The problem of the effects of compressibility and large-scale anisotropy on anomalous scaling behavior is considered for two models describing passive advection of scalar density and tracer fields. The advecting velocity field is Gaussian, delta correlated in time, and scales with a positive exponent epsilon. Explicit inertial-range expressions for the… (More)
Instanton analysis is applied to model A of critical dynamics. It is shown that the static instanton of the massless φ 4 model determines the large-order asymptotes of the perturbation expansion of the dynamic model.
— It is generally believed that the first experiment on bimetallic electric stimulation of living body was made by Luigi Galvani with frog leg in 1786. Galvani however succeeded to produce electric stimulation of the frog leg already in 1781 with electricity produced with electric machine. It has been suggested by Rowbottom and Susskind that the first… (More)
Stochastic dynamics of a nonconserved scalar order parameter near its critical point, subject to random stirring and mixing, is studied using the field theoretic renormalization group. The stirring and mixing are modelled by a random external Gaussian noise with the correlation function ∝ δ(t − t ′)k 4−d−y and the divergence-free (due to incompressibility)… (More)
Inertial-range scaling behavior of high-order (up to order N=51 ) two-point correlation functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. Exponents of the power-like asymptotic behavior of… (More)
The renormalization group and operator product expansion are applied to the model of a passive scalar quantity advected by the Gaussian self-similar velocity field with finite, and not small, correlation time. The inertial-range energy spectrum of the velocity is chosen in the form E(k) proportional, variant k(1-2 epsilon ), and the correlation time at the… (More)