Design and operation of an autosampler controlled flow-injection preconcentration system for lead determination by flame atomic absorption spectrometry

Flow-injection manifolds are described which allow the preconcentration of lead for flame atomic absorption determinations, using columns contained within the sample loop of an injection valve. An interface was designed which allowed the valves and pump in the system to be controlled by an autosampler which enabled precise timing of preconcentration and elution steps. The effects of sample flow rate, buffer pH and buffer type for preconcentration and eluent concentration and flow rate were investigated in order to obtain optimum performance of the system. A 50-times improvement in detection limits over conventional sample introduction was obtained for a sample volume of approximately 12 ml, preconcentrated for 150 s. The injection of eluent, as opposed to the use of a continuously flowing eluent stream, enabled this reagent to be conserved

Tests of Bayesian Model Selection Techniques for Gravitational Wave Astronomy

The analysis of gravitational wave data involves many model selection problems. The most important example is the detection problem of selecting between the data being consistent with instrument noise alone, or instrument noise and a gravitational wave signal. The analysis of data from ground based gravitational wave detectors is mostly conducted using classical statistics, and methods such as the Neyman-Pearson criteria are used for model selection. Future space based detectors, such as the \emph{Laser Interferometer Space Antenna} (LISA), are expected to produced rich data streams containing the signals from many millions of sources. Determining the number of sources that are resolvable, and the most appropriate description of each source poses a challenging model selection problem that may best be addressed in a Bayesian framework. An important class of LISA sources are the millions of low-mass binary systems within our own galaxy, tens of thousands of which will be detectable. Not only are the number of sources unknown, but so are the number of parameters required to model the waveforms. For example, a significant subset of the resolvable galactic binaries will exhibit orbital frequency evolution, while a smaller number will have measurable eccentricity. In the Bayesian approach to model selection one needs to compute the Bayes factor between competing models. Here we explore various methods for computing Bayes factors in the context of determining which galactic binaries have measurable frequency evolution. The methods explored include a Reverse Jump Markov Chain Monte Carlo (RJMCMC) algorithm, Savage-Dickie density ratios, the Schwarz-Bayes Information Criterion (BIC), and the Laplace approximation to the model evidence. We find good agreement between all of the approaches.Comment: 11 pages, 6 figure

Theory of Spike Spiral Waves in a Reaction-Diffusion System

We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in Gray-Scott model. We derive the kinematic relations describing the shape of this spiral and find the dependence of its main parameters on the control parameters. The theory does not rely on the specific features of Gray-Scott model and thus is expected to be applicable to a broad range of reaction-diffusion systems.Comment: 4 pages (REVTeX), 2 figures (postscript), submitted to Phys. Rev. Let

Validation and Calibration of Models for Reaction-Diffusion Systems

Space and time scales are not independent in diffusion. In fact, numerical simulations show that different patterns are obtained when space and time steps ($\Delta x$ and $\Delta t$) are varied independently. On the other hand, anisotropy effects due to the symmetries of the discretization lattice prevent the quantitative calibration of models. We introduce a new class of explicit difference methods for numerical integration of diffusion and reaction-diffusion equations, where the dependence on space and time scales occurs naturally. Numerical solutions approach the exact solution of the continuous diffusion equation for finite $\Delta x$ and $\Delta t$, if the parameter $\gamma_N=D \Delta t/(\Delta x)^2$ assumes a fixed constant value, where $N$ is an odd positive integer parametrizing the alghorithm. The error between the solutions of the discrete and the continuous equations goes to zero as $(\Delta x)^{2(N+2)}$ and the values of $\gamma_N$ are dimension independent. With these new integration methods, anisotropy effects resulting from the finite differences are minimized, defining a standard for validation and calibration of numerical solutions of diffusion and reaction-diffusion equations. Comparison between numerical and analytical solutions of reaction-diffusion equations give global discretization errors of the order of $10^{-6}$ in the sup norm. Circular patterns of travelling waves have a maximum relative random deviation from the spherical symmetry of the order of 0.2%, and the standard deviation of the fluctuations around the mean circular wave front is of the order of $10^{-3}$.Comment: 33 pages, 8 figures, to appear in Int. J. Bifurcation and Chao

Detection of weak gravitational lensing distortions of distant galaxies by cosmic dark matter at large scales

Most of the matter in the universe is not luminous and can be observed directly only through its gravitational effect. An emerging technique called weak gravitational lensing uses background galaxies to reveal the foreground dark matter distribution on large scales. Light from very distant galaxies travels to us through many intervening overdensities which gravitationally distort their apparent shapes. The observed ellipticity pattern of these distant galaxies thus encodes information about the large-scale structure of the universe, but attempts to measure this effect have been inconclusive due to systematic errors. We report the first detection of this ``cosmic shear'' using 145,000 background galaxies to reveal the dark matter distribution on angular scales up to half a degree in three separate lines of sight. The observed angular dependence of this effect is consistent with that predicted by two leading cosmological models, providing new and independent support for these models.Comment: 18 pages, 5 figures: To appear in Nature. (This replacement fixes tex errors and typos.

Synoptic Sky Surveys and the Diffuse Supernova Neutrino Background: Removing Astrophysical Uncertainties and Revealing Invisible Supernovae

The cumulative (anti)neutrino production from all core-collapse supernovae within our cosmic horizon gives rise to the diffuse supernova neutrino background (DSNB), which is on the verge of detectability. The observed flux depends on supernova physics, but also on the cosmic history of supernova explosions; currently, the cosmic supernova rate introduces a substantial (+/-40%) uncertainty, largely through its absolute normalization. However, a new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming online, and will map the sky in the time domain with unprecedented depth, completeness, and dynamic range. We show that these surveys will obtain the cosmic supernova rate by direct counting, in an unbiased way and with high statistics, and thus will allow for precise predictions of the DSNB. Upcoming sky surveys will substantially reduce the uncertainties in the DSNB source history to an anticipated +/-5% that is dominated by systematics, so that the observed high-energy flux thus will test supernova neutrino physics. The portion of the universe (z < 1) accessible to upcoming sky surveys includes the progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event rate. We show that precision determination of the (optically detected) cosmic supernova history will also make the DSNB into a strong probe of an extra flux of neutrinos from optically invisible supernovae, which may be unseen either due to unexpected large dust obscuration in host galaxies, or because some core-collapse events proceed directly to black hole formation and fail to give an optical outburst.Comment: 11 pages, 6 figure

Towards Precision LSST Weak-Lensing Measurement - I: Impacts of Atmospheric Turbulence and Optical Aberration

The weak-lensing science of the LSST project drives the need to carefully model and separate the instrumental artifacts from the intrinsic lensing signal. The dominant source of the systematics for all ground based telescopes is the spatial correlation of the PSF modulated by both atmospheric turbulence and optical aberrations. In this paper, we present a full FOV simulation of the LSST images by modeling both the atmosphere and the telescope optics with the most current data for the telescope specifications and the environment. To simulate the effects of atmospheric turbulence, we generated six-layer phase screens with the parameters estimated from the on-site measurements. For the optics, we combined the ray-tracing tool ZEMAX and our simulated focal plane data to introduce realistic aberrations and focal plane height fluctuations. Although this expected flatness deviation for LSST is small compared with that of other existing cameras, the fast f-ratio of the LSST optics makes this focal plane flatness variation and the resulting PSF discontinuities across the CCD boundaries significant challenges in our removal of the systematics. We resolve this complication by performing PCA CCD-by-CCD, and interpolating the basis functions using conventional polynomials. We demonstrate that this PSF correction scheme reduces the residual PSF ellipticity correlation below 10^-7 over the cosmologically interesting scale. From a null test using HST/UDF galaxy images without input shear, we verify that the amplitude of the galaxy ellipticity correlation function, after the PSF correction, is consistent with the shot noise set by the finite number of objects. Therefore, we conclude that the current optical design and specification for the accuracy in the focal plane assembly are sufficient to enable the control of the PSF systematics required for weak-lensing science with the LSST.Comment: Accepted to PASP. High-resolution version is available at http://dls.physics.ucdavis.edu/~mkjee/LSST_weak_lensing_simulation.pd

Galaxy Peculiar Velocities From Large-Scale Supernova Surveys as a Dark Energy Probe

Upcoming imaging surveys such as the Large Synoptic Survey Telescope will repeatedly scan large areas of sky and have the potential to yield million-supernova catalogs. Type Ia supernovae are excellent standard candles and will provide distance measures that suffice to detect mean pairwise velocities of their host galaxies. We show that when combining these distance measures with photometric redshifts for either the supernovae or their host galaxies, the mean pairwise velocities of the host galaxies will provide a dark energy probe which is competitive with other widely discussed methods. Adding information from this test to type Ia supernova photometric luminosity distances from the same experiment, plus the cosmic microwave background power spectrum from the Planck satellite, improves the Dark Energy Task Force Figure of Merit by a factor of 1.8. Pairwise velocity measurements require no additional observational effort beyond that required to perform the traditional supernova luminosity distance test, but may provide complementary constraints on dark energy parameters and the nature of gravity. Incorporating additional spectroscopic redshift follow-up observations could provide important dark energy constraints from pairwise velocities alone. Mean pairwise velocities are much less sensitive to systematic redshift errors than the luminosity distance test or weak lensing techniques, and also are only mildly affected by systematic evolution of supernova luminosity.Comment: 18 pages; 4 figures; 4 tables; replaced to match the accepted versio