Eulerian Statistically Preserved Structures in Passive Scalar Advection

We analyze numerically the time-dependent linear operators that govern the dynamics of Eulerian correlation functions of a decaying passive scalar advected by a stationary, forced 2-dimensional Navier-Stokes turbulence. We show how to naturally discuss the dynamics in terms of effective compact operators that display Eulerian Statistically Preserved Structures which determine the anomalous scaling of the correlation functions. In passing we point out a bonus of the present approach, in providing analytic predictions for the time-dependent correlation functions in decaying turbulent transport.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.

The Schwinger mechanism and graphene

The Schwinger mechanism, the production of charged particle-antiparticle pairs in a macroscopic external electric field, is derived for 2+1 dimensional theories. The rate of pair production per unit area for four species of massless fermions, with charge $q$, in a constant electric field $E$ is given by $\pi^{-2} \hbar^{-3/2} \tilde{c}^{-1/2} (q E)^{3/2}$ where $\tilde{c}$ is the speed of light for the two-dimensional system. To the extent undoped graphene behaves like the quantum field-theoretic vacuum for massless fermions in 2+1 dimensions, the Schwinger mechanism should be testable experimentally. A possible experimental configuration for this is proposed. Effects due to deviations from this idealized picture of graphene are briefly considered. It is argued that with present day samples of graphene, tests of the Schwinger formula may be possible.Comment: Extensive revisions. The distinction between the vacuum decay rate and the pair production rate in the Schwinger mechanism is now stressed. The discussion of quality of sample needed for a viable experimental test has been significantly expanded. References adde

An improved lower bound for (1,<=2)-identifying codes in the king grid

We call a subset $C$ of vertices of a graph $G$ a $(1,\leq \ell)$-identifying code if for all subsets $X$ of vertices with size at most $\ell$, the sets $\{c\in C |\exists u \in X, d(u,c)\leq 1\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging procedure, we improve the lower bound by showing that any $(1,\leq 2)$-identifying code of the king grid has density at least 47/111

Model Independent Extraction of ∣Vbc∣|V_{\rm bc}| Without Heavy Quark Symmetry

A new method to extract $|V_{\rm bc}|$ is proposed based on a sum--rule for semileptonic decays of the $B$ meson. The method relies on much weaker assumptions than previous approaches which are based on heavy--quark symmetry. This sum--rule only relies on the assumption that the virtual $c \overline{c}$ pair content of the $B$ meson can be neglected. The extraction of the CKM matrix element also requires that the sum--rule saturates in the kinematically accessible region.Comment: 10 pages revtex3 manuscript. No figures, U. of MD PP #94--086. With our apologies, some innocuous errors corrected and some references added that had been brought to our attentio

Sub-au imaging of water vapour clouds around four Asymptotic Giant Branch stars

We present MERLIN maps of the 22-GHz H2O masers around four low-mass late-type stars (IK Tau U Ori, RT Vir and U Her), made with an angular resolution of ~ 15 milliarcsec and a velocity resolution of 0.1 km s-1. The H2O masers are found in thick expanding shells with inner radii ~ 6 to 16 au and outer radii four times larger. The expansion velocity increases radially through the H2O maser regions, with logarithmic velocity gradients of 0.5--0.9. IK Tau and RT Vir have well-filled H2O maser shells with a spatial offset between the near and far sides of the shell, which suggests that the masers are distributed in oblate spheroids inclined to the line of sight. U Ori and U Her have elongated poorly-filled shells with indications that the masers at the inner edge have been compressed by shocks; these stars also show OH maser flares. MERLIN resolves individual maser clouds, which have diameters of 2 -- 4 au and filling factors of only ~ 0.01 with respect to the whole H2O maser shells. The CSE velocity structure gives additional evidence the maser clouds are density bounded. Masing clouds can be identified over a similar timescale to their sound crossing time (~2 yr) but not longer. The sizes and observed lifetimes of these clouds are an order of magnitude smaller than those around red supergiants, similar to the ratio of low-mass:high-mass stellar masses and sizes. This suggests that cloud size is determined by stellar properties, not local physical phenomena in the wind.Comment: 21 pages, including 14 figures and 8 tables. Accepted for publication in MNRA

Random Walks in Local Dynamics of Network Losses

We suggest a model for data losses in a single node of a packet-switched network (like the Internet) which reduces to one-dimensional discrete random walks with unusual boundary conditions. The model shows critical behavior with an abrupt transition from exponentially small to finite losses as the data arrival rate increases. The critical point is characterized by strong fluctuations of the loss rate. Although we consider the packet arrival being a Markovian process, the loss rate exhibits non-Markovian power-law correlations in time at the critical point.Comment: 4 pages, 2 figure

On Toroidal Horizons in Binary Black Hole Inspirals

We examine the structure of the event horizon for numerical simulations of two black holes that begin in a quasicircular orbit, inspiral, and finally merge. We find that the spatial cross section of the merged event horizon has spherical topology (to the limit of our resolution), despite the expectation that generic binary black hole mergers in the absence of symmetries should result in an event horizon that briefly has a toroidal cross section. Using insight gained from our numerical simulations, we investigate how the choice of time slicing affects both the spatial cross section of the event horizon and the locus of points at which generators of the event horizon cross. To ensure the robustness of our conclusions, our results are checked at multiple numerical resolutions. 3D visualization data for these resolutions are available for public access online. We find that the structure of the horizon generators in our simulations is consistent with expectations, and the lack of toroidal horizons in our simulations is due to our choice of time slicing.Comment: Submitted to Phys. Rev.

NICMOS Imaging of the Dusty Microjansky Radio Source VLA J123642+621331 at z = 4.424

We present the discovery of a radio galaxy at a likely redshift of z = 4.424 in one of the flanking fields of the Hubble Deep Field. Radio observations with the VLA and MERLIN centered on the HDF yielded a complete sample of microjansky radio sources, of which about 20% have no optical counterpart to I < 25 mag. In this Letter, we address the possible nature of one of these sources, through deep HST NICMOS images in the F110W (J) and F160W (H) filters. VLA J123642+621331 has a single emission line at 6595-A, which we identify with Lyman-alpha at z = 4.424. We argue that this faint (H = 23.9 mag), compact (r = 0.2 arcsec), red (I - K = 2.0) object is most likely a dusty, star-forming galaxy with an embedded active nucleus.Comment: Accepted for publication in Astrophysical Journal Letters. 11 pages, 4 figures, uses aastex v5.0 and psfi

Moller operators and Lippmann-Schwinger equations for step-like potentials

The Moller operators and the asociated Lippman-Schwinger equations obtained from different partitionings of the Hamiltonian for a step-like potential barrier are worked out, compared and related.Comment: 15 pages, 1 inlined figure, iopart.cl