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Full-Text Articles in Physics
Self-Organized Criticality As An Absorbing-State Phase Transition, R Dickman, A Vespignani, S Zapperi
Self-Organized Criticality As An Absorbing-State Phase Transition, R Dickman, A Vespignani, S Zapperi
Alessandro Vespignani
We explore the connection between self-organized criticality and phase transitions in models with absorbing states. Sandpile models are found to exhibit criticality only when a pair of relevant parameters - dissipation epsilon and driving field h - are set to their critical values. The critical values of epsilon and h are both equal to zero. The first result is due to the absence of saturation (no bound on energy) in the sandpile model, while the second result is common to other absorbing-state transitions. The original definition of the sandpile model places it at the point (epsilon = 0,h = 0(+)): …
How Self-Organized Criticality Works: A Unified Mean-Field Picture, A Vespignani, S Zapperi
How Self-Organized Criticality Works: A Unified Mean-Field Picture, A Vespignani, S Zapperi
Alessandro Vespignani
We present a unified dynamical mean-field theory, based on the single site approximation to the master-equation, for stochastic self-organized critical models. In particular, we analyze in detail the properties of sandpile and forest-fire (FF) models. In analogy with other nonequilibrium critical phenomena, we identify an order parameter with the density of ''active'' sites, and control parameters with the driving rates. Depending on the values of the control parameters, the system is shown to reach a subcritical (absorbing) or supercritical (active) stationary state. Criticality is analyzed in terms of the singularities of the zero-field susceptibility. In the limit of vanishing control …
Universality In Sandpiles, A Chessa, H E. Stanley, A Vespignani, S Zapperi
Universality In Sandpiles, A Chessa, H E. Stanley, A Vespignani, S Zapperi
Alessandro Vespignani
We perform extensive numerical simulations of different versions of the sandpile model. We find that previous claims about universality classes are unfounded, since the method previously employed to analyze the data suffered from a systematic bias. We identify the correct scaling behavior and provide evidences suggesting that sandpiles with stochastic and deterministic toppling rules belong to the same universality class.
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.
Mean-Field Behavior Of The Sandpile Model Below The Upper Critical Dimension, A Chessa, E Marinari, A Vespignani, S Zapperi
Mean-Field Behavior Of The Sandpile Model Below The Upper Critical Dimension, A Chessa, E Marinari, A Vespignani, S Zapperi
Alessandro Vespignani
We present results of large scale numerical simulations of the Bak, Tang, and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] sandpile model. We analyze the critical behavior of the model in Euclidean dimensions 2 less than or equal to d less than or equal to 6. We consider a dissipative generalization of the model and study the avalanche size and duration distributions for different values of the lattice size and dissipation. We find that the scaling exponents in d=4 significantly differ from mean-field predictions, thus Suggesting an upper critical dimension d(c)greater than or equal …
Energy Constrained Sandpile Models, A Chessa, E Marinari, A Vespignani
Energy Constrained Sandpile Models, A Chessa, E Marinari, A Vespignani
Alessandro Vespignani
We study two driven dynamical systems with conserved energy. The two automata contain the basic dynamical rules of the Bak, Tang, and Wiesenfeld sandpile model. In addition a global constraint on the energy contained in the lattice is imposed. In the limit of an infinitely slow driving of the system, the conserved energy E becomes the only parameter governing the dynamical behavior of the system. Both models show scale-fret behavior at a critical value E-c of the fixed energy. The scaling with respect to the relevant scaling field points out that the developing of critical correlations is in a different …
Absorbing-State Phase Transitions In Fixed-Energy Sandpiles, A Vespignani, R Dickman, M A. Munoz, S Zapperi
Absorbing-State Phase Transitions In Fixed-Energy Sandpiles, A Vespignani, R Dickman, M A. Munoz, S Zapperi
Alessandro Vespignani
We study sandpile models as closed systems, with the conserved energy density zeta playing the role of an external parameter. The critical energy density zeta (c) marks a nonequilibrium phase transition between active and absorbing states. Several fixed-energy sandpiles are studied in extensive simulations of stationary and transient properties, as well as the dynamics of roughening in an interface-height representation. Our primary goal is to identify the universality classes of such models, in hopes of assessing the validity of two recently proposed approaches to sandpiles: a phenomenological continuum Langevin description with absorbing states, and a mapping to driven interface dynamics …
Renormalization Approach To The Self-Organized Critical-Behavior Of Sandpile Models, A Vespignani, S Zapperi, L Pietronero
Renormalization Approach To The Self-Organized Critical-Behavior Of Sandpile Models, A Vespignani, S Zapperi, L Pietronero
Alessandro Vespignani
No abstract provided.
Dynamical Real Space Renormalization Group Applied To Sandpile Models, E V. Ivashkevich, A M. Povolotsky, A Vespignani, S Zapperi
Dynamical Real Space Renormalization Group Applied To Sandpile Models, E V. Ivashkevich, A M. Povolotsky, A Vespignani, S Zapperi
Alessandro Vespignani
A general framework for the renormalization group analysis of self-organized critical sandpile models is formulated. The usual real space renormalization scheme for lattice models when applied to nonequilibrium dynamical models must be supplemented by feedback relations coming from the stationarity conditions. On the basis of these ideas the dynamically driven renormalization group is applied to describe the boundary and bulk critical behavior of sandpile models. A detailed description of the branching nature of sandpile avalanches is given in terms of the generating functions of the underlying branching process.
Renormalization Scheme For Self-Organized Criticality In Sandpile Models, L Pietronero, A Vespignani, S Zapperi
Renormalization Scheme For Self-Organized Criticality In Sandpile Models, L Pietronero, A Vespignani, S Zapperi
Alessandro Vespignani
We introduce a renormalization scheme of novel type that allows us to characterize the critical state and the scale invariant dynamics in sandpile models. The attractive fixed point clarifies the nature of self-organization in these systems. Universality classes can be identified and the critical exponents can be computed analytically. We obtain tau = 1.253 for the avalanche exponent and z = 1.234 for the dynamical exponent. These results are in good agreement with computer simulations. The method can be naturally extended to other problems with nonequilibrium stationary states.
Driving, Conservation, And Absorbing States In Sandpiles, A Vespignani, R Dickman, M A. Munoz, S Zapperi
Driving, Conservation, And Absorbing States In Sandpiles, A Vespignani, R Dickman, M A. Munoz, S Zapperi
Alessandro Vespignani
We use a phenomenological field theory, reflecting the symmetries and conservation laws of sandpiles, to compare the driven dissipative sandpile, widely studied in the context of self-organized criticality, with the corresponding fixed-energy model. The latter displays an absorbing-state phase transition with upper critical dimension d(c) = 4. We show that the driven model exhibits a fundamentally different approach to the critical point, and compute a subset of critical exponents. We present numerical simulations in support of our theoretical predictions.