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

Nonlinear nanomechanical resonators for quantum optoelectromechanics

We present a scheme for tuning and controlling nano mechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a novel regime of optomechanics, where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields allow to control the motional state of the nanoresonator at the single phonon level. Some applications of this platform have been presented previously [New J. Phys. 14, 023042 (2012), Phys. Rev. Lett. 110, 120503 (2013)]. Here, we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms, together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.Comment: 15 pages, 6 figure

Anomalous latent heat in non-equilibrium phase transitions

We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc) are well-defined. The sign of the latent heat is found to be counterintuitive: it is positive when going from the phase where the temperatures and the entropy are higher to the one where these quantities are lower. The effect exists only out of equilibrium and requires conflicting interactions. It is displayed on a lattice gas model of ferromagnetically interacting spin-1/2 particles.Comment: 4 pages, 2 figure

Phase transitions in diluted negative-weight percolation models

We investigate the geometric properties of loops on two-dimensional lattice graphs, where edge weights are drawn from a distribution that allows for positive and negative weights. We are interested in the appearance of spanning loops of total negative weight. The resulting percolation problem is fundamentally different from conventional percolation, as we have seen in a previous study of this model for the undiluted case. Here, we investigate how the percolation transition is affected by additional dilution. We consider two types of dilution: either a certain fraction of edges exhibit zero weight, or a fraction of edges is even absent. We study these systems numerically using exact combinatorial optimization techniques based on suitable transformations of the graphs and applying matching algorithms. We perform a finite-size scaling analysis to obtain the phase diagram and determine the critical properties of the phase boundary. We find that the first type of dilution does not change the universality class compared to the undiluted case whereas the second type of dilution leads to a change of the universality class.Comment: 8 pages, 7 figure

Magnetized Non-linear Thin Shell Instability: Numerical Studies in 2D

We revisit the analysis of the Non-linear Thin Shell Instability (NTSI) numerically, including magnetic fields. The magnetic tension force is expected to work against the main driver of the NTSI -- namely transverse momentum transport. However, depending on the field strength and orientation, the instability may grow. For fields aligned with the inflow, we find that the NTSI is suppressed only when the Alfv\'en speed surpasses the (supersonic) velocities generated along the collision interface. Even for fields perpendicular to the inflow, which are the most effective at preventing the NTSI from developing, internal structures form within the expanding slab interface, probably leading to fragmentation in the presence of self-gravity or thermal instabilities. High Reynolds numbers result in local turbulence within the perturbed slab, which in turn triggers reconnection and dissipation of the excess magnetic flux. We find that when the magnetic field is initially aligned with the flow, there exists a (weak) correlation between field strength and gas density. However, for transverse fields, this correlation essentially vanishes. In light of these results, our general conclusion is that instabilities are unlikely to be erased unless the magnetic energy in clouds is much larger than the turbulent energy. Finally, while our study is motivated by the scenario of molecular cloud formation in colliding flows, our results span a larger range of applicability, from supernovae shells to colliding stellar winds.Comment: 12 pages, 17 figures, some of them at low resolution. Submitted to ApJ, comments welcom