Magnetism in the Square Kilometre Array Era

The unprecedented sensitivity, angular resolution and broad bandwidth coverage of Square Kilometre Array (SKA) radio polarimetric observations will allow us to address many long-standing mysteries in cosmic magnetism science. I will highlight the unique capabilities of the SKA to map the warm hot intergalactic medium, reveal detailed 3-dimensional structures of magnetic fields in local galaxies and trace the redshift evolution of galactic magnetic fields.Comment: 4 pages, Invited paper, Proceedings of FM8 "New Insights in Extragalactic Magnetic Fields", XXXth General Assembly of the IAU, Vienna, August 20-31, 201

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

Empirical Study of Simulated Two-planet Microlensing Event

We undertake the first study of two-planet microlensing models recovered from simulations of microlensing events generated by realistic multi-planet systems in which 292 planetary events including 16 two-planet events were detected from 6690 simulated light curves. We find that when two planets are recovered, their parameters are usually close to those of the two planets in the system most responsible for the perturbations. However, in one of the 16 examples, the apparent mass of both detected planets was more than doubled by the unmodeled influence of a third, massive planet. This fraction is larger than, but statistically consistent with, the roughly 1.5% rate of serious mass errors due to unmodeled planetary companions for the 274 cases from the same simulation in which a single planet is recovered. We conjecture that an analogous effect due to unmodeled stellar companions may occur more frequently. For seven out of 23 cases in which two planets in the system would have been detected separately, only one planet was recovered because the perturbations due to the two planets had similar forms. This is a small fraction (7/274) of all recovered single-planet models, but almost a third of all events that might plausibly have led to two-planet models. Still, in these cases, the recovered planet tends to have parameters similar to one of the two real planets most responsible for the anomaly.Comment: 21 pages, 9 figures, 2 tables; submitted to ApJ; for a short video introducing the key results, see https://www.youtube.com/watch?v=qhK4a6sbfO

A New Photometric Model of the Galactic Bar using Red Clump Giants

We present a study of the luminosity density distribution of the Galactic bar using number counts of red clump giants (RCGs) from the OGLE-III survey. The data were recently published by Nataf et al. (2013) for 9019 fields towards the bulge and have $2.94\times 10^6$ RC stars over a viewing area of $90.25 \,\textrm{deg}^2$. The data include the number counts, mean distance modulus ($\mu$), dispersion in $\mu$ and full error matrix, from which we fit the data with several tri-axial parametric models. We use the Markov Chain Monte Carlo (MCMC) method to explore the parameter space and find that the best-fit model is the $E_3$ model, with the distance to the GC is 8.13 kpc, the ratio of semi-major and semi-minor bar axis scale lengths in the Galactic plane $x_{0},y_{0}$, and vertical bar scale length $z_0$, is $x_0:y_0:z_0 \approx 1.00:0.43:0.40$ (close to being prolate). The scale length of the stellar density profile along the bar's major axis is $\sim$ 0.67 kpc and has an angle of $29.4^\circ$, slightly larger than the value obtained from a similar study based on OGLE-II data. The number of estimated RC stars within the field of view is $2.78 \times 10^6$, which is systematically lower than the observed value. We subtract the smooth parametric model from the observed counts and find that the residuals are consistent with the presence of an X-shaped structure in the Galactic centre, the excess to the estimated mass content is $\sim 5.8$. We estimate the total mass of the bar is $\sim 1.8 \times 10^{10} M_\odot$. Our results can be used as a key ingredient to construct new density models of the Milky Way and will have implications on the predictions of the optical depth to gravitational microlensing and the patterns of hydrodynamical gas flow in the Milky Way.Comment: 15 pages, 6 figures, 4 tables. MNRAS accepte

Approximate solutions of stochastic differential delay equations with Markovian switching

Our main aim is to develop the existence theory for the solutions to stochastic differential delay equations with Markovian switching (SDDEwMSs) and to establish the convergence theory for the Euler-Maruyama approximate solutions under the local Lipschitz condition. As an application, our results are used to discuss a stochastic delay population system with Markovian switching

Robustness of Majorana Modes and Minigaps in a Spin-Orbit-Coupled Semiconductor-Superconductor Heterostructure

We study the robustness of Majorana zero energy modes and minigaps of quasiparticle excitations in a vortex by numerically solving Bogoliubov-deGennes equations in a heterostructure composed of an \textit{s} -wave superconductor, a spin-orbit-coupled semiconductor thin film, and a magnetic insulator. This heterostructure was proposed recently as a platform for observing non-Abelian statistics and performing topological quantum computation. The dependence of the Majorana zero energy states and the minigaps on various physics parameters (Zeeman field, chemical potential, spin-orbit coupling strength) is characterized. We find the minigaps depend strongly on the spin-orbit coupling strength. In certain parameter region, the minigaps are linearly proportional to the \textit{s}-wave superconducting pairing gap $\Delta_{s}$, which is very different from the $\Delta_{s}^{2}$ dependence in a regular \textit{s-} or \textit{\p}-wave superconductor. We characterize the zero energy chiral edge state at the boundary and calculate the STM signal in the vortex core that shows a pronounced zero energy peak. We show that the Majorana zero energy states are robust in the presence of various types of impurities. We find the existence of impurity potential may increase the minigaps and thus benefit topological quantum computation.Comment: 11 pages, 15 figure

The Effect of Buying versus Leasing on Entry Deterrence

Monopoly; Entry Deterrence

Site evaluation for laser satellite-tracking stations

Twenty-six locations for potential laser satellite-tracking stations, four of them actually already occupied in this role, are reviewed in terms of their known local and regional geology and geophysics. The sites are also considered briefly in terms of weather and operational factors. Fifteen of the sites qualify as suitable for a stable station whose motions are likely to reflect only gross plate motion. The others, including two of the present laser station sites (Arequipa and Athens), fail to qualify unless extra monitoring schemes can be included, such as precise geodetic surveying of ground deformation

Stabilisation and destabilisation of nonlinear differential equations by noise

This paper considers the stabilisation and destabilisa- tion by a Brownian noise perturbation which preserves the equilibrium of the ordinary dierential equation x0(t) = f(x(t)). In an extension of earlier work, we lift the restriction that f obeys a global linear bound, and show that when f is locally Lipschitz, a function g can always be found so that the noise perturbation g(X(t)) dB(t) either stabilises an unstable equilibrium, or destabilises a stable equilibrium. When the equilibrium of the deterministic equation is non{hyperbolic, we show that a non{hyperbolic perturbation suffices to change the stability properties of the solution.