Surrogates with random Fourier Phases

The method of surrogates is widely used in the field of nonlinear data analysis for testing for weak nonlinearities. The two most commonly used algorithms for generating surrogates are the amplitude adjusted Fourier transform (AAFT) and the iterated amplitude adjusted Fourier transfom (IAAFT) algorithm. Both the AAFT and IAAFT algorithm conserve the amplitude distribution in real space and reproduce the power spectrum (PS) of the original data set very accurately. The basic assumption in both algorithms is that higher-order correlations can be wiped out using a Fourier phase randomization procedure. In both cases, however, the randomness of the Fourier phases is only imposed before the (first) Fourier back tranformation. Until now, it has not been studied how the subsequent remapping and iteration steps may affect the randomness of the phases. Using the Lorenz system as an example, we show that both algorithms may create surrogate realizations containing Fourier phase correlations. We present two new iterative surrogate data generating methods being able to control the randomization of Fourier phases at every iteration step. The resulting surrogate realizations which are truly linear by construction display all properties needed for surrogate data.Comment: To appear in: "Topics on Chaotic Systems: Selected Papers from Chaos 2008 International Conference", World Scientifi

Long term persistence in the sea surface temperature fluctuations

We study the temporal correlations in the sea surface temperature (SST) fluctuations around the seasonal mean values in the Atlantic and Pacific oceans. We apply a method that systematically overcome possible trends in the data. We find that the SST persistence, characterized by the correlation $C(s)$ of temperature fluctuations separated by a time period $s$, displays two different regimes. In the short-time regime which extends up to roughly 10 months, the temperature fluctuations display a nonstationary behavior for both oceans, while in the asymptotic regime it becomes stationary. The long term correlations decay as $C(s) \sim s^{-\gamma}$ with $\gamma \sim 0.4$ for both oceans which is different from $\gamma \sim 0.7$ found for atmospheric land temperature.Comment: 14 pages, 5 fiure

Application of a renormalization group algorithm to nonequilibrium cellular automata with one absorbing state

We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the renormalization group scheme considering three different approximations which take into account correlations in the stationary probability distribution. The improved scheme is applied to a probabilistic cellular automaton already introduced in the literature.Comment: 7 pages, 4 figures, to be published in Phys. Rev.

Study of the one-dimensional off-lattice hot-monomer reaction model

Hot monomers are particles having a transient mobility (a ballistic flight) prior to being definitely absorbed on a surface. After arriving at a surface, the excess energy coming from the kinetic energy in the gas phase is dissipated through degrees of freedom parallel to the surface plane. In this paper we study the hot monomer-monomer adsorption-reaction process on a continuum (off-lattice) one-dimensional space by means of Monte Carlo simulations. The system exhibits second-order irreversible phase transition between a reactive and saturated (absorbing) phases which belong to the directed percolation (DP) universality class. This result is interpreted by means of a coarse-grained Langevin description which allows as to extend the DP conjecture to transitions occurring in continuous media.Comment: 13 pages, 5 figures, final version to appear in J. Phys.

Critical behavior of a one-dimensional monomer-dimer reaction model with lateral interactions

A monomer-dimer reaction lattice model with lateral repulsion among the same species is studied using a mean-field analysis and Monte Carlo simulations. For weak repulsions, the model exhibits a first-order irreversible phase transition between two absorbing states saturated by each different species. Increasing the repulsion, a reactive stationary state appears in addition to the saturated states. The irreversible phase transitions from the reactive phase to any of the saturated states are continuous and belong to the directed percolation universality class. However, a different critical behavior is found at the point where the directed percolation phase boundaries meet. The values of the critical exponents calculated at the bicritical point are in good agreement with the exponents corresponding to the parity-conserving universality class. Since the adsorption-reaction processes does not lead to a non-trivial local parity-conserving dynamics, this result confirms that the twofold symmetry between absorbing states plays a relevant role in determining the universality class. The value of the exponent $\delta_2$, which characterizes the fluctuations of an interface at the bicritical point, supports the Bassler-Brown's conjecture which states that this is a new exponent in the parity-conserving universality class.Comment: 19 pages, 22 figures, to be published in Phys. Rev