695 research outputs found
Influence of the nonlinearity parameter on the solar-wind sub-ion magnetic energy spectrum: FLR-Landau fluid simulations
The cascade of kinetic Alfv\'en waves (KAWs) at the sub-ion scales in the
solar wind is numerically simulated using a fluid approach that retains ion and
electron Landau damping, together with ion finite Larmor radius corrections.
Assuming initially equal and isotropic ion and electron temperatures, and an
ion beta equal to unity, different simulations are performed by varying the
propagation direction and the amplitude of KAWs that are randomly driven at a
transverse scale of about one fifth of the proton gyroradius in order to
maintain a prescribed level of turbulent fluctuations. The resulting turbulent
regimes are characterized by the nonlinearity parameter, defined as the ratio
of the characteristic times of Alfv\'en wave propagation and of the transverse
nonlinear dynamics. The corresponding transverse magnetic energy spectra
display power laws with exponents spanning a range of values consistent with
spacecraft observations. The meandering of the magnetic field lines together
with the ion temperature homogenization along these lines are shown to be
related to the strength of the turbulence, measured by the nonlinearity
parameter. The results are interpreted in terms of a recently proposed
phenomenological model where the homogenization process along field lines
induced by Landau damping plays a central role
Finite time collapse of N classical fields described by coupled nonlinear Schrodinger equations
We prove the finite-time collapse of a system of N classical fields, which
are described by N coupled nonlinear Schrodinger equations. We derive the
conditions under which all of the fields experiences this finite-time collapse.
Finally, for two-dimensional systems, we derive constraints on the number of
particles associated with each field that are necessary to prevent collapse.Comment: v2: corrected typo on equation
Nonlinear Schroedinger Equation in the Presence of Uniform Acceleration
We consider a recently proposed nonlinear Schroedinger equation exhibiting
soliton-like solutions of the power-law form , involving the
-exponential function which naturally emerges within nonextensive
thermostatistics [, with ]. Since
these basic solutions behave like free particles, obeying , and (), it is relevant to investigate how they
change under the effect of uniform acceleration, thus providing the first steps
towards the application of the aforementioned nonlinear equation to the study
of physical scenarios beyond free particle dynamics. We investigate first the
behaviour of the power-law solutions under Galilean transformation and discuss
the ensuing Doppler-like effects. We consider then constant acceleration,
obtaining new solutions that can be equivalently regarded as describing a free
particle viewed from an uniformly accelerated reference frame (with
acceleration ) or a particle moving under a constant force . The latter
interpretation naturally leads to the evolution equation with .
Remarkably enough, the potential couples to , instead of coupling
to , as happens in the familiar linear case ().Comment: 4 pages, no figure
Instabilities in Zakharov Equations for Laser Propagation in a Plasma
F.Linares, G.Ponce, J-C.Saut have proved that a non-fully dispersive Zakharov
system arising in the study of Laser-plasma interaction, is locally well posed
in the whole space, for fields vanishing at infinity. Here we show that in the
periodic case, seen as a model for fields non-vanishing at infinity, the system
develops strong instabilities of Hadamard's type, implying that the Cauchy
problem is strongly ill-posed
Distribution of eigenfrequencies for oscillations of the ground state in the Thomas--Fermi limit
In this work, we present a systematic derivation of the distribution of
eigenfrequencies for oscillations of the ground state of a repulsive
Bose-Einstein condensate in the semi-classical (Thomas-Fermi) limit. Our
calculations are performed in 1-, 2- and 3-dimensional settings. Connections
with the earlier work of Stringari, with numerical computations, and with
theoretical expectations for invariant frequencies based on symmetry principles
are also given.Comment: 8 pages, 1 figur
Symmetry Breaking in Symmetric and Asymmetric Double-Well Potentials
Motivated by recent experimental studies of matter-waves and optical beams in
double well potentials, we study the solutions of the nonlinear Schr\"{o}dinger
equation in such a context. Using a Galerkin-type approach, we obtain a
detailed handle on the nonlinear solution branches of the problem, starting
from the corresponding linear ones and predict the relevant bifurcations of
solutions for both attractive and repulsive nonlinearities. The results
illustrate the nontrivial differences that arise between the steady
states/bifurcations emerging in symmetric and asymmetric double wells
Vortices in attractive Bose-Einstein condensates in two dimensions
The form and stability of quantum vortices in Bose-Einstein condensates with
attractive atomic interactions is elucidated. They appear as ring bright
solitons, and are a generalization of the Townes soliton to nonzero winding
number . An infinite sequence of radially excited stationary states appear
for each value of , which are characterized by concentric matter-wave rings
separated by nodes, in contrast to repulsive condensates, where no such set of
states exists. It is shown that robustly stable as well as unstable regimes may
be achieved in confined geometries, thereby suggesting that vortices and their
radial excited states can be observed in experiments on attractive condensates
in two dimensions.Comment: 4 pages, 3 figure
On a fourth order nonlinear Helmholtz equation
In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz
equation in for positive, bounded and -periodic functions . Using
the dual method of Evequoz and Weth, we find solutions to this equation and
establish some of their qualitative properties
Stabilization of BEC droplet in free space by feedback control of interatomic interaction
A self-trapped Bose-Einstein condensate in three-dimensional free space is
shown to be stabilized by feedback control of the interatomic interaction
through nondestructive measurement of the condensate's peak column density. The
stability is found to be robust against poor resolution and experimental errors
in the measurement.Comment: 7 pages, 6 figure
Nonlinear Relativistic and Quantum Equations with a Common Type of Solution
Generalizations of the three main equations of quantum physics, namely, the
Schr\"odinger, Klein-Gordon, and Dirac equations, are proposed. Nonlinear
terms, characterized by exponents depending on an index , are considered in
such a way that the standard linear equations are recovered in the limit . Interestingly, these equations present a common, soliton-like,
travelling solution, which is written in terms of the -exponential function
that naturally emerges within nonextensive statistical mechanics. In all cases,
the well-known Einstein energy-momentum relation is preserved for arbitrary
values of
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