2,087 research outputs found
Nonlinear dynamics of flexural wave turbulence
The Kolmogorov-Zakharov spectrum predicted by the Weak Turbulence Theory
remains elusive for wave turbulence of flexural waves at the surface of an thin
elastic plate. We report a direct measurement of the nonlinear timescale
related to energy transfer between waves. This time scale is extracted
from the space-time measurement of the deformation of the plate by studying the
temporal dynamics of wavelet coefficients of the turbulent field. The central
hypothesis of the theory is the time scale separation between dissipative time
scale, nonlinear time scale and the period of the wave (). We
observe that this scale separation is valid in our system. The discrete modes
due to the finite size effects are responsible for the disagreement between
observations and theory. A crossover from continuous weak turbulence and
discrete turbulence is observed when the nonlinear time scale is of the same
order of magnitude as the frequency separation of the discrete modes. The
Kolmogorov-Zakharov energy cascade is then strongly altered and is frozen
before reaching the dissipative regime expected in the theory.Comment: accepted for publication in Physical Review
Quadratic invariants for discrete clusters of weakly interacting waves
We consider discrete clusters of quasi-resonant triads arising from a Hamiltonian three-wave equation. A cluster consists of N modes forming a total of M connected triads. We investigate the problem of constructing a functionally independent set of quadratic constants of motion. We show that this problem is equivalent to an underlying basic linear problem, consisting of finding the null space of a rectangular M × N matrix with entries 1, −1 and 0. In particular, we prove that the number of independent quadratic invariants is equal to J ≡ N − M* ≥ N − M, where M* is the number of linearly independent rows in Thus, the problem of finding all independent quadratic invariants is reduced to a linear algebra problem in the Hamiltonian case. We establish that the properties of the quadratic invariants (e.g., locality) are related to the topological properties of the clusters (e.g., types of linkage). To do so, we formulate an algorithm for decomposing large clusters into smaller ones and show how various invariants are related to certain parts of a cluster, including the basic structures leading to M* < M. We illustrate our findings by presenting examples from the Charney–Hasegawa–Mima wave model, and by showing a classification of small (up to three-triad) clusters
Triple cascade behaviour in QG and drift turbulence and generation of zonal jets
We study quasigeostrophic (QG) and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus on the zonostrophy, an extra invariant in the CHM model, and on its role in the formation of zonal jets. We use a generalized Fjørtoft argument for the energy, enstrophy, and zonostrophy and show that they cascade anisotropically into nonintersecting sectors in k space with the energy cascading towards large zonal scales. Using direct numerical simulations of the CHM equation, we show that zonostrophy is well conserved, and the three invariants cascade as predicted by the Fjørtoft argument
Superconductivity in the Cuprates as a Consequence of Antiferromagnetism and a Large Hole Density of States
We briefly review a theory for the cuprates that has been recently proposed
based on the movement and interaction of holes in antiferromagnetic (AF)
backgrounds. A robust peak in the hole density of states (DOS) is crucial to
produce a large critical temperature once a source of hole attraction is
identified. The predictions of this scenario are compared with experiments. The
stability of the calculations after modifying some of the original assumptions
is addressed. We find that if the dispersion is changed from an
antiferromagnetic band at half-filling to a tight binding
narrow band at , the main conclusions of the approach remain
basically the same i.e. superconductivity appears in the -channel and is enhanced by a large DOS. The main features
distinguishing these ideas from more standard theories based on
antiferromagnetic correlations are here discussed.Comment: RevTex, 7 pages, 5 figures are available on reques
Directed Random Walk on the Lattices of Genus Two
The object of the present investigation is an ensemble of self-avoiding and
directed graphs belonging to eight-branching Cayley tree (Bethe lattice)
generated by the Fucsian group of a Riemann surface of genus two and embedded
in the Pincar\'e unit disk. We consider two-parametric lattices and calculate
the multifractal scaling exponents for the moments of the graph lengths
distribution as functions of these parameters. We show the results of numerical
and statistical computations, where the latter are based on a random walk
model.Comment: 17 pages, 8 figure
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
Gravity wave turbulence in a laboratory flume
We present an experimental study of the statistics of surface gravity wave turbulence in a flume of a horizontal size 12×6 m. For a wide range of amplitudes the wave energy spectrum was found to scale as Eω∼ω-ν in a frequency range of up to one decade. However, ν appears to be nonuniversal: it depends on the wave intensity and ranges from about 6 to 4. We discuss our results in the context of existing theories and argue that at low wave amplitudes the wave statistics is affected by the flume finite size, and at high amplitudes the wave breaking effect dominates
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