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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)
The field theoretic renormalization group (RG) and the operator-product expansion are applied to the model of a transverse (divergence-free) vector quantity, passively advected by the "synthetic" turbulent flow with a finite (and not small) correlation time. The vector field is described by the stochastic advection-diffusion equation with the most general… (More)
An improved epsilon expansion in the d -dimensional (d > 2) stochastic theory of turbulence is constructed at two-loop order, which incorporates the effect of pole singularities at d--> 2 in coefficients of the epsilon expansion of universal quantities. For a proper account of the effect of these singularities, two different approaches to the… (More)
This paper is an attempt to relate two vast areas of the applicability of the renormalization group (RG): field-theoretic models and partial differential equations. It is shown that the Green function of a nonlinear diffusion equation can be viewed as a correlation function in a field-theoretic model with an ultralocal term, concentrated at a space-time… (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.
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)
Interplay of kinematic and magnetic forcing in a model of a conducting fluid with randomly driven magnetohydrodynamic equations has been studied in space dimensions d > or =2 by means of the renormalization group. A perturbative expansion scheme, parameters of which are the deviation of the spatial dimension from two and the deviation of the exponent of the… (More)
An improved epsilon expansion in the d-dimensional (d>2) stochastic theory of turbulence is constructed by taking into account pole singularities at d-->2 in coefficients of the epsilon expansion of universal quantities. Effectiveness of the method is illustrated by a two-loop calculation of the Kolmogorov constant in three dimensions.
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)
— 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)