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## Normal and anomalous scaling of the fourth-order correlation function of a randomly advected passive scalar

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 1995. Vol. 52. No. 5. P. 4924-4941.

For a delta-correlated velocity field, simultaneous correlation functions
of a passive scalar satisfy closed equations. We analyze the equation for the
four-point function. To describe a solution completely, one has to solve the
matching problems at the scale of the source and at the diffusion scale.
We solve both the matching problems and thus
find the dependence of the four-point correlation function on the diffusion
and pumping scale for large space dimensionality $d$.
It is shown that anomalous scaling
appears in the first order of $1/d$ perturbation theory.
Anomalous dimensions are found analytically both for the scalar field and for
it's derivatives, in particular, for the dissipation field.

Kolokolov I., Chertkov M., Vergassola M., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1997 Vol. 56 No. 5 P. 5483-5499

Random advection of a Lagrangian tracer scalar field u (t,x) by a one-dimensional, spatially smooth and
short-correlated in time velocity field is considered. Scalar fluctuations are maintained by a source concentrated
at the integral scale L. The statistical properties of both scalar differences and the dissipation field are analytically
determined, exploiting the dynamical formulation of the model. The ...

Added: March 6, 2017

Kolokolov I., Lebedev V., Chertkov M., Physics of Fluids 2007 Vol. 19 P. 101703-1-101703-4

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale L,
injection scale l, and diffusive scale rd. The scales are well separated if the diffusivity is small,
rdl ,L, and one normally says that effects of diffusion are confined to smaller scales, rrd.
However, if the velocity is single scale, one finds that a weak ...

Added: February 10, 2017

Kolokolov I., Lebedev V., Chertkov M. et al., International Journal of Modern Physics B 1996 Vol. 10 No. 18-19 P. 2273-2309

The steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described at scales less than the correlation length of the flow and larger than the diffusion scale. The probability distribution of the scalar is expressed via the probability distribution of the line stretching rate. The description of ...

Added: March 28, 2017

Kolokolov I., Lebedev V., Balkovsky E. et al., JETP Letters 1995 Vol. 61 No. 12 P. 1049-1054

Advection of a passive scalar $\theta$ in $d=2$ by a large-scale velocity
field rapidly changing in time is considered. The Gaussian feature of the
passive scalar statistics in the convective interval was discovered in
\cite{95CFKLa}. Here we examine deviations from the Gaussianity: we obtain
analytically the simultaneous fourth-order correlation function of $\theta$.
Explicit expressions for fourth-order objects,
like $\langle(\theta_1-\theta_2)^4\rangle$ are ...

Added: March 27, 2017

Kolokolov I., Chertkov M., Gamba A., Physics Letters A 1994 Vol. 192 No. 5-6 P. 435-443

We describe a new functional integral method for the computation of averages containing chronological exponentials of random matrices of arbitrary dimension. We apply these results to the rigorous study of the statistics of a passive scalar advected by a large-scale N-dimensional flow. In the delta-correlated case the statistics of the rate of line stretching appears to ...

Added: March 28, 2017

Kolokolov I., Chertkov M., Falkovich G., Physical Review Letters 1998 Vol. 80 No. 10 P. 2121-2124

The probability density function (PDF) of passive scalar dissipation P sed is found analytically in
the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The
tail of PDF is shown to be stretched exponent. ...

Added: March 5, 2017

Kolokolov I., Lebedev V., Chertkov M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1995 Vol. 51 No. 6 P. 5609-5627

Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. This corresponds to the so-called Batchelor regime where the velocity is replaced by its large-scale gradient. The probability distribution of the ...

Added: March 28, 2017

Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1996 Vol. 54 No. 5 P. 4896

We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is ...

Added: March 8, 2017

Kolokolov I., Chertkov M., Vergassola M., Physical Review Letters 1998 Vol. 80 P. 512

A model of scalar turbulent advection in compressible flow is analytically investigated. It is shown that, depending on the dimensionality d of space and the degree of compressibility of the smooth advecting velocity field, the cascade of the scalar is direct or inverse. If d>4 the cascade is always direct. For a small enough degree of compressibility, the cascade ...

Added: March 5, 2017

Kolokolov I., Gamba A., Journal of Statistical Physics 1999 Vol. 94 No. 5/6 P. 759-777

We compute analytically the probability distribution function PP(ε) of the dissipation field ε=(∇θ)2 of a passive scalar θ advected by a d-dimensional random flow, in the limit of large Peclet and Prandtl numbers (Batchelor–Kraichnan regime). The tail of the distribution is a stretched exponential: for ε→∞, ln PP(ε)∼−(d2ε)1/3. ...

Added: March 5, 2017

Kolokolov I., JETP Letters 2010 Vol. 92 No. 2 P. 107-109

The joint distribution function of two distances between three Lagrangian particles has been calculated in the
problem of chaotic twodimensional transport ...

Added: February 2, 2017

Belan S., Journal of Chemical Physics 2019 Vol. 150 No. 6 P. 064907

Ensembles of biological and artificial microswimmers produce long-range velocity fields with strong nonequilibrium fluctuations, which result in a dramatic increase in diffusivity of embedded particles (tracers). While such enhanced diffusivity may point to enhanced mixing of the fluid, a rigorous quantification of the mixing efficiency requires analysis of pair dispersion of tracers, rather than simple ...

Added: February 5, 2020

Kolokolov I., Nguyen Thanh T., Physics Letters A 2012 Vol. 376 P. 1836-1838

We study mixing of passive scalar by a chaotic velocity field with a relatively strong regular shear
component. We show that the tail of partition distribution function (PDF) of coarse-grained passive scalar
field differs qualitatively from the corresponding asymptotics in the case of isotropic flow statistics. ...

Added: December 28, 2016

Kolokolov I., Journal of Physics A: Mathematical and Theoretical 2017 Vol. 50 No. 155501 P. 1-12

The two-point correlation tensor of small-scale fluctuations of magnetic field B in a two-dimensional chaotic flow is studied. The analytic approach is developed in the framework of the Kraichnan–Kazantsev model. It is shown that the growth of the field fluctuations takes place in an essentially resistive regime and stops at large times in accordance with ...

Added: March 28, 2017

Lebedev V., Vergeles S. S., / Cornell University. Series Physics "arxiv.org". 2023.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar ...

Added: December 28, 2023

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1-8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

Andrew G. Semenov, Zaikin A., Physical Review B: Condensed Matter and Materials Physics 2013 Vol. 88 No. 5 P. 054505-1-054505-10

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current ...

Added: February 9, 2015

Slunyaev A., Кокорина А. В., Water Waves, Springer 2019 P. 1-20

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate ...

Added: October 13, 2019

Marshakov A., Миронов А. Д., Морозов А. Ю., Journal of Geometry and Physics 2011 Vol. 61 P. 1203-1222

We present a summary of current knowledge about the AGT relations for conformal blocks with additional insertion of the simplest degenerate operator, and a special choice of the corresponding intermediate dimension, when the conformal blocks satisfy hypergeometric-type differential equations in position of the degenerate operator. A special attention is devoted to representation of conformal block ...

Added: February 28, 2013

Prazdnichnykh A., Glazov M., Ren L. et al., Physical Review B: Condensed Matter and Materials Physics 2021 Vol. 103 No. 8 P. 085302-1-085302-12

The exciton valley dynamics in van der Waals heterostructures with transition metal dichalcogenide monolayers is driven by the long-range exchange interaction between the electron and the hole in the exciton. It couples the states active in the opposite circular polarizations resulting in the longitudinal-transverse splitting of excitons propagating in the monolayer plane. Here we study ...

Added: March 5, 2021

Pelinovsky E., Didenkulova I., Rybkin A., Journal of Fluid Mechanics 2014 Vol. 748 P. 416-432

We present an exact analytical solution of the nonlinear shallow water theory for wave run-up in inclined channels of arbitrary cross-section, which generalizes previous studies on wave run-up for a plane beach and channels of parabolic cross-section. The solution is found using a hodograph-type transform, which extends the well-known Carrier–Greenspan transform for wave run-up on ...

Added: November 19, 2014

Pelinovsky E., Kurkin A. A., Kozelkov A. et al., European Journal of Mechanics - B/Fluids 2018 Vol. 72 P. 616-623

The paper presents results of numerical simulations of freely rising solid spheres in a viscous fluid. The
diameter of spheres was 5 mm, 7 mm, 10 mm, and 20 mm, and the corresponding Reynolds numbers
varies in the interval 1400 < Re < 10100. It has been found that the free rise path varies, as the
Galileo number ...

Added: October 21, 2018

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Bodrova A., Osinsky A., Brilliantov N., Scientific Reports 2020 Vol. 10 Article 693

We study analytically and numerically the distribution of granular temperatures in granular mixtures for
different dissipation mechanisms of inelastic inter-particle collisions. Both driven and force-free systems
are analyzed. We demonstrate that the simplified model of a constant restitution coefficient fails to
predict even qualitatively a granular temperature distribution in a homogeneous cooling state. At the
same time we reveal ...

Added: February 25, 2020