Research output: Contribution to journal › Article › peer-review
Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise: Emergence of Induced Nonlinearity. / Какинь, Полина Игоревна; Рейтер, Михаил Алексеевич; Тумакова, Мария Михайловна; Гулицкий, Николай Михайлович; Антонов, Николай Викторович.
In: Universe, Vol. 8, No. 2, 72, 26.01.2022.Research output: Contribution to journal › Article › peer-review
}
TY - JOUR
T1 - Stirred Kardar-Parisi-Zhang Equation with Quenched Random Noise: Emergence of Induced Nonlinearity
AU - Какинь, Полина Игоревна
AU - Рейтер, Михаил Алексеевич
AU - Тумакова, Мария Михайловна
AU - Гулицкий, Николай Михайлович
AU - Антонов, Николай Викторович
N1 - Publisher Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland.
PY - 2022/1/26
Y1 - 2022/1/26
N2 - We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f (t, x) is specified by the pair correlation function 〈 f (t, x) f (t ′, x ′)〉 ∝ δ (d) (x − x ′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε = 4 − d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.
AB - We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise f (t, x) is specified by the pair correlation function 〈 f (t, x) f (t ′, x ′)〉 ∝ δ (d) (x − x ′), d being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this “induced” nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in ε = 4 − d and the velocity exponent ξ (one-loop approximation). As is the case with most “descendants” of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in “forbidden zones”, i.e., in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.
KW - Critical behaviour
KW - Kinetic roughening
KW - Renormalization group
KW - Turbulence
KW - MULTIFRACTALS
KW - FIELD-THEORY
KW - BEHAVIOR
KW - UPPER CRITICAL DIMENSION
KW - MODEL
KW - turbulence
KW - critical behaviour
KW - RENORMALIZATION-GROUP ANALYSIS
KW - SCALE PROPERTIES
KW - GROWTH
KW - kinetic roughening
KW - OPERATOR PRODUCT EXPANSION
KW - renormalization group
KW - DYNAMIC PHASE-TRANSITIONS
UR - http://www.scopus.com/inward/record.url?scp=85123759327&partnerID=8YFLogxK
UR - https://www.mendeley.com/catalogue/b7fc4ac9-76b7-38c9-86a6-f5b170b2b4be/
U2 - 10.3390/universe8020072
DO - 10.3390/universe8020072
M3 - Article
VL - 8
JO - Universe
JF - Universe
SN - 2218-1997
IS - 2
M1 - 72
ER -
ID: 92115752