Variational approach to KPZ: Fluctuation theorems and large deviation function for entropy production.

Motivated by the time behavior of the functional arising in the variational approach to the Kardar-Parisi-Zhang (KPZ) equation, and in order to study fluctuation theorems in such a system, we have adapted a path-integral scheme that adequately fits to this kind of study dealing with unstable systems. As the KPZ system has no stationary probability distribution, we show how to proceed for obtaining detailed as well as integral fluctuation theorems. This path-integral methodology, together with the variational approach, in addition to allowing analyze fluctuation theorems, can be exploited to determine a large deviation function for entropy production.

Stochastic entropies and fluctuation theorems for a discrete one-dimensional Kardar-Parisi-Zhang system.

The statistical properties of stochastic entropies in a discrete stationary one-dimensional Kardar-Parisi-Zhang system are numerically studied. As the usual time-independent solution of the associated Fokker-Planck equation is not strictly stationary, it is necessary to transform the current variables to other variables with zero spatial mean. We resorted to discrete representations in order to prove the statistical properties of entropies, and we performed a direct test of the fluctuation theorem.

Waves of seed propagation induced by delayed animal dispersion.

We study a model of seed dispersal that considers the inclusion of an animal disperser moving diffusively, feeding on fruits and transporting the seeds, which are later deposited and capable of germination. The dynamics depends on several population parameters of growth, decay, harvesting, transport, digestion and germination. In particular, the deposition of transported seeds at places away from their collection sites produces a delay in the dynamics, whose effects are the focus of this work.

Enhanced transport through desorption-mediated diffusion.

We present a master equation approach to the study of the bulk-mediated surface diffusion mechanism in a three-dimensional confined domain. The proposed scheme allowed us to evaluate analytically a number of magnitudes that were used to characterize the efficiency of the bulk-mediated surface transport mechanism, for instance, the mean escape time from the domain, and the mean number of distinct visited sites on the confined domain boundary.

Narrow-escape-time problem: the imperfect trapping case.

We present a master equation approach to the narrow escape time (NET) problem, i.e., the time needed for a particle contained in a confining domain with a single narrow opening to exit the domain for the first time.

Recent developments on the Kardar-Parisi-Zhang surface-growth equation.

The stochastic nonlinear partial differential equation known as the Kardar-Parisi-Zhang (KPZ) equation is a highly successful phenomenological mesoscopic model of surface and interface growth processes. Its suitability for analytical work, its explicit symmetries and its prediction of an exact dynamic scaling relation for a one-dimensional substratum led people to adopt it as a 'standard' model in the field during the last quarter of a century. At the same time, several conjectures deserving closer scrutiny were established as dogmas throughout the community.

Discretization-related issues in the Kardar-Parisi-Zhang equation: consistency, Galilean-invariance violation, and fluctuation-dissipation relation.

In order to perform numerical simulations of the Kardar-Parisi-Zhang (KPZ) equation, in any dimensionality, a spatial discretization scheme must be prescribed. The known fact that the KPZ equation can be obtained as a result of a Hopf-Cole transformation applied to a diffusion equation (with multiplicative noise) is shown here to strongly restrict the arbitrariness in the choice of spatial discretization schemes. On one hand, the discretization prescriptions for the Laplacian and the nonlinear (KPZ) term cannot be independently chosen.

System size stochastic resonance: general nonequilibrium potential framework.

We study the phenomenon of system size stochastic resonance within the nonequilibrium potential framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing that through the analysis of that potential we can obtain a clear physical interpretation of this phenomenon in wide classes of extended systems. Depending on the characteristics of the system, the phenomenon is associated with a breaking of the symmetry of the nonequilibrium potential or a deepening of the potential minima yielding an effective scaling of the noise intensity with the system size.

Interplay between noise and boundary conditions in pattern formation in adsorbed substances.

We have studied the interplay between noise and boundary conditions on the possibility of noise induced pattern formation. With this aim, we have exploited a deterministic model for pattern formation in adsorbed substances--including the effect of lateral interactions--used to describe the phenomenon of adsorption in surfaces, where a multiplicative noise fulfilling a fluctuation-dissipation relation was added. We have found solutions for different boundary conditions, particularly corresponding to two stable and one unstable patterns, where one of the stable and the unstable one, are purely induced by the multiplicative noise.

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.

Limit cycle induced by multiplicative noise in a system of coupled Brownian motors.

We study a model consisting of N nonlinear oscillators with global periodic coupling, and local multiplicative and additive noises. The model was shown to undergo a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced "ratchet" behavior. A previous study [H.

Coupling-reentrant phase transition, complex hysteretic behavior, and efficiency optimization in coupled phase oscillators submitted to colored flashing potentials.

A recent mean-field analysis of a model consisting of N nonlinear phase oscillators-under the joint influence of global periodic coupling with strength K0 and of local multiplicative and additive noises-has shown a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced transport, or "ratchet" behavior. In a previous paper we focused on the relationship between the character of the (mean velocity vs load force F) hysteresis loop, the number of "homogeneous" mean-field solutions, and the shape of the stationary mean-field probability distribution function (PDF). Here we assume that the multiplicative noises of the model are Ornstein-Uhlenbeck with common strength Q and self-correlation time tau.

Reaction kinetics of diffusing particles injected into a reactive substrate.

We analyze the kinetics of trapping (A+B-->B) and annihilation (A+B-->0) processes on a one-dimensional substrate with homogeneous distribution of immobile B particles while the A particles are supplied by a localized source. For the imperfect reaction case, we analyze both problems by means of a stochastic model and compare the results with numerical simulations. In addition, we present the exact analytical results of the stochastic model for the case of perfect trapping.

Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials.

We have obtained the exact expression of the diffusion propagator in the time-dependent anharmonic potential V(x,t)=1 / 2a(t)x(2)+b ln x. The underlying Euclidean metric of the problem allows us to obtain analytical solutions for a whole family of the elastic parameter a(t), exploiting the relation between the path integral representation of the short time propagator and the modified Bessel functions. We have also analyzed the conditions for the appearance of a nonzero flow of particles through the infinite barrier located at the origin (b<0).

Stochastic resonance in extended bistable systems: the role of potential symmetry.

We study the role of potential symmetry in a three-field reaction-diffusion system presenting bistability by means of a two-state theory for stochastic resonance in general asymmetric systems. By analyzing the influence of different parameters in the optimization of the signal-to-noise ratio, we observe that this magnitude always increases with the symmetry of the system's potential, indicating that it is this feature which governs the optimization of the system's response to periodic signals.

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.

Pattern dynamics in bidimensional oscillatory media with bistable inhomogeneities.

By means of numerical simulations, we study pattern dynamics in selected examples of inhomogeneous active media described by a reaction diffusion model of the activator-inhibitor type. We consider inhomogeneities corresponding to a variation in space of the (nonlinear) reaction characteristics of the system or the diffusion constants. Three different bidimensional systems are analyzed: an oscillatory medium in a square reactor with a circular central bistable domain, and cases of a bistable stripe immersed in an oscillatory medium in a trapezoidal reactor and in a rectangular reactor with inhomogeneous diffusion.

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.

Stochastic resonance driven by time-modulated correlated white noise sources.

We analyze the effects caused by the simultaneous presence of correlated additive and multiplicative noises for stochastic resonance. Besides the standard potential modulation we also consider a time-periodic variation of the correlation between the two noise sources. As a foremost result we find that stochastic resonance, as characterized by the signal-to-noise ratio and the spectral amplification, becomes characteristically broadened.

Anomalous diffusion with absorption: exact time-dependent solutions.

Recently, analytical solutions of a nonlinear Fokker-Planck equation describing anomalous diffusion with an external linear force were found using a nonextensive thermostatistical Ansatz. We have extended these solutions to the case when an homogeneous absorption process is also present. Some peculiar aspects of the interrelation between the deterministic force, the nonlinear diffusion, and the absorption process are discussed.

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.

Enhancement of stochastic resonance in distributed systems due to a selective coupling.

Recent massive numerical simulations have shown that the response of a "stochastic resonator" is enhanced as a consequence of spatial coupling. Similar results have been analytically obtained in a reaction-diffusion model, using nonequilibrium potential techniques. We now consider a field-dependent diffusivity and show that the selectivity of the coupling is more efficient for achieving stochastic-resonance enhancement than its overall value in the constant-diffusivity case.

An exact analytical solution of a three-component model for competitive coexistence.

A three-component competition system is modeled as a reaction-diffusion process. An exact analytical solution has been found that indicates that in certain situations the classical results on extinction and coexistence of Lotka-Volterra-type equations are no longer valid. Cases with one or both predators diffuse are analyzed, and the stability question is discussed.