Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of first order Euler and Prandtl corrections plus a further error term. The equation for the error term is weakly nonlinear; its linear part is the time dependent Stokes equation. This error equation is solved by inversion of the Stokes equation, through expressing the solution as a regular (Euler-like) part plus a boundary layer (Prandtl-like) part. The main technical tool in this analysis is the Abstract Cauchy-Kowalewski Theorem. Received: 5 September 1996 / Accepted: 14 July 1997     

CEMS of nitride coatings in agressive environments

The corrosion properties of single layered TiN and CrN films have been compared to bi-layered and multi-layered Ti/TiN films. XPS has showed that in humid SO₂ atmosphere the best corrosion properties have been achieved by a multi-layered Ti/TiN coating. Cyclic voltammetry in acetate buffer has been applied to measure the porousity and corrosion resistance of coatings. The best results have been achieved by multi-layered Ti/TiN and CrN films. Conversion electron Mössbauer spectroscopy has been used to study the changes in the interface Fe/TiN during thermal treatment in UHV. It has been shown that the amount of iron nitrides in the interface increases with increasing temperature.     

Hadron masses and matrix elements from the QCD Schrödinger functional

We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.     

The corrosion of weathering steel by SO2 polluted atmospheres at its very early stages

CEMS was used in conjunction with AES to study the protective film formed on a weathering steel by exposure to a highly SO₂-polluted atmosphere. Ferrous species (sulphite) and ferric oxyhydroxides (ferrihydrite and α-FeOOH) were identified as corrosion products. From the correlation of CEMS and AES results the evolution with time of the different compounds is obtained, and a possible reaction sequence is outlined.     

Lateral IBIC characterization of single crystal synthetic diamond detectors

In order to evaluate the charge collection efficiency (CCE) profile of single‐crystal diamond devices based on a p‐type/intrinsic/metal configuration, a lateral Ion Beam Induced Charge (IBIC) analysis was performed over their cleaved cross sections using a 2 MeV proton microbeam. CCE profiles in the depth direction were extracted from the cross‐sectional maps at variable bias voltage. IBIC spectra relevant to the depletion region extending beneath the frontal Schottky electrode show a 100% CCE, with a spectral resolution of about 1.5%. The dependence of the width of the high efficiency region from applied bias voltage allows the constant residual doping concentration of the active region to be evaluated. The region where the electric field is absent shows an exponentially decreasing CCE profile, from which it is possible to estimate the diffusion length of the minority carriers by means of a drift–diffusion model. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Precision measurement of gravity with cold atoms in an optical lattice and comparison with a classical gravimeter

We report on a precision measurement of gravitational acceleration using ultracold strontium atoms confined in an amplitude-modulated vertical optical lattice. An uncertainty Δg/g ≈ 10(-7) is reached by measuring at the 5th harmonic of the Bloch frequency. The value obtained with this microscopic quantum system is consistent with the one measured with a classical gravimeter. Using lattice modulation to prepare the atomic sample, we also achieve high visibility of Bloch oscillations for ～ 20 s. These results can be of relevance for testing gravitational redshift and Newtonian law at micrometer scale.     

X‐Tream quality assurance in synchrotron X‐ray microbeam radiation therapy

Microbeam radiation therapy (MRT) is a novel irradiation technique for brain tumours treatment currently under development at the European Synchrotron Radiation Facility in Grenoble, France. The technique is based on the spatial fractionation of a highly brilliant synchrotron X‐ray beam into an array of microbeams using a multi‐slit collimator (MSC). After promising pre‐clinical results, veterinary trials have recently commenced requiring the need for dedicated quality assurance (QA) procedures. The quality of MRT treatment demands reproducible and precise spatial fractionation of the incoming synchrotron beam. The intensity profile of the microbeams must also be quickly and quantitatively characterized prior to each treatment for comparison with that used for input to the dose‐planning calculations. The Centre for Medical Radiation Physics (University of Wollongong, Australia) has developed an X‐ray treatment monitoring system (X‐Tream) which incorporates a high‐spatial‐resolution silicon strip detector (SSD) specifically designed for MRT. In‐air measurements of the horizontal profile of the intrinsic microbeam X‐ray field in order to determine the relative intensity of each microbeam are presented, and the alignment of the MSC is also assessed. The results show that the SSD is able to resolve individual microbeams which therefore provides invaluable QA of the horizontal field size and microbeam number and shape. They also demonstrate that the SSD used in the X‐Tream system is very sensitive to any small misalignment of the MSC. In order to allow as rapid QA as possible, a fast alignment procedure of the SSD based on X‐ray imaging with a low‐intensity low‐energy beam has been developed and is presented in this publication.