- Palma de Mallorca, Balearic Islands, Spain
Raul Toral
Universitat de les Illes Balears, IFISC, Department Member
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We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical and efficient algorithm like the... more
We present a simple and general framework to simulate statistically correct realizations of a system of non-Markovian discrete stochastic processes. We give the exact analytical solution and a practical and efficient algorithm like the Gillespie algorithm for Markovian processes, with the difference being that now the occurrence rates of the events depend on the time elapsed since the event last took place. We use our non-Markovian generalized Gillespie stochastic simulation methodology to investigate the effects of nonexponential interevent time distributions in the susceptible-infected-susceptible model of epidemic spreading. Strikingly, our results unveil the drastic effects that very subtle differences in the modeling of non-Markovian processes have on the global behavior of complex systems, with important implications for their understanding and prediction. We also assess our generalized Gillespie algorithm on a system of biochemical reactions with time delays. As compared to other existing methods, we find that the generalized Gillespie algorithm is the most general because it can be implemented very easily in cases (such as for delays coupled to the evolution of the system) in which other algorithms do not work or need adapted versions that are less efficient in computational terms.
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Toral and Salazar Reply: The fact that mean-field theory is appropriate to describe an Ising model with long-range interactions within the context of Gibbs statistics has already been shown by Cannas and Tamarit [1]. Although not... more
Toral and Salazar Reply: The fact that mean-field theory is appropriate to describe an Ising model with long-range interactions within the context of Gibbs statistics has already been shown by Cannas and Tamarit [1]. Although not explicitly stated in our Letter [2], we have used periodic boundary conditions in all of our simulations, such that the maximum possible distance between two lattice sites is L/2. ... Raul Toral and Rafael Salazar Instituto Mediterráneo de Estudios Avanzados (CSIC-UIB) and Department de Física ... Universitat de les Illes Balears E-07071 Palma ...
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(4) where d is the dimensionality of the system. The functions g (x) and F (x) and the growth exponent a define the different dynamical universality classes and their theoretical determination is one of the most challenging problems in... more
(4) where d is the dimensionality of the system. The functions g (x) and F (x) and the growth exponent a define the different dynamical universality classes and their theoretical determination is one of the most challenging problems in the kinetics of first-order phase transitions. The scaling Ansatz (4) has been analyzed in Fig. 1 with use of the spherically averaged correlation function G (r, t) R (t) is defi. ned here as the coordinate of the first zero of G (r, t). This figure seems to indicate that scaling is satisfied for all r, at late times. ...
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Research Interests: Electron Microscopy, Morphology, Block Copolymer, SAXS, TEM, and 4 morePhysical sciences, Pi, Phase Separation, and G
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We numerically show that extreme events induced by parameter mismatches or noise in coupled oscillatory systems can be anticipated and suppressed before they actually occur. We show this in a main system unidirectionally coupled to an... more
We numerically show that extreme events induced by parameter mismatches or noise in coupled oscillatory systems can be anticipated and suppressed before they actually occur. We show this in a main system unidirectionally coupled to an auxiliary system subject to a negative delayed feedback. Each system consists of two electronic oscillators coupled in a master-slave configuration. Extreme events are observed in this coupled system as large and sporadic desynchronization events. Under certain conditions, the auxiliary system can predict the dynamics of the main system. We use this to efficiently suppress the extreme events by applying a direct corrective reset to the main system.
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Department ofPhysics, Lehigh Uniuersity, Bethlehem, Pennsylvania 18015 (Received 23August 1991)%'e present results of a numerical study of the Cahn-Billiard model of phase separation for a binary mixture quenched deep in the... more
Department ofPhysics, Lehigh Uniuersity, Bethlehem, Pennsylvania 18015 (Received 23August 1991)%'e present results of a numerical study of the Cahn-Billiard model of phase separation for a binary mixture quenched deep in the nucleation regime.% e study the volume-fraction dependence of the scal-ing functions for the pair correlation function and the structure factor. Our results indicate that for small volume fraction P the shape of the scaling functions depends strongly on P, whereas for larger volume fractions the scaling functions ...