R. R. Deza

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.

KPZ equation: Galilean-invariance violation, consistency, and fluctuation-dissipation issues in real-space discretization

Strong constraints are drawn for the choice of real-space discretization schemes, using the known fact that the KPZ equation results from a diffusion equation (with multiplicative noise) through a Hopf-Cole transformation. Whereas the nearest-neighbor discretization passes the consistency tests, known examples in the literature do not. We emphasize the importance of the Lyapunov functional as natural starting point for real-space discretization and, in the light of these findings, challenge the mainstream opinion on the relevance of Galilean invariance.

Replication of noise-sustained autocatalytic chemical structures.

Autocatalytic systems in a differential-flow reactor may undergo a differential-flow-induced chemical instability toward a convectively unstable regime, in which noise-sustained structures may appear. This is the case of a system with Gray-Scott kinetics in a packed-bed reactor, as reported in [B. von Haeften and G. Izus, Phys. Rev. E 67, 056207 (2003)]. In this work, two identical copies of such a system are coupled in master-slave configuration and submitted to independent spatiotemporal Gaussian white noise sources. Numerical simulation of two-dimensional reactors with uniform and Poiseuille flows reveals that the slave system replicates to a very high degree of precision and the convective patterns arising in the master one due to the presence of noise. The quality of this synchronization is assessed through several measures. A convective instability in the synchronization manifold is theoretically predicted and numerically confirmed.

Stochastic resonance between propagating extended attractors

The nonequilibrium Ising—Bloch (NIB) bifurcation of the FitzHugh—Nagumo (FHN) model with nondiffusing inhibitor provides a beautiful instance of an extended bistable system with counterpropagating fronts or Bloch walls (BW) as stable attractors. Moreover, these fronts are chiral and parity‐related, and the barrier between them is the unstable stationary front or Ising wall (IW). Here we show by means of numerical simulation the presence of stochastic resonance in the transition between 1D BW of opposite chiralities when an additive noise is included. A scaling law of the signal‐to‐noise ratio (SNR) with the distance to the critical point is numerically observed and theoretically characterized in terms of an effective nonequilibrium potential.

On the role of Galilean invariance in KPZ

Starting from a variational formulation of the Kardar‐Parisi‐Zhang (KPZ) equation, we point out some strong constraints and consistency tests, to be fulfilled by real‐space discretization schemes. In the light of these findings, the mainstream opinion on the relevance of Galilean invariance and the fluctuation—dissipation theorem (peculiar of 1D) is challenged.

Modular system for data acquisition and control of experiments with digital output.

In the present work, the design of an efficient, modular, and scalable data acquisition and control system is described. It consists of an array of microcontrollers and memories, which feed a single concentrating unit whose information can be accessed by means of a universal series bus (USB) interface to be processed later on. Signal levels can be controlled through a set of digital potentiometers. This system is ideal for experiments with a large number of digital outputs.

Fluctuation theorems from non-equilibrium Onsager-Machlup theory for a Brownian particle in a time-dependent harmonic potential

We discuss the case of a Brownian particle which is harmonically bound and multiplicatively forced-namely bound by V(x,t)=1/2 a(t)x2 where a(t)is externally controlled-as another instance that provides a generalization of Onsager-Machlup’s theory to non-equilibrium states, thus allowing establishment of several fluctuation theorems. In particular, we outline the derivation of a fluctuation theorem for work, through the calculation of the work probability distribution as a functional integral over stochastic trajectories.