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 (ɛ,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.

Active-to-absorbing phase transition subjected to the velocity fluctuations in the frozen limit case

“…From (3) one can expect that the parameter η formally drops out of the theory. However, RG analysis [14] shows that η affects the boundaries of fixed points. Note that in the blank space other regimes, e.g.…”

Advanced field-theoretical methods in stochastic dynamics and theory of developed turbulence

“…For α = 0 there is a region of stability for FP II 7 , which shrinks for the immediate value α = 3.5 to a smaller area. Numerical analysis [271] shows that this shrinking continues well down to the value α = 6. A further increase of α leads to a substantially larger region of stability for the given FP.…”

“…It should be noted, however, the rapid change limit discussed below corresponds to the white-noise problem in the Stratonovich interpretation. The stochastic problem (5.2.1-5.2.5) can be cast into a field-theoretic form and the resulting dynamic functional [271] reads…”

“…Therefore, it is convenient to consider a new charge g 20 It turns out [271] that for some fixed points the computation of the eigenvalues of the matrix (2.4.8) is cumbersome and rather unpractical. In those cases it is possible to obtain information about the stability from analyzing RG flow equations (2.4.4).…”

“…Finally, let us take look at the nontrivial regime, which means that no special requirements were laid upon the parameter u 1 . The corresponding differential equations for the RG flow (2.4.4) have been analyzed numerically [271]. The behavior of the RG flows has been found as follows.…”