5,665 research outputs found
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
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
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