Phase Synchronization and Polarization Ordering of Globally-Coupled Oscillators

We introduce a prototype model for globally-coupled oscillators in which each element is given an oscillation frequency and a preferential oscillation direction (polarization), both randomly distributed. We found two collective transitions: to phase synchronization and to polarization ordering. Introducing a global-phase and a polarization order parameters, we show that the transition to global-phase synchrony is found when the coupling overcomes a critical value and that polarization order enhancement can not take place before global-phase synchrony. We develop a self-consistent theory to determine both order parameters in good agreement with numerical results

Divergent Time Scale in Axelrod Model Dynamics

We study the evolution of the Axelrod model for cultural diversity. We consider a simple version of the model in which each individual is characterized by two features, each of which can assume q possibilities. Within a mean-field description, we find a transition at a critical value q_c between an active state of diversity and a frozen state. For q just below q_c, the density of active links between interaction partners is non-monotonic in time and the asymptotic approach to the steady state is controlled by a time scale that diverges as (q-q_c)^{-1/2}.Comment: 4 pages, 5 figures, 2-column revtex4 forma

Determinación de vitaminas del Complejo B en Arthrospira maxima por cromatografía líquida de alta resolución

Se diseñan dos métodos para la extracción de las vitaminas del complejo B en muestras de Arthrospira maximacubana. Para la determinación, se emplea un sistema HPLC formado por una columna de octadecilsilano y fasesmóviles de metanol - agua - ácido fosfórico 0.1 mol/L (20:79.5:0.5) para el análisis de la cianocobalamina y (30:69.5:0.5)para el resto de las vitaminas, empleando hexanosulfonato sódico 5 mM en ambos casos. Las velocidades de flujoson de 1 y 0.8 mL/min respectivamente. La determinación se realiza a 362 y 270 nm. Se observó que la Arthrospiramaxima cultivada en Cuba constituye una rica fuente de vitaminas del grupo B presentando un contenido promediode 3.1 mg/10g de tiamina, 4.0 mg/10g de riboflavina, 9.0 mg/10g de piridoxina, 0.29 mg/10g de cianocobalamina, 21mg/10g de ácido nicotínico y 26 mg/10g de nicotinamida

Conservation laws for the voter model in complex networks

We consider the voter model dynamics in random networks with an arbitrary distribution of the degree of the nodes. We find that for the usual node-update dynamics the average magnetization is not conserved, while an average magnetization weighted by the degree of the node is conserved. However, for a link-update dynamics the average magnetization is still conserved. For the particular case of a Barabasi-Albert scale-free network the voter model dynamics leads to a partially ordered metastable state with a finite size survival time. This characteristic time scales linearly with system size only when the updating rule respects the conservation law of the average magnetization. This scaling identifies a universal or generic property of the voter model dynamics associated with the conservation law of the magnetization.Comment: 5 pages, 4 figures; for related material please visit http://www.imedea.uib.e

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

Growing pains: can family policies revert the decline of fertility in Spain?

This article aims to analyze the capability of family policies to reverse the sharp decline in fertility that has been observed in Spain in recent decades. The analysis was carried out by applying two mathematical techniques: the genetic algorithm and the strategic scenarios. Firstly, a mathematical model was designed and validated adjusting the combined performance of fertility and family policies during the 2008–2019 period. Subsequently, this model was applied to the future (2020–2060) to extrapolate the evolution of fertility considering different models of family policies. The results demonstrate that a model of family policies that is coherent with other socially desirable objectives, such as gender and social equality, will be insufficient to reverse the current downward trend in fertility. Therefore, these outcomes point to the need to articulate and harmonize diverse public policies considering the principles of equality and well‐being to modify the recent decline in fertility. An increase in fertility must therefore be identified as a socially desirable goal and public policies must be adapted to this objective, in the understanding that fertility not only requires family policies but also their coherence with the employment and educational policies and work–life balance mechanisms offered by public institutions.This study was conducted under the competitive research project Problemas no Lineales en Ciencias Naturales y Ciencias Sociales (Nonlinear Problems in Natural Sciences and Social Sciences; PID2020- 112517GB-I00), funded by the Spanish Ministry of Sciences and Innovation. It was also supported by the Department of Social Analysis of the Carlos III University of Madrid

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

Selfsimilar Domain Growth, Localized Structures and Labyrinthine Patterns in Vectorial Kerr Resonators

We study domain growth in a nonlinear optical system useful to explore different scenarios that might occur in systems which do not relax to thermodynamic equilibrium. Domains correspond to equivalent states of different circular polarization of light. We describe three dynamical regimes: a coarsening regime in which dynamical scaling holds with a growth law dictated by curvature effects, a regime in which localized structures form, and a regime in which polarization domain walls are modulationally unstable and the system freezes in a labyrinthine pattern.Comment: 13 pages, 6 figure

In situ growth of Ag nanoparticles on alpha-Ag2WO4 under electron irradiation: probing the physical principles

Exploiting the plasmonic behavior of Ag nanoparticles grown on α-Ag2WO4 is a widely employed strategy to produce efficient photocatalysts, ozone sensors, and bactericides. However, a description of the atomic and electronic structure of the semiconductor sites irradiated by electrons is still not available. Such a description is of great importance to understand the mechanisms underlying these physical processes and to improve the design of silver nanoparticles to enhance their activities. Motivated by this, we studied the growth of silver nanoparticles to investigate this novel class of phenomena using both transmission electron microscopy and field emission scanning electron microscopy. A theoretical framework based on density functional theory calculations (DFT), together with experimental analysis and measurements, were developed to examine the changes in the local geometrical and electronic structure of the materials. The physical principles for the formation of Ag nanoparticles on α-Ag2WO4 by electron beam irradiation are described. Quantum mechanical calculations based on DFT show that the (001) of α-Ag2WO4 displays Ag atoms with different coordination numbers. Some of them are able to diffuse out of the surface with a very low energy barrier (less than 0.1 eV), thus, initiating the growth of metallic Ag nanostructures and leaving Ag vacancies in the bulk material. These processes increase the structural disorder of α-Ag2WO4 as well as its electrical resistance as observed in the experimental measurements.The authors are grateful to Generalitat Valenciana (Spain) for PrometeoII/2014/022 and ACOMP/2014/270 projects, Ministerio de Economia y Competitividad (Spain), CTQ2012-36253-C03-02, and to the Spanish Brazilian Program (PHB2009-0065-PC), CAPES (203038 009607/2013- 56 088/2013), INCTMN (2008/57872-1), FAPESP (2013/ 07296-2; 2012/14468-1; 2010/16970-0) and CNPq (147001/2013-7; 573636/2008-7) for financially supporting this research. Most of the calculations were performed using IFGW-UNICAMP computer facilities and the National Center for High Performance Computing in São Paulo (CENAPAD- SP)