The optimal convergence of the h–p version of the boundary element method with quasiuniform meshes for elliptic problems on polygonal domains

In the framework of the Jacobi-weighted Besov spaces, we analyze the lower and upper bounds of errors in the h–p version of boundary element solutions on quasiuniform meshes for elliptic problems on polygons. Both lower bound and upper bound are optimal in h and p, and they are of the same order. The optimal convergence of the h–p version of boundary element method with quasiuniform meshes is proved, which includes the optimal rates for h version with quasiuniform meshes and the p version with quasiuniform degrees as two special cases. Dedicated to Professor Charles Micchelli on the occasion of his sixtieth birthday Mathematics subject classification (2000) 65N38. Benqi Guo: The work of this author was supported by NSERC of Canada under Grant OGP0046726 and was complete during visiting Newton Institute for Mathematical Sciences, Cambridge University for participating in special program “Computational Challenges in PDEs” in 2003. Norbert Heuer: This author is supported by Fondecyt project No. 1010220 and by the FONDAP Program (Chile) on Numerical Analysis. Current address: Mathematical Sciences, Brunel University, Uxbridge, U.K.     

A posteriori error analysis for a boundary element method with nonconforming domain decomposition

We present and analyze an a posteriori error estimator based on mesh refinement for the solution of the hypersingular boundary integral equation governing the Laplacian in three dimensions. The discretization under consideration is a nonconforming domain decomposition method based on the Nitsche technique. Assuming a saturation property, we establish quasireliability and efficiency of the error estimator in comparison with the error in a natural (nonconforming) norm. Numerical experiments with uniform and adaptively refined meshes confirm our theoretical results. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 947–963, 2014     

Coupling of mixed finite element and stabilized boundary element methods for a fluid–solid interaction problem in 3D

We introduce and analyze the coupling of a mixed finite element and a boundary element for a three‐dimensional time‐harmonic fluid–solid interaction problem. We consider a formulation in which the Cauchy stress tensor and the rotation are the main variables in the elastic structure and use the usual pressure formulation in the acoustic fluid. The mixed variational formulation in the solid is completed with boundary integral equations relating the Cauchy data of the acoustic problem on the coupling interface. A crucial point in our formulation is the stabilization technique introduced by Hiptmair and coworkers to avoid the well‐known instability issue appearing in the boundary element method treatment of the exterior Helmholtz problem. The main novelty of this formulation, with respect to a previous approach, consists in reducing the computational domain to the solid media and providing a more accurate treatment of the far field effect. We show that the continuous problem is well‐posed and propose a conforming Galerkin method based on the lowest‐order Arnold–Falk–Winther mixed finite element. Finally, we prove that the numerical scheme is convergent with optimal order.Copyright © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1211–1233, 2014     

An hp‐adaptive refinement strategy for hypersingular operators on surfaces

An adaptive refinement strategy for the hp‐version of the boundary element method with hypersingular operators on surfaces is presented. The error indicators are based on local projections provided by two‐level decompositions of ansatz spaces with additional bubble functions. Assuming a saturation property and locally quasi‐uniform meshes, efficiency and reliability of the resulting error estimator is proved. A second error estimator based on mesh refinement and overlapping decompositions that better fulfills the saturation property is presented. The performance of the algorithm and the estimators is demonstrated for a model problem. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 396–419, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10011     

Odds versus evens in Silverman-type games

A class of Silverman-like games is considered where the players need not choose numbers from the same set. The case where Player I chooses from the positive odd integers and Player II from the positive even integers is analyzed for all threshold and penalty values. Optimal strategies, involving only finitely many pure strategies, exist in all cases and are obtained explicitly. The game value is found in all cases. The game never favors the evens, almost always favors the odds, but in a curious sequence of special cases is fair.     

Structural relaxation of polymers at the glass transition: conformational memory in poly(n-alkylmethacrylates)

Conformational memory is introduced as a new aspect of structural relaxation of polymers. In poly(n-alkylmethacrylates) extended backbone chain conformations are identified by advanced NMR techniques as the molecular units involved in structural relaxation. They retain conformational memory over many steps of restricted axial chain motion. Randomization of conformation and isotropization of backbone orientation occur on the same time scale, yet much slower than the slowest relaxation process identified so far. Behavior typical of fragile glass formers is found for this new process of chain relaxation.     

New dicarboxylic acid bipyridine ligand for ruthenium polypyridyl sensitization of TiO2

An ambidentate dicarboxylic acid bipyridine ligand, (4,5-diazafluoren-9-ylidene) malonic acid (dfm), was synthesized for coordination to Ru(II) and mesoporous nanocrystalline (anatase) TiO(2) thin films. The dfm ligand provides a conjugated pathway from the pyridyl rings to the carbonyl carbons of the carboxylic acid groups. X-ray crystal structures of [Ru(bpy)(2)(dfm)]Cl(2) and the corresponding diethyl ester compound, [Ru(bpy)(2)(defm)](PF(6))(2), were obtained. The compounds displayed intense metal-to-ligand charge transfer (MLCT) absorption bands in the visible region (ε > 11,000 M(-1) cm(-1) for [Ru(bpy)(2)(dfm)](PF(6))(2) in acetonitrile). Significant room temperature photoluminescence, PL, was absent in CH(3)CN but was observed at 77 K in a 4:1 EtOH:MeOH (v:v) glass. Cyclic voltammetry measurements revealed quasi-reversible Ru(III/II) electrochemistry. Ligand reductions were quasi-reversible for the diethyl ester compound [Ru(bpy)(2)(defm)](2+), but were irreversible for [Ru(bpy)(2)(dfm)](2+). Both compounds were anchored to TiO(2) thin films by overnight reactions in CH(3)CN to yield saturation surface coverages of 3 × 10(-8) mol/cm(2). Attenuated total reflection infrared measurements revealed that the [Ru(bpy)(2)(dfm)](2+) compound was present in the deprotonated carboxylate form when anchored to the TiO(2) surface. The MLCT excited states of both compounds injected electrons into TiO(2) with quantum yields of 0.70 in 0.1 M LiClO(4) CH(3)CN. Micro- to milli-second charge recombination yielded ground state products. In regenerative solar cells with 0.5 M LiI/0.05 M I(2) in CH(3)CN, the Ru(bpy)(2)(dfm)/TiO(2) displayed incident photon-to-current efficiencies of 0.7 at the absorption maximum. Under the same conditions, the diethylester compound was found to rapidly desorb from the TiO(2) surface.     

Fitness,chance, and myths: an objective view on soccer results

We analyze the time series of soccer matches in a model-free way using data for the German soccer league (Bundesliga). We argue that the goal difference is a better measure for the overall fitness of a team than the number of points. It is shown that the time evolution of the table during a season can be interpreted as a random walk with an underlying constant drift. Variations of the overall fitness mainly occur during the summer break but not during a season. The fitness correlation shows a long-time decay on the scale of a quarter century. Some typical soccer myths are analyzed in detail. It is shown that losing but no winning streaks exist. For this analysis ideas from multidimensional NMR experiments have been borrowed. Furthermore, beyond the general home advantage there is no statistically relevant indication of a team-specific home fitness. Based on these insights a framework for a statistical characterization of the results of a soccer league is introduced and some general consequences for the prediction of soccer results are formulated.     

Origin of complex fragments from32S+natAg reaction at 37.5 A·MeV

Fragment emission from collisions of³²S with^natAg at 37.5 A·MeV has been studied with the 4π multi-detector AMPHORA. Production of intermediate mass and heavy fragments as well as of light charged particles has been measured. The total charged particle multiplicity and polar angular distributions have been used to select various classes of collisions. Analysis of angular and energy distributions of fragments and light particles in central collisions indicates the formation of a hot source (excitation energy of≈4.4 A·MeV) with an additional contribution from a preequilibrium process at more forward angles. Azimuthal angle correlations of He-Li, Li-Li, B-B, and C-C pairs have been used as a tool to study the origin of complex fragments. Data at backward angles are well described by considering a thermalized emitter with an angular momentum around 70? and a fragment emission time of the order of 200 fm/c. A microscopic approach of BNV type confirms these emission times and angular momenta indicating the persistence of an incomplete fusion process responsible for the emission of complex fragments at backward angles.     

Measurements of total fast neutron cross sections for aluminum and barium by application of Si(Li)-detectors

Total neutron cross sections of²⁷Al and natural barium have been determined at bombarding energies in the range between 5.5 MeV and 9.6 MeV by transmission measurements. Si(Li)-detectors were used for neutron spectroscopy via charged particle reactions in the active volumes of the detectors. Inscattering corrections have been made by means of a Monte Carlo computer program. In most cases the measured cross sections have root-mean-square uncertainties of 1% to 3%. Cross sections of barium not yet measured have been calculated using optical model potential parameters obtained from an analysis of the experimental results.