Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Measurement of the Azimuthal Angle Dependence of Inclusive Jet Yields in Pb+Pb Collisions at sqrts_NN= 2.76 TeV with the ATLAS detector

Measurements of the variation of inclusive jet suppression as a function of relative azimuthal angle, Delta phi, with respect to the elliptic event plane provide insight into the path-length dependence of jet quenching. ATLAS has measured the Delta phi dependence of jet yields in 0.14 nb(-1) of root s(NN) = 2.76 TeV Pb + Pb collisions at the LHC for jet transverse momenta p(T) > 45 GeV in different collision centrality bins using an underlying event subtraction procedure that accounts for elliptic flow. The variation of the jet yield with Delta phi was characterized by the parameter, nu(jet)(2), and the ratio of out-of-plane (Delta phi similar to pi/2) to in-plane (Delta phi similar to 0) yields. Nonzero nu(jet)(2) values were measured in all centrality bins for p(T) < 160 GeV. The jet yields are observed to vary by as much as 20% between in-plane and out-of-plane directions.

Measurement of ℤ boson Production in Pb+Pb Collision at sqrtsNN=2.76 TeV with the ATLAS Detector

The ATLAS experiment has observed 1995 Z boson candidates in data corresponding to 0.15 nb(-1) of integrated luminosity obtained in the 2011 LHC Pb + Pb run at root s(NN) = 2.76 TeV. The Z bosons are reconstructed via dielectron and dimuon decay channels, with a background contamination of less than 3%. Results from the two channels are consistent and are combined. Within the statistical and systematic uncertainties, the per-event Z boson yield is proportional to the number of binary collisions estimated by the Glauber model. The elliptic anisotropy of the azimuthal distribution of the Z boson with respect to the event plane is found to be consistent with zero.

Are We Sims? How Computer Simulations Represent and What this Means for the Simulation Argument

N. Bostrom’s simulation argument and two additional assumptions imply that we are likely to live in a computer simulation. The argument is based upon the following assumption about the workings of realistic brain simulations: The hardware of a computer on which a brain simulation is run bears a close analogy to the brain itself. To inquire whether this is so, I analyze how computer simulations trace processes in their targets. I describe simulations as fictional, mathematical, pictorial, and material models. Even though the computer hardware does provide a material model of the target, this does not suffice to underwrite the simulation argument because the ways in which parts of the computer hardware interact during simulations do not resemble the ways in which neurons interact in the brain. Further, there are computer simulations of all kinds of systems, and it would be unreasonable to infer that some computers display consciousness just because they simulate brains rather than, say, galaxies.

The hp-adaptive FEM based on continuous Sobolev embeddings: isotropic refinements

The aim of this paper is to present a new class of smoothness testing strategies in the context of hp-adaptive refinements based on continuous Sobolev embeddings. In addition to deriving a modified form of the 1d smoothness indicators introduced in [26], they will be extended and applied to a higher dimensional framework. A few numerical experiments in the context of the hp-adaptive FEM for a linear elliptic PDE will be performed.

Measurement of flow harmonics with multi-particle cumulants in Pb+Pb collisions at √sNN=2.76 TeV with the ATLAS detector

ATLAS measurements of the azimuthal anisotropy in lead–lead collisions at √sNN = 2.76 TeV are shown using a dataset of approximately 7μb−1 collected at the LHC in 2010. The measurements are performed for charged particles with transversemomenta 0.5 < pT < 20 GeV and in the pseudorapidity range |η| < 2.5. The anisotropy is characterized by the Fourier coefficients, vn, of the charged-particle azimuthal angle distribution for n = 2–4. The Fourier coefficients are evaluated using multi-particle cumulants calculated with the generating function method. Results on the transverse momentum, pseudorapidity and centrality dependence of the vn coefficients are presented. The elliptic flow, v2, is obtained from the two-, four-, six- and eight-particle cumulants while higher-order coefficients, v3 and v4, are determined with two- and four-particle cumulants. Flow harmonics vn measured with four-particle cumulants are significantly reduced compared to the measurement involving two-particle cumulants. A comparison to vn measurements obtained using different analysis methods and previously reported by the LHC experiments is also shown. Results of measurements of flow fluctuations evaluated with multiparticle cumulants are shown as a function of transverse momentum and the collision centrality. Models of the initial spatial geometry and its fluctuations fail to describe the flow fluctuations measurements.

Orbital elements of the material surrounding comet 67P/Churyumov-Gerasimenko

Context. We investigate the dust coma within the Hill sphere of comet 67P/Churyumov-Gerasimenko. Aims. We aim to determine osculating orbital elements for individual distinguishable but unresolved slow-moving grains in the vicinity of the nucleus. In addition, we perform photometry and constrain grain sizes. Methods. We performed astrometry and photometry using images acquired by the OSIRIS Wide Angle Camera on the European Space Agency spacecraft Rosetta. Based on these measurements, we employed standard orbit determination and orbit improvement techniques. Results. Orbital elements and effective diameters of four grains were constrained, but we were unable to uniquely determine them. Two of the grains have light curves that indicate grain rotation. Conclusions. The four grains have diameters nominally in the range 0.14-0.50 m. For three of the grains, we found elliptic orbits, which is consistent with a cloud of bound particles around the nucleus. However, hyperbolic escape trajectories cannot be excluded for any of the grains, and for one grain this is the only known option. One grain may have originated from the surface shortly before observation. These results have possible implications for the understanding of the dispersal of the cloud of bound debris around comet nuclei, as well as for understanding the ejection of large grains far from the Sun.