TY - JOUR

T1 - RANDOM INTERFACE GROWTH IN A RANDOM ENVIRONMENT: RENORMALIZATION GROUP ANALYSIS OF A SIMPLE MODEL

AU - Antonov, N.V.

AU - Kakin, P.I.

PY - 2015

Y1 - 2015

N2 - We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known Kardar–Parisi– Zhang model. The turbulent advecting velocity field is modeled by the Kraichnan rapid-change ensemble: Gaussian statistics with the correlation function hvvi ∝ δ(t − t ′ )k −d−ξ , where k is the wave number and ξ is a free parameter, 0 <ξ <2. We study the effects of the fluid compressibility. Using the field theory renormalization group, we show that depending on the relation between the exponent ξ and the spatial dimension d, the system manifests different types of large-scale, long-time asymptotic behavior associated with four possible fixed points of the renormalization group equations. In addition to the known regimes (ordinary diffusion, the ordinary growth process, and a passively advected scalar field), we establish the existence of a new nonequilibrium universality class. We calculate the fixed-point coord

AB - We study the effects of turbulent mixing on the random growth of an interface in the problem of the deposition of a substance on a substrate. The growth is modeled by the well-known Kardar–Parisi– Zhang model. The turbulent advecting velocity field is modeled by the Kraichnan rapid-change ensemble: Gaussian statistics with the correlation function hvvi ∝ δ(t − t ′ )k −d−ξ , where k is the wave number and ξ is a free parameter, 0 <ξ <2. We study the effects of the fluid compressibility. Using the field theory renormalization group, we show that depending on the relation between the exponent ξ and the spatial dimension d, the system manifests different types of large-scale, long-time asymptotic behavior associated with four possible fixed points of the renormalization group equations. In addition to the known regimes (ordinary diffusion, the ordinary growth process, and a passively advected scalar field), we establish the existence of a new nonequilibrium universality class. We calculate the fixed-point coord

KW - statistical mechanics

KW - critical behavior

KW - renormalization group

KW - nonequilibrium system

KW - turbulence

U2 - 10.1007/s11232-015-0348-1

DO - 10.1007/s11232-015-0348-1

M3 - Article

VL - 185

SP - 1391

EP - 1407

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -