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R. Toral

Publications and source records attributed to R. Toral.

At least 37 records · Page 2Linked to original sources
arXiv2004

Efficiency of discrete-time ratchets

Recently there has been much interest in discrete forms of Brownian ratchets, using a game-theoretic formalism. Using the approach pioneered by Parrondo, we develop a new method for obtaining the stationary probabilities and probability current for the case of discrete-time and discrete-space ratchets. We then use this result to calculate the Parrondian ratchet efficiency in two cases: firstly, for Parrondo's original system and, secondly, for a set of probabilities derived from a discretized ratchet potential.

cond-mat.stat-mech↗
arXiv2004

Neighborhood models of minority opinion spreading

We study the effect of finite size population in Galam's model [Eur. Phys. J. B 25 (2002) 403] of minority opinion spreading and introduce neighborhood models that account for local spatial effects. For systems of different sizes N, the time to reach consensus is shown to scale as ln N in the original version, while the evolution is much slower in the new neighborhood models. The threshold value of the initial concentration of minority supporters for the defeat of the initial majority, which is independent of N in Galam's model, goes to zero with growing system size in the neighborhood models. This is a consequence of the existence of a critical size for the growth of a local domain of minority supporters.

cond-mat.other↗
arXiv2004

Exact Solution of Ising Model on a Small-World Network

We present an exact solution of a one-dimensional Ising chain with both nearest neighbor and random long-range interactions. Not surprisingly, the solution confirms the mean field character of the transition. This solution also predicts the finite-size scaling that we observe in numerical simulations.

cond-mat.stat-mech↗
arXiv2003

On the derivation of amplitude equations for nonlinear oscillators subject to arbitrary forcing

By using a generalization of the multiple scales technique we develop a method to derive amplitude equations for zero--dimensional forced systems. The method allows to consider either additive or multiplicative forcing terms and can be straightforwardly applied to the case that the forcing is white noise. We give examples of the use of this method to the case of the van der Pol--Duffing oscillator. The writing of the amplitude equations in terms of a Lyapunov potential allow us to obtain an analytical expression for the probability distribution function which reproduces reasonably well the numerical simulation results.

cond-mat↗
arXiv2003

Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.

cond-mat.stat-mech↗
arXiv2003

A Fokker--Planck description for Parrondo's games

We discuss in detail two recently proposed relations between the Parrondo's games and the Fokker--Planck equation describing the flashing ratchet as the overdamped motion of a particle in a potential landscape. In both cases it is possible to relate exactly the probabilities of the games to the potential in which the overdamped particle moves. We will discuss under which conditions current-less potentials correspond to fair games and vice versa.

cond-mat.stat-mech↗
arXiv2003

Experimental study of high frequency stochastic resonance in Chua circuits

We study the stochastic resonance phenomenon occurring in electronic Chua circuits operating in the chaotic regime when the forcing signal is modulated at relatively high frequency, of the order of magnitude of the main Chua frequency in the absence of forcing ($f_o$). In all the cases, a clear maximum in the signal-to-noise ratio for an intermediate noise level is observed. When modulating with a frequency smaller than $f_o$ we also observe a resonance at a harmonic of the external frequency which is closer to $f_o$ or to one of its harmonic. If the modulating frequency is larger than $f_o$ we only observe the resonance at the modulating frequency.

cond-mat↗
arXiv2001

Numerical Determination of the Distribution of Energies for the XY-model

We compute numerically the distribution of energies W(E,N) for the XY-model with short-range and long-range interactions. We find that in both cases the distribution can be fitted to the functional form: W(E,N) ~ exp(N f(E,N)), with f(E,N) an intensive function of the energy.

cond-mat.stat-mech↗
arXiv2001

Experimental Observation of Coherence and Stochastic Resonances in an Electronic Chua Circuit

Stochastic and coherence resonances appear in nonlinear systems subjected to an external source of noise and are characterized by a maximum response at the optimal value of the noise intensity. This paper shows experimentally that it is possible to observe them in a chaotic system. To this end we have analysed an electronic Chua circuit running in the chaotic regime and added noise to its dynamics. In the case of coherence resonance, we observe an optimal periodicity for the jumps between chaotic attractors, whereas in the case of stochastic resonance we observe a maximum in the signal-to-noise ratio at the frequency of an external sinusoidal perturbation.

cond-mat↗
arXiv2001

"Fuzzy" stochastic resonance: robustness against noise tuning due to non Gaussian noises

We have analyzed the phenomenon of stochastic resonance in a system driven by non Gaussian noises. We have considered both white and colored noises. In the latter case we have obtained a consistent Markovian approximation that enables us to get quasi-analytical results for the signal-to-noise ratio. As the system departs from Gaussian behavior, our main findings are: an enhancement of the response together with a notable robustness against noise tuning. These remarkable findings are supported by extensive numerical simulations. We also discuss the relation with some experiments in sensory systems.

cond-mat.stat-mech↗
arXiv2001

Space and Scale Localization in a Model of a Direct Transition to Spatiotemporal Chaos

We present the results of a wavelet-based approach to the study of the chaotic dynamics of a one dimensional model that shows a direct transition to spatiotemporal chaos. We find that the dynamics of this model in the spatiotemporally chaotic regime may be understood in terms of localized dynamics in both space and scale (wavenumber). A projection onto a Daubechies basis yields a good separation of scales, as shown by an examination of the contribution of different wavelet levels to the power spectrum. At most scales, including the most energetic ones, we find essentially Gaussian dynamics. We also show that removal of certain wavelet modes can be made without altering the dynamics of the system as described by the Lyapunov spectrum.

nlin.CD↗
arXiv2001

Cooperative Parrondo's Games

We introduce a new family of Parrondo's games of alternating losing strategies in order to get a winning result. In our version of the games we consider an ensemble of players and use "social" rules in which the probabilities of the games are defined in terms of the actual state of the neighbors of a given player.

cond-mat↗
arXiv2000

Coherence Resonance in Chaotic Systems

We show that it is possible for chaotic systems to display the main features of coherence resonance. In particular, we show that a Chua model, operating in a chaotic regime and in the presence of noise, can exhibit oscillations whose regularity is optimal for some intermediate value of the noise intensity. We find that the power spectrum of the signal develops a peak at finite frequency at intermediate values of the noise. These are all signatures of coherence resonance. We also experimentally study a Chua circuit and corroborate the above simulation results. Finally, we analyze a simple model composed of two separate limit cycles which still exhibits coherence resonance, and show that its behavior is qualitatively similar to that of the chaotic Chua system

cond-mat↗
arXiv2000

An entropy-driven noise-induced phase transition

We introduce a class of exactly solvable models which exhibit an ordering noise-induced phase transition driven by an entropic mechanism. In contrast with previous studies, order does not appear in this case as a result of an instability of the disordered phase produced by noise, but of a balance between the relaxing deterministic dynamics and the randomizing (entropic) 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 derived analytically. The relevance of our result as a possible scenario of the so-called Lower Critical Solution Temperature (LCST) transitions is analysed.

cond-mat↗
arXiv2000

Dynamics and Scaling of Noise-Induced Domain Growth

The domain growth processes originating from noise-induced nonequilibrium phase transitions are analyzed, both for non-conserved and conserved dynamics. The existence of a dynamical scaling regime is established in the two cases, and the corresponding growth laws are determined. The resulting universal dynamical scaling scenarios are those of Allen-Cahn and Lifshitz-Slyozov, respectively. Additionally, the effect of noise sources on the behaviour of the pair correlation function at short distances is studied.

cond-mat↗
arXiv2000

Reply to the Comment on``Scaling Laws for a System with Long--Range Interactions within Tsallis Statistics''

The fact that mean field theory is appropriate to describe an Ising model with long-range interactions has been already shown by Cannas and Tamarit. Although not explicited in our Letter, we have used periodic boundary conditions in all our simulations, such that the maximum possible distance between two lattice sites is L/2. We make no specific comments about the validity (or lack of validity) of Boltzmann-Gibbs statistical mechanics to describe long-range systems. Our paper does nothing but to compare the scaling functions derived from Boltzman-Gibbs statistics from those derived from the use of Tsallis entropy.

cond-mat.stat-mech↗
arXiv2000

Weakly Nonextensive Thermostatistics and the Ising Model with Long--range Interactions

We introduce a nonextensive entropic measure $S_χ$ that grows like $N^χ$, where $N$ is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some $N$-body systems endowed with long-range interactions described by $r^{-α}$ interparticle potentials. The power law (weakly nonextensive) behavior exhibited by $S_χ$ is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and the (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized $q$-entropies. The functional $S_χ $ is parametrized by the real number $χ\in[1,2]$ in such a way that the standard logarithmic entropy is recovered when $χ=1$ >. We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., $S_χ$ possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since $S_χ$ is nonextensive. For $1<χ<2$, the entropy $S_χ$ becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions.

cond-mat.stat-mech↗