Cover pebbling numbers and bounds for certain families of graphs

Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph, gamma(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are initially distributed. The cover pebbling number for complete multipartite graphs and wheel graphs is determined. We also prove a sharp bound for gamma(G) given the diameter and number of vertices of G.Comment: 10 pages, 1 figure, submitted to Discrete Mathematic

Domination Cover Pebbling: Structural Results

This paper continues the results of "Domination Cover Pebbling: Graph Families." An almost sharp bound for the domination cover pebbling (DCP) number for graphs G with specified diameter has been computed. For graphs of diameter two, a bound for the ratio between the cover pebbling number of G and the DCP number of G has been computed. A variant of domination cover pebbling, called subversion DCP is introducted, and preliminary results are discussed.Comment: 15 page

Materials technology for an advanced space power nuclear reactor concept: Program summary

The results of a materials technology program for a long-life (50,000 hr), high-temperature (950 C coolant outlet), lithium-cooled, nuclear space power reactor concept are reviewed and discussed. Fabrication methods and compatibility and property data were developed for candidate materials for fuel pins and, to a lesser extent, for potential control systems, reflectors, reactor vessel and piping, and other reactor structural materials. The effects of selected materials variables on fuel pin irradiation performance were determined. The most promising materials for fuel pins were found to be 85 percent dense uranium mononitride (UN) fuel clad with tungsten-lined T-111 (Ta-8W-2Hf)

A radial mode ultrasonic horn for the inactivation of <i>Escherichia coli</i> K12

Tuned cylindrical radial mode ultrasonic horns offer advantages over ultrasonic probes in the design of flow-through devices for bacterial inactivation. This study presents a comparison of the effectiveness of a radial horn and probe in the inactivation of Escherichia coli K12. The radial horn is designed using finite element analysis and the predicted modal parameters are validated using experimental modal analysis. A validated finite element model of the probe is also presented. Visual studies of the cavitation fields produced by the radial horn and probe are carried out using luminol and also backlighting to demonstrate the advantages of radial horns in producing a more focused cavitation field with widely dispersed streamers. Microbiological studies show that, for the same power density, better inactivation of E. coli K12 is achieved using the radial horn and, also, the radial horn offers greater achievable power density resulting in further improvements in bacterial inactivation. The radial horn is shown to be more effective than the probe device and offers opportunities to design in-line flow-through devices for processing applications

The shape of primordial non-Gaussianity and the CMB bispectrum

We present a set of formalisms for comparing, evolving and constraining primordial non-Gaussian models through the CMB bispectrum. We describe improved methods for efficient computation of the full CMB bispectrum for any general (non-separable) primordial bispectrum, incorporating a flat sky approximation and a new cubic interpolation. We review all the primordial non-Gaussian models in the present literature and calculate the CMB bispectrum up to l <2000 for each different model. This allows us to determine the observational independence of these models by calculating the cross-correlation of their CMB bispectra. We are able to identify several distinct classes of primordial shapes - including equilateral, local, warm, flat and feature (non-scale invariant) - which should be distinguishable given a significant detection of CMB non-Gaussianity. We demonstrate that a simple shape correlator provides a fast and reliable method for determining whether or not CMB shapes are well correlated. We use an eigenmode decomposition of the primordial shape to characterise and understand model independence. Finally, we advocate a standardised normalisation method for $f_{NL}$ based on the shape autocorrelator, so that observational limits and errors can be consistently compared for different models.Comment: 32 pages, 20 figure

Primordial non-Gaussianity and the CMB bispectrum

We present a new formalism, together with efficient numerical methods, to directly calculate the CMB bispectrum today from a given primordial bispectrum using the full linear radiation transfer functions. Unlike previous analyses which have assumed simple separable ansatze for the bispectrum, this work applies to a primordial bispectrum of almost arbitrary functional form, for which there may have been both horizon-crossing and superhorizon contributions. We employ adaptive methods on a hierarchical triangular grid and we establish their accuracy by direct comparison with an exact analytic solution, valid on large angular scales. We demonstrate that we can calculate the full CMB bispectrum to greater than 1% precision out to multipoles l<1800 on reasonable computational timescales. We plot the bispectrum for both the superhorizon ('local') and horizon-crossing ('equilateral') asymptotic limits, illustrating its oscillatory nature which is analogous to the CMB power spectrum

Assessment of Axial Wave Number and Mean Flow Uncertainty on Acoustic Liner Impedance Eduction

International audienceA key parameter in designing and assessing advanced broadband acoustic liners to achieve the current and future noise reduction goals is the acoustic impedance presented by the liner. This parameter, intrinsic to a specific liner configuration, is dependent on sound pressure level and grazing flow velocity. Current impedance eduction approaches have, in general, provided excellent results and continue to be employed throughout the acoustic liner community. However, some recent applications have indicated a possible dependence of the educed impedance on the direction of incident waves relative to the mean flow. The purpose of the current study is to investigate this unexpected behavior for various impedance eduction methods based on the Pridmore-Brown and convected Helmholtz equations. Specifically, the effects of flow profile and axial wavenumber uncertainties on educed impedances for upstream and downstream sources are investigated. The uniform flow results demonstrate the importance of setting a correct Mach number value in obtaining consistent educed impedances for upstream and downstream sources. In fact, the consistency of results over the two source locations was greatly improved by a slight modification of the uniform flow Mach number. In addition, uncertainty in educed axial wavenumber was also illustrated to correlate well with differences in the educed impedances, even with modified uniform flow Mach number. Finally, while less straightforward than in the uniform flow case, it appears that modification of the mean flow profile may also improve consistency of results for upstream and downstream results when shear flow is included

Roman military bookkeeping

This work is divided into two parts. Part I examines the system of documentation practised in the Roman Army from the foundation of the Empire to the accession of Diocletian. This examination includes a discussion of the administrative personnel and their functions and of the documents they issued and received. In Chapter I the orderly-room staffs are considered in ascending order of seniority. This method has the advantage of proceeding from the simple to the complex, and is perhaps better adapted than the opposite order for illustrating the gradual elaboration of the organization. In Chapter II complete texts, with variant readings, are given of the more important documents, in the order in which they might appear in the documentation of an imaginary soldier from the day when he first considers enlistment to the day of his discharge. These documents fall into three broad categories. One contains those which belong to the period when the soldier is a recruit or would-be recruit, and consists of letters of recommendation, posting orders, etc. The second includes matriculae of various types, the acta diurnal, pridiana, and other administrative documents. The third category is limited to financial documents, mainly soldiers' pay accounts and military receipts. Part II contains, besides the notes to the first part, a summary catalogue of Roman military documents, arranged in order of the media on which they were written, papyrus, parchment, wax tablets, bronze tablets, and ostraca. Inscriptions on stone are excluded. The catalogue includes not only such documents as are obviously official, but also a number of others which bear indirectly upon the general problem