28,473 research outputs found
Almost sure exponential stability of numerical solutions for stochastic delay differential equations
Using techniques based on the continuous and discrete semimartingale convergence theorems, this paper investigates if numerical methods may reproduce the almost sure exponential stability of the exact solutions to stochastic delay differential equations (SDDEs). The important feature of this technique is that it enables us to study the almost sure exponential stability of numerical solutions of SDDEs directly. This is significantly different from most traditional methods by which the almost sure exponential stability is derived from the moment stability by the Chebyshev inequality and the BorelâCantelli lemma
Is J 133658.3-295105 a Radio Source at z >= 1.0 or at the Distance of M 83?
We present Gemini optical imaging and spectroscopy of the radio source J
133658.3-295105. This source has been suggested to be the core of an FR II
radio source with two detected lobes. J 133658.3-295105 and its lobes are
aligned with the optical nucleus of M 83 and with three other radio sources at
the M 83 bulge outer region. These radio sources are neither supernova remnants
nor H II regions. This curious configuration prompted us to try to determine
the distance to J 133658.3-295105. We detected H_alpha emission redshifted by ~
130 km s^-1 with respect to an M 83 H II region 2.5" east-southeast of the
radio source. We do not detect other redshifted emission lines of an optical
counterpart down to m_i = 22.2 +/- 0.8. Two different scenarios are proposed:
the radio source is at z >= 2.5, a much larger distance than the previously
proposed lower limit z >= 1.0, or the object was ejected by a gravitational
recoil event from the M 83 nucleus. This nucleus is undergoing a strong
dynamical evolution, judging from previous three-dimensional spectroscopy.Comment: 6 pages, 4 figure
Almost sure exponential stability of the EulerâMaruyama approximations for stochastic functional differential equations
By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the EulerâMaruyama (EM) approximations of stochastic functional differential equations (SFDEs) can share the almost sure exponential stability of the exact solution. Moreover, for sufficiently small stepsize, the decay rate as measured by the Lyapunov exponent can be reproduced arbitrarily accurately
Hole-doped semiconductor nanowire on top of an s-wave superconductor: A new and experimentally accessible system for Majorana fermions
Majorana fermions were envisioned by E. Majorana in 1935 to describe
neutrinos. Recently it has been shown that they can be realized even in a class
of electron-doped semiconductors, on which ordinary s-wave superconductivity is
proximity induced, provided the time reversal symmetry is broken by an external
Zeeman field above a threshold. Here we show that in a hole-doped semiconductor
nanowire the threshold Zeeman field for Majorana fermions can be very small for
some magic values of the hole density. In contrast to the electron-doped
systems, smaller Zeeman fields and much stronger spin-orbit coupling and
effective mass of holes allow the hole-doped systems to support Majorana
fermions in a parameter regime which is routinely realized in current
experiments.Comment: 5 pages, 3 figures, accepted for publication in Phys. Rev. Let
The X-ray light curve of Gamma-ray bursts: clues to the central engine
We present the analysis of a large sample of gamma-ray burst (GRB) X-ray
light curves in the rest frame to characterise their intrinsic properties in
the context of different theoretical scenarios. We determine the morphology,
time scales, and energetics of 64 long GRBs observed by \emph{Swift}/XRT
\emph{without} flaring activity. We furthermore provide a one-to-one comparison
to the properties of GRBs \emph{with} X-ray flares. We find that the steep
decay morphology and its connection with X-ray flares favour a scenario in
which a central engine origin. We show that this scenario can also account for
the shallow decay phase, provided that the GRB progenitor star has a
self-similar structure with a constant envelope-to-core mass ratio . However, difficulties arise for very long duration
( s) shallow phases. Alternatively, a spinning-down magnetar
whose emitted power refreshes the forward shock can quantitatively account for
the shallow decay properties. In particular we demonstrate that this model can
account for the plateau luminosity vs. end time anticorrelation.Comment: 12 pages, 8 figures, accepted for publication in A&
Optimization of graded multilayer designs for astronomical x-ray telescopes
We developed a systematic method for optimizing the design of depth-graded multilayers for astronomical hard-x-ray and soft-Îł-ray telescopes based on the instrumentâs bandpass and the field of view. We apply these methods to the design of the conical-approximation Wolter I optics employed by the balloon-borne High Energy Focusing Telescope, using W/Si as the multilayer materials. In addition, we present optimized performance calculations of mirrors, using other material pairs that are capable of extending performance to photon energies above the W K-absorption edge (69.5 keV), including Pt/C, Ni/C, Cu/Si, and Mo/Si
Constraints on the average magnetic field strength of relic radio sources 0917+75 and 1401-33 from XMM-Newton observations
We observed two relic radio sources, 0917+75 and 1401-33, with the XMM-Newton
X-ray observatory. We did not detect any X-ray emission, thermal or
non-thermal, in excess of the local background level from either target. This
imposes new upper limits on the X-ray flux due to inverse Compton scattering of
photons from the cosmic microwave background by relativistic electrons in the
relic sources, and new lower limits on the magnetic field strength from the
relative strength of the radio and X-ray emission. The combination of radio and
X-ray observations provides a measure of the magnetic field independent of
equipartition or minimum energy assumptions. Due to increasing sensitivity of
radio observations, the known population of cluster relics has been growing;
however, studies of non-thermal X-ray emission from relics remain scarce. Our
study adds to the small sample of relics studied in X-rays. In both relics, our
field strength lower limits are slightly larger than estimates of the
equipartition magnetic field.Comment: 11 pages, 5 figures. Accepted by MNRA
Microlensing of collimated Gamma-Ray Burst afterglows
We investigate stellar microlensing of the collimated gamma-ray burst
afterglows. A spherical afterglow appears on the sky as a superluminally
expanding thin ring (``ring-like'' image), which is maximally amplified as it
crosses the lens. We find that the image of the collimated afterglow becomes
quite uniform (``disk-like'' image) after the jet break time (after the Lorentz
factor of the jet drops below the inverse of the jet opening angle).
Consequently, the amplification peak in the light curve after the break time is
lower and broader. Therefore detailed monitoring of the amplification history
will be able to test whether the afterglows are jets or not, i.e.,
``disk-like'' or not, if the lensing occurs after the break time. We also show
that some proper motion and polarization is expected, peaking around the
maximum amplification. The simultaneous detection of the proper motion and the
polarization will strengthen that the brightening of the light curve is due to
microlensing.Comment: 16 pages, 6 figures, accepted for publication in Ap
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