Influence of turbulent mixing on critical behavior of directed percolation process : effect of compressibility
arXiv:1802.02036 · doi:10.1103/PhysRevE.97.022123
Abstract
Universal behavior is a typical emergent feature of critical systems. A paramount model of the non-equilibrium critical behavior is the directed bond percolation process that exhibits an active- to-absorbing state phase transition in the vicinity of a percolation threshold. Fluctuations of the ambient environment might affect or destroy the universality properties completely. In this work we assume that the random environment can be described by means of compressible velocity fluctu- ations. Using field-theoretic models and renormalization group methods we investigate large-scale and long-time behavior. Altogether eleven universality classes are found, out of which four are stable in the infrared limit and thus macroscopically accessible. In contrast to the model without veloc- ity fluctuations a possible candidate for a realistic three-dimensional case, a regime with relevant short-range noise, is identified. Depending on the dimensionality of space and the structure of the turbulent flow we calculate critical exponents of the directed percolation process. In the limit of the purely transversal velocity field random force critical exponents comply with the incompressible results obtained by previous authors. We have found intriguing non-universal behavior related to the mutual effect of compressibility and advection.
References in corpus (38)
- Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
- Particles and fields in fluid turbulence
- Universality classes in nonequilibrium lattice systems
- Directed percolation criticality in turbulent liquid crystals
- A Universal Transition to Turbulence in Channel Flow
- The Field Theory Approach to Percolation Processes
- Critical Dynamics of the Contact Process with Quenched Disorder
- Levy-flight spreading of epidemic processes leading to percolating clusters
- Critical behavior and Griffiths effects in the disordered contact process
- Anomalous scaling regimes of a passive scalar advected by the synthetic velocity field
- Non Perturbative Renormalization Group study of reaction-diffusion processes and directed percolation
- General framework of the non-perturbative renormalization group for non-equilibrium steady states
- Renormalization group and anomalous scaling in a simple model of passive scalar advection in compressible flow
- Anomalous scaling of a passive scalar advected by the synthetic compressible flow
- Fully developed isotropic turbulence: nonperturbative renormalization group formalism and fixed point solution
- Study of the disordered one-dimensional contact process
- Critical exponents of directed percolation measured in spatiotemporal intermittency
- Non-equilibrium Phase Transitions with Long-Range Interactions
- Population genetics in compressible flows
- Nonequilibrium phase transition on a randomly diluted lattice
- Coherent-state path integral versus coarse-grained effective stochastic equation of motion: From reaction diffusion to stochastic sandpiles
- An improved $\eps$ expansion for three-dimensional turbulence: two-loop renormalization near two dimensions
- Effects of turbulent mixing on the nonequilibrium critical behaviour
- Anomalous scaling of passive scalar fields advected by the Navier-Stokes velocity ensemble: Effects of strong compressibility and large-scale anisotropy
- Effects of turbulent mixing on critical behaviour in the presence of compressibility: Renormalization group analysis of two models
- Langevin equations for reaction-diffusion processes
- Reaction-diffusion processes and non-perturbative renormalisation group
- Chaotic mixing in effective compressible flows
- Fisher equation with turbulence in one dimension
- Effects of turbulent transfer on the critical behaviour
- Turbulent compressible fluid: renormalization group analysis, scaling regimes, and anomalous scaling of advected scalar fields
- Clustering of vertically constrained passive particles in homogeneous, isotropic turbulence
- Stochastic magnetohydrodynamic turbulence in space dimensions
- Functional renormalization-group approach to decaying turbulence
- Effects of Turbulent Mixing on the Critical Behavior
- Directed percolation process in the presence of velocity fluctuations: Effect of compressibility and finite correlation time
- Influence of diffusion on models for non-equilibrium wetting
- Critical Behavior of Percolation Process Influenced by Random Velocity Field: One-Loop Approximation