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V. Lebedev

Publications and source records attributed to V. Lebedev.

At least 73 records · Page 4Linked to original sources
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↗
arXiv2004

A New 76Ge Double Beta Decay Experiment at LNGS

This Letter of Intent has been submitted to the Scientific Committee of the INFN Laboratori Nazionali del Gran Sasso (LNGS) in March 2004. It describes a novel facility at the LNGS to study the double beta decay of 76Ge using an (optionally active) cryogenic fluid shield. The setup will allow to scrutinize with high significance on a short time scale the current evidence for neutrinoless double beta decay of 76Ge using the existing 76Ge diodes from the previous Heidelberg-Moscow and IGEX experiments. An increase in the lifetime limit can be achieved by adding more enriched detectors, remaining thereby background-free up to a few 100 kg-years of exposure.

hep-ex↗
arXiv2003

Acceleration of chemical reaction by chaotic mixing

Theory of fast binary chemical reaction, ${\cal A}+{\cal B}\to{\cal C}$, in a statistically stationary chaotic flow at large Schmidt number ${Sc}$ and large Damköhler number ${Da}$ is developed. For stoichiometric condition we identify subsequent stages of the chemical reaction. The first stage corresponds to the exponential decay, $\propto\exp(-λt)$ (where $λ$ is the Lyapunov exponent of the flow), of the chemicals in the bulk part of the flow. The second and the third stages are related to the chemicals remaining in the boundary region. During the second stage the amounts of ${\cal A}$ and ${\cal B}$ decay $\propto 1/\sqrt{t}$, whereas the decay law during the third stage is exponential, $\propto\exp(-γt)$, where $γ\simλ/\sqrt{Sc}$.

nlin.CD↗
arXiv2002

Decay of scalar turbulence revisited

We demonstrate that at long times the rate of passive scalar decay in a turbulent, or simply chaotic, flow is dominated by regions (in real space or in inverse space) where mixing is less efficient. We examine two situations. The first is of a spatially homogeneous stationary turbulent flow with both viscous and inertial scales present. It is shown that at large times scalar fluctuations decay algebraically in time at all spatial scales (particularly in the viscous range, where the velocity is smooth). The second example explains chaotic stationary flow in a disk/pipe. The boundary region of the flow controls the long-time decay, which is algebraic at some transient times, but becomes exponential, with the decay rate dependent on the scalar diffusion coefficient, at longer times.

nlin.CD↗
arXiv2002

Spectra of turbulence in dilute polymer solutions

We investigate turbulence in dilute polymer solutions when polymers are strongly stretched by the flow. We establish power-law spectrum of velocity, which is not associated with a flux of a conserved quantity, in two cases. The first case is the elastic waves range of high Reynolds number turbulence of polymer solutions above the coil-stretch transition. The second case is the elastic turbulence, where chaotic flow is excited due to elastic instabilities at small Reynolds numbers.

nlin.CD↗
arXiv2002

Study of the K- -> mu- nu pi0 decay

The decay $K^{-} \to μ^{-} \barν π^{0}$ has been studied using in-flight decays detected with ``ISTRA+'' setup operating in the 25 GeV negative secondary beam of the U-70 PS. About 112K events were used for the analysis. The $λ_{+}$ and $λ_{0}$ slope parameters of the decay formfactors $f_{+}(t)$, $f_{0}(t)$ have been measured : $λ_{+}= 0.0321 \pm 0.004$(stat) $\pm 0.002$(syst) $λ_{0}= 0.0209 \pm 0.004$(stat) $\pm 0.002$(syst); the correlation $d λ_{0}/d λ_{+}=-0.46$ The limits on the possible tensor and scalar couplings have been derived: $f_{T}/f_{+}(0)=-0.021 \pm 0.028$(stat) $\pm 0.014$(theory); $f_{S}/f_{+}(0)=0.004 \pm 0.005$(stat) $\pm 0.005$(theory)

hep-ph↗
arXiv2001

The Timing Synchronization System at Jefferson Lab

This paper presents the requirements and design of a Timing Synchronization System (TSS) for the Continuous Electron Beam Accelerator Facility (CEBAF) control system at Thomas Jefferson National Accelerator Facility. A clock module has been designed which resides in a VME crate. The clock module can be a communications master or a slave depending on its configuration, which is software and jumper selectable. As a master, the clock module sends out messages in response to an external synchronization signal over a serial fiber optic line. As a slave, it receives the messages and interrupts an associated computer in its VME crate. The application that motivated the development of the TSS, the Accelerator 30 Hz Measurement System, will be described. Operational experience with the TSS will also be discussed.

physics.acc-ph↗
arXiv2001

On Turbulence of Polymer Solutions

We investigate high-Reynolds number turbulence in dilute polymer solutions. We show the existence of a critical value of the Reynolds number which separates two different regimes. In the first regime, below the transition, the influence of the polymer molecules on the flow is negligible and they can be regarded as passively embedded in the flow. This case admits a detailed investigation of the statistics of the polymer elongations. The second state is realized when the Reynolds number is larger than the critical value. This regime is characterized by the strong back reaction of polymers on the flow. We establish some properties of the statistics of the stress and velocity in this regime and discuss its relation to the drag reduction phenomenon.

nlin.CD↗
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↗
arXiv2000

On the Turbulent Dynamics of Polymer Solutions

We study properties of dilute polymer solutions which are known to depend strongly on polymer elongation. The probability density function (PDF) of polymer end-to-end extensions $R$ in turbulent flows is examined. We demonstrate that if the value of the Lyapunov exponent $λ$ is smaller than the inverse molecular relaxation time $1/τ$ then the PDF has a strong peak at the equilibrium size $R_0$ and a power tail at $R\gg R_0$. This confirms and extends the results of \cite{Lumley72}. There is no essential influence of polymers on the flow in the regime $λτ<1$. At $λ>1/τ$ the majority of molecules is stretched to the linear size $R_{\rm op}\gg R_0$. The value of $R_{\rm op}$ can be much smaller than the maximal length of the molecules because of back reaction of the polymers on the flow, which suppresses velocity gradients thus preventing the polymers from maximal possible stretching.

chao-dyn↗
arXiv1999

Large-scale properties of passive scalar advection

We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close. At the Batchelor limit of spatially smooth velocity, the breakdown of scale invariance is established for scalar statistics.

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↗
arXiv1998

Instanton for the Kraichnan Passive Scalar Problem

We consider high-order correlation functions of the passive scalar in the Kraichnan model. Using the instanton formalism we find the scaling exponents $ζ_n$ of the structure functions $S_n$ for $n\gg1$ under the additional condition $dζ_2\gg1$ (where $d$ is the dimensionality of space). At $n n_c$ they are $n$-independent: $ζ_n=ζ_2 n_c/4$. We also estimate $n$-dependent factors in $S_n$, particularly their behavior at $n$ close to $n_c$.

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↗
arXiv1996

Non-universality of the scaling exponents of a passive scalar convected by a random flow

We consider passive scalar convected by multi-scale random velocity field with short yet finite temporal correlations. Taking Kraichnan's limit of a white Gaussian velocity as a zero approximation we develop perturbation theory with respect to a small correlation time and small non-Gaussianity of the velocity. We derive the renormalization (due to temporal correlations and non-Gaussianity) of the operator of turbulent diffusion. That allows us to calculate the respective corrections to the anomalous scaling exponents of the scalar field and show that they continuously depend on velocity correlation time and the degree of non-Gaussianity. The scalar exponents are thus non universal as was predicted by Shraiman and Siggia on a phenomenological ground (CRAS {\bf 321}, 279, 1995).

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↗