Optimal Moments for the Analysis of Peculiar Velocity Surveys

We present a new method for the analysis of peculiar velocity surveys which removes contributions to velocities from small scale, nonlinear velocity modes while retaining information about large scale motions. Our method utilizes Karhunen--Lo\`eve methods of data compression to construct a set of moments out of the velocities which are minimally sensitive to small scale power. The set of moments are then used in a likelihood analysis. We develop criteria for the selection of moments, as well as a statistic to quantify the overall sensitivity of a set of moments to small scale power. Although we discuss our method in the context of peculiar velocity surveys, it may also prove useful in other situations where data filtering is required.Comment: 25 Pages, 3 figures. Submitted to Ap

Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection

We investigate the utility of the convex hull of many Lagrangian tracers to analyze transport properties of turbulent flows with different anisotropy. In direct numerical simulations of statistically homogeneous and stationary Navier-Stokes turbulence, neutral fluid Boussinesq convection, and MHD Boussinesq convection a comparison with Lagrangian pair dispersion shows that convex hull statistics capture the asymptotic dispersive behavior of a large group of passive tracer particles. Moreover, convex hull analysis provides additional information on the sub-ensemble of tracers that on average disperse most efficiently in the form of extreme value statistics and flow anisotropy via the geometric properties of the convex hulls. We use the convex hull surface geometry to examine the anisotropy that occurs in turbulent convection. Applying extreme value theory, we show that the maximal square extensions of convex hull vertices are well described by a classic extreme value distribution, the Gumbel distribution. During turbulent convection, intermittent convective plumes grow and accelerate the dispersion of Lagrangian tracers. Convex hull analysis yields information that supplements standard Lagrangian analysis of coherent turbulent structures and their influence on the global statistics of the flow.Comment: 18 pages, 10 figures, preprin

Interpreting New Data on Large Scale Bulk Flows

We study the implications of a recent estimate of the bulk flow of a sample of galaxies containing supernovae type Ia by Riess, Press, and Kirshner. We find that their results are quite consistent with power spectra from several currently popular models of structure formation, but that the sample is as yet too sparse to put significant constraints on the power spectrum. We compare this new result with that of Lauer and Postman, with which there is apparent disagreement. We find that for the power spectra we consider, the difference in window functions between the two samples used for the measurements results in a low level of expected correlation between the estimated bulk flows. We calculate a $\chi^2$ for the two measurements taken together and find that their lack of agreement tends to disfavor spectra with excessive power on large scales, but not at a level sufficient to rule them out. A sample consisting of other SN type Ia's found in the Asiago catalog is used to study how the sensitivity of the method used by RPK will improve with increasing sample size. We conclude that the local group motion should be able to be determined with a sample of $\sim 100$ SN Ia light curve shapes.Comment: 13 pages, 2 figures included in a self-unpacking uudecoded gzipped postscript file. We changed some of the power spectra analyzed and expanded the discussion. The postscript file is available at http://pupgga.princeton.edu/disk20/anonymous/feldman/bflows.p

Ranks of quadratic twists of elliptic curves

We report on a large-scale project to investigate the ranks of elliptic curves in a quadratic twist family, focussing on the congruent number curve. Our methods to exclude candidate curves include 2-Selmer, 4-Selmer, and 8-Selmer tests, the use of the Guinand-Weil explicit formula, and even 3-descent in a couple of cases. We find that rank 6 quadratic twists are reasonably common (though still quite difficult to find), while rank 7 twists seem much more rare. We also describe our inability to find a rank 8 twist, and discuss how our results here compare to some predictions of rank growth vis-à-vis conductor. Finally we explicate a heuristic of Granville, which when interpreted judiciously could predict that 7 is indeed the maximal rank in this quadratic twist family

Dynamically triggered star formation in giant molecular clouds

A Lagrangian, particle-based numerical method (tree code gravity plus smoothed particle hydrodynamics) was used to simulate clump-clump collisions occurring within GMCs. The collisions formed shock-compressed layers, out of which condensed approximately co-planar protostellar discs of 7-60 solar masses and 500-1000AU radius. Binary and multiple systems were the usual final state. Lower mass objects were also produced, but commonly underwent disruption or merger. Such objects occasionally survived by being ejected via a three-body slingshot event resulting from an encounter with a binary system. Varying the impact parameter, b, altered the processes by which the protostellar systems formed. At low b a single central disc formed initially, and was then spun-up by an accretion flow, causing it to produce secondaries via rotational instabilities. At mid b the shocked layer w hich formed initially broke up into fragments, and discs were then formed via fragment merger. At large b single objects formed within the compressed leading edge of each clump. These became unbound from each other as b was increased further. The effect of changing numerical factors was examined by : (i) colliding clumps which had been re-oriented before the collision (thus altering the initial particle noise), and (ii) by quadrupling the number of particles in each clump (thus increasing the resolution of the simulation). Both changes were found to affect the small-scale details of a collision, but leave the large scale morphology largely unaltered. It was concluded that clump-clump collisions provide a natural mechanism by which multiple protostellar systems may form.Comment: 15 pages, 12 low resolution figures in 50 files, accepted by MNRA

Preliminary Results from an Experimental Assessment of a Natural Laminar Flow Design Method

A 5.2% scale semispan model of the new Common Research Model with Natural Laminar Flow (CRM-NLF) was tested in the National Transonic Facility (NTF) at the NASA Langley Research Center. The model was tested at transonic cruise flight conditions with Reynolds numbers based on mean aerodynamic chord ranging from 10 to 30 million. The goal of the test was to experimentally validate a new design method, referred to as Crossflow Attenuated NLF (CATNLF), which shapes airfoils to have pressure distributions that delay transition on wings with high sweep and Reynolds numbers. Additionally, the test aimed to characterize the NTF laminar flow testing capabilities, as well as establish best practices for laminar flow wind tunnel testing. Preliminary results regarding the first goal of validating the new design method are presented in this paper. Experimental data analyzed in this assessment include surface pressure data and transition images. The surface pressure data acquired during the test agree well with computational fluid dynamics (CFD) results. Transition images at a variety of Reynolds numbers and angles of attack are presented and compared to computational transition predictions. The experimental data are used to assess transition due to a turbulent attachment line, as well as crossflow and Tollmien-Schlichting modal instabilities. Preliminary results suggest the CATNLF design method is successful at delaying transition on wings with high sweep. Initial analysis of the transition front images showed transition Reynolds numbers that exceed historic experimental values at similar sweep angles. , section lif

A New Approach to Probing Large Scale Power with Peculiar Velocities

We propose a new strategy to probe the power spectrum on large scales using galaxy peculiar velocities. We explore the properties of surveys that cover only two small fields in opposing directions on the sky. Surveys of this type have several advantages over those that attempt to cover the entire sky; in particular, by concentrating galaxies in narrow cones these surveys are able to achieve the density needed to measure several moments of the velocity field with only a modest number of objects, even for surveys designed to probe scales \gtwid 100\hmpc. We construct mock surveys with this geometry and analyze them in terms of the three moments to which they are most sensitive. We calculate window functions for these moments and construct a $\chi^2$ statistic which can be used to put constraints on the power spectrum. In order to explore the sensitivity of these surveys, we calculate the expectation values of the moments and their associated measurement noise as a function of the survey parameters such as density and depth and for several popular models of structure formation. In addition, we have studied how well these kind of surveys can distinguish between different power spectra and found that, for the same number of objects, cone surveys are as good or better than full-sky surveys in distinguishing between popular cosmological models. We find that a survey with $200-300$ galaxy peculiar velocities with distance errors of 15% in two cones with opening angle of $\sim 10^\circ$ could put significant constraints on the power spectrum on scales of $100-300$\hmpc, where few other constraints exist.Comment: 15 pages, 3 figures, Some revisions and different figure. Accepted for publication at ApJ letter