposition in Fe-V thin-film alloys

We investigate the origin of ferromagnetism induced in thin-film (similar to 20 nm) Fe-V alloys by their irradiation with subpicosecond laser pulses. We find with Rutherford backscattering that the magnetic modifications follow a thermally stimulated process of diffusion decomposition, with formation of a-few-nm-thick Fe enriched layer inside the film. Surprisingly, similar transformations in the samples were also found after their long-time (similar to 10(3) s) thermal annealing. However, the laser action provides much higher diffusion coefficients (similar to 4 orders of magnitude) than those obtained under standard heat treatments. We get a hint that this ultrafast diffusion decomposition occurs in the metallic glassy state achievable in laser-quenched samples. This vitrification is thought to be a prerequisite for the laser-induced onset of ferromagnetism that we observe. 2014 Elsevier B.V. All rights reserved.

Viscosity and self-diffusion coefficients of dialkyl adipates: a correlation scheme with predictive capabilities

A correlation and predictive scheme for the viscosity and self-diffusivity of liquid dialkyl adipates is presented. The scheme is based on the kinetic theory for dense hard-sphere fluids, applied to the van der Waals model of a liquid to predict the transport properties. A "universal" curve for a dimensionless viscosity of dialkyl adipates was obtained using recently published experimental viscosity and density data of compressed liquid dimethyl (DMA), dipropyl (DPA), and dibutyl (DBA) adipates. The experimental data are described by the correlation scheme with a root-mean-square deviation of +/- 0.34 %. The parameters describing the temperature dependence of the characteristic volume, V-0, and the roughness parameter, R-eta, for each adipate are well correlated with one single molecular parameter. Recently published experimental self-diffusion coefficients of the same set of liquid dialkyl adipates at atmospheric pressure were correlated using the characteristic volumes obtained from the viscosity data. The roughness factors, R-D, are well correlated with the same single molecular parameter found for viscosity. The root-mean-square deviation of the data from the correlation is less than 1.07 %. Tests are presented in order to assess the capability of the correlation scheme to estimate the viscosity of compressed liquid diethyl adipate (DEA) in a range of temperatures and pressures by comparison with literature data and of its self-diffusivity at atmospheric pressure in a range of temperatures. It is noteworthy that no data for DEA were used to build the correlation scheme. The deviations encountered between predicted and experimental data for the viscosity and self-diffusivity do not exceed 2.0 % and 2.2 %, respectively, which are commensurate with the estimated experimental measurement uncertainty, in both cases.