Fine structure of Vavilov-Cherenkov radiation near the Cherenkov threshold

We analyze the Vavilov-Cherenkov radiation (VCR) in a dispersive nontransparent dielectric air-like medium both below and above the Cherenkov threshold, in the framework of classical electrodynamics. It is shown that the transition to the subthreshold energies leads to the destruction of electromagnetic shock waves and to the sharp reduction of the frequency domain where VCR is emitted. The fine wake-like structure of the Vavilov-Cherenkov radiation survives and manifests the existence of the subthreshold radiation in the domain of anomalous dispersion. These domains can approximately be defined by the two phenomenological parameters of the medium, namely, the effective frequency of oscillators and the damping describing an interaction with the other degrees of freedom.Comment: 9 pages, 6 figure

Thin film dynamics on a vertically rotating disk partially immersed in a liquid bath

The axisymmetric flow of a thin liquid film is considered for the problem of a vertically rotating disk that is partially immersed in a liquid bath. A model for the fully three-dimensional free-boundary problem of the rotating disk, that drags a thin film out of the bath is set up. From this, a dimension-reduced extended lubrication approximation that includes the meniscus region is derived. This problem constitutes a generalization of the classic drag-out and drag-in problem to the case of axisymmetric flow. The resulting nonlinear fourth-order partial differential equation for the film profile is solved numerically using a finite element scheme. For a range of parameters steady states are found and compared to asymptotic solutions. Patterns of the film profile, as a function of immersion depth and angular velocity are discussed.Comment: 31 pages, 19 figures accepted: Applied Mathematical Modellin

System Size and Centrality Dependence of the Electric Charge Correlations in A+A and p+p Collisions at the SPS Energies

The Balance Function analysis method was developed in order to study the long range correlations in pseudo-rapidity of charged particle. The final results on p+p, C+C, Si+Si and centrality selected Pb+Pb collisions at $\sqrt{s_{NN}} = 17.2$ GeV and the preliminary data at $\sqrt{s_{NN}} = 8.8$ GeV are presented. The width of the Balance Function decreases with increasing system size and centrality of the collisions. This could suggest a delayed hadronization scenario.Comment: To appear in the proceedings of NPDC18, Prague, Czech Republic, 23-28 Aug. 200