3,446 research outputs found
Coexistence of Weak and Strong Wave Turbulence in a Swell Propagation
By performing two parallel numerical experiments -- solving the dynamical
Hamiltonian equations and solving the Hasselmann kinetic equation -- we
examined the applicability of the theory of weak turbulence to the description
of the time evolution of an ensemble of free surface waves (a swell) on deep
water. We observed qualitative coincidence of the results.
To achieve quantitative coincidence, we augmented the kinetic equation by an
empirical dissipation term modelling the strongly nonlinear process of
white-capping. Fitting the two experiments, we determined the dissipation
function due to wave breaking and found that it depends very sharply on the
parameter of nonlinearity (the surface steepness). The onset of white-capping
can be compared to a second-order phase transition. This result corroborates
with experimental observations by Banner, Babanin, Young.Comment: 5 pages, 5 figures, Submitted in Phys. Rev. Letter
Quantum Many-Body Dynamics of Dark Solitons in Optical Lattices
We present a fully quantum many-body treatment of dark solitons formed by
ultracold bosonic atoms in one-dimensional optical lattices. Using
time-evolving block decimation to simulate the single-band Bose-Hubbard
Hamiltonian, we consider the quantum dynamics of density and phase engineered
dark solitons as well as the quantum evolution of mean-field dark solitons
injected into the quantum model. The former approach directly models how one
may create quantum entangled dark solitons in experiment. While we have already
presented results regarding the latter approach elsewhere [Phys. Rev. Lett.
{\bf 103}, 140403 (2009)], we expand upon those results in this work. In both
cases, quantum fluctuations cause the dark soliton to fill in and may induce an
inelasticity in soliton-soliton collisions. Comparisons are made to the
Bogoliubov theory which predicts depletion into an anomalous mode that fills in
the soliton. Our many-body treatment allows us to go beyond the Bogoliubov
approximation and calculate explicitly the dynamics of the system's natural
orbitals.Comment: 14 pages, 11 figures -- v3 has only minor changes from v2 -- this is
the print versio
Weak compressible magnetohydrodynamic turbulence in the solar corona
This Letter presents a calculation of the power spectra of weakly turbulent
Alfven waves and fast magnetosonic waves ("fast waves") in low-beta plasmas. It
is shown that three-wave interactions transfer energy to high-frequency fast
waves and, to a lesser extent, high-frequency Alfven waves. MHD turbulence is
thus a promising mechanism for producing the high-frequency waves needed to
explain the anisotropic heating of minor ions in the solar corona.Comment: 4 pages, 3 figures, accepted, Phys. Rev. Let
Integrable turbulence generated from modulational instability of cnoidal waves
We study numerically the nonlinear stage of modulational instability (MI) of
cnoidal waves, in the framework of the focusing one-dimensional Nonlinear
Schrodinger (NLS) equation. Cnoidal waves are the exact periodic solutions of
the NLS equation and can be represented as a lattice of overlapping solitons.
MI of these lattices lead to development of "integrable turbulence" [Zakharov
V.E., Stud. Appl. Math. 122, 219-234 (2009)]. We study the major
characteristics of the turbulence for dn-branch of cnoidal waves and
demonstrate how these characteristics depend on the degree of "overlapping"
between the solitons within the cnoidal wave.
Integrable turbulence, that develops from MI of dn-branch of cnoidal waves,
asymptotically approaches to it's stationary state in oscillatory way. During
this process kinetic and potential energies oscillate around their asymptotic
values. The amplitudes of these oscillations decay with time as t^{-a},
1<a<1.5, the phases contain nonlinear phase shift decaying as t^{-1/2}, and the
frequency of the oscillations is equal to the double maximal growth rate of the
MI, s=2g_{max}. In the asymptotic stationary state the ratio of potential to
kinetic energy is equal to -2. The asymptotic PDF of wave amplitudes is close
to Rayleigh distribution for cnoidal waves with strong overlapping, and is
significantly non-Rayleigh one for cnoidal waves with weak overlapping of
solitons. In the latter case the dynamics of the system reduces to two-soliton
collisions, which occur with exponentially small rate and provide up to
two-fold increase in amplitude compared with the original cnoidal wave.Comment: 36 pages, 25 figure
Weak Wave Turbulence Scaling Theory for Diffusion and Relative Diffusion in Turbulent Surface Waves
We examine the applicability of the weak wave turbulence theory in explaining
experimental scaling results obtained for the diffusion and relative diffusion
of particles moving on turbulent surface waves. For capillary waves our
theoretical results are shown to be in good agreement with experimental
results, where a distinct crossover in diffusive behavior is observed at the
driving frequency. For gravity waves our results are discussed in the light of
ocean wave studies.Comment: 5 pages; for related work visit http://www.imedea.uib.es/~victo
Second generation diffusion model of interacting gravity waves on the surface of deep fluid
We propose a second generation phenomenological model for nonlinear interaction of gravity waves on the surface of deep water. This model takes into account the effects of non-locality of the original Hasselmann diffusion equation still preserving important properties of the first generation model: physically consistent scaling, adherence to conservation laws and the existence of Kolmogorov-Zakharov solutions. Numerical comparison of both models with the original Hasselmann equation shows that the second generation models improves the angular distribution in the evolving wave energy spectrum
An all-optical event horizon in an optical analogue of a Laval nozzle
Exploiting the fact that light propagation in defocusing nonlinear media can
mimic the transonic flow of an equivalent fluid, we demonstrate experimentally
the formation of an all-optical event horizon in a waveguide structure akin to
a hydrodynamic Laval nozzle. The analogue event horizon, which forms at the
nozzle throat is suggested as a novel platform for analogous gravity
experiments
Solitary waves of Bose-Einstein condensed atoms confined in finite rings
Motivated by recent progress in trapping Bose-Einstein condensed atoms in
toroidal potentials, we examine solitary-wave solutions of the nonlinear
Schr\"odinger equation subject to periodic boundary conditions. When the
circumference of the ring is much larger than the size of the wave, the density
profile is well approximated by that of an infinite ring, however the density
and the velocity of propagation cannot vanish simultaneously. When the size of
the ring becomes comparable to the size of the wave, the density variation
becomes sinusoidal and the velocity of propagation saturates to a constant
value.Comment: 6 pages, 2 figure
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