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 Borel–Cantelli 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 Euler–Maruyama approximations for stochastic functional differential equations

By the continuous and discrete nonnegative semimartingale convergence theorems, this paper investigates conditions under which the Euler–Maruyama (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 $\sim 0.02-0.03$. However, difficulties arise for very long duration ($t_p\gtrsim10^4$ 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-γ-ray telescopes based on the instrument’s 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