Formation Rates of Black Hole Accretion Disk Gamma-Ray Bursts

While many models have been proposed for GRBs, those currently favored are all based upon the formation of and/or rapid accretion into stellar mass black holes. We present population synthesis calculations of these models using a Monte Carlo approach in which the many uncertain parameters intrinsic to such calculations are varied. We estimate the event rate for each class of model as well as the propagation distance for those having significant delay between formation and burst production, i.e., double neutron star (DNS) mergers and black hole-neutron star (BH/NS) mergers. For reasonable assumptions regarding the many uncertainties in population synthesis, we calculate a daily event rate in the universe for i) merging neutron stars: ~100/day; ii) neutron-star black hole mergers: ~450/day; iii) collapsars: ~10,000/day; iv) helium star black hole mergers: ~1000/day; and v) white dwarf black hole mergers: ~20/day. The range of uncertainty in these numbers however, is very large, typically two to three orders of magnitude. These rates must additionally be multiplied by any relevant beaming factor and sampling fraction (if the entire universal set of models is not being observed). Depending upon the mass of the host galaxy, half of the DNS and BH/NS mergers will happen within 60kpc (for a Milky-Way massed galaxy) to 5Mpc (for a galaxy with negligible mass) from the galactic center. Because of the delay time, neutron star and black hole mergers will happen at a redshift 0.5 to 0.8 times that of the other classes of models. Information is still lacking regarding the hosts of short hard bursts, but we suggest that they are due to DNS and BH/NS mergers and thus will ultimately be determined to lie outside of galaxies and at a closer mean distance than long complex bursts (which we attribute to collapsars).Comment: 57 pages total, 23 figures, submitted by Ap

Analysis of the loop length distribution for the negative weight percolation problem in dimensions d=2 through 6

We consider the negative weight percolation (NWP) problem on hypercubic lattice graphs with fully periodic boundary conditions in all relevant dimensions from d=2 to the upper critical dimension d=6. The problem exhibits edge weights drawn from disorder distributions that allow for weights of either sign. We are interested in in the full ensemble of loops with negative weight, i.e. non-trivial (system spanning) loops as well as topologically trivial ("small") loops. The NWP phenomenon refers to the disorder driven proliferation of system spanning loops of total negative weight. While previous studies where focused on the latter loops, we here put under scrutiny the ensemble of small loops. Our aim is to characterize -using this extensive and exhaustive numerical study- the loop length distribution of the small loops right at and below the critical point of the hypercubic setups by means of two independent critical exponents. These can further be related to the results of previous finite-size scaling analyses carried out for the system spanning loops. For the numerical simulations we employed a mapping of the NWP model to a combinatorial optimization problem that can be solved exactly by using sophisticated matching algorithms. This allowed us to study here numerically exact very large systems with high statistics.Comment: 7 pages, 4 figures, 2 tables, paper summary available at http://www.papercore.org/Kajantie2000. arXiv admin note: substantial text overlap with arXiv:1003.1591, arXiv:1005.5637, arXiv:1107.174

Pioneer Mars 1979 mission options

A preliminary investigation of lower cost Mars missions which perform useful exploration objectives after the Viking/75 mission was conducted. As a study guideline, it was assumed that significant cost savings would be realized by utilizing Pioneer hardware currently being developed for a pair of 1978 Venus missions. This in turn led to the additional constraint of a 1979 launch with the Atlas/Centaur launch vehicle which has been designated for the Pioneer Venus missions. Two concepts, using an orbiter bus platform, were identified which have both good science potential and mission simplicity indicative of lower cost. These are: (1) an aeronomy/geology orbiter, and (2) a remote sensing orbiter with a number of deployable surface penetrometers

F-8C digital CCV flight control laws

A set of digital flight control laws were designed for the NASA F-8C digital fly-by-wire aircraft. The control laws emphasize Control Configured Vehicle (CCV) benefits. Specific pitch axis objectives were improved handling qualities, angle-of-attack limiting, gust alleviation, drag reduction in steady and maneuvering flight, and a capability to fly with reduced static stability. The lateral-directional design objectives were improved Dutch roll damping and turn coordination over a wide range in angle-of-attack. An overall program objective was to explore the use of modern control design methodilogy to achieve these specific CCV benefits. Tests for verifying system integrity, an experimental design for handling qualities evaluation, and recommended flight test investigations were specified

Effective dynamics using conditional expectations

The question of coarse-graining is ubiquitous in molecular dynamics. In this article, we are interested in deriving effective properties for the dynamics of a coarse-grained variable $\xi(x)$, where $x$ describes the configuration of the system in a high-dimensional space $\R^n$, and $\xi$ is a smooth function with value in $\R$ (typically a reaction coordinate). It is well known that, given a Boltzmann-Gibbs distribution on $x \in \R^n$, the equilibrium properties on $\xi(x)$ are completely determined by the free energy. On the other hand, the question of the effective dynamics on $\xi(x)$ is much more difficult to address. Starting from an overdamped Langevin equation on $x \in \R^n$, we propose an effective dynamics for $\xi(x) \in \R$ using conditional expectations. Using entropy methods, we give sufficient conditions for the time marginals of the effective dynamics to be close to the original ones. We check numerically on some toy examples that these sufficient conditions yield an effective dynamics which accurately reproduces the residence times in the potential energy wells. We also discuss the accuracy of the effective dynamics in a pathwise sense, and the relevance of the free energy to build a coarse-grained dynamics

Directed polymers in random media under confining force

The scaling behavior of a directed polymer in a two-dimensional (2D) random potential under confining force is investigated. The energy of a polymer with configuration $\{y(x)\}$ is given by H\big(\{y(x)\}\big) = \sum_{x=1}^N \exyx + \epsilon \Wa^\alpha, where $\eta(x,y)$ is an uncorrelated random potential and \Wa is the width of the polymer. Using an energy argument, it is conjectured that the radius of gyration $R_g(N)$ and the energy fluctuation $\Delta E(N)$ of the polymer of length $N$ in the ground state increase as $R_g(N)\sim N^{\nu}$ and $\Delta E(N)\sim N^\omega$ respectively with $\nu = 1/(1+\alpha)$ and $\omega = (1+2\alpha)/(4+4\alpha)$ for $\alpha\ge 1/2$. A novel algorithm of finding the exact ground state, with the effective time complexity of \cO(N^3), is introduced and used to confirm the conjecture numerically.Comment: 9 pages, 7 figure

Maternal and infant infections stimulate a rapid leukocyte response in breastmilk

Breastmilk protects infants against infections; however, specific responses of breastmilk immune factors to different infections of either the mother or the infant are not well understood. Here, we examined the baseline range of breastmilk leukocytes and immunomodulatory biomolecules in healthy mother/infant dyads and how they are influenced by infections of the dyad. Consistent with a greater immunological need in the early postpartum period, colostrum contained considerable numbers of leukocytes (13–70% out of total cells) and high levels of immunoglobulins and lactoferrin. Within the first 1–2 weeks postpartum, leukocyte numbers decreased significantly to a low baseline level in mature breastmilk (0–2%) (P\u3c0.001). This baseline level was maintained throughout lactation unless the mother and/or her infant became infected, when leukocyte numbers significantly increased up to 94% leukocytes out of total cells (P\u3c0.001). Upon recovery from the infection, baseline values were restored. The strong leukocyte response to infection was accompanied by a more variable humoral immune response. Exclusive breastfeeding was associated with a greater baseline level of leukocytes in mature breastmilk. Collectively, our results suggest a strong association between the health status of the mother/infant dyad and breastmilk leukocyte levels. This could be used as a diagnostic tool for assessment of the health status of the lactating breast as well as the breastfeeding mother and infant

Renormalization algorithm with graph enhancement

We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states. States within this class may (i) possess arbitrarily long-ranged two-point correlations, (ii) exhibit an arbitrary degree of block entanglement entropy up to a volume law, (iii) may be taken translationally invariant, while at the same time (iv) local properties and two-point correlations can be computed efficiently. This new variational class of states can be thought of as being prepared from matrix product states, followed by commuting unitaries on arbitrary constituents, hence truly generalizing both matrix product and weighted graph states. We use this class of states to formulate a renormalization algorithm with graph enhancement (RAGE) and present numerical examples demonstrating that improvements over density-matrix renormalization group simulations can be achieved in the simulation of ground states and quantum algorithms. Further generalizations, e.g., to higher spatial dimensions, are outlined.Comment: 4 pages, 1 figur