Topology of the Galaxy Distribution in the Hubble Deep Fields

We have studied topology of the distribution of the high redshift galaxies identified in the Hubble Deep Field (HDF) North and South. The two-dimensional genus is measured from the projected distributions of the HDF galaxies at angular scales from $3.8''$ to $6.1''$. We have also divided the samples into three redshift slices with roughly equal number of galaxies using photometric redshifts to see possible evolutionary effects on the topology. The genus curve of the HDF North clearly indicates clustering of galaxies over the Poisson distribution while the clustering is somewhat weaker in the HDF South. This clustering is mainly due to the nearer galaxies in the samples. We have also found that the genus curve of galaxies in the HDF is consistent with the Gaussian random phase distribution with no significant redshift dependence.Comment: 14 pages, 4 figures, submitted to Ap

The Fast Multipole Method and Point Dipole Moment Polarizable Force Fields

We present an implementation of the fast multipole method for computing coulombic electrostatic and polarization forces from polarizable force-fields based on induced point dipole moments. We demonstrate the expected $O(N)$ scaling of that approach by performing single energy point calculations on hexamer protein subunits of the mature HIV-1 capsid. We also show the long time energy conservation in molecular dynamics at the nanosecond scale by performing simulations of a protein complex embedded in a coarse-grained solvent using a standard integrator and a multiple time step integrator. Our tests show the applicability of FMM combined with state-of-the-art chemical models in molecular dynamical systems.Comment: 11 pages, 8 figures, accepted by J. Chem. Phy

Experiments on single oblique laminar-instability waves in a boundary layer: Introduction, growth, and transition

The laminar-turbulent transition in an incompressible flat-plate boundary layer was studied experimentally by using a spanwise array of computer-controlled surface heating elements to generate small disturbances. Oblique Tollmien-Schlichting waves were successfully introduced, and their downstream development into the intermittent region was studied using flush-mounted hot-film wall-shear sensors and dye flow visualization. Comparative studies of the development of single oblique waves were made for various wave angles, frequencies, and amplitudes. As these single oblique waves grew and began to break down, higher harmonics and subharmonics appeared in the wall shear. The amplitude of the subharmonic component decreased rapidly with increasing oblique-wave angle, so that a 10 degrees oblique wave had a subharmonic amplitude an order of magnitude below that for a two-dimensional (2-D) wave. Thus, the nonlinear mechanism that produces the subharmonic is affected by the symmetry of the primary wave. Intermittency measurements, carried out farther downstream, show that a 2-D wave is most effective in moving the transition point upstream, for a given power input

Error Estimates for Measurements of Cosmic Shear

In the very near future, weak lensing surveys will map the projected density of the universe in an unbiased way over large regions of the sky. In order to interpret the results of studies it is helpful to develop an understanding of the errors associated with quantities extracted from the observations. In a generalization of one of our earlier works, we present estimators of the cumulants and cumulant correlators of the weak lensing convergence field, and compute the variance associated with these estimators. By restricting ourselves to so-called compensated filters we are able to derive quite simple expressions for the errors on these estimates. We also separate contributions from cosmic variance, shot noise and intrinsic ellipticity of the source galaxies.Comment: 12 pages, including 5 figures, uses mn.sty. Substantially revised version accepted by MNRA

Effects of Foreground Contamination on the Cosmic Microwave Background Anisotropy Measured by MAP

We study the effects of diffuse Galactic, far-infrared extragalactic source, and radio point source emission on the cosmic microwave background (CMB) anisotropy data anticipated from the MAP experiment. We focus on the correlation function and genus statistics measured from mock MAP foreground-contaminated CMB anisotropy maps generated in a spatially-flat cosmological constant dominated cosmological model. Analyses of the simulated MAP data at 90 GHz (0.3 deg FWHM resolution smoothed) show that foreground effects on the correlation function are small compared with cosmic variance. However, the Galactic emission, even just from the region with |b| > 20 deg, significantly affects the topology of CMB anisotropy, causing a negative genus shift non-Gaussianity signal. Given the expected level of cosmic variance, this effect can be effectively reduced by subtracting existing Galactic foreground emission models from the observed data. IRAS and DIRBE far-infrared extragalactic sources have little effect on the CMB anisotropy. Radio point sources raise the amplitude of the correlation function considerably on scales below 0.5 deg. Removal of bright radio sources above a 5 \sigma detection limit effectively eliminates this effect. Radio sources also result in a positive genus curve asymmetry (significant at 2 \sigma) on 0.5 deg scales. Accurate radio point source data is essential for an unambiguous detection of CMB anisotropy non-Gaussianity on these scales. Non-Gaussianity of cosmological origin can be detected from the foreground-subtracted CMB anisotropy map at the 2 \sigma level if the measured genus shift parameter |\Delta\nu| >= 0.02 (0.04) or if the measured genus asymmetry parameter |\Delta g| >= 0.03 (0.08) on a 0.3 (1.0) deg FWHM scale.Comment: 26 pages, 7 figures, Accepted for Publication in Astrophysical Journal (Some sentences and figures modified

Topology of Neutral Hydrogen Within the Small Magellanic Cloud

In this paper, genus statistics have been applied to an HI column density map of the Small Magellanic Cloud in order to study its topology. To learn how topology changes with the scale of the system, we provide the study of topology for column density maps at varying resolution. To evaluate the statistical error of the genus we randomly reassign the phases of the Fourier modes while keeping the amplitudes. We find, that at the smallest scales studied ($40 {pc}\leq\lambda\leq 80 {pc}$) the genus shift is in all regions negative, implying a clump topology. At the larger scales ($110 {pc}\leq\lambda\leq 250 {pc}$) the topology shift is detected to be negative in 4 cases and positive (``swiss cheese'' topology) in 2 cases. In 4 regions there is no statistically significant topology shift at large scales

Testing for Non-Gaussianity in the Wilkinson Microwave Anisotropy Probe Data: Minkowski Functionals and the Length of the Skeleton

The three Minkowski functionals and the recently defined length of the skeleton are estimated for the co-added first-year Wilkinson Microwave Anisotropy Probe (WMAP) data and compared with 5000 Monte Carlo simulations, based on Gaussian fluctuations with the a-priori best-fit running-index power spectrum and WMAP-like beam and noise properties. Several power spectrum-dependent quantities, such as the number of stationary points, the total length of the skeleton, and a spectral parameter, gamma, are also estimated. While the area and length Minkowski functionals and the length of the skeleton show no evidence for departures from the Gaussian hypothesis, the northern hemisphere genus has a chi^2 that is large at the 95% level for all scales. For the particular smoothing scale of 3.40 degrees FWHM it is larger than that found in 99.5% of the simulations. In addition, the WMAP genus for negative thresholds in the northern hemisphere has an amplitude that is larger than in the simulations with a significance of more than 3 sigma. On the smallest angular scales considered, the number of extrema in the WMAP data is high at the 3 sigma level. However, this can probably be attributed to the effect of point sources. Finally, the spectral parameter gamma is high at the 99% level in the northern Galactic hemisphere, while perfectly acceptable in the southern hemisphere. The results provide strong evidence for the presence of both non-Gaussian behavior and an unexpected power asymmetry between the northern and southern hemispheres in the WMAP data.Comment: 17 pages, 10 figures, accepted for publication in Ap

A low CMB variance in the WMAP data

We have estimated the CMB variance from the three-year WMAP data, finding a value which is significantly lower than the one expected from Gaussian simulations using the WMAP best-fit cosmological model, at a significance level of 98.7 per cent. This result is even more prominent if we consider only the north ecliptic hemisphere (99.8 per cent). Different analyses have been performed in order to identify a possible origin for this anomaly. In particular we have studied the behaviour of single radiometers and single year data as well as the effect of residual foregrounds and 1/f noise, finding that none of these possibilities can explain the low value of the variance. We have also tested the effect of varying the cosmological parameters, finding that the estimated CMB variance tends to favour higher values of $n_s$ than the one of the WMAP best-fit model. In addition, we have also tested the consistency between the estimated CMB variance and the actual measured CMB power spectrum of the WMAP data, finding a strong discrepancy. A possible interpretation of this result could be a deviation from Gaussianity and/or isotropy of the CMB.Comment: 13 pages, 5 figures. Some new tests added. Section 5 largely modified. Accepted for publication in MNRA

On Recovering the Nonlinear Bias Function from Counts in Cells Measurements

We present a simple and accurate method to constrain galaxy bias based on the distribution of counts in cells. The most unique feature of our technique is that it is applicable to non-linear scales, where both dark matter statistics and the nature of galaxy bias are fairly complex. First, we estimate the underlying continuous distribution function from precise counts-in-cells measurements assuming local Poisson sampling. Then a robust, non-parametric inversion of the bias function is recovered from the comparison of the cumulative distributions in simulated dark matter and galaxy catalogs. Obtaining continuous statistics from the discrete counts is the most delicate novel part of our recipe. It corresponds to a deconvolution of a (Poisson) kernel. For this we present two alternatives: a model independent algorithm based on Richardson-Lucy iteration, and a solution using a parametric skewed lognormal model. We find that the latter is an excellent approximation for the dark matter distribution, but the model independent iterative procedure is more suitable for galaxies. Tests based on high resolution dark matter simulations and corresponding mock galaxy catalogs show that we can reconstruct the non-linear bias function down to highly non-linear scales with high precision in the range of $-1 \le \delta \le 5$. As far as the stochasticity of the bias, we have found a remarkably simple and accurate formula based on Poisson noise, which provides an excellent approximation for the scatter around the mean non-linear bias function. In addition we have found that redshift distortions have a negligible effect on our bias reconstruction, therefore our recipe can be safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap