Array of femtosecond plasma channels in fused silica

We have shown experimentally and confirmed by means of full dimensional (3D + 1) numerical simulations, the possibility to create an array of refractive index modification zones inside a fused silica sample using a 43 fs, 2 mJ, 800 nm laser pulse and a periodic mesh introduced in front of the sample. Robust filaments and the corresponding refractive index modification zones preserve their transverse positions for more than 10 Rayleigh lengths (∼500 μm). Numerical simulations prove that each mesh unit is an independent source of the background energy for a filament formed within this unit. The effect of the simultaneous formation of many extended periodically spaced filaments can be used to accelerate the fabrication of microoptics devices.     

On the almost automorphy of bounded solutions of differential equations with piecewise constant argument

In this paper we give sufficient spectral conditions for the almost automorphy of bounded solutions to differential equations with piecewise constant argument of the form x^′(t)=Ax([t])+f(t), t∈R, where A is a bounded linear operator in X and f is an X-valued almost automorphic function.     

Ferromagnetism in transition-metal-doped semiconducting oxide thin films

A rather complete work on transition-metal (TM)-doped TiO₂ thin films has been done and room ferromagnetism (FM) is found in the whole series of Sc/V/Cr/Mn/Fe/Co/Ni-doped TiO₂ films. Not only is it remarkable that for the first time, FM at high temperature was achieved in TM-doped TiO₂, but also a very big magnetic moment of 4.2μ_B/atom could be obtained, and direct evidences of real ferromagnets with big domains were shown as well. A similar chemical trend was achieved in TM-doped In₂O₃ films, however, the observed magnetic moment is rather modest, with the maximal value is of only 0.7μ_B/atom for Ni-doped In₂O₃ films. As regards TM-doped SnO₂ films, observed magnetic moments could be very large, with the maximum saturation of 6μ_B per impurity atom for Cr-doped SnO₂ thin films, but it could be influenced very much depending on substrate types. On the other hand, results on TM-doped ZnO films interestingly have revealed that in these systems, the magnetism more likely resulted from defects and/or oxygen vacancies.     

Dendrite-like texture growth in the nematic liquid crystal phase of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids aligned by a polyimide coating

An oriented dendrite-like texture is reported, appearing at a definite temperature in the nematic phase range of 4-n-heptyl- and 4-n-octyl-oxybenzoic acids (HOBA and OOBA), aligned by rubbed polyimide and preceding the smectic C phase, on cooling. Two preferred directions with respect to the 'easy' axis are indicated in the dendrites grown of HOBA and OOBA. We discuss a possible mechanism, at molecular and supramolecular levels, for this dendrite growth; and assume that the building 'blocks' of the dendrites are oligomers, or mixture of oligomers with 'free' closed and open dimers, constituting a detached crystalline layered state (named by us SmX, a smectic state intermediate between the N₁ ordinary nematic and SmC phases). The study of the dynamics of the dendrite growth demonstrates a scaling relationship typical for non-equilibrium systems. The observed dendrites can be considered as patterns formed in complex non-linear dissipative systems, driven outside of equilibrium.     

On Grushin’s equation

The paper deals with nonlinear problems for equations of Grushin type. We prove some nonexistence results via Pokhozhaev’s identity. In the rest of the paper we prove some results on smoothness near the boundary of eigenfunctions by using an explicit formula for fundamental solutions and the Kelvin transform for the operator.     

The stationary three‐dimensional Navier–Stokes equations with a non‐zero constant velocity at infinity

This paper is devoted to some mathematical questions related to the three‐dimensional stationary Navier–Stokes equations. Our approach is based on a combination of properties of Oseen problems in ?³. Copyright © 2008 John Wiley & Sons, Ltd.     

Studies on the deposition of acid and of ecotoxic heavy metals with precipitates from the atmosphere

Summary For the input of ecotoxic heavy metals (Cd, Pb, Cu, Zn and Ni) from the atmosphere into terrestrial and aquatic ecosystems their wet deposition with rain (and snow) has been established as the deposition type of predominant significance. The wet deposition situation in the Federal Republic of Germany has been observed systematically since 1980 with a network of automated samplers of own construction distributed over the various regions of the country (German Wet Deposition Program). These regions include rural areas from the North Sea coast to the Alps as well as urban agglomerations, industrial zones and locations with particular heavy metal emissions. The analysis of the heavy metals is carried out by differential pulse stripping voltammetry or for Ni by adsorption differential pulse voltammetry. At the same time the determination of the H⁺-concentration by electrometric high precision pH-measurements provides for the observation period 1980–1982 a survey on the acid deposition in the various regions of the Federal Republic of Germany. Based on reliable experimental data the main contours and the dimensions of the present burden by the deposition of acid rain and the wet deposition of ecotoxic heavy metals emerge.

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Untersuchungen über die Deposition von Säure und ökotoxischen Schwermetallen mit Niederschlägen aus der Atmosphäre

Zusammenfassung Für den Eintrag ökotoxischer Schwermetalle (Cd, Pb, Cu, Zn und Ni) aus der Atmosphäre in terrestrische und aquatische Ökosysteme hat sich die Naßdeposition als die vorherrschende Depositionsart erwiesen. Die Situation hinsichtlich der Naßdeposition in der Bundesrepublik Deutschland wird seit 1980 systematisch mit einem über das gesamte Bundesgebiet verteilten Netz automatischer Sammler eigener Entwicklung verfolgt (Deutsches Naßdepositionsprogramm). Die untersuchten Regionen schließen ländliche Gebiete von der Nordseeküste bis zu den Alpen ein sowie Ballungsräume, Industriezonen und Orte mit besonderer Schwermetallemission. Die Schwermetallanalyse erfolgt mit differentieller Pulsinversvoltammetrie oder für Ni mit differentieller Adsorptions-Pulsvoltammetrie. Gleichzeitig resultiert auf Grund präziser elektrometrischer pH-Messungen ein Überblick über die Säuredeposition in den verschiedenen Regionen des Bundesgebietes für den Beobachtungszeitraum 1980–1982. Basierend auf zuverlässigen experimentellen Daten ergaben sich die wesentlichen Konturen und die Dimensionen der gegenwärtigen Belastung der Bundesrepublik durch die Deposition von saurem Regen und die Naßdeposition ökotoxisch wirksamer Schwermetalle.

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Dedicated to Prof. Dr. W. Fresenius on the occasion of his 70th birthday

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Guest scientist from Univ. Fed. do Ceara, Fortaleza, Brasil     

Solution domain decomposition with finite difference methods for partial differential equations

The Solution Domain Decomposition method of Nguyen and Paik [J. Sci. Comput. 4 , 357 (1993)] originally developed in a pseudospectral context is extended for use with finite difference techniques to solve partial differential equations. The essential idea behind this method lies in an application of the superposition principle, which allows interactions between adjacent subdomains to be decoupled and the resulting equations to be solved in parallel. Several tests are performed to assess its accuracy and efficiency based on a model problem arising from thermal convection inside a fluid-saturated porous cavity with heating from a side. The results reveal a well adaptation of the methodology into the framework of finite differences. © 1995 John Wiley & Sons, Inc.