Testing equality of variances in the analysis of repeated measurements

The problem of comparing the precisions of two instruments using repeated measurements can be cast as an extension of the Pitman-Morgan problem of testing equality of variances of a bivariate normal distribution. Hawkins (1981) decomposes the hypothesis of equal variances in this model into two subhypotheses for which simple tests exist. For the overall hypothesis he proposes to combine the tests of the subhypotheses using Fisher's method and empirically compares the component tests and their combination with the likelihood ratio test. In this paper an attempt is made to resolve some discrepancies and puzzling conclusions in Hawkins's study and to propose simple modifications.\ud \ud The new tests are compared to the tests discussed by Hawkins and to each other both in terms of the finite sample power (estimated by Monte Carlo simulation) and theoretically in terms of asymptotic relative efficiencies

An integral equation method for a boundary value problem arising in unsteady water wave problems

In this paper we consider the 2D Dirichlet boundary value problem for Laplace’s equation in a non-locally perturbed half-plane, with data in the space of bounded and continuous functions. We show uniqueness of solution, using standard Phragmen-Lindelof arguments. The main result is to propose a boundary integral equation formulation, to prove equivalence with the boundary value problem, and to show that the integral equation is well posed by applying a recent partial generalisation of the Fredholm alternative in Arens et al [J. Int. Equ. Appl. 15 (2003) pp. 1-35]. This then leads to an existence proof for the boundary value problem. Keywords. Boundary integral equation method, Water waves, Laplace’

11 W narrow linewidth laser source at 780nm for laser cooling and manipulation of Rubidium

We present a narrow linewidth continuous laser source with over 11 Watts of output power at 780nm, based on single-pass frequency doubling of an amplified 1560nm fibre laser with 36% efficiency. This source offers a combination of high power, simplicity, mode quality and stability. Without any active stabilization, the linewidth is measured to be below 10kHz. The fibre seed is tunable over 60GHz, which allows access to the D2 transitions in 87Rb and 85Rb, providing a viable high-power source for laser cooling as well as for large-momentum-transfer beamsplitters in atom interferometry. Sources of this type will pave the way for a new generation of high flux, high duty-cycle degenerate quantum gas experiments.Comment: 5 pages, 3 figure

Current-Induced Polarization and the Spin Hall Effect at Room Temperature

Electrically-induced electron spin polarization is imaged in n-type ZnSe epilayers using Kerr rotation spectroscopy. Despite no evidence for an electrically-induced internal magnetic field, current-induced in-plane spin polarization is observed with characteristic spin lifetimes that decrease with doping density. The spin Hall effect is also observed, indicated by an electrically-induced out-of-plane spin polarization with opposite sign for spins accumulating on opposite edges of the sample. The spin Hall conductivity is estimated as 3 +/- 1.5 Ohms**-1 m**-1/|e| at 20 K, which is consistent with the extrinsic mechanism. Both the current-induced spin polarization and the spin Hall effect are observed at temperatures from 10 K to 295 K.Comment: 5 pages, 4 figure

Internal magnetic fields in thin ZnSe epilayers

Strain induced spin-splitting is observed and characterized using pump-probe Kerr rotation spectroscopy in n-ZnSe epilayers grown on GaAs substrates. The spin-splitting energies are mapped out as a function of pump-probe separation, applied voltage, and temperature in a series of samples of varying epilayer thicknesses and compressive strain arising from epilayer-substrate lattice mismatch. The strain is independently quantified using photoluminescence and x-ray diffraction measurements. We observe that the magnitude of the spin splitting increases with applied voltage and temperature, and is highly crystal direction dependent, vanishing along [1 1-bar 0].Comment: 9 pages, 3 figure

Chandra Detects a Rapid Flare in the Gravitationally Lensed Mini-BALQSO RX J0911.4+0551

The mini Broad Absorption Line (BAL) quasar RX J0911.4+0551 was observed with the Advanced CCD Imaging Spectrometer (ACIS) of the Chandra X-ray Observatory for ~ 29 ks as part of a gravitational lens (GL) survey aimed at measuring time-delays. Timing analysis of the light-curve of the lensed image A2 shows a rapid flux variation with a duration of about 2000s. A Kolmogorov-Smirnov test shows that the probability that a constant-intensity source would produce the observed variability is less than ~ 0.2 percent. We discuss possible origins for the observed short-term X-ray variability. Our gravitational lens models for the RX J0911.4+0551 GL system predict a time-delay of less than a day between images A1 and A2. The rapid variability combined with the predicted short-time delay make RX J0911.4+0551 an ideal system to apply the GL method for estimating the Hubble constant. We describe the prospects of measuring H_0 within single X-ray observations of GL systems with relatively short time delays. Modeling of the spectrum of the mini-BAL quasar RX J0911.4+0551 suggests the presence of an intrinsic absorber. Partial covering models are slightly preferred over models that contain absorption due to intrinsic ionized or neutral gas.Comment: 17 pages, includes 5 figures, Accepted for publication in Ap

Exact static solutions for discrete ϕ4\phi^4 models free of the Peierls-Nabarro barrier: Discretized first integral approach

We propose a generalization of the discrete Klein-Gordon models free of the Peierls-Nabarro barrier derived in Nonlinearity {\bf 12}, 1373 (1999) and Phys. Rev. E {\bf 72}, 035602(R) (2005), such that they support not only kinks but a one-parameter set of exact static solutions. These solutions can be obtained iteratively from a two-point nonlinear map whose role is played by the discretized first integral of the static Klein-Gordon field, as suggested in J. Phys. A {\bf 38}, 7617 (2005). We then discuss some discrete $\phi^4$ models free of the Peierls-Nabarro barrier and identify for them the full space of available static solutions, including those derived recently in Phys. Rev. E {\bf 72} 036605 (2005) but not limited to them. These findings are also relevant to standing wave solutions of discrete nonlinear Schr{\"o}dinger models. We also study stability of the obtained solutions. As an interesting aside, we derive the list of solutions to the continuum $\phi^4$ equation that fill the entire two-dimensional space of parameters obtained as the continuum limit of the corresponding space of the discrete models.Comment: Accepted for publication in PRE; the M/S has been revised in line with the referee repor