Dimension-Dependence of the Critical Exponent in Spherically Symmetric Gravitational Collapse

We study the critical behaviour of spherically symmetric scalar field collapse to black holes in spacetime dimensions other than four. We obtain reliable values for the scaling exponent in the supercritical region for dimensions in the range $3.5\leq D\leq 14$. The critical exponent increases monotonically to an asymptotic value at large $D$ of $\gamma\sim0.466$. The data is well fit by a simple exponential of the form: $\gamma \sim 0.466(1-e^{-0.408 D})$.Comment: 5 pages, including 7 figures New version contains more data points, one extra graph and more accurate error bars. No changes to result

Spherically symmetric scalar field collapse in any dimension

We describe a formalism and numerical approach for studying spherically symmetric scalar field collapse for arbitrary spacetime dimension d and cosmological constant Lambda. The presciption uses a double null formalism, and is based on field redefinitions first used to simplify the field equations in generic two-dimensional dilaton gravity. The formalism is used to construct code in which d and Lambda are input parameters. The code reproduces known results in d = 4 and d = 6 with Lambda = 0. We present new results for d = 5 with zero and negative Lambda.Comment: 16 pages, 6 figures, typos corrected, presentational changes, PRD in pres

Dynamic range of nanotube- and nanowire-based electromechanical systems

Nanomechanical resonators with high aspect ratio, such as nanotubes and nanowires are of interest due to their expected high sensitivity. However, a strongly nonlinear response combined with a high thermomechanical noise level limits the useful linear dynamic range of this type of device. We derive the equations governing this behavior and find a strong dependence [[proportional]dsqrt((d/L)[sup 5])] of the dynamic range on aspect ratio

Scalar field collapse in three-dimensional AdS spacetime

We describe results of a numerical calculation of circularly symmetric scalar field collapse in three spacetime dimensions with negative cosmological constant. The procedure uses a double null formulation of the Einstein-scalar equations. We see evidence of black hole formation on first implosion of a scalar pulse if the initial pulse amplitude $A$ is greater than a critical value $A_*$. Sufficiently near criticality the apparent horizon radius $r_{AH}$ grows with pulse amplitude according to the formula $r_{AH} \sim (A-A_*)^{0.81}$.Comment: 10 pages, 1 figure; references added, to appear in CQG(L

Two dimensional general covariance from three dimensions

A 3d generally covariant field theory having some unusual properties is described. The theory has a degenerate 3-metric which effectively makes it a 2d field theory in disguise. For 2-manifolds without boundary, it has an infinite number of conserved charges that are associated with graphs in two dimensions and the Poisson algebra of the charges is closed. For 2-manifolds with boundary there are additional observables that have a Kac-Moody Poisson algebra. It is further shown that the theory is classically integrable and the general solution of the equations of motion is given. The quantum theory is described using Dirac quantization, and it is shown that there are quantum states associated with graphs in two dimensions.Comment: 10 pages (Latex), Alberta-Thy-19-9

Constants of motion for vacuum general relativity

The 3+1 Hamiltonian Einstein equations, reduced by imposing two commuting spacelike Killing vector fields, may be written as the equations of the $SL(2,R)$ principal chiral model with certain `source' terms. Using this formulation, we give a procedure for generating an infinite number of non-local constants of motion for this sector of the Einstein equations. The constants of motion arise as explicit functionals on the phase space of Einstein gravity, and are labelled by sl(2,R) indices.Comment: 10 pages, latex, version to appear in Phys. Rev. D

Basins of attraction of a nonlinear nanomechanical resonator

We present an experiment that systematically probes the basins of attraction of two fixed points of a nonlinear nanomechanical resonator and maps them out with high resolution. We observe a separatrix which progressively alters shape for varying drive strength and changes the relative areas of the two basins of attraction. The observed separatrix is blurred due to ambient fluctuations, including residual noise in the drive system, which cause uncertainty in the preparation of an initial state close to the separatrix. We find a good agreement between the experimentally mapped and theoretically calculated basins of attraction

Nanowire-based very-high-frequency electromechanical resonator

Fabrication and readout of devices with progressively smaller size, ultimately down to the molecular scale, is critical for the development of very-high-frequency nanoelectromechanical systems (NEMS). Nanomaterials, such as carbon nanotubes or nanowires, offer immense prospects as active elements for these applications. We report the fabrication and measurement of a platinum nanowire resonator, 43 nm in diameter and 1.3 µm in length. This device, among the smallest NEMS reported, has a fundamental vibration frequency of 105.3 MHz, with a quality factor of 8500 at 4 K. Its resonant motion is transduced by a technique that is well suited to ultrasmall mechanical structures

Einstein's equations and the chiral model

The vacuum Einstein equations for spacetimes with two commuting spacelike Killing field symmetries are studied using the Ashtekar variables. The case of compact spacelike hypersurfaces which are three-tori is considered, and the determinant of the Killing two-torus metric is chosen as the time gauge. The Hamiltonian evolution equations in this gauge may be rewritten as those of a modified SL(2) principal chiral model with a time dependent `coupling constant', or equivalently, with time dependent SL(2) structure constants. The evolution equations have a generalized zero-curvature formulation. Using this form, the explicit time dependence of an infinite number of spatial-diffeomorphism invariant phase space functionals is extracted, and it is shown that these are observables in the sense that they Poisson commute with the reduced Hamiltonian. An infinite set of observables that have SL(2) indices are also found. This determination of the explicit time dependence of an infinite set of spatial-diffeomorphism invariant observables amounts to the solutions of the Hamiltonian Einstein equations for these observables.Comment: 22 pages, RevTeX, to appear in Phys. Rev.

Identification of genes required for the survival of B. fragilis using massive parallel sequencing of a saturated transposon mutant library

BACKGROUND: Bacteroides fragilis is a Gram-negative anaerobe that is normally a human gut commensal; it comprises a small percentage of the gut Bacteroides but is the most frequently isolated Bacteroides from human infections. Identification of the essential genes necessary for the survival of B. fragilis provides novel information which can be exploited for the treatment of bacterial infections. RESULTS: Massive parallel sequencing of saturated transposon mutant libraries (two mutant pools of approximately 50,000 mutants each) was used to determine the essential genes for the growth of B. fragilis 638R on nutrient rich medium. Among the 4326 protein coding genes, 550 genes (12.7%) were found to be essential for the survival of B. fragilis 638R. Of the 550 essential genes, only 367 genes were assigned to a Cluster of Orthologous Genes, and about 290 genes had Kyoto Encyclopedia of Genes and Genomes orthologous members. Interestingly, genes with hypothetical functions accounted for 41.3% of essential genes (227 genes), indicating that the functions of a significant percentage of the genes used by B. fragilis 638R are still unknown. Global transcriptome analysis using RNA-Seq indicated that most of the essential genes (92%) are, in fact, transcribed in B. fragilis 638R including most of those coding for hypothetical proteins. Three hundred fifty of the 550 essential genes of B. fragilis 638R are present in Database of Essential Genes. 10.02 and 31% of those are genes included as essential genes for nine species (including Gram-positive pathogenic bacteria). CONCLUSIONS: The essential gene data described in this investigation provides a valuable resource to study gene function and pathways involved in B. fragilis survival. Thorough examination of the B. fragilis-specific essential genes and genes that are shared between divergent organisms opens new research avenues that will lead to enhanced understanding of survival strategies used by bacteria in different microniches and under different stress situations. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi: 10.1186/1471-2164-15-429) contains supplementary material, which is available to authorized users