192 research outputs found
Dynamics of coreless vortices and rotation-induced dissipation peak in superfluid films on rotating porous substrates
We analyze dynamics of 3D coreless vortices in superfluid films covering
porous substrates. The 3D vortex dynamics is derived from the 2D dynamics of
the film. The motion of a 3D vortex is a sequence of jumps between neighboring
substrate cells, which can be described, nevertheless, in terms of
quasi-continuous motion with average vortex velocity. The vortex velocity is
derived from the dissociation rate of vortex-antivortex pairs in a 2D film,
which was developed in the past on the basis of the Kosterlitz-Thouless theory.
The theory explains the rotation-induced dissipation peak in torsion-oscillator
experiments on He films on rotating porous substrates and can be used in
the analysis of other phenomena related to vortex motion in films on porous
substrates.Comment: 8 pages, 3 figures submitted to Phys. Rev.
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
Mirror Descent and Convex Optimization Problems With Non-Smooth Inequality Constraints
We consider the problem of minimization of a convex function on a simple set
with convex non-smooth inequality constraint and describe first-order methods
to solve such problems in different situations: smooth or non-smooth objective
function; convex or strongly convex objective and constraint; deterministic or
randomized information about the objective and constraint. We hope that it is
convenient for a reader to have all the methods for different settings in one
place. Described methods are based on Mirror Descent algorithm and switching
subgradient scheme. One of our focus is to propose, for the listed different
settings, a Mirror Descent with adaptive stepsizes and adaptive stopping rule.
This means that neither stepsize nor stopping rule require to know the
Lipschitz constant of the objective or constraint. We also construct Mirror
Descent for problems with objective function, which is not Lipschitz
continuous, e.g. is a quadratic function. Besides that, we address the problem
of recovering the solution of the dual problem
General model selection estimation of a periodic regression with a Gaussian noise
This paper considers the problem of estimating a periodic function in a
continuous time regression model with an additive stationary gaussian noise
having unknown correlation function. A general model selection procedure on the
basis of arbitrary projective estimates, which does not need the knowledge of
the noise correlation function, is proposed. A non-asymptotic upper bound for
quadratic risk (oracle inequality) has been derived under mild conditions on
the noise. For the Ornstein-Uhlenbeck noise the risk upper bound is shown to be
uniform in the nuisance parameter. In the case of gaussian white noise the
constructed procedure has some advantages as compared with the procedure based
on the least squares estimates (LSE). The asymptotic minimaxity of the
estimates has been proved. The proposed model selection scheme is extended also
to the estimation problem based on the discrete data applicably to the
situation when high frequency sampling can not be provided
Kinetics of a Network of Vortex Loops in He II and a Theory of Superfluid Turbulence
A theory is developed to describe the superfluid turbulence on the base of
kinetics of the merging and splitting vortex loops. Because of very frequent
reconnections the vortex loops (as a whole) do not live long enough to perform
any essential evolution due to the deterministic motion. On the contrary, they
rapidly merge and split, and these random recombination processes prevail over
other slower dynamic processes. To develop quantitative description we take the
vortex loops to have a Brownian structure with the only degree of freedom,
which is the length of the loop. We perform investigation on the base of
the Boltzmann type kinetic equation for the distribution function of
number of loops with length . By use of the special ansatz in the collision
integral we have found the exact power-like solution to kinetic equation in the
stationary case. This solution is not (thermodynamically) equilibrium, but on
the contrary, it describes the state with two mutual fluxes of the length (or
energy) in space of sizes of the vortex loops. The term flux means just
redistribution of length (or energy) among the loops of different sizes due to
reconnections. Analyzing this solution we drew several results on the structure
and dynamics of the vortex tangle in the turbulent superfluid helium. In
particular, we evaluated the mean radius of the curvature and the full rate of
the reconnection events. We also studied the evolution of the full length of
vortex loops per unit volume-the so-called vortex line density. It is shown
this evolution to obey the famous Vinen equation. The properties of the Vinen
equation from the point of view of the developed approach had been discussed.Comment: 34 pages, 9 Postscript figures, [aps,preprint,12pt]{revtex4
Scattering of first and second sound waves by quantum vorticity in superfluid Helium
We study the scattering of first and second sound waves by quantum vorticity
in superfluid Helium using two-fluid hydrodynamics. The vorticity of the
superfluid component and the sound interact because of the nonlinear character
of these equations. Explicit expressions for the scattered pressure and
temperature are worked out in a first Born approximation, and care is exercised
in delimiting the range of validity of the assumptions needed for this
approximation to hold. An incident second sound wave will partly convert into
first sound, and an incident first sound wave will partly convert into second
sound. General considerations show that most incident first sound converts into
second sound, but not the other way around. These considerations are validated
using a vortex dipole as an explicitely worked out example.Comment: 24 pages, Latex, to appear in Journal of Low Temperature Physic
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
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