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- Sandpile models (11)
- Infectious disease (6)
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- Complex networks (3)
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- Diffusion-limited aggregation (DLA) (3)
- Numerical simulations (3)
- Phase transition (3)
- Universality classes (3)
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- Epidemics (2)
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- Internet maps (2)
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- Absorbing states (1)
- Amplitude distribution (1)
- Andrade's law (1)
- Avalanche events (1)
- Avalanche exponents (1)
- Axelrod's model for social influence (1)
- Born model (1)
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- Conserved energy (1)
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Articles 1 - 30 of 46
Full-Text Articles in Physics
Field Theory Of Absorbing Phase Transitions With A Nondiffusive Conserved Field, R Pastor-Satorras, A Vespignani
Field Theory Of Absorbing Phase Transitions With A Nondiffusive Conserved Field, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
We investigate the critical behavior of a reaction-diffusion system exhibiting a continuous absorbing-state phase transition. The reaction-diffusion system strictly conserves the total density of particles, represented as a nondiffusive conserved field, and allows an infinite number of absorbing configurations. Numerical results show that it belongs to a wide universality class that also includes stochastic sandpile models. We derive microscopically the field theory representing this universality class.
Parallel Diffusion-Limited Aggregation, H Kaufman, A Vespignani, B B. Mandelbrot, L Woog
Parallel Diffusion-Limited Aggregation, H Kaufman, A Vespignani, B B. Mandelbrot, L Woog
Alessandro Vespignani
We present methods for simulating very large diffusion-limited aggregation (DLA) clusters using parallel processing (PDLA). With our techniques, we have been able to simulate clusters of up to 130 million particles. The time required for generating a 100 million particle PDLA is approximately 13 h. The fractal behavior of these ''parallel'' clusters changes from a multiparticle aggregation dynamics to the usual DLA dynamics. The transition is described by simple scaling assumptions that define a characteristic cluster size separating the two dynamical regimes. We also use DLA clusters as seeds for parallel processing. In this case, the transient regime disappears and …
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(+)): …
Dislocation Jamming And Andrade Creep, M C. Miguel, A Vespignani, M Zaiser, S Zapperi
Dislocation Jamming And Andrade Creep, M C. Miguel, A Vespignani, M Zaiser, S Zapperi
Alessandro Vespignani
We simulate the glide motion of an assembly of interacting dislocations under the action of an external shear stress and show that the associated plastic creep relaxation follows Andrade's law. Our results indicate that Andrade creep in plastically deforming crystals involves the correlated motion of dislocation structures near a dynamic transition separating a flowing from a jammed phase. Simulations in the presence of dislocation multiplication and noise confirm the robustness of this finding and highlight the importance of metastable structure formation for the relaxation process.
The Fixed-Scale Transformation Approach To Fractal Growth, A Erzan, L Pietronero, A Vespignani
The Fixed-Scale Transformation Approach To Fractal Growth, A Erzan, L Pietronero, A Vespignani
Alessandro Vespignani
Irreversible fractal-growth models like diffusion-limited aggregation (DLA) and the dielectric breakdown model (DBM) have confronted us with theoretical problems of a new type for which standard concepts like field theory and renormalization group do not seem to be suitable. The fixed-scale transformation (FST) is a theoretical scheme of a novel type that can deal with such problems in a reasonably systematic way. The main idea is to focus on the irreversible dynamics at a given scale and to compute accurately the nearest-neighbor correlations at this scale by suitable lattice path integrals. The next basic step is to identify the scale-invariant …
Fractal And Topological Properties Of Directed Fractures, G Caldarelli, C Castellano, A Vespignani
Fractal And Topological Properties Of Directed Fractures, G Caldarelli, C Castellano, A Vespignani
Alessandro Vespignani
We use the Born model for the energy of elastic networks to simulate ''directed'' fracture growth. We define directed fractures as crack patterns showing a preferential evolution direction imposed by the type of stress and boundary conditions applied. This type of fracture allows a more realistic description of some kinds of experimental cracks and presents several advantages in order to distinguish between the various growth regimes. By choosing this growth geometry it is also possible to use without ambiguity the box-counting method to obtain the fractal dimension for different subsets of the patterns and for a wide range of the …
Avalanche And Spreading Exponents In Systems With Absorbing States, M A. Munoz, R Dickman, A Vespignani, S Zapperi
Avalanche And Spreading Exponents In Systems With Absorbing States, M A. Munoz, R Dickman, A Vespignani, S Zapperi
Alessandro Vespignani
We present generic scaling laws relating spreading critical exponents and avalanche exponents (in the sense of self-organized criticality) in general systems with absorbing states. Using these scaling laws we present a collection of the state-of-the-art exponents for directed percolation, dynamical percolation, and other universality classes. This collection of results should help to elucidate the connections of self-organized criticality and systems with absorbing states. In particular, some nonuniversality in avalanche exponents is predicted for systems with many absorbing states.
Renormalization Of Nonequilibrium Systems With Critical Stationary States, A Vespignani, S Zapperi, V Loreto
Renormalization Of Nonequilibrium Systems With Critical Stationary States, A Vespignani, S Zapperi, V Loreto
Alessandro Vespignani
We introduce the general formulation of a renormalization method suitable to study the critical properties of nonequilibrium systems with steady states: the dynamically driven renormalization group. We renormalize the time evolution operator by computing the rescaled time transition rate between coarse grained states. The obtained renormalization equations are coupled to a stationarity condition which provides the approximate nonequilibrium statistical weights of steady-state configurations to be used in the calculations. in this way we are able to write recursion relations for the parameter evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework …
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 …
Efficiency And Reliability Of Epidemic Data Dissemination In Complex Networks, Y Moreno, M Nekovee, A Vespignani
Efficiency And Reliability Of Epidemic Data Dissemination In Complex Networks, Y Moreno, M Nekovee, A Vespignani
Alessandro Vespignani
We study the dynamics of epidemic spreading processes aimed at spontaneous dissemination of information updates in populations with complex connectivity patterns. The influence of the topological structure of the network in these processes is studied by analyzing the behavior of several global parameters, such as reliability, efficiency, and load. Large-scale numerical simulations of update-spreading processes show that while networks with homogeneous connectivity patterns permit a higher reliability, scale-free topologies allow for a better efficiency.
Epidemic Spreading In Scale-Free Networks, R Pastor-Satorras, A Vespignani
Epidemic Spreading In Scale-Free Networks, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
The Internet has a very complex connectivity recently modeled by the class of scale-free networks. This feature, which appears to be very efficient for a communications network, favors at the same time the spreading of computer viruses. We analyze real data from computer virus infections and find the average lifetime and persistence of viral strains on the Internet. We define a dynamical model for the spreading of infections on scale-free networks. finding the absence of an epidemic threshold and its associated critical behavior. This new epidemiological framework rationalizes data of computer viruses and could help in the understanding of other …
Modeling The Evolution Of Weighted Networks, A Barrat, M Barthelemy, A Vespignani
Modeling The Evolution Of Weighted Networks, A Barrat, M Barthelemy, A Vespignani
Alessandro Vespignani
We present a general model for the growth of weighted networks in which the structural growth is coupled with the edges' weight dynamical evolution. The model is based on a simple weight-driven dynamics and a weights' reinforcement mechanism coupled to the local network growth. That coupling can be generalized in order to include the effect of additional randomness and nonlinearities which can be present in real-world networks. The model generates weighted graphs exhibiting the statistical properties observed in several real-world systems. In particular, the model yields a nontrivial time evolution of vertices' properties and scale-free behavior with exponents depending on …
Immunization Of Complex Networks, R Pastor-Satorras, A Vespignani
Immunization Of Complex Networks, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity provides an ideal environment for the spreading of infective agents. Here we show that the random uniform immunization of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scale-free properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunized individuals. The absence of any critical immunization threshold is due to the unbounded connectivity fluctuations of …
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.
Critical Behavior And Conservation In Directed Sandpiles, R Pastor-Satorras, A Vespignani
Critical Behavior And Conservation In Directed Sandpiles, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
We perform large-scale simulations of directed sandpile models with both deterministic and stochastic toppling rules. Our results show the existence of two distinct universality classes. We also provide numerical simulations of directed models in the presence of bulk dissipation. The numerical results indicate that the way in which dissipation is implemented is irrelevant for the determination of the critical behavior. The analysis of the self-affine properties of avalanches shows the existence of a subset of superuniversal exponents, whose value is independent of the universality class. This feature is accounted for by means of a phenomenological description of the energy balance …
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 …
Experimental Evidence For Critical-Dynamics In Microfracturing Processes, A Petri, G Paparo, A Vespignani, A Alippi, M Costantini
Experimental Evidence For Critical-Dynamics In Microfracturing Processes, A Petri, G Paparo, A Vespignani, A Alippi, M Costantini
Alessandro Vespignani
No abstract provided.
Avalanches In Breakdown And Fracture Processes, S Zapperi, P Ray, H E. Stanley, A Vespignani
Avalanches In Breakdown And Fracture Processes, S Zapperi, P Ray, H E. Stanley, A Vespignani
Alessandro Vespignani
We investigate the breakdown of disordered networks under the action of an increasing external-mechanical or electrical-force. We perform a mean-field analysis and estimate scaling exponents for the approach to the instability. By simulating two-dimensional models of electric breakdown and fracture we observe that the breakdown is preceded by avalanche events. The avalanches can be described by scaling laws, and the estimated values of the exponents are consistent with those found in mean-field theory. The breakdown point is characterized by a discontinuity in the macroscopic properties of the material, such as conductivity or elasticity, indicative of a first-order transition. The scaling …
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.
Persistence Of Screening And Self-Criticality In The Scale-Invariant Dynamics Of Diffusion-Limited Aggregation, R Cafiero, L Pietronero, A Vespignani
Persistence Of Screening And Self-Criticality In The Scale-Invariant Dynamics Of Diffusion-Limited Aggregation, R Cafiero, L Pietronero, A Vespignani
Alessandro Vespignani
The origin of fractal properties in diffusion limited aggregation is related to the persistence of screening in the scale invariant growth regime. This effect is described by the effective noise reduction parameter S spontaneously generated by the scale invariant dynamics. The renormalization of this parameter under scale transformation shows the following: (i) The fixed point is attractive, implying the self-critical nature of the process. (ii) The fixed point value S* is of the order of unity, showing that the small scale growth rules are already close to the scale invariant ones and that screening effects persist in the asymptotic regime.
First-Order Transition In The Breakdown Of Disordered Media, S Zapperi, P Ray, H Stanley, A Vespignani
First-Order Transition In The Breakdown Of Disordered Media, S Zapperi, P Ray, H Stanley, A Vespignani
Alessandro Vespignani
We study the approach to global breakdown in disordered media driven by increasing external forces. We first analyze the problem by mean-field theory, showing that the failure process can be described as a first-order phase transition, similarly to the case of thermally activated fracture in homogeneous media. Then we quantitatively confirm the predictions of the mean-field theory using numerical simulations of discrete models. Widely distributed avalanches and the corresponding mean-field scaling are explained by the long-range nature of elastic interactions. We discuss the analogy of our results to driven disordered first-order transitions and spinodal nucleation in magnetic systems.
Monte Carlo Fixed Scale Transformation For Nonlocal Fractal Growth Models, M Piccioni, R Cafiero, A Vespignani
Monte Carlo Fixed Scale Transformation For Nonlocal Fractal Growth Models, M Piccioni, R Cafiero, A Vespignani
Alessandro Vespignani
The fixed scale transformation (FST) is a theoretical framework developed for the evaluation of scaling dimensions in a vast class of complex systems showing fractal geometric correlations. For models with long range interactions, such as Laplacian growth models, the identification by analytical methods of the transformation's basic elements is a very difficult task. Here we present a Monte Carlo renormalization approach which allows the direct numerical evaluation of the FST transfer matrix, overcoming the usual problems of analytical and numerical treatments. The scheme is explicitly applied to the diffusion limited aggregation case where a scale invariant regime is identified and …
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.
Large-Scale Topological And Dynamical Properties Of The Internet, A Vazquez, R Pastor-Satorras, A Vespignani
Large-Scale Topological And Dynamical Properties Of The Internet, A Vazquez, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
We study the large-scale topological and dynamical properties of real Internet maps at the autonomous system level, collected in a 3-yr time interval. We find that the connectivity structure of the Internet presents statistical distributions settled in a well-defined stationary state. The large-scale properties are characterized by a scale-free topology consistent with previous observations. Correlation functions and clustering coefficients exhibit a remarkable structure due to the underlying hierarchical organization of the Internet. The study of the Internet time evolution shows a growth dynamics with aging features typical of recently proposed growing network models. We compare the properties of growing network …
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 …
Universality Class Of Absorbing Phase Transitions With A Conserved Field, M Rossi, R Pastor-Satorras, A Vespignani
Universality Class Of Absorbing Phase Transitions With A Conserved Field, M Rossi, R Pastor-Satorras, A Vespignani
Alessandro Vespignani
We investigate the critical behavior of systems exhibiting a continuous absorbing phase transition in the presence of a conserved field coupled to the order parameter. The results obtained point out the existence of a new universality class of nonequilibrium phase transitions that characterizes a vast set of systems including conserved threshold transfer processes and stochastic sandpile models.
Diffusion Of Scientific Credits And The Ranking Of Scientists, Filippo Radicchi, Santo Fortunato, Benjamin Markines, Alessandro Vespignani
Diffusion Of Scientific Credits And The Ranking Of Scientists, Filippo Radicchi, Santo Fortunato, Benjamin Markines, Alessandro Vespignani
Alessandro Vespignani
Recently, the abundance of digital data is enabling the implementation of graph-based ranking algorithms that provide system level analysis for ranking publications and authors. Here, we take advantage of the entire Physical Review publication archive (1893-2006) to construct authors' networks where weighted edges, as measured from opportunely normalized citation counts, define a proxy for the mechanism of scientific credit transfer. On this network, we define a ranking method based on a diffusion algorithm that mimics the spreading of scientific credits on the network. We compare the results obtained with our algorithm with those obtained by local measures such as the …