Effects of turbulent transfer on critical behavior

Abstract

Using the field theory renormalization group, we study the critical behavior of two systems subjected to turbulent mixing. The first system, described by the equilibrium model A, corresponds to the relaxational dynamics of a nonconserved order parameter. The second system is the strongly nonequilibrium reactiondiffusion system, known as the Gribov process or directed percolation process. The turbulent mixing is modeled by the stochastic Navier-Stokes equation with a random stirring force with the correlator ∝ δ(t − t )p 4−d−y , where p is the wave number, d is the space dimension, and y is an arbitrary exponent. We show that the systems exhibit various types of critical behavior depending on the relation between y and d. In addition to known regimes (original systems without mixing and a passively advected scalar field), we establish the existence of new strongly nonequilibrium universality classes and calculate the corresponding critical dimensions to the first order of the double expansion in y and ε = 4 − d (one-loop approximation).

Active-to-absorbing-state phase transition in the presence of fluctuating environments: Weak and strong dynamic scaling

“…Agreement of our results for the scaling exponents and the phase diagram with those in Ref. [17] shows the general robustness of the perturbation theory, despite our using (slightly) different choices for the coupling constants. It also shows how such choices may be exploited to infer the large-length-scale, long-time-limit physics of the system in a simple manner.…”

“…It may be noted that AAPT in contact with a randomly stirred velocity field has been considered in Ref. [17]. We compare our results and scheme of calculations with Ref.…”

“…[17] and our results lie essentially in the details: Our choice for the coupling constants is slightly different from Ref. [17]. Let us reconsider our choice for the effective coupling constants as used in the calculations above: The expressions of the Z factors in Eq.…”

“…Let us now compare with Ref. [17] where AAPT in contact with a randomly stirred fluid described by the NS equation with a long-ranged force is considered within a one-loop renormalized perturbation theory as above.…”

“…In contrast to us, Ref. [17] worked with u, w, and e (θ in our notation) as coupling constants in which the perturbative expansions are made. Our main operational motivation of expanding in terms of u, w, and w is that u andw (or rather their renormalized counterparts u R andw R ) directly describe the relative importance of the original DP nonlinearity vis-à-vis the advective nonlinearity.…”