The sdfem on Shishkin meshes for linear convection-diffusion problems

Summary. We consider singularly perturbed linear elliptic problems in two dimensions. The solutions of such problems typically exhibit layers and are difficult to solve numerically. The streamline diffusion finite element method (SDFEM) has been proved to produce accurate solutions away from any layers on uniform meshes, but fails to compute the boundary layers precisely. Our modified SDFEM is implemented with piecewise linear functions on a Shishkin mesh that resolves boundary layers, and we prove that it yields an accurate approximation of the solution both inside and outside these layers. The analysis is complicated by the severe nonuniformity of the mesh. We give local error estimates that hold true uniformly in the perturbation parameter , provided only that , where mesh points are used. Numerical experiments support these theoretical results. Received February 19, 1999 / Revised version received January 27, 2000 / Published online August 2, 2000     

Two types of limit cycles of a resonant converter modelled by a three-dimensional system

In this paper, the long-run dynamics of a resonant converter is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the long-run dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.     

Iterative Algorithms for Multiscale State Estimation, Part 2: Numerical Investigations

Usually, direct methods are employed for the solution of linear systems arising in the context of optimization. However, motivated by the potential of multiscale refinement schemes for large problems of dynamic state estimation, we investigate in this paper the application of iterative solvers based on the concepts developed in Ref. 1. Specifically, we explore the effect of different system reductions for various Krylov-space iteration methods as well as three concepts of preconditioning. The first one is the normalization of states and outputs, which also favors error analysis. Next, diagonal scale-dependent preconditioners are compared; they all bound the condition numbers independently of the refinement scale, but exhibit significant quantitative differences. Finally, the effect of the regularization parameter on condition numbers and iteration numbers is analyzed. It turns out that a so-called simplified Uzawa scheme with Jacobi preconditioning and suitable regularization parameter is most efficient. The experiments also reveal that further improvements are necessary.     

Photometrische Messung der Konzentration und Dispersität in kolloiden Lösungen. I. Lichtschwächungsmessung

Ohne Zusammenfassung     

Synthesis of rigid photoswitchable hemithioindigo ω-amino acids

The synthesis of novel N-Boc- and N-Fmoc protected hemithioindigo-based ω-amino acids is described. An approach to modulate the thermal stability of a hemithioindigo subunit is presented. Placing the amino-group in the stilbene part from the para- to meta-position leads to an increase of the half-life of the thermally labile E-form from 19 h to 47 h.     

Nondestructive three-dimensional analysis of layered polymer structures with chemical imaging

Three-dimensional (3D) chemical information was obtained by means of a combination of two-dimensional attenuated total reflection Fourier transform infrared (ATR-FT-IR) imaging with a focal plane array detector and variable angle depth profiling. Since the penetration depth of the evanescent wave in ATR spectroscopy is not limited by diffraction, it was possible to resolve thin sandwiched polymer layers nondestructively within a stack of polymer layers. Chemical images were obtained from layers of different thickness of the laminate by moving a custom-made aperture to specific positions on the condenser lens of the ATR accessory. Sequences of absorption images detect the successive appearance of thin, buried layers of polybutylmethacrylate (d(PBMA) = 400 nm) and polycarbonate (d(TMPC) = 300 nm) in different depths of the stack of polymer layers. The depth resolution of variable-angle ATR-FT-IR imaging is sufficiently high to detect surface roughness at the interface between different polymer layers. Two different stacks of polymers with reordered sandwich-layers were imaged simultaneously, demonstrating the potential of variable angle ATR-FT-IR for 3D-imaging of a sample with xyz-heterogeneity, which can be a powerful analytical technique for materials science and biomedical research.     

Ordered mesoporous MFe(2)O(4) (M = Co, Cu, Mg, Ni, Zn) thin films with nanocrystalline walls, uniform 16 nm diameter pores and high thermal stability: template-directed synthesis and characterization of redox active trevorite

In this paper, we report on ordered mesoporous NiFe(2)O(4) thin films synthesized via co-assembly of hydrated ferric nitrate and nickel chloride with an amphiphilic diblock copolymer, referred to as KLE. We establish that the NiFe(2)O(4) samples are highly crystalline after calcination at 600 °C, and that the conversion of the amorphous inorganic framework comes at little cost to the ordering of the high quality cubic network of pores averaging 16 nm in diameter. We further show that the synthesis method employed in this work can be readily extended to other ferrites, such as CoFe(2)O(4), CuFe(2)O(4), MgFe(2)O(4), and ZnFe(2)O(4), which could pave the way for innovative device design. While this article focuses on the self-assembly and characterization of these materials using various state-of-the-art techniques, including electron microscopy, grazing incidence small-angle X-ray scattering (GISAXS), time-of-flight secondary ion mass spectrometry (TOF-SIMS), X-ray photoelectron spectroscopy (XPS), as well as UV-vis and Raman spectroscopy, we also examine the electrochemical properties and show the benefits of combining a continuous mesoporosity with nanocrystalline films. KLE-templated NiFe(2)O(4) electrodes exhibit reasonable levels of lithium ion storage at short charging times which stem from facile pseudocapacitance.