Physics – Condensed Matter – Statistical Mechanics
Scientific paper
1998-03-19
Physics
Condensed Matter
Statistical Mechanics
RevTeX, 18 pages, 19 eps-figures, To appear in Phys. Rev. E
Scientific paper
10.1103/PhysRevE.57.2949
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 which 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 which 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 which 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 succesive time steps is correlated, 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.
Barma Mustansir
Krishnamurthy Supriya
No associations
LandOfFree
Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pattern Formation in Interface Depinning and Other Models: Erratically Moving Spatial Structures will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-528681