On the analytical solutions of the Hindmarsh-Rose neuronal model

In this article we analytically solve the Hindmarsh-Rose model (Proc R Soc Lond B221:87-102, 1984) by means of a technique developed for strongly nonlinear problems-the step homotopy analysis method. This analytical algorithm, based on a modification of the standard homotopy analysis method, allows us to obtain a one-parameter family of explicit series solutions for the studied neuronal model. The Hindmarsh-Rose system represents a paradigmatic example of models developed to qualitatively reproduce the electrical activity of cell membranes. By using the homotopy solutions, we investigate the dynamical effect of two chosen biologically meaningful bifurcation parameters: the injected current I and the parameter r, representing the ratio of time scales between spiking (fast dynamics) and resting (slow dynamics). The auxiliary parameter involved in the analytical method provides us with an elegant way to ensure convergent series solutions of the neuronal model. Our analytical results are found to be in excellent agreement with the numerical simulations.

The condensation and ordering of models of empty liquids

We consider a simple model consisting of particles with four bonding sites ("patches"), two of type A and two of type B, on the square lattice, and investigate its global phase behavior by simulations and theory. We set the interaction between B patches to zero and calculate the phase diagram as the ratio between the AB and the AA interactions, epsilon(AB)*, varies. In line with previous work, on three-dimensional off-lattice models, we show that the liquid-vapor phase diagram exhibits a re-entrant or "pinched" shape for the same range of epsilon(AB)*, suggesting that the ratio of the energy scales - and the corresponding empty fluid regime - is independent of the dimensionality of the system and of the lattice structure. In addition, the model exhibits an order-disorder transition that is ferromagnetic in the re-entrant regime. The use of low-dimensional lattice models allows the simulation of sufficiently large systems to establish the nature of the liquid-vapor critical points and to describe the structure of the liquid phase in the empty fluid regime, where the size of the "voids" increases as the temperature decreases. We have found that the liquid-vapor critical point is in the 2D Ising universality class, with a scaling region that decreases rapidly as the temperature decreases. The results of simulations and theoretical analysis suggest that the line of order-disorder transitions intersects the condensation line at a multi-critical point at zero temperature and density, for patchy particle models with a re-entrant, empty fluid, regime. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3657406]

Electrochemical and analytical investigation of passive films formed on stainless steels in alkaline media

Passive films were grown in potentiodynamic mode, by cyclic voltammetry on AISI 316 and AISI 304 stainless steels. The composition of these films was investigated by X-ray photoelectron spectroscopy (XPS). The electrochemical behaviour and the chemical composition of the passive films formed by cyclic voltammetry were compared to those of films grown under natural conditions (by immersion at open circuit potential, OCP) in alkaline solutions simulating concrete. The study included the effect of pH of the electrolyte and the effect of the presence of chloride ions. The XPS results revealed important changes in the passive film composition, which becomes enriched in chromium and depleted in magnetite as the pH decreases. On the other hand, the presence of chlorides promotes a more oxidised passive layer. The XPS results also showed relevant differences on the composition of the oxide layers for the films formed under cyclic voltammetry and/or under OCP.