Almost sure and moment exponential stability of Euler-Maruyama discretizations for hybrid stochastic differential equations

Positive results are derived concerning the long time dynamics of numerical simulations of stochastic differential equation systems with Markovian switching. Euler-Maruyama discretizations are shown to capture almost sure and momente xponential stability for all sufficiently small timesteps under appropriate conditions

Asymptotic properties of stochastic population dynamics

In this paper we stochastically perturb the classical Lotka{Volterra model x_ (t) = diag(x1(t); ; xn(t))[b + Ax(t)] into the stochastic dierential equation dx(t) = diag(x1(t); ; xn(t))[(b + Ax(t))dt + dw(t)]: The main aim is to study the asymptotic properties of the solution. It is known (see e.g. [3, 20]) if the noise is too large then the population may become extinct with probability one. Our main aim here is to nd out what happens if the noise is relatively small. In this paper we will establish some new asymptotic properties for the moments as well as for the sample paths of the solution. In particular, we will discuss the limit of the average in time of the sample paths

Observation of the TeV gamma-ray source MGRO J1908+06 with ARGO-YBJ

The extended gamma ray source MGRO J1908+06, discovered by the Milagro air shower detector in 2007, has been observed for about 4 years by the ARGO-YBJ experiment at TeV energies, with a statistical significance of 6.2 standard deviations. The peak of the signal is found at a position consistent with the pulsar PSR J1907+0602. Parametrizing the source shape with a two-dimensional Gauss function we estimate an extension \sigma = 0.49 \pm 0.22 degrees, consistent with a previous measurement by the Cherenkov Array H.E.S.S.. The observed energy spectrum is dN/dE = 6.1 \pm 1.4 \times 10^-13 (E/4 TeV)^{-2.54 \pm 0.36} photons cm^-2 s^-1 TeV^-1, in the energy range 1-20 TeV. The measured gamma ray flux is consistent with the results of the Milagro detector, but is 2-3 times larger than the flux previously derived by H.E.S.S. at energies of a few TeV. The continuity of the Milagro and ARGO-YBJ observations and the stable excess rate observed by ARGO-YBJ along 4 years of data taking support the identification of MGRO J1908+06 as the steady powerful TeV pulsar wind nebula of PSR J1907+0602, with an integrated luminosity above 1 TeV about 1.8 times the Crab Nebula luminosity.Comment: 6 pages, accepted for pubblication by ApJ. Replaced to correct the author lis

Long-term Monitoring on Mrk 501 for Its VHE gamma Emission and a Flare in October 2011

As one of the brightest active blazars in both X-ray and very high energy $\gamma$-ray bands, Mrk 501 is very useful for physics associated with jets from AGNs. The ARGO-YBJ experiment is monitoring it for $\gamma$-rays above 0.3 TeV since November 2007. Starting from October 2011 the largest flare since 2005 is observed, which lasts to about April 2012. In this paper, a detailed analysis is reported. During the brightest $\gamma$-rays flaring episodes from October 17 to November 22, 2011, an excess of the event rate over 6 $\sigma$ is detected by ARGO-YBJ in the direction of Mrk 501, corresponding to an increase of the $\gamma$-ray flux above 1 TeV by a factor of 6.6$\pm$2.2 from its steady emission. In particular, the $\gamma$-ray flux above 8 TeV is detected with a significance better than 4 $\sigma$. Based on time-dependent synchrotron self-Compton (SSC) processes, the broad-band energy spectrum is interpreted as the emission from an electron energy distribution parameterized with a single power-law function with an exponential cutoff at its high energy end. The average spectral energy distribution for the steady emission is well described by this simple one-zone SSC model. However, the detection of $\gamma$-rays above 8 TeV during the flare challenges this model due to the hardness of the spectra. Correlations between X-rays and $\gamma$-rays are also investigated.Comment: have been accepted for publication at Ap

Dataset for "Quantitative analysis of anti-resonance in single-ring, hollow-core fibres"

This dataset contains the data used to create Figures 2 to 5 in the paper, "Quantitative analysis of anti-resonance in single-ring, hollow-core fibres". The data represents the confinement loss of jacketed and unjacketed single-ring, hollow-core fibres and of a reference model consisting of concentric glass and air layers. The different Figures, and the related datasets, show the dependence of the confinement loss on the structural parameters of the fibres. Data for jacketed and unjacketed fibres is calculated using the commercial finite-element solver, COMSOL Multiphysics. Data for the reference model is calculated with an in-house code

Dataset for "Quantitative analysis of anti-resonance in single-ring, hollow-core fibres"

This dataset contains the data used to create Figures 2 to 5 in the paper, "Quantitative analysis of anti-resonance in single-ring, hollow-core fibres". The data represents the confinement loss of jacketed and unjacketed single-ring, hollow-core fibres and of a reference model consisting of concentric glass and air layers. The different Figures, and the related datasets, show the dependence of the confinement loss on the structural parameters of the fibres. Data for jacketed and unjacketed fibres is calculated using the commercial finite-element solver, COMSOL Multiphysics. Data for the reference model is calculated with an in-house code

Dataset for "Birefringent Anti-resonant Hollow-core Fiber"

This dataset contains data supporting the results presented in the paper "Birefringent Anti-resonant Hollow-core Fiber" and the supplementary material. It includes the data used to plot each figure (in .xlsx format), together with simulated data obtained using COMSOL. Hollow-core fibres have demonstrated record performance in applications such as high-power pulse delivery, quantum computing, and sensing. However, their routine use is yet to become reality. A major obstacle is the ability to maintain the polarisation state of light over a broad range of wavelengths, while also ensuring single-mode guidance and attenuation that is low enough for practical applications that require only a few meters of fibre length (<1 dB/m). Here we simulated, fabricated and characterized a single-mode birefringent anti-resonant hollow-core fibre. The birefringence was achieved by introducing capillary tubes of different thicknesses, thereby creating reduced symmetry in the structure. The measured group birefringence is in good agreement with the calculated group birefringence from simulations across the fibre guidance band within the telecommunications C-band. At 1550 nm, we measured a group birefringence of 4.4E-5, which corresponds to a phase birefringence of 2.5E-5. The measured loss of the fibre was 0.46 dB/m at 1550 nm. The measured polarisation extinction ratio of the fibre at 1550 nm was 23.1 dB (25.7 dB) along the x-(y-) polarisation axis, relating to an h-parameter of 9.8E-4 (5.3E-4)