Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results

The absolutely continuous spectrum of one-dimensional Schrödinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectra of free and periodic Schrödinger operators are preserved under all perturbations satisfying This result is optimal in the power scale. Slightly more general classes of perturbing potentials are also treated. A general criterion for stability of the absolutely continuous spectrum of one-dimensional Schrödinger operators is established. In all cases analyzed, the main term of the asymptotic behavior of the generalized eigenfunctions is shown to have WKB form for almost all energies. The proofs rely on maximal function and norm estimates, and on almost everywhere convergence results for certain multilinear integral operators.

     

Thermal relaxation of glycerol and propylene glycol studied by photothermal spectroscopy

In this paper we report on experimental data for the frequency and temperature dependence of the thermal properties of supercooled glycerol and propylene glycol. By using a photopyroelectric method the specific heat capacity and thermal conductivity were separately determined in a bandwidth of several decades. We have recently shown that the thermal conductivity has no relaxation behavior, which simplifies the analysis of our results. The relaxation behavior of the specific heat capacity is compared with literature results for other physical quantities and a detailed analysis of the temperature dependence of the relaxation parameters is presented.     

Addition-elimination reactions between phenyllithium and some perfluorovinylether compounds

Reactions between C₆H₅Li and C₃F₇OCFCF₂ (I) yield phenyl substituted perfluorovinylethers. Stoichiometry and reaction temperature dictate the degree of substitution. With each replacement of F^θ by C₆H₅^θ the subsequent substitutions require more forcing conditions. The F^θ is substituted easier than the C₃F₇O^θ during the addition-elimination reactions.     

Numerical Simulation of the Application of NiTi Alloys in Medical Technologies

Shape memory alloys are nowadays already established as a material which is able to solve exceptional tasks in practical applications. Particularly, its utilization in the field of medical technologies increases steadily. For example micro tools (staple, catheters) and implants (coronary stents) are made out of Nickel-Titanium well known as a basic shape memory alloy. Apart from the advantages like the avoidance of auxiliary components and joints in the system and to utilize the high volume specific work of shape memory alloys, NiTi alloys exhibit a good biocompatibility. This property is necessary with regard to either permanent or temporary implants. To optimize the use of NiTi alloys in the scope of medical technologies, the support of the development of applicable tools by numerical simulations is highly recommended. However the complex material behaviour containing a profoundly thermomechanical coupling poses indeed a big challenge to the material modeling and its implementation into a finite element code. Particularly, the material model proposed by Helm [1] proves to be a firm model containing the most common properties of shape memory alloys, as the pseudoelasticity, the shape memory effect and the two-way effect. In the present contribution the FE modelling of a medical staple used in foot surgery is presented by considering the model of Helm which was investigated by the authors to improve its performance in the finite element method [2]. The foot staple, produced by a group of members of the SFB 459 which is funded by the DFG, avails the shape memory effect to excite the desired clamping effect [3]. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Production of highly aligned microfiber bundles from polymethyl methacrylate via stable jet electrospinning for organic solid-state lasers

The fabrication of micron-sized poly(methyl methacrylate) (PMMA) polymer optical fibers doped with rhodamine B as an organic dye is demonstrated. Highly aligned and defect-free fibers are fabricated by using the stable jet electrospinning (SJES) method and systematically varying critical parameters such as solvent type and polymer concentration. At optimal conditions, for example, a polymer concentration of 35 wt% of PMMA in butanone, ribbon-shaped fibers with a smooth surface and diameter of about 20 μm could be spun using SJES mode and deposited on a rotating drum as target in a highly aligned manner. Photoluminescence spectra of the doped fibers excited longitudinally and transversely with a laser show an excitation peak with full-width-at-half-maximum of only 5.05 nm and a low lasing threshold at a pump energy of 0.55 μJ, indicating that SJES could become a new source of amplified optics components or organic solid-state fiber lasers.     

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Mixed norm estimates for certain generalized Radon transforms

We obtain essentially optimal local mixed norm inequalities for certain generalized Radon transforms defined by integration over curves.

     

On the delamination and crack formation in a thin wall fabricated using laser solid freeform fabrication process: An experimental–numerical investigation

Parts fabricated using laser solid freeform fabrication (LSFF) are subject to thermal stresses due to the layer-by-layer material deposition and the temperature distribution characteristic throughout the process domain. The thermal stress patterns and intensity contribute significantly to potential delamination and crack formation. In this paper, the temperature distribution and stress field induced during the multilayer LSFF process, and their correlation with delamination and crack formation are studied. This is performed by a numerical and experimental investigation in the fabrication of a thin wall of 304L stainless steel. For time-dependent predictions on the locations of maximum temperatures and thermal stresses and their patterns, a three-dimensional (3D) transient finite element model is employed to simulate the process, including the geometry of the deposited materials as well as coupled temperature and stress distributions across the process domain. The experimental results are used to verify the numerical results as well as to investigate the correlation between the numerical results and micro-crack formations across the fabricated parts. The experiments are conducted with the same process parameters used in the numerical analyses using a 1 kW Nd:YAG pulsed laser. The trend of numerical and experimental results reveals that by preheating the substrate prior to the fabrication process, it is possible to substantially reduce the micro-cracks formed across the part. To demonstrate the feasibility of preheating on the reduction of micro-cracks, several simulations and experiments are performed in which a crack-free result is obtained when the substrate is preheated to 800 K. For this case, 22% reduction in thermal stresses is obtained throughout the process domain.     

XPS analyses of lanthanides phosphates

XPS measurements were performed on lanthanide orthophosphates LnPO₄ (Ln: La, Ce, Nd, Gd), and correlated with XRD and some EDS analyses. Single lanthanide phosphates LnPO₄ and mixed lanthanide phosphates LnxLn^′1−xPO₄, all crystallized in a monoclinic structure similar to the monazite mineral. Results were examined qualitatively and quantitatively, by considering the Ln 3d lines, P 2p line and O 1s line.Ionic sputtering does not induce significant broadening nor an additional shift of the lanthanide peaks and does not have an effect on their chemical environments, except in the case of cerium. However, sputtering seems to significantly reduce the intensity of the O 1s and P 2p peaks, while Auger peaks of carbon and oxygen atoms interfere, respectively, with the 3d line of gadolinium and neodymium. Those phenomena are all the more important when the Nd and Gd content is weak and must be taken into account for a quantitative analysis of the spectra.The quantitative analyses reveal the expected results for single monazites. On mixed phosphates, the measured phosphorous and oxygen amounts are generally more valid for non-sputtered sample surfaces than for sputtered surfaces, while the calculated relative amount of lanthanides [Ln]/[Ln′] are correct in all the cases.One of the important goals of this work was to have a satisfactory value for the atomic ratio La/Gd, and particularly in the case of (La,Ce)PO₄ and (La,Gd)PO₄, to obtain good agreement between the calculated lanthanides ratio Nd/Gd and ratios estimated from XRD and EDS measurements.