Emergent spatial structures in critical sandpiles

We introduce and study a new directed sandpile model with threshold dynamics and stochastic toppling rules. We show that particle conservation law and the directed percolation-like local evolution of avalanches lead to the formation of a spatial structure in the steady state, with the density developing a power law tail away from the top. We determine the scaling exponents characterizing the avalanche distributions in terms of the critical exponents of directed percolation in all dimensions.Comment: 4 pages, 4 Postscript figures, to appear in Phys. Rev. Let

Stability and chaos in coupled two-dimensional maps on Gene Regulatory Network of bacterium E.Coli

The collective dynamics of coupled two-dimensional chaotic maps on complex networks is known to exhibit a rich variety of emergent properties which crucially depend on the underlying network topology. We investigate the collective motion of Chirikov standard maps interacting with time delay through directed links of Gene Regulatory Network of bacterium Escherichia Coli. Departures from strongly chaotic behavior of the isolated maps are studied in relation to different coupling forms and strengths. At smaller coupling intensities the network induces stable and coherent emergent dynamics. The unstable behavior appearing with increase of coupling strength remains confined within a connected sub-network. For the appropriate coupling, network exhibits statistically robust self-organized dynamics in a weakly chaotic regime

Dynamic criticality in driven disordered systems: Role of depinning and driving rate in Barkhausen noise

We study Barkhausen noise in a diluted two-dimensional Ising model with the extended domain wall and weak random fields occurring due to coarse graining. We report two types of scaling behavior corresponding to (a) low disorder regime where a single domain wall slips through a series of positions when the external field is increased, and (b) large disorder regime, which is characterized with nucleation of many domains. The effects of finite concentration of nonmagnetic ions and variable driving rate on the scaling exponents is discussed in both regimes. The universal scaling behavior at low disorder is shown to belong to a class of critical dynamic systems, which are described by a fixed point of the stochastic transport equation with self-consistent disorder correlations.Comment: Revtex, 4 PostScript figure

Transport Processes on Homogeneous Planar Graphs with Scale-Free Loops

We consider the role of network geometry in two types of diffusion processes: transport of constant-density information packets with queuing on nodes, and constant voltage-driven tunneling of electrons. The underlying network is a homogeneous graph with scale-free distribution of loops, which is constrained to a planar geometry and fixed node connectivity $k=3$. We determine properties of noise, flow and return-times statistics for both processes on this graph and relate the observed differences to the microscopic process details. Our main findings are: (i) Through the local interaction between packets queuing at the same node, long-range correlations build up in traffic streams, which are practically absent in the case of electron transport; (ii) Noise fluctuations in the number of packets and in the number of tunnelings recorded at each node appear to obey the scaling laws in two distinct universality classes; (iii) The topological inhomogeneity of betweenness plays the key role in the occurrence of broad distributions of return times and in the dynamic flow. The maximum-flow spanning trees are characteristic for each process type.Comment: 14 pages, 5 figure

Criticality in driven cellular automata with defects

We study three models of driven sandpile-type automata in the presence of quenched random defects. When the dynamics is conservative, all these models, termed the random sites (A), random bonds (B), and random slopes (C), self-organize into a critical state. For Model C the concentration-dependent exponents are nonuniversal. In the case of nonconservative defects, the asymptotic state is subcritical. Possible defect-mediated nonequilibrium phase transitions are also discussed.Comment: 13 pages, Latex, 6 PostScript figures included, all uuencoded Z-compressed ta

Dynamics of directed graphs: the world-wide Web

We introduce and simulate a growth model of the world-wide Web based on the dynamics of outgoing links that is motivated by the conduct of the agents in the real Web to update outgoing links (re)directing them towards constantly changing selected nodes. Emergent statistical correlation between the distributions of outgoing and incoming links is a key feature of the dynamics of the Web. The growth phase is characterized by temporal fractal structures which are manifested in the hierarchical organization of links. We obtain quantitative agreement with the recent empirical data in the real Web for the distributions of in- and out-links and for the size of connected component. In a fully grown network of $N$ nodes we study the structure of connected clusters of nodes that are accessible along outgoing links from a randomly selected node. The distributions of size and depth of the connected clusters with a giant component exhibit supercritical behavior. By decreasing the control parameter---average fraction $\beta$ of updated and added links per time step---towards $\beta_c(N) < 10$ the Web can resume a critical structure with no giant component in it. We find a different universality class when the updates of links are not allowed, i.e., for $\beta \equiv 0$, corresponding to the network of science citations.Comment: Revtex, 4 PostScript figures, small changes in the tex