1,848 research outputs found
Predictions of ultra-harmonic oscillations in coupled arrays of limit cycle oscillators
Coupled distinct arrays of nonlinear oscillators have been shown to have a
regime of high frequency, or ultra-harmonic, oscillations that are at multiples
of the natural frequency of individual oscillators. The coupled array
architectures generate an in-phase high-frequency state by coupling with an
array in an anti-phase state. The underlying mechanism for the creation and
stability of the ultra-harmonic oscillations is analyzed. A class of
inter-array coupling is shown to create a stable, in-phase oscillation having
frequency that increases linearly with the number of oscillators, but with an
amplitude that stays fairly constant. The analysis of the theory is illustrated
by numerical simulation of coupled arrays of Stuart-Landau limit cycle
oscillators.Comment: 24 pages, 9 figures, accepted to Phys. Rev. E, in pres
Complete chaotic synchronization in mutually coupled time-delay systems
Complete chaotic synchronization of end lasers has been observed in a line of
mutually coupled, time-delayed system of three lasers, with no direct
communication between the end lasers. The present paper uses ideas from
generalized synchronization to explain the complete synchronization in the
presence of long coupling delays, applied to a model of mutually coupled
semiconductor lasers in a line. These ideas significantly simplify the analysis
by casting the stability in terms of the local dynamics of each laser. The
variational equations near the synchronization manifold are analyzed, and used
to derive the synchronization condition that is a function of the parameters.
The results explain and predict the dependence of synchronization on various
parameters, such as time-delays, strength of coupling and dissipation. The
ideas can be applied to understand complete synchronization in other chaotic
systems with coupling delays and no direct communication between synchronized
sub-systems.Comment: 22 pages, 6 figure
A Bayesian approach to the estimation of maps between riemannian manifolds
Let \Theta be a smooth compact oriented manifold without boundary, embedded
in a euclidean space and let \gamma be a smooth map \Theta into a riemannian
manifold \Lambda. An unknown state \theta \in \Theta is observed via
X=\theta+\epsilon \xi where \epsilon>0 is a small parameter and \xi is a white
Gaussian noise. For a given smooth prior on \Theta and smooth estimator g of
the map \gamma we derive a second-order asymptotic expansion for the related
Bayesian risk. The calculation involves the geometry of the underlying spaces
\Theta and \Lambda, in particular, the integration-by-parts formula. Using this
result, a second-order minimax estimator of \gamma is found based on the modern
theory of harmonic maps and hypo-elliptic differential operators.Comment: 20 pages, no figures published version includes correction to eq.s
31, 41, 4
Refined Algebraic Quantization in the oscillator representation of SL(2,R)
We investigate Refined Algebraic Quantization (RAQ) with group averaging in a
constrained Hamiltonian system with unreduced phase space T^*R^4 and gauge
group SL(2,R). The reduced phase space M is connected and contains four
mutually disconnected `regular' sectors with topology R x S^1, but these
sectors are connected to each other through an exceptional set where M is not a
manifold and where M has non-Hausdorff topology. The RAQ physical Hilbert space
H_{phys} decomposes as H_{phys} = (direct sum of) H_i, where the four subspaces
H_i naturally correspond to the four regular sectors of M. The RAQ observable
algebra A_{obs}, represented on H_{phys}, contains natural subalgebras
represented on each H_i. The group averaging takes place in the oscillator
representation of SL(2,R) on L^2(R^{2,2}), and ensuring convergence requires a
subtle choice for the test state space: the classical analogue of this choice
is to excise from M the exceptional set while nevertheless retaining
information about the connections between the regular sectors. A quantum theory
with the Hilbert space H_{phys} and a finitely-generated observable subalgebra
of A_{obs} is recovered through both Ashtekar's Algebraic Quantization and
Isham's group theoretic quantization.Comment: 30 pages, REVTeX v3.1 with amsfonts. (v4: Published version.
Hot Populations in M87 Globular Clusters
We have obtained HST/STIS far- and near-UV photometry of globular clusters in
four fields in the gE galaxy M87. To a limit of m(FUV) = 25 we detect a total
of 66 globular clusters (GCs) in common with the deep HST optical-band study of
Kundu et al. (1999). Despite strong overlap in V- and I-band properties, the
M87 GCs have UV/optical properties that are distinct from clusters in the Milky
Way and in M31. M87 clusters, especially metal-poor ones, produce larger hot HB
populations than do Milky Way analogues. Cluster mass is probably not a factor
in these distinctions. The most metal-rich M87 GCs in our sample are near Z_sun
and overlap the local E galaxy sample in estimated Mg_2 line indices.
Nonetheless, the clusters produce much more UV light at a given Mg_2, being up
to 1 mag bluer than any gE galaxy in (FUV-V) color. The M87 GCs do not appear
to represent a transition between Milky Way-type clusters and E galaxies. The
differences are in the correct sense if the clusters are significantly older
than the E galaxies. Comparisons with Galactic open clusters indicate that the
hot stars lie on the extreme horizontal branch, rather than being blue
stragglers, and that the EHB becomes well populated for ages > 5 Gyr. We find
that 43 of our UV detections have no optical-band counterparts. Most appear to
be UV-bright background galaxies, seen through M87. Eleven NUV variable sources
detected at only one epoch in the central field are probably classical novae.
[Abridged]Comment: 70 pages, 25 figures (including 4 jpgs), 7 tables. To appear in AJ.
Full resolution version available at
http://www.astro.virginia.edu/~rwo/m87/m87-hotpops.pd
The Rapidly Rotating, Hydrogen Deficient, Hot Post-Asymptotic Giant Branch Star ZNG 1 in the Globular Cluster M5
We report observations of the hot post-asymptotic giant branch star ZNG 1 in
the globular cluster M5 (NGC 5904) with the Far Ultraviolet Spectroscopic
Explorer (FUSE). From the resulting spectrum, we derive an effective
temperature T_eff = 44300 +/- 300 K, a surface gravity log g = 4.3 +/- 0.1, a
rotational velocity v sin i = 170 +/- 20 km/s, and a luminosity log (L/L_sun) =
3.52 +/- 0.04. The atmosphere is helium-rich (Y = 0.93), with enhanced carbon
(2.6% by mass), nitrogen (0.51%) and oxygen (0.37%) abundances. The spectrum
shows evidence for a wind with terminal velocity near 1000 km/s and an
expanding shell of carbon- and nitrogen-rich material around the star. The
abundance pattern of ZNG 1 is suggestive of the ``born-again'' scenario,
whereby a star on the white-dwarf cooling curve undergoes a very late shell
flash and returns to the AGB, but the star's rapid rotation is more easily
explained by a previous interaction with a binary companion.Comment: 8 pages, 2 PostScript figures, Latex with emulateapj5. Accepted for
publication in ApJ Letter
SN 2005hj: Evidence for Two Classes of Normal-Bright SNe Ia and Implications for Cosmology
HET Optical spectra covering the evolution from about 6 days before to about
5 weeks after maximum light and the ROTSE-IIIb unfiltered light curve of the
"Branch-normal" Type Ia Supernova SN 2005hj are presented. The host galaxy
shows HII region lines at redshift of z=0.0574, which puts the peak unfiltered
absolute magnitude at a somewhat over-luminous -19.6. The spectra show weak and
narrow SiII lines, and for a period of at least 10 days beginning around
maximum light these profiles do not change in width or depth and they indicate
a constant expansion velocity of ~10,600 km/s. We analyzed the observations
based on detailed radiation dynamical models in the literature. Whereas delayed
detonation and deflagration models have been used to explain the majority of
SNe Ia, they do not predict a long velocity plateau in the SiII minimum with an
unvarying line profile. Pulsating delayed detonations and merger scenarios form
shell-like density structures with properties mostly related to the mass of the
shell, M_shell, and we discuss how these models may explain the observed SiII
line evolution; however, these models are based on spherical calculations and
other possibilities may exist. SN 2005hj is consistent with respect to the
onset, duration, and velocity of the plateau, the peak luminosity and, within
the uncertainties, with the intrinsic colors for models with M_shell=0.2 M_sun.
Our analysis suggests a distinct class of events hidden within the
Branch-normal SNe Ia. If the predicted relations between observables are
confirmed, they may provide a way to separate these two groups. We discuss the
implications of two distinct progenitor classes on cosmological studies
employing SNe Ia, including possible differences in the peak luminosity to
light curve width relation.Comment: ApJ accepted, 31 page
- …