On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems

Consider a linear ordinary differential equation of the 2nd order which has a singularity at the origin; according to the nature of this singularity we must consider either the two-point boundary-value problem or the one-point boundary value problem. Finite-difference schemes are studied; results are given concerning error analysis and monotone convergence.The material of this paper is taken from the author's doctoral thesis [2]. The author is greatly indebted to his adviser S. V. Parter. - Sponsored by the Mathematics Research Center, United States Army, Madison, Wisconsin, under Contract No.: DA-31-124-ARO-D-462.     

Quantitative determination of tertatolol in biological fluids by gas chromatography-mass spectrometry

Quantitative determination of tertatolol concentrations in plasma and urine was performed by gas chromatography-mass spectrometry in the chemical-ionization mode with ammonia after successive extractions of the beta-blocking drug in alkaline, acid and final alkaline medium. [2H9]Tertatolol, isotopically stable under the operating conditions employed, was used as an internal standard, thus allowing quantities of 1 ng/ml to be specifically determined. Overall analytical error was less than 10%. Prior to isothermal chromatography at 240 degrees C on a column packed with 3% SE-30, both compounds were silylated with bis(trimethylsilyl)trifluoroacetamide. Detection was performed by monitoring the quasimolecular ions of tertatolol, m/z 368 and m/z 377, for the [2H9]tertatolol in the chemical-ionization mode with ammonia. The calibration curves obtained had linear characteristics for the concentration range 1-1125 ng/ml.     

Exploration of the ultimate patterning potential achievable with high resolution focused ion beams

Controlled and reproducible fabrication of nano-structured materials will be one of the main industrial challenges in the next few years. We have recently proposed exploitation of the nano-structuring potential of a high resolution Focused Ion Beam Tool, to overcome basic limitations of current nano-fabrication techniques. The aim of this article is to present some new routes for material patterning, which benefit from ion-induced local property modifications or damage. In the experiments we describe hereafter an ultra-sharp pencil of 30 keV gallium ions is used to tailor the characteristics of several materials at a scale of a few nanometres. The experimental results are then compared to simulations. First, we simulate the control of collisional defects generated in a thin magnetic layer under FIB irradiation. The results explain the stable magnetic structures we have obtained experimentally. This was achieved with a low surface ion dose (10¹² to 10¹⁴ ions/cm²). In addition we have explored the promising direction of Bottom-up or self-organization processes using a FIB instrument. We have defined artificial surface defects. These defects created by the impact of an 8-nm FWHM probe were used to pin the diffusion and to organize nanometre-sized gold clusters on a graphite surface. PACS 79.20.Rf; 81.07.-b     

Deroughening of domain wall pairs by dipolar repulsion

As a magnetic domain wall propagates under small fields through a random potential, it roughens as a result of weak collective pinning, known as creep. Using Kerr microscopy, we report experimental evidence of a surprising deroughening of wall pairs in the creep regime, in a 0.5 nm thick Co layer with perpendicular anisotropy. A bound state is found in cases where two rough domains nucleated far away from one another and first growing under the action of a magnetic field eventually do not merge. The two domains remain separated by a strip of unreversed magnetization, characterized by flat edges and stabilized by dipolar fields. A creep theory that includes dipolar interactions between domains successfully accounts for (i) the domain wall deroughening as the width of the strip decreases and (ii) the quasistatic and dynamic field dependence of the strip width s.     

Magnetic anisotropy of a single cobalt nanocluster

Using a new micro-SQUID setup, we investigate magnetic anisotropy in a single 1000-atom cobalt cluster. This system opens new fields in the characterization and understanding of the origin of magnetic anisotropy in such nanoparticles. For this purpose, we report three-dimensional switching field measurements performed on a 3 nm cobalt cluster embedded in a niobium matrix. We are able to separate the different magnetic anisotropy contributions and evidence the dominating role of the cluster surface.     

Photorefractive effect applied to flatten Gaussian beam profiles of near infrared lasers

The resonant behaviour of the two-wave mixing gain as a function of the intensity in photorefractive InP:Fe crystals is applied to flatten the Gaussian profiles of a beam emitted by a Nd:YAG laser at λ=1.06 μm. This can be extended efficiently to other wavelengths in the spectral range where InP:Fe is photosensitive.     

Structural and magnetic properties of FIB-irradiated microstructures on a Pt/Co multilayer

We present a study of the structural and magnetic effects induced by focused 30 keV Ga⁺ ion beam irradiation on a Pt(2.8 nm)/[Pt(0.6 nm)/Co(0.3 nm)]₆/Pt(6.5 nm) ferromagnetic multilayer, using transmission electron microscopy, optical and magneto-optical microscopy. The work is of relevance to high-density data-storage applications, where media planarity is crucial for device reliability.     

Critical behaviour of the linear birefringence in 3d-Heisenberg antiferromagnets : RbMnF3, KNiF3 and KCoF3

The linear birefringence of stress induced single antiferromagnetic T-domains of RbMnF₃, KNiF₃ and KCoF₃ has been measured in the vicinity of T_N. We deduce the critical behaviour in such 3d-Heisenberg systems, showing a symmetry breaking at the transition involving a unique wave vector of the order parameter in the Brillouin zone. The critical exponent $\text{β}$ of the linear birefringence has been found to be larger than 2β, in agreement with the theoretical predictions of G. Gehring.