Horacio S. Wio

Experimental evidence of stochastic resonance without tuning due to non-Gaussian noises.

In order to test theoretical predictions, we have studied the phenomenon of stochastic resonance in an electronic experimental system driven by white non-Gaussian noise. In agreement with the theoretical predictions our main findings are an enhancement of the sensibility of the system together with a remarkable widening of the response (robustness). This implies that even a single resonant unit can reach a marked reduction in the need for noise tuning.

Transition from anomalous to normal hysteresis in a system of coupled Brownian motors: a mean-field approach.

We address a recently introduced model describing a system of periodically coupled nonlinear phase oscillators submitted to multiplicative white noises, wherein a ratchetlike transport mechanism arises through a symmetry-breaking noise-induced nonequilibrium phase transition. Numerical simulations of this system reveal amazing novel features such as negative zero-bias conductance and anomalous hysteresis, explained by performing a strong-coupling analysis in the thermodynamic limit. Using an explicit mean-field approximation, we explore the whole ordered phase finding a transition from anomalous to normal hysteresis inside this phase, estimating its locus, and identifying (within this scheme) a mechanism whereby it takes place.

Critical slowing-down in the FitzHugh–Nagumo model: A non-equilibrium potential approach

Abstract We exploit our recent finding of an exact non-equilibrium potential (NEP) for the space-independent FitzHugh–Nagumo (FHN) model [Phys. Rev. E 58 (1998) 93], to characterize the transition from the bistable regime towards the excitable one. The critical slowing-down (CSD) is clearly seen in the time-evolution of the NEP.

Evolution of reaction-diffusion patterns in infinite and bounded domains

We introduce a semi-analytical method to study the evolution of spatial structures in reaction-diffusion systems. It consists in writing an integral equation for the relevant densities, from the propagator of the linear part of the evolution operator. In order to test the method, we perform an exhaustive study of a one-dimensional reaction-diffusion model associated to an electrical device - the ballast resistor. We consider the evolution of step and bubble-shaped initial density profiles in free space as well as in a semi-infinite domain with Dirichlet and Neumann boundary conditions. The piecewise-linear form of the reaction term, which preserves the basic ingredients of more complex nonlinear models, makes it possible to obtain exact wave-front solutions in free space and stationary solutions in the bounded domain. Short and long-time behaviour can also be analytically studied, whereas the evolution at intermediate times is analyzed by numerical techniques. We paid particular attention to the features introduced in the evolution by boundary conditions.

STOCHASTIC RESONANCE IN AN ACTIVATOR-INHIBITOR SYSTEM THROUGH ADIABATIC AND QUASI-VARIATIONAL APPROACHES

We study the phenomenon of stochastic resonance in a spatially extended system. An activator–inhibitor reaction–diffusion model is analyzed through two different approximations: an adiabatic one leading to a known form of the Graham’s nonequilibrium potential, and a quasi-variational approach that allows to obtain an approximated form of Graham’s potential for a different parameter region. Those potentials have been exploited to obtain, firstly the probability for the decay of the metastable extended states, and secondly expressions for the correlation function and for the signal-to-noise ratio, within the framework of a two state description. The analytical results show how this ratio depends on both local and nonlocal coupling parameters.

Non-Markovian diffusion-like equation for transport processes with anisotropic scattering

Abstract In order to describe particles diffusing in a medium with anisotropic scattering, we have derived a non-Markovian pseudo-diffusion equation starting from the solution of the one-dimensional persistent random walk model. The differential equation has a space-time convolution with a well-defined kernel. The analytic solution of this non-Markovian diffusion equation, in Fourier space, gives the conditional probability (essentially a renormalized Gaussian distribution) which is a function of the order parameter ( p − q ) ( p and q being the forward and backward scattering probabilities respectively). The velocity autocorrelation function has also been obtained analytically, showing the dependence with the order parameter.

Global analysis of pattern selection and bifurcations in monostable reaction-diffusion systems

We study a piecewise linear version of a one-component monostable reaction diffusion model in a bounded domain, subjected to partially reflecting boundary conditions (“albedo” b.c.). We analyze the local and the global stability of the merging patterns and detect a bifurcation of the uniform solution induced by changes in the reflectivity of the boundaries.

Disordering effects of colour in a system of coupled Brownian motors: phase diagram and anomalous to normal hysteresis transition

Abstract A system of periodically coupled nonlinear phase oscillators—submitted to both additive and multiplicative white noises—has been recently shown to exhibit ratchetlike transport, negative zero-bias conductance, and anomalous hysteresis. These features stem from the asymmetry of the stationary probability distribution function, arising through a noise-induced non-equilibrium phase transition which is re-entrant as a function of the multiplicative noise intensity. Using an explicit mean-field approximation we analyse the effect of the multiplicative noises being coloured, finding a contraction of the ordered phase (and a re-entrance as a function of the coupling) on one hand, and a shift of the transition from anomalous to normal hysteresis inside this phase on the other.

Separation factor of membranes used for isotopic separation by gaseous diffusion: pore morphology influence and effect of cracks

Abstract The control of membrane pore size is critical for the separation efficiency of the isotopic separation of 235/238 U in the conventional uranium enrichment process by gaseous diffusion. Theoretical evaluations generally assume that the pores are cylindrical, however the actual pore morphology could be completely different. Here, we consider the case of pores with rectangular slit morphology (‘groove-like’ pores) of width l and length D (when D≫l). We evaluate the separation factor α for membranes consisting of a mixture of ‘cylindrical’ and ‘rectangular’ pores. These two shapes may be considered as two extreme cases of pore morphology, and it is possible to represent any arbitrary actual morphology approximately as a mixture of such pores. In addition, the existence of defects on membranes, such cracks, crevices, grooves, etc. may severely affect membrane performance; and this will be more critical the smaller the pores. Here, we also use this ‘rectangular’ model to study the influence of such cracks on the separation efficiency of membranes.

TRAPPING KINETICS IN DIFFUSION-LIMITED BIMOLECULAR REACTIONS. SOURCES WITHIN THE GALANIN MODEL

We have introduced the effect of particle sources within a previously developed model of diffusion-limited bimolecular reactions. We have considered two kinds of sources: extended and point-like ones in the case of a trapping process by fixed traps. We have studied not only the asymptotic behaviour but the whole time regime as well, in the case of a single trap. Also the short and long time regime in a system of an infinite number of periodically located traps has been studied. The comparison with simulations shows that both theoretical regimes yield a rather good agreement indicating that the description is adequate for the whole time regime.