hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

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.

Northern Hemisphere temperature reconstruction during the last millennium using multiple annual proxies

Previous studies have either exclusively used annual tree-ring data or have combined tree-ring series with other, lower temporal resolution proxy series. Both approaches can lead to significant uncertainties, as tree-rings may underestimate the amplitude of past temperature variations, and the validity of non-annual records cannot be clearly assessed. In this study, we assembled 45 published Northern Hemisphere (NH) temperature proxy records covering the past millennium, each of which satisfied 3 essential criteria: the series must be of annual resolution, span at least a thousand years, and represent an explicit temperature signal. Suitable climate archives included ice cores, varved lake sediments, tree-rings and speleothems. We reconstructed the average annual land temperature series for the NH over the last millennium by applying 3 different reconstruction techniques: (1) principal components (PC) plus second-order autoregressive model (AR2), (2) composite plus scale (CPS) and (3) regularized errors-in-variables approach (EIV). Our reconstruction is in excellent agreement with 6 climate model simulations (including the first 5 models derived from the fifth phase of the Coupled Model Intercomparison Project (CMIP5) and an earth system model of intermediate complexity (LOVECLIM), showing similar temperatures at multi-decadal timescales; however, all simulations appear to underestimate the temperature during the Medieval Warm Period (MWP). A comparison with other NH reconstructions shows that our results are consistent with earlier studies. These results indicate that well-validated annual proxy series should be used to minimize proxy-based artifacts, and that these proxy series contain sufficient information to reconstruct the low-frequency climate variability over the past millennium.

Performance on auditory and visual temporal informationprocessing is related to psychometric intelligence

The present study investigated the relationship between psychometric intelligence and temporal resolution power (TRP) as simultaneously assessed by auditory and visual psychophysical timing tasks. In addition, three different theoretical models of the functional relationship between TRP and psychometric intelligence as assessed by means of the Adaptive Matrices Test (AMT) were developed. To test the validity of these models, structural equation modeling was applied. Empirical data supported a hierarchical model that assumed auditory and visual modality-specific temporal processing at a first level and amodal temporal processing at a second level. This second-order latent variable was substantially correlated with psychometric intelligence. Therefore, the relationship between psychometric intelligence and psychophysical timing performance can be explained best by a hierarchical model of temporal information processing.

Measurement with the ATLAS detector of multi-particle azimuthal correlations in p+Pb collisions at sqrtsNN=5.02 TeV

In order to study further the long-range correlations ("ridge") observed recently in p+Pb collisions at sqrt(s_NN) =5.02 TeV, the second-order azimuthal anisotropy parameter of charged particles, v_2, has been measured with the cumulant method using the ATLAS detector at the LHC. In a data sample corresponding to an integrated luminosity of approximately 1 microb^(-1), the parameter v_2 has been obtained using two- and four-particle cumulants over the pseudorapidity range |eta|<2.5. The results are presented as a function of transverse momentum and the event activity, defined in terms of the transverse energy summed over 3.1models of p+Pb collisions. Despite the small transverse spatial extent of the p+Pb collision system, the large magnitude of v_2 and its similarity to hydrodynamic predictions provide additional evidence for the importance of final-state effects in p+Pb reactions.

A potential application of sludge-based catalysts for the anaerobic bio-decolorization of tartrazine dye.

Two highly efficient (K2CO3/sludge carbon and ZnCl2/sludge carbon) solids were prepared by chemical addition following carbonization at 800 °C and were tested for anaerobic reduction of tartrazine dye in a continuous upflow packed-bed biological reactor, and their performance was compared to that of commercial activated carbon (CAC). The chemical and structural information of the solids was subjected to various characterizations in order to understand the mechanism for anaerobic decolorization, and efficiency for SBCZN800 and SBCPC800 materials was 87% and 74%, respectively, at a short space time (τ) of 2.0 min. A first-order kinetic model fitted the experimental points and kinetic constants of 0.40, 0.92 and 1.46 min(-1) were obtained for SBCZN800, SBCPC800 and CAC, respectively. The experimental results revealed that performance of solids in the anaerobic reduction of tartrazine dye can depend on several factors including chemical agents, carbonization, microbial population, chemical groups and surface chemistry. The Langmuir and Freundlich models are successfully described in the batch adsorption data. Based on these observations, a cost-effective sludge-based catalyst can be produced from harmful sewage sludge for the treatment of industrial effluents.