Noise-induced scenario for inverted phase diagrams

We introduce a class of exactly solvable models exhibiting an ordering noise-induced phase transition in which order arises as a result of a balance between the relaxing deterministic dynamics and the randomizing character of the fluctuations. A finite-size scaling analysis of the phase transition reveals that it belongs to the universality class of the equilibrium Ising model. All these results are analyzed in the light of the nonequilibrium probability distribution of the system, which can be obtained analytically. Our results could constitute a possible scenario of inverted phase diagrams in the so-called lower critical solution temperature transitions.

Effects of external noise on the Swift-Hohenberg Equation

The Swift-Hohenberg equation is studied in the presence of a multiplicative noise. This stochastic equation could describe a situation in which a noise has been superimposed on the temperature gradient between the two plates of a Rayleigh-Bnard cell. A linear stability analysis and numerical simulations show that, in constrast to the additive-noise case, convective structures appear in a regime in which a deterministic analysis predicts a homogeneous solution.

Regular wave propagation out of noise in chemical active media

A pacemaker, regularly emitting chemical waves, is created out of noise when an excitable photosensitive Belousov-Zhabotinsky medium, strictly unable to autonomously initiate autowaves, is forced with a spatiotemporal patterned random illumination. These experimental observations are also reproduced numerically by using a set of reaction-diffusion equations for an activator-inhibitor model, and further analytically interpreted in terms of genuine coupling effects arising from parametric fluctuations. Within the same framework we also address situations of noise-sustained propagation in subexcitable media.

Spatiotemporal order out of noise

Experimental observations of self-organized behavior arising out of noise are also described, and details on the numerical algorithms needed in the computer simulation of these problems are given.

Mapping, organic matter mass and water volume of a peatland in Serra do Espinhaço Meridional

Peatlands form in areas where net primary of organic matter production exceeds losses due to the decomposition, leaching or disturbance. Due to their chemical and physical characteristics, bogs can influence water dynamics because they can store large volumes of water in the rainy season and gradually release this water during the other months of the year. In Diamantina, Minas Gerais, Brazil, a peatland in the environmental protection area of Pau-de-Fruta ensures the water supply of 40,000 inhabitants. The hypothesis of this study is that the peat bogs in Pau-de-Fruta act as an environment for carbon storage and a regulator of water flow in the Córrego das Pedras basin. The objective of this study was to estimate the water volume and organic matter mass in this peatland and to study the influence of this environment on the water flow in the Córrego das Pedras basin. The peatland was mapped using 57 transects, at intervals of 100 m. Along all transects, the depth of the peat bog, the Universal Transverse Mercator (UTM) coordinates and altitude were recorded every 20 m and used to calculate the area and volume of the peatland. The water volume was estimated, using a method developed in this study, and the mass of organic matter based on samples from 106 profiles. The peatland covered 81.7 hectares (ha), and stored 497,767 m³ of water, representing 83.7 % of the total volume of the peat bog. The total amount of organic matter (OM) was 45,148 t, corresponding to 552 t ha-1 of OM. The peat bog occupies 11.9 % of the area covered by the Córrego das Pedras basin and stores 77.6 % of the annual water surplus, thus controlling the water flow in the basin and consequently regulating the water course.

Noise-induced phase separation: Mean-field results

We present a study of a phase-separation process induced by the presence of spatially correlated multiplicative noise. We develop a mean-field approach suitable for conserved-order-parameter systems and use it to obtain the phase diagram of the model. Mean-field results are compared with numerical simulations of the complete model in two dimensions. Additionally, a comparison between the noise-driven dynamics of conserved and nonconserved systems is made at the level of the mean-field approximation.

Kinematic reduction of reaction-diffusion fronts with multiplicative noise. Derivation of stochastic sharp-interface equations

We study the dynamics of generic reaction-diffusion fronts, including pulses and chemical waves, in the presence of multiplicative noise. We discuss the connection between the reaction-diffusion Langevin-like field equations and the kinematic (eikonal) description in terms of a stochastic moving-boundary or sharp-interface approximation. We find that the effective noise is additive and we relate its strength to the noise parameters in the original field equations, to first order in noise strength, but including a partial resummation to all orders which captures the singular dependence on the microscopic cutoff associated with the spatial correlation of the noise. This dependence is essential for a quantitative and qualitative understanding of fluctuating fronts, affecting both scaling properties and nonuniversal quantities. Our results predict phenomena such as the shift of the transition point between the pushed and pulled regimes of front propagation, in terms of the noise parameters, and the corresponding transition to a non-Kardar-Parisi-Zhang universality class. We assess the quantitative validity of the results in several examples including equilibrium fluctuations and kinetic roughening. We also predict and observe a noise-induced pushed-pulled transition. The analytical predictions are successfully tested against rigorous results and show excellent agreement with numerical simulations of reaction-diffusion field equations with multiplicative noise.

Coherence and anticoherence resonance tunned by noise

We present numerical evidence and a theoretical analysis of the appearance of anticoherence resonance induced by noise, not predicted in former analysis of coherence resonance. We have found that this phenomenon occurs for very small values of the intensity of the noise acting on an excitable system, and we claim that this is a universal signature of a nonmonotonous relaxational behavior near its oscillatory regime. Moreover, we demonstrate that this new phenomenon is totally compatible with the standard situation of coherence resonance appearing at intermediate values of noise intensity.

Noise Induced Fronts

A simple model is introduced that exhibits a noise-induced front propagation and where the noise enters multiplicatively. The invasion of the unstable state is studied, both theoretically and numerically. A good agreement is obtained for the mean value of the order parameter and the mean front velocity using the analytical predictions of the linear marginal stability analysis.

Digital soil mapping: strategy for data pre-processing

The region of greatest variability on soil maps is along the edge of their polygons, causing disagreement among pedologists about the appropriate description of soil classes at these locations. The objective of this work was to propose a strategy for data pre-processing applied to digital soil mapping (DSM). Soil polygons on a training map were shrunk by 100 and 160 m. This strategy prevented the use of covariates located near the edge of the soil classes for the Decision Tree (DT) models. Three DT models derived from eight predictive covariates, related to relief and organism factors sampled on the original polygons of a soil map and on polygons shrunk by 100 and 160 m were used to predict soil classes. The DT model derived from observations 160 m away from the edge of the polygons on the original map is less complex and has a better predictive performance.

Mean field model for spatially extended systems in the presence of multiplicative noise

We present a mean field model that describes the effect of multiplicative noise in spatially extended systems. The model can be solved analytically. For the case of the phi4 potential it predicts that the phase transition is shifted. This conclusion is supported by numerical simulations of this model in two dimensions.

Excitability transitions and wave dynamics under spatiotemporal structured noise

We present an analytic and numerical study of the effects of external fluctuations in active media. Our analytical methodology transforms the initial stochastic partial differential equations into an effective set of deterministic reaction-diffusion equations. As a result we are able to explain and make quantitative predictions on the systematic and constructive effects of the noise, for example, target patterns created out of noise and traveling or spiral waves sustained by noise. Our study includes the case of realistic noises with temporal and spatial structures.

Effect of External Noise Correlation in Optical Coherence Resonance

Coherence resonance occurring in semiconductor lasers with optical feedback is studied via the Lang-Kobayashi model with external nonwhite noise in the pumping current. The temporal correlation and the amplitude of the noise have a highly relevant influence in the system, leading to an optimal coherent response for suitable values of both the noise amplitude and correlation time. This phenomenon is quantitatively characterized by means of several statistical measures.

Suppression of scroll wave turbulence by noise

Rotating scroll waves are dynamical spatiotemporal structures characteristic of three-dimensional active media. It is well known that, under low excitability conditions, scroll waves develop an intrinsically unstable dynamical regime that leads to a highly disorganized pattern of wave propagation. Such a ¿turbulent¿ state bears some resemblance to fibrillation states in cardiac tissue. We show here that this unstable regime can be controlled by using a spatially distributed random forcing superimposed on a control parameter of the system. Our results are obtained from numerical simulations but an explicit analytical argument that rationalizes our observations is also presented.

Noise-enhanced excitability in bistable activator-inhibitor media

We show that external fluctuations induce excitable behavior in a bistable spatially extended system with activator-inhibitor dynamics of the FitzHugh-Nagumo type. This can be understood as a mechanism for sustained signal propagation in bistable media. The phase diagram of the stochastic system is analytically obtained and numerically verified. For small-noise intensities, front propagation becomes unstable, and excitable pulses arise as the only possible spatiotemporal behavior of the system. For large-noise intensities, on the other hand, the system enters an effective regime of oscillatory behavior, where it exhibits spontaneous nucleation of pulses and synchronized firing.