On the scaling of temperature fluctuations induced by frictional heating

The temperature fluctuations generated by viscous dissipation in an isotropic turbulent flow are studied using direct numerical simulation. It is shown that their scaling with Reynolds number is at odds with predictions from recent investigations. The origin of the discrepancy is traced back to the anomalous scaling of the dissipation rate fluctuations. Phenomenological arguments are presented which explain the observed results. The study shows that previously proposed models underpredict the variance of frictional temperature fluctuations by a factor proportional to the square of the Taylor-scale Reynolds number

Multifrequency Method for Mapping Active Galactic Nuclei with Allowance for the Frequency-Dependent Image Shift

We consider the problem of multifrequency VLBA image synthesis and spectral-index mapping for active galactic nuclei related to the necessity of taking into account the frequency-dependent image shift. We describe our generalized multifrequency synthesis algorithm with a spectral correction based on the maximum entropy method. The results of our processing of multifrequency VLBI data for the radio sources J2202+4216, J0336+3218, and J1419+5423 are presented.Comment: 12 pages, 2 tables, 6 figure

Numerical Verification of the Weak Turbulent Model for Swell Evolution

The purpose of this article is numerical verification of the theory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading and formation of Zakharov-Filonenko spectrum $I_{\omega} \sim \omega^{-4}$. To achieve quantitative coincidence of the results obtained by different methods, one has to supply the Hasselmann kinetic equation by an empirical dissipation term $S_{diss}$ modeling the coherent effects of white-capping. Using of the standard dissipation terms from operational wave predicting model ({\it WAM}) leads to significant improvement on short times, but not resolve the discrepancy completely, leaving the question about optimal choice of $S_{diss}$ open. In a long run {\it WAM} dissipative terms overestimate dissipation essentially.Comment: 41 pages, 37 figures, 1 table. Submitted in European Journal of Mechanics B/Fluid

A lower bound for Garsia's entropy for certain Bernoulli convolutions

Let $\beta\in(1,2)$ be a Pisot number and let $H_\beta$ denote Garsia's entropy for the Bernoulli convolution associated with $\beta$. Garsia, in 1963 showed that $H_\beta<1$ for any Pisot $\beta$. For the Pisot numbers which satisfy $x^m=x^{m-1}+x^{m-2}+...+x+1$ (with $m\ge2$) Garsia's entropy has been evaluated with high precision by Alexander and Zagier and later improved by Grabner, Kirschenhofer and Tichy, and it proves to be close to 1. No other numerical values for $H_\beta$ are known. In the present paper we show that $H_\beta>0.81$ for all Pisot $\beta$, and improve this lower bound for certain ranges of $\beta$. Our method is computational in nature.Comment: 16 pages, 4 figure