65 research outputs found
Note on the paper of Fu and Wong on strictly pseudoconvex domains with K\"ahler--Einstein Bergman metrics
It is shown that the Ramadanov conjecture implies the Cheng conjecture. In
particular it follows that the Cheng conjecture holds in dimension two
Three dimensionality of pulsed second-sound waves in He II
Three dimensionality of 3D pulsed second sound wave in He II emitted from a
finite size heater is experimentally investigated and theoretically studied
based on two-fluid model in this study. The detailed propagation of 3D pulsed
second sound wave is presented and reasonable agreement between the
experimental and theoretical results is obtained. Heater size has a big
influence on the profile of 3D second sound wave. The counterflow between the
superfluid and normal fluid components becomes inverse in the rarefaction of 3D
second sound wave. The amplitude of rarefaction decreases due to the
interaction between second sound wave and quantized vortices, which explains
the experimental results about second sound wave near [Phys. Rev. Lett. 73,
2480 (1994)]. The accumulation of dense quantized vortices in the vicinity of
heater surface leads to the formation of a thermal boundary layer, and further
increase of heating duration results in the occurrence of boiling phenomena.
PACS numbers: 67.40.Pm 43.25.+y 67.40.BzComment: 30 pages, 9 figures. Physical Review B, Accepte
Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics
We report the experimental studies of a parametric excitation of a second
sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity.
The results on several topics in this system are presented: (i) The linear
properties of the instability, namely, the threshold, its temperature and
geometrical dependencies, and the spectra of SS just above the onset were
measured. They were found to be in a good quantitative agreement with the
theory. (ii) It was shown that the mechanism of SS amplitude saturation is due
to the nonlinear attenuation of SS via three wave interactions between the SS
waves. Strong low frequency amplitude fluctuations of SS above the threshold
were observed. The spectra of these fluctuations had a universal shape with
exponentially decaying tails. Furthermore, the spectral width grew continuously
with the FS amplitude. The role of three and four wave interactions are
discussed with respect to the nonlinear SS behavior. The first evidence of
Gaussian statistics of the wave amplitudes for the parametrically generated
wave ensemble was obtained. (iii) The experiments on simultaneous pumping of
the FS and independent SS waves revealed new effects. Below the instability
threshold, the SS phase conjugation as a result of three-wave interactions
between the FS and SS waves was observed. Above the threshold two new effects
were found: a giant amplification of the SS wave intensity and strong resonance
oscillations of the SS wave amplitude as a function of the FS amplitude.
Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001
Rational choice of parameters of pressurized vessels made from ideally plastic materials
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