Moment inequalities and high-energy tails for the Boltzmann equations with inelastic interactions

We study the high-energy asymptotics of the steady velocity distributions for model systems of granular media in various regimes. The main results obtained are integral estimates of solutions of the hard-sphere Boltzmann equations, which imply that the velocity distribution functions $f(v)$ behave in a certain sense as $C\exp(-r|v|^s)$ for $|v|$ large. The values of $s$, which we call {\em the orders of tails}, range from $s=1$ to $s=2$, depending on the model of external forcing. The method we use is based on the moment inequalities and careful estimating of constants in the integral form of the Povzner-type inequalities.Comment: 22 page

The McKean-Vlasov Equation in Finite Volume

We study the McKean--Vlasov equation on the finite tori of length scale $L$ in $d$--dimensions. We derive the necessary and sufficient conditions for the existence of a phase transition, which are based on the criteria first uncovered in \cite{GP} and \cite{KM}. Therein and in subsequent works, one finds indications pointing to critical transitions at a particular model dependent value, $\theta^{\sharp}$ of the interaction parameter. We show that the uniform density (which may be interpreted as the liquid phase) is dynamically stable for $\theta < \theta^{\sharp}$ and prove, abstractly, that a {\it critical} transition must occur at $\theta = \theta^{\sharp}$. However for this system we show that under generic conditions -- $L$ large, $d \geq 2$ and isotropic interactions -- the phase transition is in fact discontinuous and occurs at some \theta\t < \theta^{\sharp}. Finally, for H--stable, bounded interactions with discontinuous transitions we show that, with suitable scaling, the \theta\t(L) tend to a definitive non--trivial limit as $L\to\infty$

Spectral Components of SS 433

We present results from new optical and UV spectroscopy of the unusual binary system SS 433, and we discuss the relationship of the particular spectral components we observe to the properties of the binary. (1) The continuum spectrum which we associate with flux from the super-Eddington accretion disk and the dense part of its wind. (2) H-alpha moving components which are formed far from the binary orbital plane in the relativistic jets. (3) H-alpha and He I "stationary" emission lines which we suggest are formed in the disk wind in a volume larger than the dimensions of the binary. (4) A weak "stationary" emission feature we identify as a C II 7231,7236 blend that attains maximum radial velocity at the orbital quadrature of disk recession. (5) Absorption and emission features from outflowing clumps in the disk wind (seen most clearly in an episode of blue-shifted Na I emission). (6) We found no clear evidence of the absorption line spectrum of the optical star, although we point out the presence of He I absorption features (blended with the stationary emission) with the expected radial velocity trend at the orbital and precessional phases when the star might best be seen. (7) A rich interstellar absorption spectrum of diffuse interstellar bands. The results suggest that the binary is embedded in an expanding thick disk (detected in recent radio observations) which is fed by the wind from the super-Eddington accretion disk.Comment: Submitted to Ap

FATTY LIVER DISEASE. MODERN PATHOGENETIC APPROACH TO THERAPY

Since 1980 when L. Ludwig et al. [1] identified changes in the liver characteristic of alcohol-induced hepatitis in persons who didn’t misuse alcohol, intense study of non-alcoholic fatty liver disease (NAFLD) started. The definition of NAFLD has two major principles: a morphological pattern in biopsy ma terial microscopy completely corresponds to changes induced by alcoholic pathology and the major etiologic factors is lacking – alcoholic at hepatotoxic dosages. Obligatory condition is to rule out viral, drug, metabolic and other reasons [2]