Absorbing Phase Transitions of Branching-Annihilating Random Walks

The phase transitions to absorbing states of the branching-annihilating reaction-diffusion processes mA --> (m+k)A, nA --> (n-l)A are studied systematically in one space dimension within a new family of models. Four universality classes of non-trivial critical behavior are found. This provides, in particular, the first evidence of universal scaling laws for pair and triplet processes.Comment: 4 pages, 4 figure

Het milieu van de filosofen: 20 jaar milieufilosofie in Nederland

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Lyapunov exponents as a dynamical indicator of a phase transition

We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results to a simple model, proposed for the DNA denaturation, which emphasizes a first order-like or second order phase transition depending on the ratio of two length scales: this is an excellent model to characterize $\lambda_1$ as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure

Pulses in the Zero-Spacing Limit of the GOY Model

We study the propagation of localised disturbances in a turbulent, but momentarily quiescent and unforced shell model (an approximation of the Navier-Stokes equations on a set of exponentially spaced momentum shells). These disturbances represent bursts of turbulence travelling down the inertial range, which is thought to be responsible for the intermittency observed in turbulence. Starting from the GOY shell model, we go to the limit where the distance between succeeding shells approaches zero (``the zero spacing limit'') and helicity conservation is retained. We obtain a discrete field theory which is numerically shown to have pulse solutions travelling with constant speed and with unchanged form. We give numerical evidence that the model might even be exactly integrable, although the continuum limit seems to be singular and the pulses show an unusual super exponential decay to zero as $\exp(- \mathrm{const} \sigma^n)$ when $n \to \infty$, where $\sigma$ is the {\em golden mean}. For finite momentum shell spacing, we argue that the pulses should accelerate, moving to infinity in a finite time. Finally we show that the maximal Lyapunov exponent of the GOY model approaches zero in this limit.Comment: 27 pages, submitted for publicatio

Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive a lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing and for sufficiently small viscosity term $\nu$, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to $\log_\lambda \nu^{-1}$ for all values of the governing parameter $\epsilon$, except for $\epsilon=1$. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, we show different scenarios of the transition to chaos for different parameters regime and for specific forcing. In the ``three-dimensional'' regime of parameters this scenario changes when the parameter $\epsilon$ becomes sufficiently close to 0 or to 1. We also show that in the ``two-dimensional'' regime of parameters for a certain non-zero forcing term the long-time dynamics of the model becomes trivial for any value of the viscosity

Universality in the pair contact process with diffusion

The pair contact process with diffusion is studied by means of multispin Monte Carlo simulations and density matrix renormalization group calculations. Effective critical exponents are found to behave nonmonotonically as functions of time or of system length and extrapolate asymptotically towards values consistent with the directed percolation universality class. We argue that an intermediate regime exists where the effective critical dynamics resembles that of a parity conserving process.Comment: 8 Pages, 9 figures, final version as publishe

Aging at Criticality in Model C Dynamics

We study the off-equilibrium two-point critical response and correlation functions for the relaxational dynamics with a coupling to a conserved density (Model C) of the O(N) vector model. They are determined in an \epsilon=4-d expansion for vanishing momentum. We briefly discuss their scaling behaviors and the associated scaling forms are determined up to first order in epsilon. The corresponding fluctuation-dissipation ratio has a non trivial large time limit in the aging regime and, up to one-loop order, it is the same as that of the Model A for the physically relevant case N=1. The comparison with predictions of local scale invariance is also discussed.Comment: 13 pages, 1 figur

Series expansion for a stochastic sandpile

Using operator algebra, we extend the series for the activity density in a one-dimensional stochastic sandpile with fixed particle density p, the first terms of which were obtained via perturbation theory [R. Dickman and R. Vidigal, J. Phys. A35, 7269 (2002)]. The expansion is in powers of the time; the coefficients are polynomials in p. We devise an algorithm for evaluating expectations of operator products and extend the series to O(t^{16}). Constructing Pade approximants to a suitably transformed series, we obtain predictions for the activity that compare well against simulations, in the supercritical regime.Comment: Extended series and improved analysi