2,284 research outputs found
Comment on "Symmetries and Interaction Coefficients of Kelvin waves" [arXiv:1005.4575] by Lebedev and L'vov
We comment on the claim by Lebedev and L'vov [arXiv:1005.4575] that the
symmetry with respect to a tilt of a quantized vortex line does not yet
prohibit coupling between Kelvin waves and the large-scale slope of the line.
Ironically, the counterexample of an effective scattering vertex in the local
induction approximation (LIA) attempted by Lebedev and L'vov invalidates their
logic all by itself being a notoriously known example of how symmetries impose
stringent constraints on kelvon kinetics---not only the coupling in question
but the kinetics in general are absent within LIA. We further explain that the
mistake arises from confusing symmetry properties of a specific mathematical
representation in terms of the canonical vortex position field w(z) = x(z) +
iy(z), which explicitly breaks the tilt symmetry due to an arbitrary choice of
the z-axis, with those of the real physical system recovered in final
expressions.Comment: comment on arXiv:1005.4575, version accepted in JLTP with minimal
changes: abstract adde
On role of symmetries in Kelvin wave turbulence
E.V. Kozik and B.V. Svistunov (KS) paper "Symmetries and Interaction
Coefficients of Kelvin waves", arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010,
contains a comment on paper "Symmetries and Interaction coefficients of Kelvin
waves", V. V. Lebedev and V. S. L'vov, arXiv:1005.4575, 25 May 2010. It relies
mainly on the KS text "Geometric Symmetries in Superfluid Vortex Dynamics}",
arXiv:1006.0506v1 [cond-mat.other] 2 Jun 2010. The main claim of KS is that a
symmetry argument prevents linear in wavenumber infrared asymptotics of the
interaction vertex and thereby implies locality of the Kelvin wave spectrum
previously obtained by these authors. In the present note we reply to their
arguments. We conclude that there is neither proof of locality nor any
refutation of the possibility of linear asymptotic behavior of interaction
vertices in the texts of KS
Robustly Solvable Constraint Satisfaction Problems
An algorithm for a constraint satisfaction problem is called robust if it
outputs an assignment satisfying at least -fraction of the
constraints given a -satisfiable instance, where
as . Guruswami and
Zhou conjectured a characterization of constraint languages for which the
corresponding constraint satisfaction problem admits an efficient robust
algorithm. This paper confirms their conjecture
Kolmogorov and Kelvin-Wave Cascades of Superfluid Turbulence at T=0: What is in Between?
As long as vorticity quantization remains irrelevant for the long-wave
physics, superfluid turbulence supports a regime macroscopically identical to
the Kolmogorov cascade of a normal liquid. At high enough wavenumbers, the
energy flux in the wavelength space is carried by individual Kelvin-wave
cascades on separate vortex lines. We analyze the transformation of the
Kolmogorov cascade into the Kelvin-wave cascade, revealing a chain of three
distinct intermediate cascades, supported by local-induction motion of the
vortex lines, and distinguished by specific reconnection mechanisms. The most
prominent qualitative feature predicted is unavoidable production of vortex
rings of the size of the order of inter-vortex distance.Comment: 4 RevTex pages, 1 figure. Quantitative analysis of the regime 2 has
been revise
The 17/5 spectrum of the Kelvin-wave cascade
Direct numeric simulation of the Biot-Savart equation readily resolves the
17/5 spectrum of the Kelvin-wave cascade from the 11/3 spectrum of the
non-local (in the wavenumber space) cascade scenario by L'vov and Nazarenko.
This result is a clear-cut visualisation of the unphysical nature of the 11/3
solution, which was established earlier on the grounds of symmetry.Comment: 2 pages, 1 figur
The analysis of structurally orthotropic shells by means of the compliance method Progress report, period ending 1 Jun. 1968
Linear shell theory elastic constant instability conditions for symmetrically loaded shells of revolutio
Comment on "Dispersive bottleneck delaying thermalization of turbulent Bose-Einstein Condensates" by Krstulovic and Brachet [arXiv:1007.4441]
We reveal the connection of the recent numerical observations of Krstulovic
and Brachet [arXiv:1007.4441] with the general theory of relaxation kinetics of
the strongly non-equilibrium Bose-Einstein condensates.Comment: comment on arXiv:1007.4441, published version, minor stylistic
change
- …