Prof. Raul Toral

Institute for Cross-Disciplinary Physics and Complex Systems, Palma, Balearic Islands, Spain

Prof. Raul Toral

Institute for Cross-Disciplinary Physics and Complex Systems, Palma, Balearic Islands, Spain

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Academic Career Length

44Years (1983-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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19 December 1994 in Physical Review Letters

Journal Article

Noise-Induced Nonequilibrium Phase Transition

C. Van Den Broeck

J. M. R. Parrondo

Raul Toral

We report on a simple model of a spatially distributed system which, subject to multiplicative noise, white in space and time, can undergo a nonequilibrium phase transition to a symmetry-breaking state, while no such transition exists in the absence of the noise term. The transition possesses features similar to those observed at second order equilibrium phase transitions: divergence of the correlation length and of the susceptibility, critical slowing down, and scaling properties. Furthermore, the transition is found to be reentrant: The ordered state appears at a critical value of the noise intensity but disappears again at a higher value of the noise strength.

29 September 2010 in Physical Review E

Journal Article

Description of stochastic and chaotic series using visibility graphs

Lucas Lacasa

Raul Toral

Nonlinear time series analysis is an active field of research that studies the structure of complex signals in order to derive information of the process that generated those series, for understanding, modeling and forecasting purposes. In the last years, some methods mapping time series to network representations have been proposed. The purpose is to investigate on the properties of the series through graph theoretical tools recently developed in the core of the celebrated complex network theory. Among some other methods, the so-called visibility algorithm has received much attention, since it has been shown that series correlations are captured by the algorithm and translated in the associated graph, opening the possibility of building fruitful connections between time series analysis, nonlinear dynamics, and graph theory. Here we use the horizontal visibility algorithm to characterize and distinguish between correlated stochastic, uncorrelated and chaotic processes. We show that in every case the series maps into a graph with exponential degree distribution P(k)$\sim${}exp($-${}$\lambda${}k), where the value of $\lambda${} characterizes the specific process. The frontier between chaotic and correlated stochastic processes, $\lambda${}=ln(3/2), can be calculated exactly, and some other analytical developments confirm the results provided by extensive numerical simulations and (short) experimental time series.

6 November 2006 in Physical Review Letters

Journal Article

Diversity-Induced Resonance

Claudio J. Tessone

Claudio R. Mirasso

Raul Toral

James D. Gunton

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.

1 April 1997 in Physical Review E

Journal Article

Nonequilibrium phase transitions induced by multiplicative noise

C. Van Den Broeck

J. M. R. Parrondo

Raul Toral

R. Kawai

We review a mean-field analysis and give the details of a correlation function approach for spatially distributed systems subject to multiplicative noise, white in space and time. We confirm the existence of a pure noise-induced reentrant nonequilibrium phase transition in the model introduced in [C. Van den Broeck et al., Phys. Rev. Lett. 73, 3395 (1994)], give an intuitive explanation of its origin, and present extensive simulations in dimension d=2. The observed critical properties are compatible with those of the Ising universality class.

26 February 2003 in Physical Review E

Journal Article

Nonequilibrium transitions in complex networks: A model of social interaction

We analyze the nonequilibrium 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.

15 April 2003 in Physical Review E

Journal Article

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 frozen configurations are found not to be stable. 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 ≲ T^{- 1}

induces monocultural configurations, whereas

r ≳ T^{- 1}

sustains disorder. In the thermodynamic limit, the relaxation time diverges and global polarization persists in spite of a dynamics of local convergence.

About Me

MSc in physics at the University of Barcelona in 1980 and PhD at the same university in 1985. Grant holder of the NATO Scientific Programme for a postdoctoral stay at the University of Edinburgh (1985–1987) with Prof. D. J. Wallace. Contract at Temple University (Philadelphia, 1987–1989) with Prof. James D. Gunton, during which time I obtained a tenured professorship at the University of the Balearic Islands. Scientific researcher at the CSIC in March 1992 and professor at the University of the Balearic Islands in January 1994. I am currently a professor in the area of Condensed Matter Physics and director of the Department of Complex Systems of IFISC. My research activity has focused on the field of statistical and non-linear physics, covering theoretical, fundamental, and methodological aspects, with an important component in the field of computational physics. I have published more than 200 articles with more than 5000 citations and two books. I have supervised 14 PhD students. I am the director of the master's degree in Physics of Complex Systems at the UIB. In 2016 I received the Prize for the Best Teaching Article in the publications of the Real Sociedad Española de Física (RSEF). I was president of the GEFENOL, thematic group of Statistical and Nonlinear Physics of the RSEF in the period 2.013-2019. Since 2016, I have been a member of the Board of the Statistical and Nonlinear Physics Division of the European Physical Society.

Prof. Raul Toral

Prof. Raul Toral

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