621 research outputs found
Controlling balance in an ensemble Kalman filter
We present a method to control unbalanced fast dynamics in an
ensemble Kalman filter by introducing a weak constraint on the imbalance in a
spatially sparse observational network. We show that the balance constraint
produces significantly more balanced analyses than ensemble Kalman filters
without balance constraints and than filters implementing incremental
analysis updates (IAU). Furthermore, our filter with the weak constraint on
imbalance produces good rms error statistics which outperform those of
ensemble Kalman filters without balance constraints for the fast fields
On finite-size Lyapunov exponents in multiscale systems
We study the effect of regime switches on finite size Lyapunov exponents
(FSLEs) in determining the error growth rates and predictability of multiscale
systems. We consider a dynamical system involving slow and fast regimes and
switches between them. The surprising result is that due to the presence of
regimes the error growth rate can be a non-monotonic function of initial error
amplitude. In particular, troughs in the large scales of FSLE spectra is shown
to be a signature of slow regimes, whereas fast regimes are shown to cause
large peaks in the spectra where error growth rates far exceed those estimated
from the maximal Lyapunov exponent. We present analytical results explaining
these signatures and corroborate them with numerical simulations. We show
further that these peaks disappear in stochastic parametrizations of the fast
chaotic processes, and the associated FSLE spectra reveal that large scale
predictability properties of the full deterministic model are well approximated
whereas small scale features are not properly resolved.Comment: Accepted for publication in Chao
Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?
We present a bifurcation analysis of a normal form for travelling waves in
one-dimensional excitable media. The normal form which has been recently
proposed on phenomenological grounds is given in form of a differential delay
equation. The normal form exhibits a symmetry preserving Hopf bifurcation which
may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry
breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf
bifurcation for the propagation of a single pulse in a ring by means of a
center manifold reduction, and for a wave train by means of a multiscale
analysis leading to a real Ginzburg-Landau equation as the corresponding
amplitude equation. Both, the center manifold reduction and the multiscale
analysis show that the Hopf bifurcation is always subcritical independent of
the parameters. This may have links to cardiac alternans which have so far been
believed to be stable oscillations emanating from a supercritical bifurcation.
We discuss the implications for cardiac alternans and revisit the instability
in some excitable media where the oscillations had been believed to be stable.
In particular, we show that our condition for the onset of the Hopf bifurcation
coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao
On the Validity of the 0-1 Test for Chaos
In this paper, we present a theoretical justification of the 0-1 test for
chaos. In particular, we show that with probability one, the test yields 0 for
periodic and quasiperiodic dynamics, and 1 for sufficiently chaotic dynamics
The Low Quiescent X-Ray Luminosity of the Transient X-Ray Burster EXO 1747-214
We report on X-ray and optical observations of the X-ray burster EXO
1747-214. This source is an X-ray transient, and its only known outburst was
observed in 1984-1985 by the EXOSAT satellite. We re-analyzed the EXOSAT data
to derive the source position, column density, and a distance upper limit using
its peak X-ray burst flux. We observed the EXO 1747-214 field in 2003 July with
the Chandra X-ray Observatory to search for the quiescent counterpart. We found
one possible candidate just outside the EXOSAT error circle, but we cannot rule
out the possibility that the source is unrelated to EXO 1747-214. Our
conclusion is that the upper limit on the unabsorbed 0.3-8 keV luminosity is L
< 7E31 erg/s, making EXO 1747-214 one of the faintest neutron star transients
in quiescence. We compare this luminosity upper limit to the quiescent
luminosities of 19 neutron star and 14 black hole systems and discuss the
results in the context of the differences between neutron stars and black
holes. Based on the theory of deep crustal heating by Brown and coworkers, the
luminosity implies an outburst recurrence time of >1300 yr unless some form of
enhanced cooling occurs within the neutron star. The position of the possible
X-ray counterpart is consistent with three blended optical/IR sources with
R-magnitudes between 19.4 and 19.8 and J-magnitudes between 17.2 and 17.6. One
of these sources could be the quiescent optical/IR counterpart of EXO 1747-214.Comment: 7 pages, accepted by the Astrophysical Journa
Spatiotemporally Localized Multidimensional Solitons in Self-Induced Transparency Media
"Light bullets" are multi-dimensional solitons which are localized in both
space and time. We show that such solitons exist in two- and three-dimensional
self-induced-transparency media and that they are fully stable. Our approximate
analytical calculation, backed and verified by direct numerical simulations,
yields the multi-dimensional generalization of the one-dimensional Sine-Gordon
soliton.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
Why do ultrasoft repulsive particles cluster and crystallize? Analytical results from density functional theory
We demonstrate the accuracy of the hypernetted chain closure and of the
mean-field approximation for the calculation of the fluid-state properties of
systems interacting by means of bounded and positive-definite pair potentials
with oscillating Fourier transforms. Subsequently, we prove the validity of a
bilinear, random-phase density functional for arbitrary inhomogeneous phases of
the same systems. On the basis of this functional, we calculate analytically
the freezing parameters of the latter. We demonstrate explicitly that the
stable crystals feature a lattice constant that is independent of density and
whose value is dictated by the position of the negative minimum of the Fourier
transform of the pair potential. This property is equivalent with the existence
of clusters, whose population scales proportionally to the density. We
establish that regardless of the form of the interaction potential and of the
location on the freezing line, all cluster crystals have a universal Lindemann
ratio L = 0.189 at freezing. We further make an explicit link between the
aforementioned density functional and the harmonic theory of crystals. This
allows us to establish an equivalence between the emergence of clusters and the
existence of negative Fourier components of the interaction potential. Finally,
we make a connection between the class of models at hand and the system of
infinite-dimensional hard spheres, when the limits of interaction steepness and
space dimension are both taken to infinity in a particularly described fashion.Comment: 19 pages, 5 figures, submitted to J. Chem. Phys; new version: minor
changes in structure of pape
Spatiotemporally localized solitons in resonantly absorbing Bragg reflectors
We predict the existence of spatiotemporal solitons (``light bullets'') in
two-dimensional self-induced transparency media embedded in a Bragg grating.
The "bullets" are found in an approximate analytical form, their stability
being confirmed by direct simulations. These findings suggest new possibilities
for signal transmission control and self-trapping of light.Comment: RevTex, 3 pages, 2 figures, to be published in PR
Regular and chaotic vibration in a piezoelectric energy harvester
We examine regular and chaotic responses of a vibrational energy harvester composed of a vertical beam and a tip mass. The beam is excited horizontally by a harmonic inertial force while mechanical vibrational energy is converted to electrical power through a piezoelectric patch. The mechanical resonator can be described by single or double well potentials depending on the gravity force from the tip mass. By changing the tip mass we examine bifurcations from single well oscillations, to regular and chaotic vibrations between the potential wells. The appearance of chaotic responses in the energy harvesting system is illustrated by the bifurcation diagram, the corresponding Fourier spectra, the phase portraits, and is confirmed by the 0–1 test. The appearance of chaotic vibrations reduces the level of harvested energy
- …