4,443 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
Collapse and stable self-trapping for Bose-Einstein condensates with 1/r^b type attractive interatomic interaction potential
We consider dynamics of Bose-Einstein condensates with long-range attractive
interaction proportional to and arbitrary angular dependence. It is
shown exactly that collapse of Bose-Einstein condensate without contact
interactions is possible only for . Case is critical and requires
number of particles to exceed critical value to allow collapse. Critical
collapse in that case is strong one trapping into collapsing region a finite
number of particles.
Case is supercritical with expected weak collapse which traps rapidly
decreasing number of particles during approach to collapse. For
singularity at is not strong enough to allow collapse but attractive
interaction admits stable self-trapping even in absence of external
trapping potential
Partially integrable systems in multidimensions by a variant of the dressing method. 1
In this paper we construct nonlinear partial differential equations in more
than 3 independent variables, possessing a manifold of analytic solutions with
high, but not full, dimensionality. For this reason we call them ``partially
integrable''. Such a construction is achieved using a suitable modification of
the classical dressing scheme, consisting in assuming that the kernel of the
basic integral operator of the dressing formalism be nontrivial. This new
hypothesis leads to the construction of: 1) a linear system of compatible
spectral problems for the solution of the integral equation in 3
independent variables each (while the usual dressing method generates spectral
problems in 1 or 2 dimensions); 2) a system of nonlinear partial differential
equations in dimensions (), possessing a manifold of analytic
solutions of dimension (), which includes one largely arbitrary relation
among the fields. These nonlinear equations can also contain an arbitrary
forcing.Comment: 21 page
Two-dimensional ring-like vortex and multisoliton nonlinear structures at the upper-hybrid resonance
Two-dimensional (2D) equations describing the nonlinear interaction between
upper-hybrid and dispersive magnetosonic waves are presented. Nonlocal
nonlinearity in the equations results in the possibility of existence of stable
2D nonlinear structures. A rigorous proof of the absence of collapse in the
model is given. We have found numerically different types of nonlinear
localized structures such as fundamental solitons, radially symmetric vortices,
nonrotating multisolitons (two-hump solitons, dipoles and quadrupoles), and
rotating multisolitons (azimuthons). By direct numerical simulations we show
that 2D fundamental solitons with negative hamiltonian are stable.Comment: 8 pages, 6 figures, submitted to Phys. Plasma
Soliton trains in Bose-Fermi mixtures
We theoretically consider the formation of bright solitons in a mixture of
Bose and Fermi degenerate gases. While we assume the forces between atoms in a
pure Bose component to be effectively repulsive, their character can be changed
from repulsive to attractive in the presence of fermions provided the Bose and
Fermi gases attract each other strongly enough. In such a regime the Bose
component becomes a gas of effectively attractive atoms. Hence, generating
bright solitons in the bosonic gas is possible. Indeed, after a sudden increase
of the strength of attraction between bosons and fermions (realized by using a
Feshbach resonance technique or by firm radial squeezing of both samples)
soliton trains appear in the Bose-Fermi mixture.Comment: 4 pages, 4 figure
Vainshtein mechanism in Gauss-Bonnet gravity and Galileon aether
We derive field equations of Gauss-Bonnet gravity in 4 dimensions after
dimensional reduction of the action and demonstrate that in this scenario
Vainshtein mechanism operates in the flat spherically symmetric background. We
show that inside this Vainshtein sphere the fifth force is negligibly small
compared to the gravitational force. We also investigate stability of the
spherically symmetric solution, clarify the vocabulary used in the literature
about the hyperbolicity of the equation and the ghost-Laplacian stability
conditions. We find superluminal behavior of the perturbation of the field in
the radial direction. However, because of the presence of the non linear terms,
the structure of the space-time is modified and as a result the field does not
propagate in the Minkowski metric but rather in an "aether" composed by the
scalar field . We thereby demonstrate that the superluminal behavior
does not create time paradoxes thank to the absence of Causal Closed Curves. We
also derive the stability conditions for Friedmann Universe in context with
scalar and tensor perturbations.Comment: 9 pages, 5 figures, references added, more details on the
cosmological analysis included, results and conclusions unchanged, final
version to appear in PR
Magnetic strings as part of Yang-Mills plasma
Magnetic strings are defined as infinitely thin surfaces which are closed in
the vacuum and can be open on an external monopole trajectory (that is, defined
by 't Hooft loop). We review briefly lattice data on the magnetic strings which
refer mostly to SU(2) and SU(3) pure Yang-Mills theories and concentrate on
implications of the strings for the Yang-Mills plasma. We argue that magnetic
strings might be a liquid component of the Yang-Mills plasma and suggest tests
of this hypothesis.Comment: 15 pages, no figures, uses ws-procs9x6 style. Talk by V.I.Z. at
SCGT06 workshop, Nagoya, Japan (November 2006
Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
We study the long-time evolution of gravity waves on deep water exited by the
stochastic external force concentrated in moderately small wave numbers. We
numerically implement the primitive Euler equations for the potential flow of
an ideal fluid with free surface written in canonical variables, using
expansion of the Hamiltonian in powers of nonlinearity of up to fourth order
terms.
We show that due to nonlinear interaction processes a stationary energy
spectrum close to is formed. The observed spectrum can be
interpreted as a weak-turbulent Kolmogorov spectrum for a direct cascade of
energy.Comment: 4 pages, 5 figure
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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