Adaptive local grid refinement algorithms for finite-element collocation

An adaptive grid refinement procedure allows accurate solutions to advection-dominated, time-dependent flows using finite-element collocation. The technique relies on a data structure that is readily amenable to parallel computing. The paper discusses computational aspects of the method.     

Duality Principles in Frame Theory

Duality principles in Gabor theory such as the Ron–Shen duality principle and the Wexler–Raz biorthogonality relations play a fundamental role for analyzing Gabor systems. In this article we present a general approach to derive duality principles in abstract frame theory. For each sequence in a separable Hilbert space we define a corresponding sequence dependent only on two orthonormal bases. Then we characterize exactly properties of the first sequence in terms of the associated one, which yields duality relations for the abstract frame setting. In the last part we apply our results to Gabor systems.     

Affine Twin Buildings

It is well known from work of Bruhat and Tits that an affinebuilding has a spherical building at infinity. The paper studiesthe structure at infinity for an affine twin building. It isshown that the twinning restricts the structure at infinityin a natural way, producing two smaller spherical buildingsthat are canonically isomorphic to one another. In the processit is shown that to each wall and panel of these buildings atinfinity is attached a twin tree.     

A very simple algorithm for estimating the number of k-colorings of a low-degree graph

A fully polynomial randomized approximation scheme is presented for estimating the number of (vertex) k-colorings of a graph of maximum degree Δ, when k ≥ 2Δ + 1. © 1995 John Wiley & Sons, Inc.     

Pseudo-Anosov foliations on periodic surfaces

We study lifts of the stable foliation of a pseudo-Anosov diffeomorphism to abelian covers. Under certain conditions, we show that it is ergodic but not uniquely ergodic and describe the ergodic measures.     

Mean curvature flow with a forcing term in minkowski space

We study the forced mean curvature flow of graphs in Minkowski space and prove longtime existence of solutions. When the forcing term is a constant, we prove convergence to either a constant mean curvature hypersurface or a translating soliton – depending on the boundary conditions at infinity. It is a pleasure to thank my PhD advisors Klaus Ecker and Gerhard Huisken for their assistance and encouragement. I also thank Maria Athanassenas, Oliver Schnürrer and Marty Ross for their interest and useful comments, and the Max Planck Gesellschaft for financial support.     

Adhesion studies of latex film surfaces on the meso- and nanoscale

In this paper the effects of surface roughness and annealing temperature (T) of latex coating films on adhesion are discussed for the different stages of the film formation process. The surface free energy of latex films was assessed in terms of practical work of adhesion (W) (or adherence) using a custom-built adhesion-testing device (ATD), atomic force microscopy (AFM), and contact angle measurements. For preannealed latex films surface roughness averages (R_a) were determined from AFM height images and were related to the values of W obtained from ATD measurements at room temperature. The results obtained using these tests exhibiting surface behavior on different length scales indicate a dependence of the measured adhesion on surface roughness and temperature, as well as on the length scale of the measurements.First preannealed samples were studied, which were obtained by heat treatment above the respective glass transition temperatures (T_g). Increasing the temperature of preannealing resulted in a decrease of the adherence observed in ATD experiments at room temperature. However, on the nanoscale, using AFM, no significant variation of the adherence was observed. This observation can be explained by roughness arguments. Preannealing decreases roughness which results in lower adherence values measured by ATD while for essentially single asperity AFM experiments roughness has an insignificant effect. Specimens were also annealed over a constant period of time (90 min) at different temperatures. At the end of the heat treatment, adhesion was measured at the treatment temperature by ATD. The amplified effect of temperature observed in this case on adherence is attributed to the combination of roughness decrease and increasing test temperature. In a third set of experiments completely annealed samples were studied by ATD as well as by AFM as a function of temperature. With increasing T values ATD showed a decrease in adherence, which is attributed to a decreasing surface free energy of the annealed films at elevated T values. AFM, on the other hand, showed an opposite trend which is assigned to increasing penetration of the tip into the tip/wetting polymer samples versus increasing temperature. Finally, annealing isotherms as a function of time were investigated by ATD in situ at different temperatures. This last set of experiments allowed us to optimize annealing time and temperature to achieve complete curing.     

New interpretations of XPS spectra of nickel metal and oxides

A current interpretation of XPS spectra of Ni metal assumes that the main 6 eV satellite is due to a two hole c3d⁹4s² (c is a core hole) final state effect. We report REELS observation in AES at low voltages of losses (plasmons and inter-band transitions) corresponding to the satellite structures in Ni metal 2p spectra. The satellite near 6 eV is attributed to a predominant surface plasmon loss. A current interpretation of Ni 2p spectra of oxides and other compounds is based on charge transfer assignments of the main peak at 854.6 eV and the broad satellite centred at around 861 eV to the cd⁹L and the unscreened cd⁸ final-state configurations, respectively (L is a ligand hole). Multiplet splittings have been shown to be necessary for assignment of Fe 2p and Cr 2p spectral profiles and chemical states. The assignments of Ni 2p states are re-examined with intra-atomic multiplet envelopes applied to Ni(OH)₂, NiOOH and NiO spectra. It is shown that the free ion multiplet envelopes for Ni²⁺ and Ni³⁺ simulate the main line and satellite structures for Ni(OH)₂ and NiOOH. Fitting the NiO Ni 2p spectral profile is not as straightforward as the hydroxide and oxyhydroxide. It may involve contributions from inter-atomic, non-local electronic coupling and screening effects with multiplet structures significantly different from the free ions as found for MnO. A scheme for fitting these spectra using multiplet envelopes is proposed.