1,721,107 research outputs found
Renormalization scheme for self-organized criticality in sandpile models
Full text linkWe 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 τ=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
Renormalization scheme for forest-fire models
No full textWe introduce a renormalization scheme for forest-fire models in order to characterize the nature of the critical state and its scale-invariant dynamics. We study one- and two-dimensional models defining a characterization of the phase space that allows us to describe the evolution of the dynamics under a scale transformation. We show the existence of a relevant critical parameter associated with a repulsive fixed point in the phase space, From the renormalization-group point of view these models are therefore critical in the usual sense, because the fixed-point value of the control parameter is crucial in order to get criticality. This general scheme allows us to calculate analytically the critical exponent nu which describes the approach to the critical point along the repulsive direction and the exponent tau that characterizes the distribution of forest clusters at the critical point. We obtain nu = 1.0, tau = 1.0 and nu = 0.65, tau = 1.16, respectively, for the one- and two-dimensional cases, in very good agreement with exact and numerical results
Computing Synthetic contact matrices through modeling of social mixing patterns relevant to infectious disease transmission
No full textSynthetic contact matrices for European countries
No full textSIMID workshop - ECDC Satellite Workshop: Modeling Varicella Transmission in the EU, Hasselt, Belgium, April 25-2
Dynamically driven renormalization group
No full textWe present a detailed discussion of a novel dynamical renormalization group scheme: the dynamically driven renormalization group (DDRG). This is a general renormalization method developed for dynamical systems with non-equilibrium critical steady state. The method is based on a real-space renormalization scheme driven by a dynamical steady-state condition which acts as a feedback on the transformation equations. This approach has been applied to open nonlinear systems such as self-organized critical phenomena, and it allows the analytical evaluation of scalling dimensions and critical exponents. Equilibrium models at the critical point can also be considered. The explicit application to some models and the corresponding results are discussed
Renormalization of non-equilibrium systems with critical stationary state
Full text linkWe introduce the general formulation of a renormalization method suitable to study the critical properties of non-equilibrium 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 non-equilibrium statistical weights of steady-state configurations to be used in the calculations. In this way we are able to write recursion relations for the parameters evolution under scale change, from which we can extract numerical values for the critical exponents. This general framework allows the systematic analysis of several models showing self-organized criticality in terms of usual concepts of phase transitions and critical phenomena
LOCAL RIGIDITY AND SELF-ORGANIZED CRITICALITY FOR AVALANCHES
No full textThe general conditions for a sandpile system to evolve spontaneously into a critical state characterized by a power law distribution of avalanches or bursts are identified as: a) the existence of a stationary state with a global conservation law; b) long-range correlations in the continuum limit (i.e. Laplacian diffusive field); c) the existence of a local rigidity for the microscopic dynamics. These conditions permit a classification of the models that have been considered up to now and the identification of the local rigidity as a new basic parameter that can lead to various possible scenarios ranging continuously from SOC behaviour to standard diffusion
Renormalization group approach for forest-fire models
No full textWe introduce a Renormalization scheme for the one- and two-dimensional Forest-Fire models 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. These models are therefore critical in the usual sense because the fixed point value of the control parameter is crucial in order to get criticality and it is not just the expression of a time scale separation. This general scheme allows us to calculate analytically the critical exponents for the one- and two-dimensional cases. The results obtained are in good agreement with exact or numerical results
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