Related papers: The Fourth-Order Correlation Function of a Randoml…
A model of the passive vector field advected by the uncorrelated in time Gaussian velocity with power-like covariance is studied by means of the renormalization group and the operator product expansion. The structure functions of the…
A Lagrangian method for the numerical simulation of the Kraichnan passive scalar model is introduced. The method is based on Monte--Carlo simulations of tracer trajectories, supplemented by a point-splitting procedure for coinciding points.…
We investigate the dispersion of a passive scalar such as the concentration of a chemical species, or temperature, in homogeneous bubbly suspensions, by determining an effective diffusivity tensor. Defining the longitudinal and transverse…
We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…
The gravitational collapse in fourth order theories of gravity defined by an arbitrary action of the scalar curvature shows significant deviations with General Relativity. The presence of a new scalar mode produces a higher initial…
The influence of compressibility on the stability of the scaling regimes of the passive scalar advected by a Gaussian velocity field with finite correlation time is investigated by the field theoretic renormalization group within two-loop…
For Kraichnan's problem of passive scalar advection by a velocity field delta-correlated in time, the limit of large space dimensionality $d\gg1$ is considered. Scaling exponents of the scalar field are analytically found to be…
We derive a simple consistency relation from the running of the tensor-to-scalar ratio. This new relation is first order in the slow-roll approximation. While for single field models we can obtain what can be found by using other…
Inertial-range scaling behavior of high-order (up to order N=51) structure 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…
Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order $1/d$-expansion by M.…
Model of a passive scalar field advected by the compressible Gaussian strongly anisotropic velocity field with the covariance $\propto \delta(t-t^{\prime})|{\bf x}-{\bf x^{\prime}}|^{2\epsilon}$ is studied by using the field theoretic…
We consider a problem whether bound states are made in a scalar theory with a fourth-order derivative term or not. After rewriting the theory to a standard scalar theory with second-order derivative terms, we calculate a correlation…
Passive scalar equation is considered in a turbulent homogeneous incompressible Gaussian velocity field. The turbulent nature of the field results in non-smooth coefficients in the equation. A strong, in the stochastic sense, solution of…
The field theoretic renormalization group and the operator product expansion are applied to the stochastic model of passively advected vector field with the most general form of the nonlinear term allowed by the Galilean symmetry. The…
The gaussian closure approximation previously used to study the growth kinetics of the non-conserved O(n) model is shown to be the zeroth-order approximation in a well-defined sequence of approximations composing a more elaborate theory.…
We consider evolution of a passive scalar (concentration of pollutants or temperature) in a chaotic (turbulent) flow. A universal asymptotic behavior of the passive scalar decay (homogenization) related to peripheral regions (near walls) is…
We study estimation of an $s$-sparse signal in the $p$-dimensional Gaussian sequence model with equicorrelated observations and derive the minimax rate. A new phenomenon emerges from correlation, namely the rate scales with respect to…
We consider inflationary models with the inflaton coupled to the Gauss-Bonnet term assuming a special relation $\delta_1=2\lambda\epsilon_1$ between the two slow-roll parameters $\delta_1$ and $\epsilon_1$. For the slow-roll inflation, the…
A simple model of a passive scalar quantity advected by a Gaussian non-solenoidal ("compressible") velocity field is considered. Large order asymptotes of quantum-field expansions are investigated by instanton approach. The existence of…
We compute analytically the probability distribution function ${\cal P}(\epsilon)$ of the dissipation field $\epsilon =(\nabla \theta)^{2}$ of a passive scalar $\theta$ advected by a $d$-dimensional random flow, in the limit of large Peclet…