arXiv subjects

I. Kolokolov

Publications and source records attributed to I. Kolokolov.

At least 19 recordsLinked to original sources

arXiv2010

Magnetic field correlations in a random flow with strong steady shear

We analyze magnetic 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 divergence of the Lagrangian trajectories. The magnetic field correlation functions are examined, we establish their growth rates and scaling behavior. General assertions are illustrated by explicit solution of the model where the velocity field is short-correlated in time.

nlin.CD↗

arXiv2009

Universal Velocity Profile for Coherent Vortices in Two-Dimensional Turbulence

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the $η=1/4$ scaling in the $V\propto r^{-η}$ law of the velocity spatial profile within a vortex, where $r$ is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the small-scale injection of turbulent fluctuations and details of the shape of the box.

nlin.CD↗

arXiv2008

Universal features of cell polarization processes

Cell polarization plays a central role in the development of complex organisms. It has been recently shown that cell polarization may follow from the proximity to a phase separation instability in a bistable network of chemical reactions. An example which has been thoroughly studied is the formation of signaling domains during eukaryotic chemotaxis. In this case, the process of domain growth may be described by the use of a constrained time-dependent Landau-Ginzburg equation, admitting scale-invariant solutions {\textit{à la}} Lifshitz and Slyozov. The constraint results here from a mechanism of fast cycling of molecules between a cytosolic, inactive state and a membrane-bound, active state, which dynamically tunes the chemical potential for membrane binding to a value corresponding to the coexistence of different phases on the cell membrane. We provide here a universal description of this process both in the presence and absence of a gradient in the external activation field. Universal power laws are derived for the time needed for the cell to polarize in a chemotactic gradient, and for the value of the smallest detectable gradient. We also describe a concrete realization of our scheme based on the analysis of available biochemical and biophysical data.

cond-mat.stat-mech↗

arXiv2008

Patch coalescence as a mechanism for eukaryotic directional sensing

Eukaryotic cells possess a sensible chemical compass allowing them to orient toward sources of soluble chemicals. The extracellular chemical signal triggers separation of the cell membrane into two domains populated by different phospholipid molecules and oriented along the signal anisotropy. We propose a theory of this polarization process, which is articulated into subsequent stages of germ nucleation, patch coarsening and merging into a single domain. We find that the polarization time, $t_ε$, depends on the anisotropy degree $ε$ through the power law $t_ε\propto ε^{-2}$, and that in a cell of radius $R$ there should exist a threshold value $ε_\mathrm{th}\propto R^{-1}$ for the smallest detectable anisotropy.

cond-mat.stat-mech↗

arXiv2007

Strong effect of weak diffusion on scalar turbulence at large scales

Passive scalar turbulence forced steadily is characterized by the velocity correlation scale, $L$, injection scale, $l$, and diffusive scale, $r_d$. The scales are well separated if the diffusivity is small, $r_d\ll l,L$, and one normally says that effects of diffusion are confined to smaller scales, $r\ll r_d$. However, if the velocity is single scale one finds that a weak dependence of the scalar correlations on the molecular diffusivity persists to even larger scales, e.g. $l\gg r\gg r_d$ \cite{95BCKL}. We consider the case of $L\gg l$ and report a counter-intuitive result -- the emergence of a new range of large scales, $L\gg r\gg l^2/r_d$, where the diffusivity shows a strong effect on scalar correlations.

nlin.CD↗

arXiv2007

Growing condensate in two-dimensional turbulence

We report a numerical study, supplemented by phenomenological explanations, of ``energy condensation'' in forced 2D turbulence in a biperiodic box. Condensation is a finite size effect which occurs after the standard inverse cascade reaches the size of the system. It leads to emergence of a coherent vortex dipole. We show that the time growth of the dipole is self-similar, and it contains most of the injected energy, thus resulting in an energy spectrum which is markedly steeper than the standard $k^{-5/3}$ one. Once the coherent component is subtracted, however, the remaining fluctuations have a spectrum close to $k^{-1}$. The fluctuations decay slowly as the coherent part grows.

nlin.CD↗

arXiv2004

Tumbling of Polymers in a Random Flow with Mean Shear

A polymer placed in chaotic flow with large mean shear tumbles, making a-periodic flips. We describe the statistics of angular orientation, as well as of tumbling time (separating two subsequent flips) of polymers in this flow. The probability distribution function (PDF) of the polymer orientation is peaked around a shear-preferred direction. The tails of this angular PDF are algebraic. The PDF of the tumbling time, $τ$, has a maximum at the value estimated as inverse Lyapunov exponent of the flow. This PDF shows an exponential tail for large $τ$ and a small-$τ$ tail determined by the simultaneous statistics of velocity PDF.

cond-mat.stat-mech↗

arXiv2004

Statistics of Polymer Extension in a Random Flow with Mean Shear

Considering the dynamics of a polymer with finite extensibility placed in a chaotic flow with large mean shear, we explain how the statistics of polymer extension changes with Weissenberg number, ${\it Wi}$, defined as the product of the polymer relaxation time and the Lyapunov exponent of the flow. Four regimes, of the ${\it Wi}$ number, are identified. One below the coil-stretched transition and three above the coil-stretched transition. Specific emphasis is given to explaining these regimes in terms of the polymer dynamics.

cond-mat.stat-mech↗

arXiv2000

Statistics of soliton-bearing systems with additive noise

We present a consistent method to calculate the probability distribution of soliton parameters in systems with additive noise. Even though a weak noise is considered, we are interested in probabilities of large fluctuations (generally non-Gaussian) which are beyond perturbation theory. Our method is a further development of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve a fundamental problem of soliton statistics governing by noisy Nonlinear Schrödinger Equation (NSE). We then apply our method to optical soliton transmission systems using signal control elements (filters, amplitude and phase modulators).

nlin.CD↗

arXiv1999

Small-scale turbulent dynamo

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 multi-point correlation functions of the magnetic field at small yet finite magnetic diffusivity. We show that the field is concentrated in long narrow strips and describe anomalous scalings and angular singularities of the multi-point correlation functions which are manifestations of field's intermittency. The growth rate of the magnetic field in a typical realization is found to be half the difference of two Lyapunov exponents of the same sign.

chao-dyn↗

arXiv1998

Notes about Passive Scalar in Large-Scale Velocity Field

We consider advection of a passive scalar theta(t,r) by an incompressible large-scale turbulent flow. In the framework of the Kraichnan model the whole PDF's (probability distribution functions) for the single-point statistics of theta and for the passive scalar difference theta(r_1)-theta(r_2) (for separations r_1-r_2 lying in the convective interval) are found.

chao-dyn↗

arXiv1997

Intermittent dissipation of a passive scalar in turbulence

Probability density function (PDF) of passive scalar dissipation ${\cal P} (ε)$ is found analytically in the limit of large Peclet and Prandtl numbers (Batchelor-Kraichnan regime) in two dimensions. The tail of PDF at $ε\gg<ε>$ is shown to be stretched exponent $\ln{\cal P}(ε)\proptoε^{1/3}$. At $ε\ll<ε>$, ${\cal P}\propto 1/\sqrtε$.

chao-dyn↗

arXiv1997

Inverse cascade and intermittency of passive scalar in 1d smooth flow

Random advection of Lagrangian tracer scalar field $θ(t,x)$ 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 Gaussianity known to be present at small scales for incompressible velocity fields emerges here at large scales ($x\gg L$). These scales are shown to be excited by an inverse cascade of $θ^{2}$ and the probability distribution function (PDF) of the corresponding scalar differences to approach the Gaussian form, as larger and larger scales are considered. Small scales ($x\ll L$) statistics is shown to be strongly non-Gaussian. Collapse of scaling exponents for scalar structure functions\thinspace takes place: moments of order $p\ge 1$ scale all linearly, independently of the order $p$. Smooth scaling $x^{p}$ is found for $-1<p<1$. Tails of scalar differences PDF are exponential while, at the center, a cusped shape tends to develop when smaller and smaller ratios $x/L$ are considered. The same tendency is present for scalar gradients PDF with respect to the inverse of the Péclet number (the pumping-to-diffusion scale ratio). The tails of the latter PDF are however much more extended, decaying as a stretched exponential of exponent 2/3, smaller than unity. This slower decay is physically associated with the strong fluctuations of the dynamical dissipative scale.

chao-dyn↗

arXiv1997

Inverse versus direct cascades in turbulent advection

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 small enough degree of compressibility, the cascade is direct again. Otherwise it is inverse, i.e. very large scales are excited. The dynamical hint for the direction of the cascade is the sign of the Lyapunov exponent for particles separation. Positive Lyapunov exponents are associated to direct cascade and Gaussianity at small scales. Negative Lyapunov exponents lead to inverse cascade, Gaussianity at large scales and strong intermittency at small scales.

chao-dyn↗

arXiv1996

Viscous Instanton for Burgers' Turbulence

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: $\ln{\cal P}(|u^{(k)}|)\propto -(|u^{(k)}|/{\rm Re}^k)^{3/(k+1)}$.

chao-dyn↗

arXiv1995

Instantons and Intermittency

We propose the new method for finding the non-Gaussian tails of probability distribution function (PDF) for solutions of a stochastic differential equation, such as convection equation for a passive scalar, random driven Navier-Stokes equation etc. Existence of such tails is generally regarded as a manifestation of intermittency phenomenon. Our formalism is based on the WKB approximation in the functional integral for the conditional probability of large fluctuation. We argue that the main contribution to the functional integral is given by a coupled field-force configuration -- {\em instanton}. As an example, we examine the correlation functions of the passive scalar $u$ advected by a large-scale velocity field $δ$-correlated in time. We find the instanton determining the tails of the generating functional and show that it is different from the instanton that determines the probability distribution function of high powers of $u$. We discuss the simplest instantons for the Navier-Stokes equation.

chao-dyn↗

arXiv1995

The Fourth-Order Correlation Function of a Randomly Advected Passive Scalar

Advection of a passive scalar $θ$ 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 $θ$. Explicit expressions for fourth-order objects, like $\langle(θ_1-θ_2)^4\rangle$ are derived.

chao-dyn↗

arXiv1995

Normal and Anomalous Scaling of the Fourth-Order Correlation Function of a Randomly Advected Passive Scalar

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.

chao-dyn↗