An optimal order collocation method for first kind boundary integral equations on polygons.

This paper discusses the convergence of the collocation method using splines of any order k for first kind integral equations with logarithmic kernels on closed polygonal boundaries in ℝ2. Before discretization the equation is transformed to an equivalent equation over [-π,π] using a nonlinear parametrization of the polygon which varies more slowly than arc-length near each corner. This has the effect of producing a transformed equation with a solution which is smooth on [-π,π]. This latter integral equation is shown to be well-posed in appropriate Sobolev spaces. The structure of the integral operator is described in detail, and can be written in terms of certain non-standard Mellin convolution operators. Using this information we are able to show that the collocation method using splines of order k (degree k-1) converges with optimal order O(hk). (The collocation points are the midpoints of subintervals when k is odd and the break-points when k is even, and stability is shown under the assumption that the method may be modified slightly.) Using the numerical solutions to the transformed equation we construct numerical solutions of the original equation which converge optimally in a certain weighted norm. Finally the method is shown to produce superconvergent approximations to interior potentials such as those used to solve harmonic boundary value problems by the boundary integral method. The convergence results are illustrated with some numerical examples

The Long-Baseline Neutrino Experiment: Exploring Fundamental Symmetries of the Universe

The preponderance of matter over antimatter in the early Universe, the dynamics of the supernova bursts that produced the heavy elements necessary for life and whether protons eventually decay --- these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our Universe, its current state and its eventual fate. The Long-Baseline Neutrino Experiment (LBNE) represents an extensively developed plan for a world-class experiment dedicated to addressing these questions. LBNE is conceived around three central components: (1) a new, high-intensity neutrino source generated from a megawatt-class proton accelerator at Fermi National Accelerator Laboratory, (2) a near neutrino detector just downstream of the source, and (3) a massive liquid argon time-projection chamber deployed as a far detector deep underground at the Sanford Underground Research Facility. This facility, located at the site of the former Homestake Mine in Lead, South Dakota, is approximately 1,300 km from the neutrino source at Fermilab -- a distance (baseline) that delivers optimal sensitivity to neutrino charge-parity symmetry violation and mass ordering effects. This ambitious yet cost-effective design incorporates scalability and flexibility and can accommodate a variety of upgrades and contributions. With its exceptional combination of experimental configuration, technical capabilities, and potential for transformative discoveries, LBNE promises to be a vital facility for the field of particle physics worldwide, providing physicists from around the globe with opportunities to collaborate in a twenty to thirty year program of exciting science. In this document we provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess.Comment: Major update of previous version. This is the reference document for LBNE science program and current status. Chapters 1, 3, and 9 provide a comprehensive overview of LBNE's scientific objectives, its place in the landscape of neutrino physics worldwide, the technologies it will incorporate and the capabilities it will possess. 288 pages, 116 figure

Azimuthal anisotropy of charged jet production in root s(NN)=2.76 TeV Pb-Pb collisions

We present measurements of the azimuthal dependence of charged jet production in central and semi-central root s(NN) = 2.76 TeV Pb-Pb collisions with respect to the second harmonic event plane, quantified as nu(ch)(2) (jet). Jet finding is performed employing the anti-k(T) algorithm with a resolution parameter R = 0.2 using charged tracks from the ALICE tracking system. The contribution of the azimuthal anisotropy of the underlying event is taken into account event-by-event. The remaining (statistical) region-to-region fluctuations are removed on an ensemble basis by unfolding the jet spectra for different event plane orientations independently. Significant non-zero nu(ch)(2) (jet) is observed in semi-central collisions (30-50% centrality) for 20 <p(T)(ch) (jet) <90 GeV/c. The azimuthal dependence of the charged jet production is similar to the dependence observed for jets comprising both charged and neutral fragments, and compatible with measurements of the nu(2) of single charged particles at high p(T). Good agreement between the data and predictions from JEWEL, an event generator simulating parton shower evolution in the presence of a dense QCD medium, is found in semi-central collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Forward-central two-particle correlations in p-Pb collisions at root s(NN)=5.02 TeV

Two-particle angular correlations between trigger particles in the forward pseudorapidity range (2.5 2GeV/c. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B. V.Peer reviewe

Event-shape engineering for inclusive spectra and elliptic flow in Pb-Pb collisions at root(NN)-N-S=2.76 TeV

Peer reviewe

Centrality evolution of the charged-particle pseudorapidity density over a broad pseudorapidity range in Pb-Pb collisions at root s(NN)=2.76TeV

Peer reviewe

Pseudorapidity and transverse-momentum distributions of charged particles in proton-proton collisions at root s=13 TeV

The pseudorapidity (eta) and transverse-momentum (p(T)) distributions of charged particles produced in proton-proton collisions are measured at the centre-of-mass energy root s = 13 TeV. The pseudorapidity distribution in vertical bar eta vertical bar <1.8 is reported for inelastic events and for events with at least one charged particle in vertical bar eta vertical bar <1. The pseudorapidity density of charged particles produced in the pseudorapidity region vertical bar eta vertical bar <0.5 is 5.31 +/- 0.18 and 6.46 +/- 0.19 for the two event classes, respectively. The transverse-momentum distribution of charged particles is measured in the range 0.15 <p(T) <20 GeV/c and vertical bar eta vertical bar <0.8 for events with at least one charged particle in vertical bar eta vertical bar <1. The evolution of the transverse momentum spectra of charged particles is also investigated as a function of event multiplicity. The results are compared with calculations from PYTHIA and EPOS Monte Carlo generators. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe

Elliptic flow of muons from heavy-flavour hadron decays at forward rapidity in Pb-Pb collisions at root s(NN)=2.76TeV

The elliptic flow, v(2), of muons from heavy-flavour hadron decays at forward rapidity (2.5 <y <4) is measured in Pb-Pb collisions at root s(NN)= 2.76TeVwith the ALICE detector at the LHC. The scalar product, two- and four-particle Q cumulants and Lee-Yang zeros methods are used. The dependence of the v(2) of muons from heavy-flavour hadron decays on the collision centrality, in the range 0-40%, and on transverse momentum, p(T), is studied in the interval 3 <p(T)<10 GeV/c. A positive v(2) is observed with the scalar product and two-particle Q cumulants in semi-central collisions (10-20% and 20-40% centrality classes) for the p(T) interval from 3 to about 5GeV/c with a significance larger than 3 sigma, based on the combination of statistical and systematic uncertainties. The v(2) magnitude tends to decrease towards more central collisions and with increasing pT. It becomes compatible with zero in the interval 6 <p(T)<10 GeV/c. The results are compared to models describing the interaction of heavy quarks and open heavy-flavour hadrons with the high-density medium formed in high-energy heavy-ion collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V.Peer reviewe