Sergio E. Mangioni

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.

Nonequilibrium phase transitions induced by multiplicative noise: Effects of self-correlation

A recently introduced lattice model, describing an extended system which exhibits a reentrant (symmetry-breaking, second-order) noise-induced nonequilibrium phase transition, is studied under the assumption that the multiplicative noise leading to the transition is colored. Within an effective Markovian approximation and a mean-field scheme it is found that when the self-correlation time tau of the noise is different from zero, the transition is also reentrant with respect to the spatial coupling D. In other words, at variance with what one expects for equilibrium phase transitions, a large enough value of D favors disorder. Moreover, except for a small region in the parameter subspace determined by the noise intensity sigma and D, an increase in tau usually prevents the formation of an ordered state. These effects are supported by numerical simulations.

A random walker on a ratchet potential: effect of a non Gaussian noise

Abstract.We analyze the effect of a colored non Gaussian noise on a model of a random walker moving along a ratchet potential. Such a model was motivated by the transport properties of motor proteins, like kinesin and myosin. Previous studies have been realized assuming white noises. However, for real situations, in general we could expect that those noises be correlated and non Gaussian. Among other aspects, in addition to a maximum in the current as the noise intensity is varied, we have also found another optimal value of the current when departing from Gaussian behavior. We show the relevant effects that arise when departing from Gaussian behavior, particularly related to currents enhancement, and discuss its relevance for both biological and technological situations.

Phase transitions and adsorption isotherm in multilayer adsorbates with lateral interactions

We analyze here a model for an adsorbate system composed of many layers by extending a theoretical approach used to describe pattern formation on a monolayer of adsorbates with lateral interactions. The approach shows, in addition to a first-order phase transition in the first layer, a transition in the second layer together with evidence of a “cascade” of transitions if more layers are included. The transition profiles, showing a staircase structure, corroborate this picture. The adsorption isotherm that came out of this approach is in qualitative agreement with numerical and experimental results.

Parrondo's games as a discrete ratchet

We write the master equation describing the Parrondos games as a consistent discretization of the Fokker–Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondos games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials correspond to fair games and winning games produce a tilted potential.

Stochastic resonance between dissipative structures in a bistable noise-sustained dynamics

We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arises. The stochastic resonance between the attractors of the noise-sustained dynamics is investigated theoretically in terms of a two-state approximation. The knowledge of the exact nonequilibrium potential allows us to obtain the output signal-to-noise ratio. Its maximum is predicted in the symmetric case for which both attractors have the same nonequilibrium potential value.

A Fokker-Planck description for Parrondo's games

We discuss in detail two recently proposed relations between the Parrondos games and the Fokker-Planck equation describing the flashing ratchet as the overdamped motion of a particle in a potential landscape. In both cases it is possible to relate exactly the probabilities of the games to the potential in which the overdamped particle moves. We will discuss under which conditions current-less potentials correspond to fair games and vie versa.

Limiting the stroke of a Schmitt trigger with multiplicative noise

We have devised an experiment whereby a bistable system is confined away from its deterministic attractors by means of multiplicative noise. Together with previous numerical results, our experimental results validate the hypothesis that the higher the slope of the noises multiplicative factor, the more it shifts the stationary states.

Stochastic dissipative solitons.

By the effect of aggregating currents, some systems display an effective diffusion coefficient that becomes negative in a range of the order parameter, giving rise to bistability among homogeneous states (HSs). By applying a proper multiplicative noise, localized (pinning) states are shown to become stable at the expense of one of the HSs. They are, however, not static, but their location fluctuates with a variance that increases with the noise intensity. The numerical results are supported by an analytical estimate in the spirit of the so-called solvability condition.

Optimization of Brownian Transport in a System of Globally Coupled Phase Oscillators by Means of Colored Noise

In a previous work[1], we performed a mean-field analysis of a model for noise-induced transport (“ratchet” behavior)[2]: a system of nonlinear phase oscillators—globally coupled with strength K 0 and submitted to local “flashing” potentials with common noise strength Q— undergoes a reentrant noise-induced non-equilibrium phase transition towards a brokensymmetry phase characterized by an asymmetric stationary mean-field probability distribution function (PDF) p st (x), and exhibiting a spontaneous particle current (\( \left\langle {\dot X} \right\rangle \ne 0 \) in the absence of a load force F) and hysteresis in its \( \left\langle {\dot X} \right\rangle \) vs F characteristic. Our focus was the relationship between the (normal or anomalous) character of the hysteresis loop, the number of “homogeneous” mean-field solutions, and the shape of p st (x). In subsequent works[3] we let the multiplicative noises that drive the “flashing” potentials be Ornstein- Uhlenbeck—with common self-correlation time τiand explored the consequences of this assumption on the (Q,K 0) phase diagram and on the transport properties, resorting to the “unified colored noise approximation” (UCNA). In this work we take a closer look to the efficiency ∈ of the mechanical rectification process (in the region where it is positive) to show that it attains a maximum for a finite value of τ. We also follow the τ-evolution of the shape of the “effective potential” at two points in the phase diagram.