Evaluation of the performance of tilt scanning interferometry for tomographic imaging and profilometry

In this paper we investigate the performance of Tilt Scanning Interferometry in tomographic imaging and profilometry applications, with an emphasis on the factors that limit the quality of image reconstruction. Depth resolution is mainly degraded by a frequency chirp that appears in the temporal interference signal when a large tilting range is scanned. It is shown through a numerical simulation that the chirp depends on the curvature of the illumination wavefront and also on the position of the pivot axis of the illumination beam. Data processing methods are proposed to overcome these limitations and their effects are illustrated with experimental measurements of opaque surfaces and a weakly scattering phantom with internal features. The effect of speckle decorrelation is also discussed.     

Gromov's Non-Squeezing Theorem and Beltrami Type Equation

We introduce a method for constructing J-complex discs. The method only uses the standard scheme for solving the Beltrami equation and the Schauder principle. As an application, we give a short self-contained proof of Gromov's Non-Squeezing Theorem.     

Quasi-Set-Theoretical Foundations of Statistical Mechanics: A Research Program

Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac) into the scope of quasi-set theory. We also show that, in order to derive Maxwell–Boltzmann statistics, it is not necessary to assume that the particles are distinguishable or individuals. In other words, Maxwell–Boltzmann statistics is possible even in an ensamble of indistinguishable particles, at least from the theoretical point of view. The main goal of this paper is to provide the mathematical grounds of a quasi-set theoretical framework for statistical mechanics.     

Stable reconstruction of regular 1-Harmonic maps with a given trace at the boundary

We consider the numerical solvability of the Dirichlet problem for the 1-Laplacian in a planar domain endowed with a metric conformal with the Euclidean one. Provided that a regular solution exists, we present a globally convergent method to find it. The global convergence allows to show a local stability in the Dirichlet problem for the 1-Laplacian nearby regular solutions. Such problems occur in conductivity imaging, when knowledge of the magnitude of the current density field (generated by an imposed boundary voltage) is available inside. Numerical experiments illustrate the feasibility of the convergent algorithm in the context of the conductivity imaging problem.     

Characterisation of tribocorrosion behaviour of multilayer PVD coatings

The effect of repassivation on tribocorrosion behaviour of two multilayer coatings of different structures is studied experimentally by measuring the variation of instantaneous open-circuit potential during friction. One coating consists of alternating Cr and CrN layers, while another consists of alternated layers of CrN and ZrN. Analysis of the results showed that friction force, i.e. the rate of the mechanical energy supplied to the material in the contact zone, has no direct influence on the tribocorrosion behaviour; however, the wear rate does strongly influence the tribocorrosion. A simple phenomenological model of repassivation of the multilayer coating is developed assuming “surface coverage” approach. This model establishes the relationship between the rate of mechanical activation of material by friction and the behaviour of the open-circuit potential.     

Pyridylalkylamine ligands and their palladium complexes: structure and reactivity revisited by NMR

Pyridylmethylamines or pma are versatile platforms for different catalytic transformations. Five pma‐ligands and their respective Pd complexes have been studied by liquid state NMR. By comparing ¹H, ¹³C and ¹⁵N chemical shifts for each pma/pma–Pd couple, a general trend for the metallacycle atoms concerns variations of the electronic distribution at the pendant arm, especially at the nitrogen atom of the ligand. Moreover, the increase of the chemical shift of the pendant arm nitrogen atom from primary to tertiary amine is also related to the increase of crowding within the complex. This statement is in good agreement with X‐ray data collected for several complexes. Catalytic results for the Suzuki–Miyaura reaction involving the pma–Pd complexes showed within this series that a sterically crowded and electron‐rich ligand in the metallacycle was essential to reach the coupling product with a good selectivity. In this context, NMR study of chemical shifts of all active nuclei especially in the metallacycle could give a trend of reactivity in the studied family of pma–Pd complexes. Copyright © 2014 John Wiley & Sons, Ltd.