Nonlinear oscillator with parametric colored noise: some analytical results

The asymptotic behavior of a nonlinear oscillator subject to a multiplicative Ornstein-Uhlenbeck noise is investigated. When the dynamics is expressed in terms of energy-angle coordinates, it is observed that the angle is a fast variable as compared to the energy. Thus, an effective stochastic dynamics for the energy can be derived if the angular variable is averaged out. However, the standard elimination procedure, performed earlier for a Gaussian white noise, fails when the noise is colored because of correlations between the noise and the fast angular variable. We develop here a specific averaging scheme that retains these correlations. This allows us to calculate the probability distribution function (P.D.F.) of the system and to derive the behavior of physical observables in the long time limit

Ratchet behavior in nonlinear Klein-Gordon systems with point-like inhomogeneities

We investigate the ratchet dynamics of nonlinear Klein-Gordon kinks in a periodic, asymmetric lattice of point-like inhomogeneities. We explain the underlying rectification mechanism within a collective coordinate framework, which shows that such system behaves as a rocking ratchet for point particles. Careful attention is given to the kink width dynamics and its role in the transport. We also analyze the robustness of our kink rocking ratchet in the presence of noise. We show that the noise activates unidirectional motion in a parameter range where such motion is not observed in the noiseless case. This is subsequently corroborated by the collective variable theory. An explanation for this new phenomenom is given

Resonance induced by repulsive interactions in a model of globally-coupled bistable systems

We show the existence of a competition-induced resonance effect for a generic globally coupled bistable system. In particular, we demonstrate that the response of the macroscopic variable to an external signal is optimal for a particular proportion of repulsive links. Furthermore, we show that a resonance also occurs for other system parameters, like the coupling strength and the number of elements. We relate this resonance to the appearance of a multistable region, and we predict the location of the resonance peaks, by a simple spectral analysis of the Laplacian matrix

Optimization of soliton ratchets in inhomogeneous sine-Gordon systems

Unidirectional motion of solitons can take place, although the applied force has zero average in time, when the spatial symmetry is broken by introducing a potential $V(x)$, which consists of periodically repeated cells with each cell containing an asymmetric array of strongly localized inhomogeneities at positions $x_{i}$. A collective coordinate approach shows that the positions, heights and widths of the inhomogeneities (in that order) are the crucial parameters so as to obtain an optimal effective potential $U_{opt}$ that yields a maximal average soliton velocity. $U_{opt}$ essentially exhibits two features: double peaks consisting of a positive and a negative peak, and long flat regions between the double peaks. Such a potential can be obtained by choosing inhomogeneities with opposite signs (e.g., microresistors and microshorts in the case of long Josephson junctions) that are positioned close to each other, while the distance between each peak pair is rather large. These results of the collective variables theory are confirmed by full simulations for the inhomogeneous sine-Gordon system

Depositional fluxes and concentrations of \u3csup\u3e7\u3c/sup\u3eBe and \u3csup\u3e210\u3c/sup\u3ePb in bulk precipitation and aerosols at the interface of Atlantic and Mediterranean coasts in Spain

Bulk depositional fluxes of 7Be and 210Pb in precipitation measured over a period of 16 months (April 2009–July 2010) in Huelva, Spain varied between 5.6 and 186 Bq m−2 month−1 (annual mean: 834 Bq m−2 year−1) and 0.8 and 8.1 Bq m−2 month−1 (annual mean: 59 Bq m−2 year−1), respectively, with the lowest depositional fluxes occurring during dry summer months. Quantitative evaluation of the precipitation-normalized seasonal depositional fluxes of 7Be and 210Pb indicates that the enrichment factor in winter is \u3c 1.0 while in 2010 spring, it is significantly higher than 1, possibly indicating input of air from the stratosphere-troposphere exchange (for 7Be). The specific activities of 7Be and 210Pb varied from 0.03 to 7.42 Bq L−1 (mean = 2.5 Bq L−1) and 0.005 to 1.07 BqL−1 (mean = 0.23 Bq L−1), respectively, with the highest values corresponding to the spring season. The spatial and temporal variations of 7Be and 210Pb in aerosols from three stations are evaluated and compared to their monthly depositional fluxes. The mean depositional velocity of aerosols using 7Be and 210Pb are similar, ∼0.5 cm s−1 and are compared to other published values. This is the first time the fractional amounts of 7Be and 210Pb in monthly bulk precipitation are compared to the fractional amount of precipitation and provides insight on how the amount of precipitation plays a key role on the scavenging of these nuclides. The importance of dry fallout is evaluated for the study site which has direct implications for other areas in the Mediterranean Climate Zone

Critical behavior of a Ginzburg-Landau model with additive quenched noise

We address a mean-field zero-temperature Ginzburg-Landau, or \phi^4, model subjected to quenched additive noise, which has been used recently as a framework for analyzing collective effects induced by diversity. We first make use of a self-consistent theory to calculate the phase diagram of the system, predicting the onset of an order-disorder critical transition at a critical value {\sigma}c of the quenched noise intensity \sigma, with critical exponents that follow Landau theory of thermal phase transitions. We subsequently perform a numerical integration of the system's dynamical variables in order to compare the analytical results (valid in the thermodynamic limit and associated to the ground state of the global Lyapunov potential) with the stationary state of the (finite size) system. In the region of the parameter space where metastability is absent (and therefore the stationary state coincide with the ground state of the Lyapunov potential), a finite-size scaling analysis of the order parameter fluctuations suggests that the magnetic susceptibility diverges quadratically in the vicinity of the transition, what constitutes a violation of the fluctuation-dissipation relation. We derive an effective Hamiltonian and accordingly argue that its functional form does not allow to straightforwardly relate the order parameter fluctuations to the linear response of the system, at odds with equilibrium theory. In the region of the parameter space where the system is susceptible to have a large number of metastable states (and therefore the stationary state does not necessarily correspond to the ground state of the global Lyapunov potential), we numerically find a phase diagram that strongly depends on the initial conditions of the dynamical variables.Comment: 8 figure

Dynamics of localized structures in vector waves

Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.Comment: 4 pages, 5 figures included in the text. To appear in Phys. Rev. Lett. (2000). Related material at http://www.imedea.uib.es/Nonlinear and http://www.imedea.uib.es/Photonics . In this new version, Fig. 3 has been replaced by a better on

Agent Based Models of Language Competition: Macroscopic descriptions and Order-Disorder transitions

We investigate the dynamics of two agent based models of language competition. In the first model, each individual can be in one of two possible states, either using language $X$ or language $Y$, while the second model incorporates a third state XY, representing individuals that use both languages (bilinguals). We analyze the models on complex networks and two-dimensional square lattices by analytical and numerical methods, and show that they exhibit a transition from one-language dominance to language coexistence. We find that the coexistence of languages is more difficult to maintain in the Bilinguals model, where the presence of bilinguals in use facilitates the ultimate dominance of one of the two languages. A stability analysis reveals that the coexistence is more unlikely to happen in poorly-connected than in fully connected networks, and that the dominance of only one language is enhanced as the connectivity decreases. This dominance effect is even stronger in a two-dimensional space, where domain coarsening tends to drive the system towards language consensus.Comment: 30 pages, 11 figure