16,866 research outputs found

    Correlated Initial Conditions in Directed Percolation

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    We investigate the influence of correlated initial conditions on the temporal evolution of a (d+1)-dimensional critical directed percolation process. Generating initial states with correlations ~r^(sigma-d) we observe that the density of active sites in Monte-Carlo simulations evolves as rho(t)~t^kappa. The exponent kappa depends continuously on sigma and varies in the range -beta/nu_{||}<=kappa<=eta. Our numerical results are confirmed by an exact field-theoretical renormalization group calculation.Comment: 10 pages, RevTeX, including 5 encapsulated postscript figure

    Geotechnical Prediction and Performance of Eastern Scheldt Storm Surge Barrier

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    The construction of the Eastern Scheldt storm surge barrier was completed in 1986. The monitoring system meant to verify the functioning of the barrier during storm conditions became operational in 1988. Data concerning the geotechnical response was collected during the 4 days storm period between February 26 and March 2, 1990. In the paper some results are described. Conclusions with respect to the expected behaviour of the barrier during more extreme storms in future will be drawn in near future

    Spontaneous Symmetry Breaking in Directed Percolation with Many Colors: Differentiation of Species in the Gribov Process

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    A general field theoretic model of directed percolation with many colors that is equivalent to a population model (Gribov process) with many species near their extinction thresholds is presented. It is shown that the multicritical behavior is always described by the well known exponents of Reggeon field theory. In addition this universal model shows an instability that leads in general to a total asymmetry between each pair of species of a cooperative society.Comment: 4 pages, 2 Postscript figures, uses multicol.sty, submitte

    Spreading with immunization in high dimensions

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    We investigate a model of epidemic spreading with partial immunization which is controlled by two probabilities, namely, for first infections, p0p_0, and reinfections, pp. When the two probabilities are equal, the model reduces to directed percolation, while for perfect immunization one obtains the general epidemic process belonging to the universality class of dynamical percolation. We focus on the critical behavior in the vicinity of the directed percolation point, especially in high dimensions d>2d>2. It is argued that the clusters of immune sites are compact for d≤4d\leq 4. This observation implies that a recently introduced scaling argument, suggesting a stretched exponential decay of the survival probability for p=pcp=p_c, p0≪pcp_0\ll p_c in one spatial dimension, where pcp_c denotes the critical threshold for directed percolation, should apply in any dimension d≤3d \leq 3 and maybe for d=4d=4 as well. Moreover, we show that the phase transition line, connecting the critical points of directed percolation and of dynamical percolation, terminates in the critical point of directed percolation with vanishing slope for d<4d<4 and with finite slope for d≥4d\geq 4. Furthermore, an exponent is identified for the temporal correlation length for the case of p=pcp=p_c and p0=pc−ϵp_0=p_c-\epsilon, ϵ≪1\epsilon\ll 1, which is different from the exponent ν∥\nu_\parallel of directed percolation. We also improve numerical estimates of several critical parameters and exponents, especially for dynamical percolation in d=4,5d=4,5.Comment: LaTeX, IOP-style, 18 pages, 9 eps figures, minor changes, additional reference

    Development of Stresses in Cohesionless Poured Sand

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    The pressure distribution beneath a conical sandpile, created by pouring sand from a point source onto a rough rigid support, shows a pronounced minimum below the apex (`the dip'). Recent work of the authors has attempted to explain this phenomenon by invoking local rules for stress propagation that depend on the local geometry, and hence on the construction history, of the medium. We discuss the fundamental difference between such approaches, which lead to hyperbolic differential equations, and elastoplastic models, for which the equations are elliptic within any elastic zones present .... This displacement field appears to be either ill-defined, or defined relative to a reference state whose physical existence is in doubt. Insofar as their predictions depend on physical factors unknown and outside experimental control, such elastoplastic models predict that the observations should be intrinsically irreproducible .... Our hyperbolic models are based instead on a physical picture of the material, in which (a) the load is supported by a skeletal network of force chains ("stress paths") whose geometry depends on construction history; (b) this network is `fragile' or marginally stable, in a sense that we define. .... We point out that our hyperbolic models can nonetheless be reconciled with elastoplastic ideas by taking the limit of an extremely anisotropic yield condition.Comment: 25 pages, latex RS.tex with rspublic.sty, 7 figures in Rsfig.ps. Philosophical Transactions A, Royal Society, submitted 02/9

    Renormalization group of probabilistic cellular automata with one absorbing state

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    We apply a recently proposed dynamically driven renormalization group scheme to probabilistic cellular automata having one absorbing state. We have found just one unstable fixed point with one relevant direction. In the limit of small transition probability one of the cellular automata reduces to the contact process revealing that the cellular automata are in the same universality class as that process, as expected. Better numerical results are obtained as the approximations for the stationary distribution are improved.Comment: Errors in some formulas have been corrected. Additional material available at http://mestre.if.usp.br/~javie

    Percolation Threshold, Fisher Exponent, and Shortest Path Exponent for 4 and 5 Dimensions

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    We develop a method of constructing percolation clusters that allows us to build very large clusters using very little computer memory by limiting the maximum number of sites for which we maintain state information to a number of the order of the number of sites in the largest chemical shell of the cluster being created. The memory required to grow a cluster of mass s is of the order of sθs^\theta bytes where θ\theta ranges from 0.4 for 2-dimensional lattices to 0.5 for 6- (or higher)-dimensional lattices. We use this method to estimate dmind_{\scriptsize min}, the exponent relating the minimum path ℓ\ell to the Euclidean distance r, for 4D and 5D hypercubic lattices. Analyzing both site and bond percolation, we find dmin=1.607±0.005d_{\scriptsize min}=1.607\pm 0.005 (4D) and dmin=1.812±0.006d_{\scriptsize min}=1.812\pm 0.006 (5D). In order to determine dmind_{\scriptsize min} to high precision, and without bias, it was necessary to first find precise values for the percolation threshold, pcp_c: pc=0.196889±0.000003p_c=0.196889\pm 0.000003 (4D) and pc=0.14081±0.00001p_c=0.14081\pm 0.00001 (5D) for site and pc=0.160130±0.000003p_c=0.160130\pm 0.000003 (4D) and pc=0.118174±0.000004p_c=0.118174\pm 0.000004 (5D) for bond percolation. We also calculate the Fisher exponent, τ\tau, determined in the course of calculating the values of pcp_c: τ=2.313±0.003\tau=2.313\pm 0.003 (4D) and τ=2.412±0.004\tau=2.412\pm 0.004 (5D)
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