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Full-Text Articles in Physics
Fluctuations And Correlations In Sandpile Models, A Barrat, A Vespignani, S Zapperi
Fluctuations And Correlations In Sandpile Models, A Barrat, A Vespignani, S Zapperi
Alessandro Vespignani
We perform numerical simulations of the sandpile model for nonvanishing driving fields it and dissipation rates epsilon. Unlike simulations performed in the slow driving limit, the unique time scale present in our system allows us to measure unambiguously the response and correlation functions. We discuss the dynamic scaling of the model and show that fluctuation-dissipation relations are not obeyed in this system.
Renormalization-Group Approach To The Critical-Behavior Of The Forest-Fire Model, V Loreto, L Pietronero, A Vespignani, S Zapperi
Renormalization-Group Approach To The Critical-Behavior Of The Forest-Fire Model, V Loreto, L Pietronero, A Vespignani, S Zapperi
Alessandro Vespignani
We introduce a renormalization scheme for the one- and two-dimensional forest-fire model in order to characterize the nature of the critical state and its scale invariant dynamics. We show the existence of a relevant scaling field associated with a repulsive fixed point. This model is therefore critical in the usual sense because the control parameter has to be tuned to its critical value in order to get criticality. It turns out that this is not just the condition for a time scale separation. The critical exponents are computed analytically and we obtain nu = 1.0, tau = 1.0 and nu …
Order Parameter And Scaling Fields In Self-Organized Criticality, A Vespignani, S Zapperi
Order Parameter And Scaling Fields In Self-Organized Criticality, A Vespignani, S Zapperi
Alessandro Vespignani
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation, and we include the details of different models by using effective parameters and constraints. We identify the order parameter and the relevant scaling fields in order to describe the critical behavior in terms of the usual concepts of nonequilibrium lattice models with steady states. We point out the inconsistencies of previous mean-field approaches, which lead to different predictions. Numerical simulations confirm the validity of our results beyond mean-field theory.