Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time

Abstract

The direct bond percolation process (Gribov process) is studied in the presence of random velocity fluctuations generated by the Gaussian self-similar ensemble with finite correlation time. We employ the renormalization group in order to analyze a combined effect of the compressibility and finite correlation time on the long-time behavior of the phase transition between an active and an absorbing state. The renormalization procedure is performed to the one-loop order. Stable fixed points of the renormalization group and their regions of stability are calculated in the one-loop approximation within the three-parameter $(\eps,y,η)$-expansion. Different regimes corresponding to the rapid-change limit and frozen velocity field are discussed, and their fixed points' structure is determined in numerical fashion.

17 pages, 7 Tables, 10 Figures

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Cited by in corpus (4)

• The symbiotic contact process: phase transitions, hysteresis cycles, and bistability
• Influence of turbulent mixing on critical behavior of directed percolation process : effect of compressibility
• Scaling behavior in interacting systems: joint effect of anisotropy and compressibility
• Active-to-absorbing phase transition subjected to the velocity fluctuations in the frozen limit case