J. Pontes

Gradient pattern analysis of Swift–Hohenberg dynamics: phase disorder characterization

In this paper, we analyze the onset of phase-dominant dynamics in a uniformly forced system. The study is based on the numerical integration of the Swift–Hohenberg equation and adresses the characterization of phase disorder detected from gradient computational operators as complex entropic form (CEF). The transition from amplitude to phase dynamics is well characterized by means of the variance of the CEF phase component.

Numerical Solution of the Walgraef-Aifantis Model for Simulation of Dislocation Dynamics in Materials Subjected to Cyclic Loading

Strain localization and dislocation pattern formation are typical features of plastic deformation in metals and alloys. Glide and climb dislocation motion along with accompanying production/ annihilation processes of dislocations lead to the occurrence of instabilities of initially uniform dislocation distributions. These instabilities result into the development of various types of dislocation micro-structures, such as dislocation cells, slip and kink bands, persistent slip bands, labyrinth structures, etc., depending on the externally applied loading and the intrinsic lattice constraints. The Walgraef-Aifantis (WA) (Walgraef and Aifanits, J. Appl. Phys., 58, 668, 1985) model is an example of a reaction-diffusion model of coupled nonlinear equations which describe 0 formation of forest (immobile) and gliding (mobile) dislocation densities in the presence of cyclic loading. This paper discuss two versions of the WA model, the first one comprising linear diffusion of the density of mobile dislocations and the second one, with nonlinear diffusion of said variable. Subsequently, the paper focus on a finite difference, second order in time Cranck-Nicholson semi-implicit scheme, with internal iterations at each time step and a spatial splitting using the Stabilizing, Correction (Christov and Pontes, Mathematical and Computer 0, 35 , 87, 2002) for solving the model evolution equations in two dimensions. The discussion on the WA model and on the numerical scheme was already presented on a conference paper by the authors (Pontes et al., AIP Conference Proceedings, Vol. 1301 pp. 511-519, 2010). The first results of four simulations, one with linear diffusion of the mobile dislocations and three with nonlinear diffusion are presented. Several phenomena were observed in the numerical simulations, like the increase of the fundamental wavelength of the structure, the increase of the walls height and the decrease of its thickness.

Modelling Hydrodynamic Stability in Electrochemical Cells

We review the key points concerning the linear stability of the classical von Karman’s solution of rotating disk flow, modified by the coupling, through the fluid viscosity, with concentration field of a chemical species. The results were recently published by Mangiavacchi et al. (Phys. Fluids, 19: 114109, 2007) and refer to electrochemical cells employing iron rotating disk electrodes, which dissolve in the 1 M H2SO4 solution of the electrolyte. Polarization curves obtained in such cells present a current instability at the beginning of the region where the current is controlled by the the hydrodynamics. The onset of the instability occurs in a range of potentials applied to the cell and disappear above and below this range. Dissolution of the iron electrode gives rise to a thin concentration boundary layer, with thickness of about 4% of the thickness of the hydrodynamic boundary layer. The concentration boundary layer increases the interfacial fluid viscosity, diminishes the diffusion coefficient and co...