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• W2065697168 abstract "We study erratically moving spatial structures that are found in a driven interface in a random medium at the depinning threshold. We introduce a bond-disordered variant of the Sneppen model and study the effect of extremal dynamics on the morphology of the interface. We find evidence for the formation of a structure that moves along with the growth site. The time average of the structure, which is defined with respect to the active spot of growth, defines an activity-centered pattern. Extensive Monte Carlo simulations show that the pattern has a tail that decays slowly, as a power law. To understand this sort of pattern formation, we write down an approximate integral equation involving the local interface dynamics and long-ranged jumps of the growth spot. We clarify the nature of the approximation by considering a model for which the integral equation is exactly derivable from an extended master equation. Improvements to the equation are considered by adding a second coupled equation that provides a self-consistent description. The pattern, which defines a one-point correlation function, is shown to have a strong effect on ordinary space-fixed two-point correlation functions. Finally we present evidence that this sort of pattern formation is not confined to the interface problem, but is generic to situations in which the activity at successive time steps is correlated, such as, for instance, in several other extremal models. We present numerical results for activity-centered patterns in the Bak-Sneppen model of evolution and the Zaitsev model of low-temperature creep." @default.
• W2065697168 created "2016-06-24" @default.
• W2065697168 creator A5048692153 @default.
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• W2065697168 date "1998-03-01" @default.
• W2065697168 modified "2023-09-23" @default.
• W2065697168 title "Pattern formation in interface depinning and other models: Erratically moving spatial structures" @default.
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• W2065697168 doi "https://doi.org/10.1103/physreve.57.2949" @default.
• W2065697168 hasPublicationYear "1998" @default.
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