Self-consistency of the Excursion Set Approach

The excursion set approach provides a framework for predicting how the abundance of dark matter halos depends on the initial conditions. A key ingredient of this formalism comes from the physics of halo formation: the specification of a critical overdensity threshold (barrier) which protohalos must exceed if they are to form bound virialized halos at a later time. Another ingredient is statistical, as it requires the specification of the appropriate statistical ensemble over which to average when making predictions. The excursion set approach explicitly averages over all initial positions, thus implicitly assuming that the appropriate ensemble is that associated with randomly chosen positions in space, rather than special positions such as peaks of the initial density field. Since halos are known to collapse around special positions, it is not clear that the physical and statistical assumptions which underlie the excursion set approach are self-consistent. We argue that they are at least for low mass halos, and illustrate by comparing our excursion set predictions with numerical data from the DEUS simulations.Comment: 5 pages, 2 figure

Flame resistant elastic elastomeric fiber

Compositions exhibit elastomeric properties and possess various degrees of flame resistance. First material polyurethane, incorporates halogen containing polyol and is flame resistant in air; second contains spandex elastomer with flame retardant additives; and third material is prepared from fluorelastomer composition of copolymer of vinylidene fluoride and hexafluoropropylene

Non-flammable elastomeric fiber from a fluorinated elastomer and containing an halogenated flame retardant

Flame retardant elastomeric compositions are described comprised of either spandex type polyurethane having incorporated into the polymer chain halogen containing polyols, conventional spandex type polyurethanes in physical admixture with flame retardant additives, or fluoroelastomeric resins in physical admixture with flame retardant additives. Methods are described for preparing fibers of the flame retardant elastomeric materials and articles of manufacture comprised of the flame retardant clastomeric materials and non elastic materials such as polybenzimidazoles, fiberglass, nylons, etc

Flame resistant elastomeric polymer development

Elastomeric products were developed for use in the space shuttle program, and investigations were conducted to improve the properties of elastomers developed in previous programs, and to evaluate the possibility of using lower-cost general purpose polymers. Products were fabricated and processed on conventional processing equipment; these products include: foams based on fluorinated rubber flame-retarded compounds with a density of 20-30 pounds/cubic foot for use as padding and in helmets; foams based on urethane for use in instrument packaging in the space shuttle; flexible and semi-rigid films of fluorinated rubber and neoprene compounds that would not burn in a 70% nitrogen, 30% oxygen atmosphere, and in a 30% nitrogen, 70% oxygen atmosphere, respectively for use in packaging or in laminates; coated fabrics which used both nylon and Kelvar fabric substrates, coated with either fluorinated or neoprene polymer compositions to meet specific levels of flame retardancy; and other flame-resistant materials

Flame retardant spandex type polyurethanes

Flame retardant elastomeric compositions were developed, comprised of: (1) spandex type polyurethane having incorporated into the polymer chain, halogen containing polyols; (2) conventional spandex type polyurethanes in physical admixture flame retardant additives; and (3) fluoroelastomeric resins in physical admixture with flame retardant additives. Methods of preparing fibers of the flame retardant elastomeric materials are presented and articles of manufacture comprised of the elastomeric materials are mentioned

Nonlinear Gravitational Clustering: dreams of a paradigm

We discuss the late time evolution of the gravitational clustering in an expanding universe, based on the nonlinear scaling relations (NSR) which connect the nonlinear and linear two point correlation functions. The existence of critical indices for the NSR suggests that the evolution may proceed towards a universal profile which does not change its shape at late times. We begin by clarifying the relation between the density profiles of the individual halo and the slope of the correlation function and discuss the conditions under which the slopes of the correlation function at the extreme nonlinear end can be independent of the initial power spectrum. If the evolution should lead to a profile which preserves the shape at late times, then the correlation function should grow as $a^2$ [in a $\Omega=1$ universe] een at nonlinear scales. We prove that such exact solutions do not exist; however, ther e exists a class of solutions (``psuedo-linear profiles'', PLP's for short) which evolve as $a^2$ to a good approximation. It turns out that the PLP's are the correlation functions which arise if the individual halos are assumed to be isothermal spheres. They are also configurations of mass in which the nonlinear effects of gravitational clustering is a minimum and hence can act as building blocks of the nonlinear universe. We discuss the implicatios of this result.Comment: 32 Pages, Submitted to Ap

Nonlinear Velocity-Density Coupling: Analysis by Second-Order Perturbation Theory

Cosmological linear perturbation theory predicts that the peculiar velocity $V(x)$ and the matter overdensity $\delta(x)$ at a same point $x$ are statistically independent quantities, as log as the initial density fluctuations are random Gaussian distributed. However nonlinear gravitational effects might change the situation. Using framework of second-order perturbation theory and the Edgeworth expansion method, we study local density dependence of bulk velocity dispersion that is coarse-grained at a weakly nonlinear scale. For a typical CDM model, the first nonlinear correction of this constrained bulk velocity dispersion amounts to $\sim 0.3\delta$ (Gaussian smoothing) at a weakly nonlinear scale with a very weak dependence on cosmological parameters. We also compare our analytical prediction with published numerical results given at nonlinear regimes.Comment: 16 pages including 2 figures, ApJ 537 in press (July 1

Searching for the earliest galaxies in the 21 cm forest

We use a model developed by Xu et al. (2010) to compute the 21 cm line absorption signatures imprinted by star-forming dwarf galaxies (DGs) and starless minihalos (MHs). The method, based on a statistical comparison of the equivalent width (W_\nu) distribution and flux correlation function, allows us to derive a simple selection criteria for candidate DGs at very high (z >= 8) redshift. We find that ~ 18% of the total number of DGs along a line of sight to a target radio source (GRB or quasar) can be identified by the condition W_\nu < 0; these objects correspond to the high-mass tail of the DG distribution at high redshift, and are embedded in large HII regions. The criterion W_\nu > 0.37 kHz instead selects ~ 11% of MHs. Selected candidate DGs could later be re-observed in the near-IR by the JWST with high efficiency, thus providing a direct probe of the most likely reionization sources.Comment: 8 pages, 3 figures. Accepted for publication in Science in China Series

Close Pairs as Proxies for Galaxy Cluster Mergers

Galaxy cluster merger statistics are an important component in understanding the formation of large-scale structure. Unfortunately, it is difficult to study merger properties and evolution directly because the identification of cluster mergers in observations is problematic. We use large N-body simulations to study the statistical properties of massive halo mergers, specifically investigating the utility of close halo pairs as proxies for mergers. We examine the relationship between pairs and mergers for a wide range of merger timescales, halo masses, and redshifts (0<z<1). We also quantify the utility of pairs in measuring merger bias. While pairs at very small separations will reliably merge, these constitute a small fraction of the total merger population. Thus, pairs do not provide a reliable direct proxy to the total merger population. We do find an intriguing universality in the relation between close pairs and mergers, which in principle could allow for an estimate of the statistical merger rate from the pair fraction within a scaled separation, but including the effects of redshift space distortions strongly degrades this relation. We find similar behavior for galaxy-mass halos, making our results applicable to field galaxy mergers at high redshift. We investigate how the halo merger rate can be statistically described by the halo mass function via the merger kernel (coagulation), finding an interesting environmental dependence of merging: halos within the mass resolution of our simulations merge less efficiently in overdense environments. Specifically, halo pairs with separations less than a few Mpc/h are more likely to merge in underdense environments; at larger separations, pairs are more likely to merge in overdense environments.Comment: 12 pages, 9 figures; Accepted for publication in ApJ. Significant additions to text and two figures changed. Added new findings on the universality of pair mergers and added analysis of the effect of FoF linking length on halo merger