We have studied the damage spreading (defined in the text) in the 'sandpile'
model of self organised criticality. We have studied the variations of the
critical time (defined in the text) and the total number of sites damaged at
critical time as a function of system size. Both shows the power law variation.
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[Show abstract][Hide abstract] ABSTRACT: This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The survey gives a general introduction to various lattice models of directed percolation and studies their scaling properties, field-theoretic aspects, numerical techniques, as well as possible experimental realizations. In addition, several examples of absorbing-state transitions which do not belong to the directed percolation universality class will be discussed. As a closely related technique, we investigate the concept of damage spreading. It is shown that this technique is ambiguous to some extent, making it impossible to define chaotic and regular phases in stochastic nonequilibrium systems. Finally, we discuss various classes of depinning transitions in models for interface growth which are related to phase transitions into absorbing states.
Full-text · Article · Feb 2000 · Advances In Physics
[Show abstract][Hide abstract] ABSTRACT: A great deal of work in recent years has been devoted to the topic of “complexity”, its measurement, and its implications. Here, the notion of algorithmic complexity is applied to the analysis of social networks. Structural features of theoretical importance — such as structural equivalence classes — are shown to be strongly related to the algorithmic complexity of graphs, and these results are explored using analytical and simulation methods. Analysis of the complexity of a variety of empirically derived networks suggests that many social networks are nearly as complex as their source entropy, and thus that their structure is roughly in line with the conditional uniform graph distribution hypothesis. Implications of these findings for network theory and methodology are also discussed.