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

Abstract

We investigate the scaling properties of phase transitions between survival and extinction (active-to-absorbing-state phase transition, AAPT) in a model that by itself belongs to the directed percolation (DP) universality class, interacting with a spatiotemporally fluctuating environment having its own nontrivial dynamics. We model the environment by (i) a randomly stirred fluid, governed by the Navier-Stokes (NS) equation, and (ii) a fluctuating surface, described either by the Kardar-Parisi-Zhang (KPZ) or the Edward-Wilkinson (EW) equations. We show, by using a one-loop perturbative field theoretic setup that, depending upon the spatial scaling of the variance of the external forces that drive the environment (i.e., the NS, KPZ, or EW equations), the system may show weak or strong dynamic scaling at the critical point of active-to-absorbing-state phase transitions. In the former case AAPT displays scaling belonging to the DP universality class, whereas in the latter case the universal behavior is different.

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

“…A positive parameter α > 0 can be interpreted as the simplest possible deviation [35] from the incompressibility condition ∇ • v = 0. The incompressible case, α = 0, was analyzed in previous works [40][41][42][43][44]. The coupling constant g 10 and the exponent y describe the equal-time velocity correlator or, equivalently, the energy spectrum [25,28,36] of the velocity fluctuations.…”

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

“…3-5.1 is related to y as follows y = 2ε. The incompressible version of the considered model, α = 0, has been studied in works [272][273][274][275][276]. The velocity field here is a coloured noise field and does not require any specification of interpretation.…”

Active-to-absorbing-state phase transition in an evolving population with mutation

“…Studies dealing with the effect of environmental fluctuations on a species undergoing AAPT has been made in Refs. [23][24][25][26]. It is now believed that nontrivial environmental dynamics and its feedback on the species undergoing an AAPT substantially alter the critical exponents at the AAPT leading to new universal behavior different from the DP universality class.…”

“…For instance, by considering the environment to follow its own fluctuating scale invariant dynamics, Refs. [23,24] generically found non-DP like critical scaling at the AAPT, often associated with weak dynamic scaling, where the species undergoing AAPT and the environment have unequal dynamic exponents. Ref.…”

“…Our model is distinguished by the feature that the density of the mutant species B does not obey any conservation law in the active state of the model, as a result of its interaction with the species A, unlike the models in Refs. [23,24]. Our model is well-suited to study whether or not the lack of conservation laws for the mutant B dynamics due to its coupling with the pure species A undergoing AAPT affects the critical scaling of the AAPT.…”