1,189,476 research outputs found
Relative dispersion analysis of GLAD surface drifters in the Gulf of Mexico
Relative dispersion analysis of the Lagrangian dataset derived from the GLAD drifter campaign in the Gulf of
Mexico was computed on pairs derived from actual triplets.
The results show that an exponential growth of the relative dispersion begins and occurs within the first two days of
deployment.
The influence of inertial motions should be taken into account in order not to overestimate turbulence diffusivities
Dispersion processes
We study a synchronous dispersion process in which particles are
initially placed at a distinguished origin vertex of a graph . At each time
step, at each vertex occupied by more than one particle at the beginning of
this step, each of these particles moves to a neighbour of chosen
independently and uniformly at random. The dispersion process ends once the
particles have all stopped moving, i.e. at the first step at which each vertex
is occupied by at most one particle.
For the complete graph and star graph , we show that for any
constant , with high probability, if , then the
process finishes in steps, whereas if , then
the process needs steps to complete (if ever). We also show
that an analogous lazy variant of the process exhibits the same behaviour but
for higher thresholds, allowing faster dispersion of more particles.
For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes
(in terms of ) we give bounds on the time to finish and the maximum distance
traveled from the origin as a function of the number of particles
Directional supercontinuum generation: the role of the soliton
In this paper we numerically study supercontinuum generation by pumping a
silicon nitride waveguide, with two zero-dispersion wavelengths, with
femtosecond pulses. The waveguide dispersion is designed so that the pump pulse
is in the normal-dispersion regime. We show that because of self-phase
modulation, the initial pulse broadens into the anomalous-dispersion regime,
which is sandwiched between the two normal-dispersion regimes, and here a
soliton is formed. The interaction of the soliton and the broadened pulse in
the normal-dispersion regime causes additional spectral broadening through
formation of dispersive waves by non-degenerate four-wave mixing and
cross-phase modulation. This broadening occurs mainly towards the second
normal-dispersion regime. We show that pumping in either normal-dispersion
regime allows broadening towards the other normal-dispersion regime. This
ability to steer the continuum extension towards the direction of the other
normal-dispersion regime beyond the sandwiched anomalous-dispersion regime
underlies the directional supercontinuum notation. We numerically confirm the
approach in a standard silica microstructured fiber geometry with two
zero-dispersion wavelengths
Improved estimators for dispersion models with dispersion covariates
In this paper we discuss improved estimators for the regression and the
dispersion parameters in an extended class of dispersion models (J{\o}rgensen,
1996). This class extends the regular dispersion models by letting the
dispersion parameter vary throughout the observations, and contains the
dispersion models as particular case. General formulae for the second-order
bias are obtained explicitly in dispersion models with dispersion covariates,
which generalize previous results by Botter and Cordeiro (1998), Cordeiro and
McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The
practical use of the formulae is that we can derive closed-form expressions for
the second-order biases of the maximum likelihood estimators of the regression
and dispersion parameters when the information matrix has a closed-form.
Various expressions for the second-order biases are given for special models.
The formulae have advantages for numerical purposes because they require only a
supplementary weighted linear regression. We also compare these bias-corrected
estimators with two different estimators which are also bias-free to the
second-order that are based on bootstrap methods. These estimators are compared
by simulation
Hamiltonian dynamics of breathers with third-order dispersion
We present a nonperturbative analysis of certain dynamical aspects of breathers (dispersion-managed solitons) including the effects of third-order dispersion. The analysis highlights the similarities to and differences from the well-known analogous procedures for second-order dispersion. We discuss in detail the phase-space evolution of breathers in dispersion-managed systems in the presence of third-order dispersion
Dispersion-managed soliton in a strong dispersion map limit
A dispersion-managed optical system with step-wise periodical variation of
dispersion is studied in a strong dispersion map limit in the framework of
path-averaged Gabitov-Turitsyn equation. The soliton solution is obtained by
iterating the path-averaged equation analytically and numerically. An efficient
numerical algorithm for obtaining of DM soliton shape is developed. The
envelope of soliton oscillating tails is found to decay exponentially in time
while the oscillations are described by a quadratic law.Comment: 11 Pages, 3 Figures; Submitted to Optics Letter
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