ANOMALOUS SCALING OF THE PASSIVE SCALAR

We establish anomalous inertial range scaling of structure functions for a model of advection of a passive scalar by a random velocity field. The velocity statistics is taken gaussian with decorrelation in time and velocity differences scaling as $|x|^{\kappa/2}$ in space, with $0\leq\kappa < 2$. The scalar is driven by a gaussian forcing acting on spatial scale $L$ and decorrelated in time. The structure functions for the scalar are well defined as the diffusivity is taken to zero and acquire anomalous scaling behavior for large pumping scales $L$. The anomalous exponent is calculated explicitly for the 4^{\m\rm th} structure function and for small $\kappa$ and it differs from previous predictions. For all but the second structure functions the anomalous exponents are nonvanishing.Comment: 8 pages, late

Strong Universality in Forced and Decaying Turbulence

The weak version of universality in turbulence refers to the independence of the scaling exponents of the $n$th order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents {\em and} the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.Comment: RevTex 4, 10 pages, 5 Figures (included), 1 Table; PRE, submitte

Yakhot's model of strong turbulence: A generalization of scaling models of turbulence

We report on some implications of the theory of turbulence developed by V. Yakhot [V. Yakhot, Phys. Rev. E {\bf 57}(2) (1998)]. In particular we focus on the expression for the scaling exponents $\zeta_{n}$. We show that Yakhot's result contains three well known scaling models as special cases, namely K41, K62 and the theory by V. L'vov and I. Procaccia [V. L'vov & I. Procaccia, Phys. Rev. E {\bf 62}(6) (2000)]. The model furthermore yields a theoretical justification for the method of extended self--similarity (ESS).Comment: 8 page

On two-dimensionalization of three-dimensional turbulence in shell models

Applying a modified version of the Gledzer-Ohkitani-Yamada (GOY) shell model, the signatures of so-called two-dimensionalization effect of three-dimensional incompressible, homogeneous, isotropic fully developed unforced turbulence have been studied and reproduced. Within the framework of shell models we have obtained the following results: (i) progressive steepening of the energy spectrum with increased strength of the rotation, and, (ii) depletion in the energy flux of the forward forward cascade, sometimes leading to an inverse cascade. The presence of extended self-similarity and self-similar PDFs for longitudinal velocity differences are also presented for the rotating 3D turbulence case

Measurement of RudsR_{\text{uds}} and RR between 3.12 and 3.72 GeV at the KEDR detector

Using the KEDR detector at the VEPP-4M $e^+e^-$ collider, we have measured the values of $R_{\text{uds}}$ and $R$ at seven points of the center-of-mass energy between 3.12 and 3.72 GeV. The total achieved accuracy is about or better than $3.3\%$ at most of energy points with a systematic uncertainty of about $2.1\%$. At the moment it is the most accurate measurement of $R(s)$ in this energy range

From Coherent Modes to Turbulence and Granulation of Trapped Gases

The process of exciting the gas of trapped bosons from an equilibrium initial state to strongly nonequilibrium states is described as a procedure of symmetry restoration caused by external perturbations. Initially, the trapped gas is cooled down to such low temperatures, when practically all atoms are in Bose-Einstein condensed state, which implies the broken global gauge symmetry. Excitations are realized either by imposing external alternating fields, modulating the trapping potential and shaking the cloud of trapped atoms, or it can be done by varying atomic interactions by means of Feshbach resonance techniques. Gradually increasing the amount of energy pumped into the system, which is realized either by strengthening the modulation amplitude or by increasing the excitation time, produces a series of nonequilibrium states, with the growing fraction of atoms for which the gauge symmetry is restored. In this way, the initial equilibrium system, with the broken gauge symmetry and all atoms condensed, can be excited to the state, where all atoms are in the normal state, with completely restored gauge symmetry. In this process, the system, starting from the regular superfluid state, passes through the states of vortex superfluid, turbulent superfluid, heterophase granular fluid, to the state of normal chaotic fluid in turbulent regime. Both theoretical and experimental studies are presented.Comment: Latex file, 25 pages, 4 figure

Search for narrow resonances in e+ e- annihilation between 1.85 and 3.1 GeV with the KEDR Detector

We report results of a search for narrow resonances in e+ e- annihilation at center-of-mass energies between 1.85 and 3.1 GeV performed with the KEDR detector at the VEPP-4M e+ e- collider. The upper limit on the leptonic width of a narrow resonance Gamma(R -> ee) Br(R -> hadr) < 120 eV has been obtained (at 90 % C.L.)

Measurement of main parameters of the \psi(2S) resonance

A high-precision determination of the main parameters of the \psi(2S) resonance has been performed with the KEDR detector at the VEPP-4M e^{+}e^{-} collider in three scans of the \psi(2S) -- \psi(3770) energy range. Fitting the energy dependence of the multihadron cross section in the vicinity of the \psi(2S) we obtained the mass value M = 3686.114 +- 0.007 +- 0.011 ^{+0.002}_{-0.012} MeV and the product of the electron partial width by the branching fraction into hadrons \Gamma_{ee}*B_{h} = 2.233 +- 0.015 +- 0.037 +- 0.020 keV. The third error quoted is an estimate of the model dependence of the result due to assumptions on the interference effects in the cross section of the single-photon e^{+}e^{-} annihilation to hadrons explicitly considered in this work. Implicitly, the same assumptions were employed to obtain the charmonium leptonic width and the absolute branching fractions in many experiments. Using the result presented and the world average values of the electron and hadron branching fractions, one obtains the electron partial width and the total width of the \psi(2S): \Gamma_{ee} =2.282 +- 0.015 +- 0.038 +- 0.021 keV, \Gamma = 296 +- 2 +- 8 +- 3 keV. These results are consistent with and more than two times more precise than any of the previous experiments