arXiv subjects

Raul Toral

Publications and source records attributed to Raul Toral.

At least 73 records · Page 4Linked to original sources

arXiv2006

Diversity-induced resonance

We present conclusive evidence showing that different sources of diversity, such as those represented by quenched disorder or noise, can induce a resonant collective behavior in an ensemble of coupled bistable or excitable systems. Our analytical and numerical results show that when such systems are subjected to an external subthreshold signal, their response is optimized for an intermediate value of the diversity. These findings show that intrinsic diversity might have a constructive role and suggest that natural systems might profit from their diversity in order to optimize the response to an external stimulus.

cond-mat.stat-mech↗

arXiv2005

Ensemble equivalence for non-Bolztmannian distributions

We discuss the possibility of using generalized canonical distributions, i.e. using other factors than $\exp(-βE)$, in order to compute the equilibrium properties of physical systems. It will be show that some other choices can, in certain cases, lead to a simpler calculation of those properties. The corresponding equivalence between the canonical and the generalized canonical distributions is derived using well-known principles of Statistical Mechanics and we exemplify the method by deriving in a simple way the equilibrium properties of the long--range Ising model.

cond-mat.stat-mech↗

arXiv2004

System size stochastic resonance in a model for opinion formation

We study a model for opinion formation which incorporates three basic ingredients for the evolution of the opinion held by an individual: imitation, influence of fashion and randomness. We show that in the absence of fashion, the model behaves as a bistable system with random jumps between the two stable states with a distribution of times following Kramer's law. We also demonstrate the existence of system size stochastic resonance, by which there is an optimal value for the number of individuals N for which the average opinion follows better the fashion.

cond-mat.stat-mech↗

arXiv2004

A Monte-Carlo and Self-Consistent Field calculations of encapsulated spherical polymer brushes

We present the results of extensive numerical self-consistent field (SCF) and 3-dimensional off-lattice Monte Carlo (MC) studies of a spherical brush confined into a spherical cavity. The monomer density profile and the cavity pressure have been measured in systems where curvature of the cavity has an important effect on the polymer brush conformation. A direct comparison between the SCF and MC methods reveals the SCF calculation to be a valuable alternative to MC simulations in the case of free and softly compressed brushes. In the case of strongly compressed systems we have proposed an extension of the Flory theory for polymer solutions, whose predictions are found to be in good agreement with the MC simulations and has the advantage of being computationally inexpensive. In the range of high compressions, we have found the monomer volume fraction $v$ to follow a scale relationship with the cavity pressure $P$, $P \sim v^α$. SCF calculations give $α=2.15 \pm 0.05$, close to {\em des Cloiseaux law ($α=9/4$)}, whereas MC simulations lead to $α=2.73 \pm 0.04$. We conclude that the higher value of $α$ obtained with MC comes from the monomer density correlations not included in the SCF formalism.

cond-mat.soft↗

arXiv2004

Parrondo's games and the zipping algorithm

We study the relation between the discrete--time version of the flashing ratchet known as Parrondo's games and a compression technique used very recently with thermal ratchets for evaluating the transfer of information -- negentropy -- between the Brownian particle and the source of fluctuations. We present some results concerning different versions of Parrondo's games, showing all of them a good qualitative agreement between the gain and the inverse of the entropy.

cond-mat.stat-mech↗

arXiv2004

Dynamical mechanism of anticipating synchronization in excitable systems

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization.

cond-mat↗

arXiv2003

On the nonextensivity of the long range X-Y model

It will be given analytical and numerical evidence supporting that the X-Y model yields an extensive, i.e. proportional to the number of degrees of freedom N, internal energy U for any value of the interaction range.

cond-mat.stat-mech↗

arXiv2003

Anticipated synchronization: a metaphorical linear view

We study the regime of anticipated synchronization recently described on a number of dynamical systems including chaotic and noisy ones. We use simple linear caricatures to show the minimal setups able to reproduce the basic facts described.

cond-mat↗

arXiv2003

Effect of Non-Gaussian Noise Sources in a Noise Induced Transition

Here we study a noise induced transition when the system is driven by a noise source taken as colored and non-Gaussian. We show--using both, a theoretical approximation and numerical simulations-- that there is a shift of the transition as the noise departs from the Gaussian behavior. Also, we confirm the reentrance effect found for colored Gaussian noise and show the behavior of the transition line in the phase-like diagram as the noise departs from Gaussianity in the large correlation time limit.

cond-mat.stat-mech↗

arXiv2003

Parrondo's games as a discrete ratchet

We write the master equation describing the Parrondo's games as a consistent discretization of the Fokker--Planck equation for an overdamped Brownian particle describing a ratchet. Our expressions, besides giving further insight on the relation between ratchets and Parrondo's games, allow us to precisely relate the games probabilities and the ratchet potential such that periodic potentials correspond to fair games and winning games produce a tilted potential.

cond-mat.stat-mech↗

arXiv2002

Apparent phase transitions in finite one-dimensional sine-Gordon lattices

We study the one-dimensional sine-Gordon model as a prototype of roughening phenomena. In spite of the fact that it has been recently proven that this model can not have any phase transition [J. A. Cuesta and A. Sanchez, J. Phys. A 35, 2373 (2002)], Langevin as well as Monte Carlo simulations strongly suggest the existence of a finite temperature separating a flat from a rough phase. We explain this result by means of the transfer operator formalism and show as a consequence that sine-Gordon lattices of any practically achievable size will exhibit this apparent phase transition at unexpectedly large temperatures.

cond-mat.stat-mech↗

arXiv2002

Nonequilibrium transitions in complex networks: a model of social interaction

We analyze the non-equilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.

cond-mat↗

arXiv2002

Characterization of the anticipated synchronization regime in the coupled FitzHugh--Nagumo model for neurons

We characterize numerically the regime of anticipated synchronization in the coupled FitzHugh-Nagumo model for neurons. We consider two neurons, coupled unidirectionally (in a master-slave configuration), subject to the same random external forcing and with a recurrent inhibitory delayed connection in the slave neuron. We show that the scheme leads to anticipated synchronization, a regime in which the slave neuron fires the same train of pulses as the master neuron, but earlier in time. We characterize the synchronization in the parameter space (coupling strength, anticipation time) and introduce several quantities to measure the degree of synchronization.

cond-mat↗

arXiv2002

Anticipating the response of excitable systems driven by random forcing

We study the regime of anticipated synchronization in unidirectionally coupled model neurons subject to a common external aperiodic forcing that makes their behavior unpredictable. We show numerically and by implementation in analog hardware electronic circuits that, under appropriate coupling conditions, the pulses fired by the slave neuron anticipate (i.e. predict) the pulses fired by the master neuron. This anticipated synchronization occurs even when the common external forcing is white noise.

cond-mat↗

arXiv2002

Cultural transmission and optimization dynamics

We study the one-dimensional version of Axelrod's model of cultural transmission from the point of view of optimization dynamics. We show the existence of a Lyapunov potential for the dynamics. The global minimum of the potential, or optimum state, is the monocultural uniform state, which is reached for an initial diversity of the population below a critical value. Above this value, the dynamics settles in a multicultural or polarized state. These multicultural attractors are not local minima of the potential, so that any small perturbation initiates the search for the optimum state. Cultural drift is modelled by such perturbations acting at a finite rate. If the noise rate is small, the system reaches the optimum monocultural state. However, if the noise rate is above a critical value, that depends on the system size, noise sustains a polarized dynamical state.

cond-mat↗

arXiv2002

System size coherence resonance

We show the existence of a system size coherence resonance effect for an ensemble of globally coupled excitable systems. Namely, we demonstrate numerically that the regularity in the signal emitted by an ensemble of globally coupled Fitzhugh-Nagumo systems, under excitation by independent noise sources, is optimal for a particular value of the number of coupled systems. This resonance is shown through several different dynamical measures: the time correlation function, correlation time and jitter.

cond-mat↗

arXiv2002

Capital Redistribution Brings Wealth by Parrondo's Paradox

We present new versions of the Parrondo's paradox by which a losing game can be turned into winning by including a mechanism that allows redistribution of the capital amongst an ensemble of players. This shows that, for this particular class of games, redistribution of the capital is beneficial for everybody. The same conclusion arises when the redistribution goes from the richer players to the poorer.

cond-mat↗

arXiv2002

Global culture: A noise induced transition in finite systems

We analyze the effect of cultural drift, modeled as noise, in Axelrod's model for the dissemination of culture. The disordered multicultural configurations are found to be metastable. This general result is proven rigorously in d=1, where the dynamics is described in terms of a Lyapunov potential. In d=2, the dynamics is governed by the average relaxation time T of perturbations. Noise at a rate r < 1/T induces monocultural configurations, whereas r > 1/T sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.

cond-mat↗