Deciding whether a planar graph has a cubic subgraph is NP-complete

AbstractWe show that the problem of deciding whether a given planar graph (complete with planar embedding) of degree at most 7 has a cubic subgraph is NP-complete

Determining the Nonperturbative Collins-Soper Kernel From Lattice QCD

At small transverse momentum $q_T$, transverse-momentum dependent parton distribution functions (TMDPDFs) arise as genuinely nonperturbative objects that describe Drell-Yan like processes in hadron collisions as well as semi-inclusive deep-inelastic scattering. TMDPDFs naturally depend on the hadron momentum, and the associated evolution is determined by the Collins-Soper equation. For $q_T \sim \Lambda_\mathrm{QCD}$ the corresponding evolution kernel (or anomalous dimension) is nonperturbative and must be determined as an independent ingredient in order to relate TMDPDFs at different scales. We propose a method to extract this kernel using lattice QCD and the Large-Momentum Effective Theory, where the physical TMD correlation involving light-like paths is approximated by a quasi TMDPDF, defined using equal-time correlation functions with a large-momentum hadron state. The kernel is determined from a ratio of quasi TMDPDFs extracted at different hadron momenta.Comment: 9 pages, 2 figures; v2: extended the review of TMDPDF commonalities, version submitted to PRD; v3: minor changes, journal versio

Constraint equations for heavy-to-light currents in SCET

A complete basis for the next-to-next-to leading order heavy-to-light currents in the soft-collinear effective theory is constructed. Reparameterization invariance is imposed by deriving constraint equations. Their solutions give the set of allowed Dirac structures as well as relations between the Wilson coefficients of operators that appear at different orders in the power expansion. The completeness of reparameterization invariance constraints derived on a projected surface is investigated. We also discuss the universality of the ultrasoft Wilson line with boundary conditions.Comment: 35 page

Editorial

An essential property of a high-quality metallic nanofilm is the quantization of the electron spectrum due to dimensional confinement in one direction. Quantum confinement has a substantial impact on the superconducting characteristics and leads to quantum-size variations of the critical temperature Tc with film thickness. We demonstrate that the Bogoliubov-de Gennes equations are able to describe the thickness-dependent Tc in nanofilms, and our results are in good agreement with recent experimental data on ${\rm Pb}$ flat terraces grown on silicon (Science, 306 (2004) 1915 and Nature Phys., 2 (2006) 173). We predict that the quantum-size oscillations of $T_{\rm c}$ will be more pronounced for ${\rm Al}$

British Geological Survey remotely operated sea bed rockdrills and vibrocorers: new advances to meet the needs of the scientific community

The British Geological Survey (BGS) have developed a number of coring and drilling systems for use in science projects in the UK and internationally. These include 3m, 4m and 6m vibrocoring systems; a 5m combined rockdrill and vibrocorer system (RD1); an oriented drill designed specifically to recover samples for use in palaeomagnetic studies; and a 55m rockdrill (RockDrill2). The BGS has recently completed a series of modifications to increase the flexibility and performance of its vibrocoring and rock-drilling capability to meet the ever increasing needs of the scientific community. The latest generation vibrocorers can be operated without an umbilical power cable. The new system not only allows vibrocoring in greater water depths, but can also be used on a wider range of vessels including those with limited deck space. The BGS RockDrill2 can core up to 55m sub-seabed by focussing on reducing the overall weight therefore extending operational water depth to 4000m