79,606 research outputs found
Reheating in the Presence of Inhomogeneous Noise
Explosive particle production due to parametric resonance is a crucial
feature of reheating in an inflationary cosmology. Coherent oscillations of the
inflaton field lead to a periodically varying mass in the evolution equation of
matter and gravitational fluctuations and often induce a parametric resonance
instability. In a previous paper (hep-ph/9709273) it was shown that homogeneous
(i.e. space independent) noise leads to an increase of the generalized Floquet
exponent for all modes, at least if the noise is temporally uncorrelated. Here
we extend the results to the physically more realistic case of spatially
inhomogeneous noise. We demonstrate - modulo some mathematical fine points
which are addressed in a companion paper - that the Floquet exponent is a non-
decreasing function of the amplitude of the noise. We provide numerical
evidence for an even stronger statement, namely that in the presence of
inhomogeneous noise, the Floquet exponent of each mode is larger than the
maximal Floquet exponent of the system in the absence of noise.Comment: 21 pages, 4 figure
Multi-valued, singular stochastic evolution inclusions
We provide an abstract variational existence and uniqueness result for
multi-valued, monotone, non-coercive stochastic evolution inclusions in Hilbert
spaces with general additive and Wiener multiplicative noise. As examples we
discuss certain singular diffusion equations such as the stochastic 1-Laplacian
evolution (total variation flow) in all space dimensions and the stochastic
singular fast diffusion equation. In case of additive Wiener noise we prove the
existence of a unique weak-* mean ergodic invariant measure.Comment: 39 pages, in press: J. Math. Pures Appl. (2013
ATLBS: the Australia Telescope Low-brightness Survey
We present a radio survey carried out with the Australia Telescope Compact
Array. A motivation for the survey was to make a complete inventory of the
diffuse emission components as a step towards a study of the cosmic evolution
in radio source structure and the contribution from radio-mode feedback on
galaxy evolution. The Australia Telescope low-brightness survey (ATLBS) at 1388
MHz covers 8.42 sq deg of the sky in an observing mode designed to yield images
with exceptional surface brightness sensitivity and low confusion. The ATLBS
radio images, made with 0.08 mJy/beam rms noise and 50" beam, detect a total of
1094 sources with peak flux exceeding 0.4 mJy/beam. The ATLBS source counts
were corrected for blending, noise bias, resolution, and primary beam
attenuation; the normalized differential source counts are consistent with no
upturn down to 0.6 mJy. The percentage integrated polarization Pi_0 was
computed after corrections for the polarization bias in integrated polarized
intensity; Pi_0 shows an increasing trend with decreasing flux density.
Simultaneous visibility measurements made with longer baselines yielded images,
with 5" beam, of compact components in sources detected in the survey. The
observations provide a measurement of the complexity and diffuse emission
associated with mJy and sub-mJy radio sources. 10% of the ATLBS sources have
more than half of their flux density in extended emission and the fractional
flux in diffuse components does not appear to vary with flux density, although
the percentage of sources that have complex structure increases with flux
density. The observations are consistent with a transition in the nature of
extended radio sources from FR-II radio source morphology, which dominates the
mJy population, to FR-I structure at sub-mJy flux density. (Abridged)Comment: 18 pages, 8 figues, 6 tables, accepted for publication in MNRA
Analytical results for a Fokker-Planck equation in the small noise limit
We present analytical results for the lowest cumulants of a stochastic
process described by a Fokker-Planck equation with nonlinear drift. We show
that, in the limit of small fluctuations, the mean, the variance and the
covariance of the process can be expressed in compact form with the help of the
Lambert W function. As an application, we discuss the interplay of noise and
nonlinearity far from equilibrium.Comment: 5 pages, 4 figure
The Emergence of Gravitational Wave Science: 100 Years of Development of Mathematical Theory, Detectors, Numerical Algorithms, and Data Analysis Tools
On September 14, 2015, the newly upgraded Laser Interferometer
Gravitational-wave Observatory (LIGO) recorded a loud gravitational-wave (GW)
signal, emitted a billion light-years away by a coalescing binary of two
stellar-mass black holes. The detection was announced in February 2016, in time
for the hundredth anniversary of Einstein's prediction of GWs within the theory
of general relativity (GR). The signal represents the first direct detection of
GWs, the first observation of a black-hole binary, and the first test of GR in
its strong-field, high-velocity, nonlinear regime. In the remainder of its
first observing run, LIGO observed two more signals from black-hole binaries,
one moderately loud, another at the boundary of statistical significance. The
detections mark the end of a decades-long quest, and the beginning of GW
astronomy: finally, we are able to probe the unseen, electromagnetically dark
Universe by listening to it. In this article, we present a short historical
overview of GW science: this young discipline combines GR, arguably the
crowning achievement of classical physics, with record-setting, ultra-low-noise
laser interferometry, and with some of the most powerful developments in the
theory of differential geometry, partial differential equations,
high-performance computation, numerical analysis, signal processing,
statistical inference, and data science. Our emphasis is on the synergy between
these disciplines, and how mathematics, broadly understood, has historically
played, and continues to play, a crucial role in the development of GW science.
We focus on black holes, which are very pure mathematical solutions of
Einstein's gravitational-field equations that are nevertheless realized in
Nature, and that provided the first observed signals.Comment: 41 pages, 5 figures. To appear in Bulletin of the American
Mathematical Societ
Detecting compact galactic binaries using a hybrid swarm-based algorithm
Compact binaries in our galaxy are expected to be one of the main sources of
gravitational waves for the future eLISA mission. During the mission lifetime,
many thousands of galactic binaries should be individually resolved. However,
the identification of the sources, and the extraction of the signal parameters
in a noisy environment are real challenges for data analysis. So far,
stochastic searches have proven to be the most successful for this problem. In
this work we present the first application of a swarm-based algorithm combining
Particle Swarm Optimization and Differential Evolution. These algorithms have
been shown to converge faster to global solutions on complicated likelihood
surfaces than other stochastic methods. We first demonstrate the effectiveness
of the algorithm for the case of a single binary in a 1 mHz search bandwidth.
This interesting problem gave the algorithm plenty of opportunity to fail, as
it can be easier to find a strong noise peak rather than the signal itself.
After a successful detection of a fictitious low-frequency source, as well as
the verification binary RXJ0806.3+1527, we then applied the algorithm to the
detection of multiple binaries, over different search bandwidths, in the cases
of low and mild source confusion. In all cases, we show that we can
successfully identify the sources, and recover the true parameters within a
99\% credible interval.Comment: 19 pages, 5 figure
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