Primitive divisors on twists of the Fermat cubic

We show that for an elliptic divisibility sequence on a twist of the Fermat cubic, u3+v3=m, with m cube-free, all the terms beyond the first have a primive divisor

The New Cornwall syenogranite, Nova Scotia: petrology and geochemistry

The New Cornwall syenogranite is a 1.7 km2 intrusion at the southern margin of the Whale Lake monzogranitc of the South Mountain Batholilh of southwestern Nova Scotia- It has a mean SiO2 content of 75 8%, and contains accessory amounts of tourmaline, andalusite, and primary muscovitc. Ratios such as A/CNK (~ 1.25). Rb/K (~215), and Nb/Ta (- 3.5) show that the syenogranitc is not highly fractionated. Although binary clement plots for some elements show the same regular trend for both monzogranite and syenogranite, variations in trace elements such as Rb, Ha, Th and LREE show that the syenogranite is not derived from the monzogranite by fractional crystalli7ation, as the syenogranite has lower Eu and HREE compared with the monzogranite. Similarities in LREE, Nd isotope composition (ℇNd ~ -2) and other geochemical indicators between monzogranite and syenogranitc suggest that they were derived by partial melting of a common source Both the Whale Lake monzogranite and the New Cornwall syenogranite then evolved independently by fractional crystallization and late fluids played only a minor role in the further evolution of the syenogranitc. This represents a third mode of development of mineralized leucogranite in the South Mountain Batholith, in addition to the previously recognized "associated" and "independent" leucogranitc RÉSUMÉ Le syénogranitc de New Cornwall constituc une intrusion de 1.7 kilomètre carré sur la limite méridionale du granite monzonitique du lac Whale, lequcl fait panic du batholithe du mont South, dans le sud-ouest de la Nouvelle-Écosse. Il a une teneur moyenne en Si02 de 75.8 %, et renferme des quantités accessoires de tourmaline, d'andalousite et de muscovite primaire. Les rapports d'A/CNK (~ 1,25), de Rb/K (~ 215) et de Nb/Ta (~ 3,5) révèlent que le syénogranite n'est pas extrémement fractionné. Même si les représentaions graphiques des éléments binaires de certains éléments révèlent la même tendance régulière dans le cas du granite monzonitique et du syénogranite, les variations des éléments traces comme le Rb, lc Ba, lc Th et les éléments de terres rares légers signalent que le syénogranite ne provient pas du granite monzonitique par cristallisation fractionnairc, car le syénogranite posséde des teneurs moindres en Eu et en éléments de terres rares légerds, la comparativement au granite monzonitique. Les similantés existantes en ce qui conceme les éléments de terres rares légers, la composition en isotopes de Nd (ℇNd ~ -2) et d'autres mdicatcurs gêochimiques entrc le granite monzonitique et le syénogranite permettent de supposer qu'ils proviennent d'une fonte partielle d'une source commune. Le granite monzonitique du lac Whale et le syénogranite de New Cornwall ont ensuite tous deux évolué indépendamment par cristallisation fractionnaire et lcs fluides tardifs ont seulement joué un rôle secondairé dans l'évolution ulténeure du syénogranite. Il s'agit la d'un troisieme mode de développemcnt du leucogranitc minéralisé dans le batholithe du mont South, qui s'ajoute aux leucogranites « assoaés » et « indépendants » dèjà rcconnus Traduit par la rédactio

Quantifying uncertainty in acoustic measurements of tidal flows using a ‘Virtual’ Doppler Current Profiler

This is the author accepted manuscript. The final version is available from Elsevier via the DOI in this record.Accurate characterisation of flows at tidal sites can enable the developers of tidal stream energy projects to design and model the loads on, and the performance of, tidal energy converters. Acoustic Doppler technology is versatile in the measurement of sea conditions; however, this technology can be limited in its effectiveness at measuring the small-scale kinematic fluctuations caused by waves and turbulence. A Virtual Doppler Current Profiler (VDCP) is used to sample a simulated tidal flow to understand the limitations of this type of measurement instrument whilst recording the small timescale kinematics of waves and turbulence in tidal currents. Results demonstrate the phase dependency of velocity measurements averaged between two acoustic beams and provide a theoretical error for wave and turbulence characteristics sampled under a range of conditions. Spectral moments of the subsurface longitudinal wave orbital velocities recorded by the VDCP can be between 0.1 and 9 times those measured at a point for certain turbulent current conditions, turbulence intensity measurements may vary between 0.2 and 1.5 times the inputted value in low wave conditions and turbulence length scale calculation can also vary hugely dependent on both current and wave conditions. The continuation of this work will enable effective comparison of a linear model for tidal flow kinematics against field measurements from UK tidal site data, and subsequently validate numerical models for the testing of tidal turbines.This work was supported by the Industrial Centre for Offshore Renewable Energy (IDCORE) with funding from the Energy Technologies Institute and the Research Councils Energy Programme [grant number EP/J500847/1] and DNV GL

Using Fluid Curtains to Improve Sealing Performance in Turbomachinery Applications

The results from an investigation into the physics of how fluid curtains can be applied to improve the aerodynamic performance of conventional turbomachinery shaft and rotor seals are described in this paper. Computational fluid dynamics and testing on two experimental facilities are used in the study. In the first part of the work, computational fluid dynamics simulations validated against experimental test data demonstrate the fundamental mechanism by which the presence of the curtain can act to reduce leakage flow through conventional seals. These results are consolidated into a single performance carpet map, showing how the leakage reduction performance and the curtain supply pressure needed to achieve it vary with changes in values of key geometrical parameters. In the second part of the work the effect of swirl in the seal inlet flow, as is often encountered in turbomachinery applications, on the performance of the fluid curtain is investigated experimentally. Test results show that if the swirl momentum in the inlet flow is greater than the momentum of the curtain flow, the performance benefit from applying the curtain is greatly diminished. Overall, the results provide some fundamental design rules for applying fluid curtains to enhance turbomachinery sealing performance for the general type of leakage path geometry (cylindrical channel, 45-degree jet angle, curtain upstream of a conventional seal) and working fluid type and conditions (air, ambient temperature, subsonic leakage channel flow), used in the study

On the eigenvalues of Cayley graphs on the symmetric group generated by a complete multipartite set of transpositions

Given a finite simple graph \cG with $n$ vertices, we can construct the Cayley graph on the symmetric group $S_n$ generated by the edges of \cG, interpreted as transpositions. We show that, if \cG is complete multipartite, the eigenvalues of the Laplacian of \Cay(\cG) have a simple expression in terms of the irreducible characters of transpositions, and of the Littlewood-Richardson coefficients. As a consequence we can prove that the Laplacians of \cG and of \Cay(\cG) have the same first nontrivial eigenvalue. This is equivalent to saying that Aldous's conjecture, asserting that the random walk and the interchange process have the same spectral gap, holds for complete multipartite graphs.Comment: 29 pages. Includes modification which appear on the published version in J. Algebraic Combi

The Invisible Thin Red Line

The aim of this paper is to argue that the adoption of an unrestricted principle of bivalence is compatible with a metaphysics that (i) denies that the future is real, (ii) adopts nomological indeterminism, and (iii) exploits a branching structure to provide a semantics for future contingent claims. To this end, we elaborate what we call Flow Fragmentalism, a view inspired by Kit Fine (2005)’s non-standard tense realism, according to which reality is divided up into maximally coherent collections of tensed facts. In this way, we show how to reconcile a genuinely A-theoretic branching-time model with the idea that there is a branch corresponding to the thin red line, that is, the branch that will turn out to be the actual future history of the world

A Distributed Multilevel Force-directed Algorithm

The wide availability of powerful and inexpensive cloud computing services naturally motivates the study of distributed graph layout algorithms, able to scale to very large graphs. Nowadays, to process Big Data, companies are increasingly relying on PaaS infrastructures rather than buying and maintaining complex and expensive hardware. So far, only a few examples of basic force-directed algorithms that work in a distributed environment have been described. Instead, the design of a distributed multilevel force-directed algorithm is a much more challenging task, not yet addressed. We present the first multilevel force-directed algorithm based on a distributed vertex-centric paradigm, and its implementation on Giraph, a popular platform for distributed graph algorithms. Experiments show the effectiveness and the scalability of the approach. Using an inexpensive cloud computing service of Amazon, we draw graphs with ten million edges in about 60 minutes.Comment: Appears in the Proceedings of the 24th International Symposium on Graph Drawing and Network Visualization (GD 2016