Synchronization universality classes and stability of smooth, coupled map lattices

We study two problems related to spatially extended systems: the dynamical stability and the universality classes of the replica synchronization transition. We use a simple model of one dimensional coupled map lattices and show that chaotic behavior implies that the synchronization transition belongs to the multiplicative noise universality class, while stable chaos implies that the synchronization transition belongs to the directed percolation universality class.Comment: 6 pages, 7 figure

Stochastic Sensitivity Analysis of Volcanic Activity

In the present paper, we study the stochastically induced behavior of a nonlinear volcanic model containing three prognostic variables: the plug velocity u, the pressure p under the plug, and the conduit volume V. The nouvelle phenomena of noise-induced transitions from the equilibrium to the cycle in the bistability parametric zone and noise-induced excitement with the generation of spike oscillations in the monostability zone are found in the presence of N-shaped friction force. To study these phenomena numerically, we used the computations of random solutions, the phase trajectories and time series, the statistics of interspike intervals, and the mean square variations. To study these phenomena analytically, we applied the stochastic sensitivity function technique and the confidence domains method. This approach is used to predict the noise-induced transition from a “dormant volcano” state to the “active volcano” mode. From the physical point of view, the volcano is capable to become active under the influence of external noises in the friction force, which model various compositions and properties of volcanic rocks. What is more, the volcanic plug can pop out when its slipping becomes heavy, and the volcano can erupt. © 2020 John Wiley & Sons, Ltd.This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project number FEUZ‐2020‐0057)

Multifractal analysis of stress time series during ultrathin lubricant film melting

Melting of an ultrathin lubricant film confined between two atomically flat surfaces is we studied using the rheological model for viscoelastic matter approximation. Phase diagram with domains, corresponding to sliding, dry, and two types of $stick-slip$ friction regimes has been built taking into account additive noises of stress, strain, and temperature of the lubricant. The stress time series have been obtained for all regimes of friction using the Stratonovich interpretation. It has been shown that self-similar regime of lubricant melting is observed when intensity of temperature noise is much larger than intensities of strain and stress noises. This regime is defined by homogenous distribution, at which characteristic stress scale is absent. We study stress time series obtained for all friction regimes using multifractal detrended fluctuation analysis. It has been shown that multifractality of these series is caused by different correlations that are present in the system and also by a power-law distribution. Since the power-law distribution is related to small stresses, this case corresponds to self-similar solid-like lubricant.Comment: 22 pages, 10 figures, 41 reference

Fronts dynamics in the presence of spatio-temporal structured noises

Front dynamics modeled by a reaction-diffusion equation are studied under the influence of spatio-temporal structured noises. An effective deterministic model is analytical derived where the noise parameters, intensity, correlation time and correlation length appear explicitely. The different effects of these parameters are discussed for the Ginzburg-Landau and Schl\"ogl models. We obtain an analytical expression for the front velocity as a function of the noise parameters. Numerical simulations results are in a good agreement with the theoretical predictions.Comment: 11 pages, 6 figures; REVTEX; to be published in Phys.Rev.E, july 200

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001