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## Viscous Instanton for Burgers' Turbulence

International Journal of Modern Physics B. 1997. Vol. 11. No. 26/27. P. 3223-3245.

We consider
the tails of probability density functions (PDF) for different characteristics
of velocity that satisfies Burgers equation driven by a large-scale force.
The saddle-point approximation is employed in the path integral
so that the calculation of the PDF tails
boils down to finding the special field-force configuration (instanton) that
realizes the extremum of probability. We calculate high moments of the velocity
gradient $\partial_xu$ and find out that they correspond to the PDF with
$\ln[{\cal P}(\partial_xu)]\propto-(-\partial_xu/{\rm Re})^{3/2}$ where
${\rm Re}$ is the Reynolds number. That stretched exponential form is valid
for negative $\partial_xu$ with the modulus much larger than its
root-mean-square (rms) value. The respective tail of PDF for negative velocity
differences $w$ is steeper than Gaussian,
$\ln{\cal P}(w)\sim-(w/u_{\rm rms})^3$, as well as single-point
velocity PDF $\ln{\cal P}(u)\sim-(|u|/u_{\rm rms})^3$.
For high velocity derivatives $u^{(k)}=\partial_x^ku$, the general
formula is found: $\ln{\cal P}(|u^{(k)}|)\propto
-(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.

Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review Letters 1997 Vol. 78 No. 8 P. 1452-1455

We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For ...

Added: March 6, 2017

Kolokolov I., JETP Letters 2000 Vol. 71 No. 1 P. 12-14

Leading terms of the asymptotic behavior of the pair and higher order correlation functions for finite times and large distances have been calculated for the Burgers equation involving thermal noise. It is shown that an intermittence phenomenon occurs, whereby certain correlation functions are much greater than their reducible parts. ...

Added: March 5, 2017

Kolokolov I., Turitsyn K., Journal of Experimental and Theoretical Physics 2002 Vol. 94 No. 6 P. 1193-1200

For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics
of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This
means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...

Added: February 25, 2017

Zybin K., Il'yn A. S., Physics-Uspekhi 2016 Vol. 59 No. 12 P. 1241-1244

This paper reviews the statistical properties and calculates the velocity structure functions of flows produced by a large-scale random scaling force in the Burgers model. ...

Added: September 22, 2017

Kolokolov I., Lebedev V., Kogan V. R., Journal of Physics A: Mathematical and Theoretical 2010 Vol. 43 P. 182001

We analyze the kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing the divergence of Lagrangian trajectories. A degree of ...

Added: February 5, 2017

Musaev E., Haupt A., Lechtenfeld O., Journal of High Energy Physics 2014 Vol. 2014 No. 11

Abstract: We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kaehler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order alpha' corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present ...

Added: December 8, 2014

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., 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., 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., Korshunov S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2009 Vol. 80 P. 031107

The free-energy distribution function of an elastic string in a quenched random potential, PLF, is investigated
with the help of the optimal fluctuation approach. The form of the far-right tail of PLF is found by
constructing the exact solution of the nonlinear saddle-point equations describing the asymptotic form of the
optimal fluctuation. The solution of the problem is ...

Added: February 8, 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., Falkovich G., Chertkov M. et al., Physical Review Letters 1999 Vol. 83 No. 20 P. 4065-4068

Kinematic dynamo theory is presented here for turbulent conductive fluids. We describe how inhomogeneous magnetic fluctuations are generated below the viscous scale of turbulence where the spatial smoothness of the velocity permits a systematic analysis of the Lagrangian path dynamics. We find analytically the moments and multipoint correlation functions of the magnetic field at small ...

Added: March 5, 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

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

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

Budkov Y., Kolesnikov A. L., Polymer Science - Series C 2018 Vol. 60 No. Supplement 1 P. 148-159

Theoretical models of the conformational behavior of flexible polymer chains in mixed solvents enunciated in the world literature during the last decade are critically reviewed. Models describing different mechanisms of coil-to-globule transitions in a good solvent induced by cosolvent addition are highlighted. Special attention is given to the analysis of theoretical approaches to describing the ...

Added: November 30, 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

М. : ИКИ РАН, 2011

Added: March 26, 2013