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

Annular electroconvection with shear

We report experiments on convection driven by a radial electrical force in suspended annular smectic A liquid crystal films. In the absence of an externally imposed azimuthal shear, a stationary one-dimensional (1D) pattern consisting of symmetric vortex pairs is formed via a supercritical transition at the onset of convection. Shearing reduces the symmetries of the base state and produces a traveling 1D pattern whose basic periodic unit is a pair of asymmetric vortices. For a sufficiently large shear, the primary bifurcation changes from supercritical to subcritical. We describe measurements of the resulting hysteresis as a function of the shear at radius ratio $\eta \sim 0.8$. This simple pattern forming system has an unusual combination of symmetries and control parameters and should be amenable to quantitative theoretical analysis.Comment: 12 preprint pages, 3 figures in 2 parts each. For more info, see http://mobydick.physics.utoronto.c

Vacuum discharge as a possible source of gamma-ray bursts

We propose that spontaneous particle--anti-particle pair creations from the discharged vacuum caused by the strong interactions in dense matter are major sources of $\gamma$-ray bursts. Two neutron star collisions or black hole-neutron star mergers at cosmological distance could produce a compact object with its density exceeding the critical density for pair creations. The emitted anti-particles annihilate with corresponding particles at the ambient medium. This releases a large amount of energy. We discuss the spontaneous $p\bar{p}$ pair creations within two neutron star collision and estimate the exploded energy from $p\bar{p}$ annihilation processes. The total energy could be around $10^{51} - 10^{53}$ erg depending on the impact parameter of colliding neutron stars. This value fits well into the range of the initial energy of the most energetic $\gamma$-ray bursts.Comment: 12 pages, Latex, 2 figures included; replaced by the revised version, Int. J. Mod. Phys. E in pres

Fractal Characterizations of MAX Statistical Distribution in Genetic Association Studies

Two non-integer parameters are defined for MAX statistics, which are maxima of $d$ simpler test statistics. The first parameter, $d_{MAX}$, is the fractional number of tests, representing the equivalent numbers of independent tests in MAX. If the $d$ tests are dependent, $d_{MAX} < d$. The second parameter is the fractional degrees of freedom $k$ of the chi-square distribution $\chi^2_k$ that fits the MAX null distribution. These two parameters, $d_{MAX}$ and $k$, can be independently defined, and $k$ can be non-integer even if $d_{MAX}$ is an integer. We illustrate these two parameters using the example of MAX2 and MAX3 statistics in genetic case-control studies. We speculate that $k$ is related to the amount of ambiguity of the model inferred by the test. In the case-control genetic association, tests with low $k$ (e.g. $k=1$) are able to provide definitive information about the disease model, as versus tests with high $k$ (e.g. $k=2$) that are completely uncertain about the disease model. Similar to Heisenberg's uncertain principle, the ability to infer disease model and the ability to detect significant association may not be simultaneously optimized, and $k$ seems to measure the level of their balance

Metallic state in La-doped YBa2_2Cu3_3Oy_y thin films with nn-type charge carriers

We report hole and electron doping in La-doped YBa$_2$Cu$_3$O$_y$(YBCO) thin films synthesized by pulsed laser deposition technique and subsequent \emph{in-situ} postannealing in oxygen ambient and vaccum. The $n$-type samples show a metallic behavior below the Mott limit and a high carrier density of $\sim2.8$ $\times$ 10$^{21}$ cm$^{-3}$ at room temperature (\emph{T}) at the optimally reduced condition. The in-plane resistivity ($\rho$$_{ab}$) of the $n$-type samples exhibits a quadratic \emph{T} dependence in the moderate-\emph{T} range and shows an anomaly at a relatively higher \emph{T} probably related to pseudogap formation analogous to underdoped Nd$_{2-x}$Ce$_x$CuO$_4$ (NCCO). Furthermore, $\rho$$_{ab}$(T), \emph{T}$_c$ and \emph{T} with minimum resistivity (\emph{T}$_{min}$) were investigated in both $p$- and $n$-side. The present results reveal the $n$-$p$ asymmetry (symmetry) within the metallic-state region in an underdoped cuprate and suggest the potential toward ambipolar superconductivity in a single YBCO system.Comment: 4 pages, 5 figure

Electroconvection in a Suspended Fluid Film: A Linear Stability Analysis

A suspended fluid film with two free surfaces convects when a sufficiently large voltage is applied across it. We present a linear stability analysis for this system. The forces driving convection are due to the interaction of the applied electric field with space charge which develops near the free surfaces. Our analysis is similar to that for the two-dimensional B\'enard problem, but with important differences due to coupling between the charge distribution and the field. We find the neutral stability boundary of a dimensionless control parameter ${\cal R}$ as a function of the dimensionless wave number ${\kappa}$. ${\cal R}$, which is proportional to the square of the applied voltage, is analogous to the Rayleigh number. The critical values ${{\cal R}_c}$ and ${\kappa_c}$ are found from the minimum of the stability boundary, and its curvature at the minimum gives the correlation length ${\xi_0}$. The characteristic time scale ${\tau_0}$, which depends on a second dimensionless parameter ${\cal P}$, analogous to the Prandtl number, is determined from the linear growth rate near onset. ${\xi_0}$ and ${\tau_0}$ are coefficients in the Ginzburg-Landau amplitude equation which describes the flow pattern near onset in this system. We compare our results to recent experiments.Comment: 36 pages, 7 included eps figures, submitted to Phys Rev E. For more info, see http://mobydick.physics.utoronto.ca

The Luminosity Function of high-redshift QSOs - A combined analysis of GOODS and SDSS

Aims: In this work the luminosity function of QSOs is measured in the redshift range 3.5<z<5.2 for the absolute magnitude interval -21<M_{145}<-28. The determination of the faint end of the luminosity function at these redshifts provides important constraints on models of joint evolution of galaxies and AGNs. Methods: We have defined suitable criteria to select faint QSOs in the GOODS fields, checking in detail their effectiveness and completeness. Spectroscopic follow-up of the resulting QSO candidates has been carried out. The confirmed sample of faint QSOs is compared with a brighter one derived from the SDSS. We have used a Monte-Carlo technique to estimate the properties of the luminosity function, checking various parameterizations for its shape and evolution. Results: Models based on Pure Density Evolution show better agreement with observation than models based on Pure Luminosity Evolution. However a different break magnitude with respect to z~2.1 is required at 3.5<z<5.2. Models with a steeper faint end score a higher probability. We do not find any evidence for a flattening of the bright end at redshift z>3.5. Conclusions: The estimated space density evolution of QSOs indicates a suppression of the formation and/or feeding of Supermassive Black Holes at these redshifts. The QSO contribution to the UV background is insufficient to ionize the IGM at 3.5<z<5.2.Comment: 17 pages, 13 ps figures, A&A accepted. Updated to journal versio