Properties of Gauss Digitized Shapes and Digital Surface Integration

This paper presents new topological and geometric properties of Gauss digitizations of Euclidean shapes, most of them holding in arbitrary dimension d. We focus on r-regular shapes sampled by Gauss digitization at gridstep h. The digitized boundary is shown to be close to the Euclidean boundary in the Hausdorff sense, the minimum distance \(\frac{\sqrt{d}}{2}h\) being achieved by the projection map \(\xi \) induced by the Euclidean distance. Although it is known that Gauss digitized boundaries may not be manifold when \(d \ge 3\), we show that non-manifoldness may only occur in places where the normal vector is almost aligned with some digitization axis, and the limit angle decreases with h. We then have a closer look at the projection of the digitized boundary onto the continuous boundary by \(\xi \). We show that the size of its non-injective part tends to zero with h. This leads us to study the classical digital surface integration scheme, which allocates a measure to each surface element that is proportional to the cosine of the angle between an estimated normal vector and the trivial surface element normal vector. We show that digital integration is convergent whenever the normal estimator is multigrid convergent, and we explicit the convergence speed. Since convergent estimators are now available in the literature, digital integration provides a convergent measure for digitized objects.     

Experimental analysis of failures in filled hole compression tests of carbon/epoxy laminate

In this study, failure modes occurring during Filled hole compression (FHC) tests were analysed using post-mortem analysis for failure pattern identification and high-speed cameras for failure scenario (damage initiation and progress). Two different failure scenario were experienced depending upon the stacking sequence:

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Net compression failure for high 0° oriented lay-ups. The crack initiation is observed near the bolt but the location differs with bolt tightening or not, enabling future validation of finite element models.     

Comparison and improvement of tangent estimators on digital curves

Many contour-based applications rely on the estimation of the geometry of the shape, such as pattern recognition or classification methods. This paper proposes a comprehensive evaluation on the problem of tangent estimators on digital curves. The methods taken into account use different paradigms: approximation and digital geometry. In the former paradigm, methods based on polynomial fitting, smoothing and filtering are reviewed. In the latter case of digital geometry, we consider two methods that mainly rely on digital straight line recognition [J.-O. Lachaud, A. Vialard, F. de Vieilleville, Fast, accurate and convergent tangent estimation on digital contours, Image and Vision Computing 25(10) (2007) 1572-1587] and optimization [B. Kerautret, J.-O. Lachaud, Robust estimation of curvature along digital contours with global optimization, in: Proceedings of Discrete Geometry for Computer Imagery, Lyon, France, Lecture Notes in Computer Science, vol. 4992, Springer, Berlin, 2008]. The comparison takes into account objective criteria such as multi-grid convergence, average error, maximum error, isotropy and length estimation. Experiments underline that adaptive methods based on digital straight line recognition often propose a good trade-off between time and precision and that if precision is to be sought, non-adaptive methods can be easily transformed into adaptive methods to get more accurate estimations.     

Convex Digital Polygons,Maximal Digital Straight Segments and Convergence of Discrete Geometric Estimators

Discrete geometric estimators approach geometric quantities on digitized shapes without any knowledge of the continuous shape. A classical yet difficult problem is to show that an estimator asymptotically converges toward the true geometric quantity as the resolution increases. For estimators of local geometric quantities based on Digital Straight Segment (DSS) recognition this problem is closely linked to the asymptotic growth of maximal DSS for which we show bounds both about their number and sizes on Convex Digital Polygons. These results not only give better insights about digitized curves but indicate that curvature estimators based on local DSS recognition are not likely to converge. We indeed invalidate a conjecture which was essential in the only known convergence theorem of a discrete curvature estimator. The proof involves results from arithmetic properties of digital lines, digital convexity, combinatorics and continued fractions.     

Chemical sensor based on a novel capacitive microwave flexible transducer with polymer nanocomposite-carbon nanotube sensitive film

Microsystem Technologies - This study presents the results on the feasibility of a resonant planar chemical capacitive sensor in the microwave frequency range suitable for gas detection and...     

Drilling of composite structures

Structural parts made of composites have frequently to be drilled in the aircraft industry. However, little is know about the interacting conditions between the drilling tool and the material, which may be multi-type and multi-size. This study proposes a model which links the axial penetration of the drill bit to the conditions of delamination (crack opening mode I) of the last few plies. Several types of tool/material contact conditions were analyzed and were compared with experimental measurements, and with a model taken from the literature. Our study shows a close correlation between experiment and calculation when the thrust force of the drill is modeled by taking into account the geometrical nature of the contact between the tool and a laminate composite material.     

Analytical models of composite material drilling

Drilling of composite material structures is widely used for aeronautical assemblies. When drilling, damage to the composite laminate is directly related to the cutter geometry and the cutting conditions. Delamination of the composite materials at the hole exit as directly related to the axial force (F _Z) of the cutter is considered to be the major such defect. To address this issue, an orthotropic analytical model is developed in order to calculate the critical force of delamination during drilling and a number of hypotheses for loading are proposed. This critical axial load is related to the delamination conditions (propagation of cracks in the last layers) and the mechanical characteristics of the composite material machined. A numerical model is also drawn up to allow for numerical validation of the analytical approach. A comparison between these analytical and numerical modellings and experimental results from quasi-static punch tests led to the choice of the loading hypothesis closest to the experimental conditions. The selection of corresponding load permits to model the drilling critical thrust force on delamination and then to optimise the cutting conditions. The dimensions and geometrical shape of the cutter are of considerable importance when it comes to choosing this load. The present article focuses on the case of the twist drill, which is commonly used to drill thick plates. However, this work can be adapted to different cutter geometries.     

Possibilites de la diffusion centrale dans l'examen d'etats alteres du ciment

After a review of the idea of specific surface in relation to x-ray diffuse scattering, we examine in a comparative way the data gathered on normal cements and on cements having been subjected to different types of modifications. We show that these modifications are very evident on pure kinds (of cement), but are much more uncertain on concrete.     

Two Plane-Probing Algorithms for the Computation of the Normal Vector to a Digital Plane

Digital planes are sets of integer points located between two parallel planes. We present a new algorithm that computes the normal vector of a digital plane given only a predicate “is a point x in the digital plane or not”. In opposition to classical recognition algorithm, this algorithm decides on-the-fly which points to test in order to output at the end the exact surface characteristics of the plane. We present two variants: the H-algorithm, which is purely local, and the R-algorithm which probes further along rays coming out from the local neighborhood tested by the H-algorithm. Both algorithms are shown to output the correct normal to the digital planes if the starting point is a lower leaning point. The worst-case time complexity is in \(O(\omega )\) for the H-algorithm and \(O(\omega \log \omega )\) for the R-algorithm, where \(\omega \) is the arithmetic thickness of the digital plane. In practice, the H-algorithm often outputs a reduced basis of the digital plane while the R-algorithm always returns a reduced basis. Both variants perform much better than the theoretical bound, with an average behavior close to \(O(\log \omega )\). Finally, we show how this algorithm can be used to analyze the geometry of arbitrary digital surfaces, by computing normals and identifying convex, concave or saddle parts of the surface. This paper is an extension of Lachaud et al. (Proceedings of 19th IAPR international conference discrete geometry for computer imagery (DGCI’2016), Nantes, France. Springer, Cham, 2016).     

Nanocomposite electrodes based on pre-synthesized organically capped platinum nanoparticles and carbon nanotubes. Part II: Determination of diffusion area for oxygen reduction reflects platinum accessibility

In this paper we report the determination of the diffusion area for oxygen reduction in porous electrode structure having a controlled platinum loading and based on capped platinum electrocatalysts and carbon nanotubes. Such a parameter is expected to be higher than the macroscopic geometrical area of the active porous layer. The oxygen diffusion area is determined by cyclic voltammetry after impregnation of the electrode structure by the electrolyte, and using the equations available for peak potential and peak current as a function of scan speed for irreversible redox couple. First it is found first that the oxygen diffusion area is dependent on the total amount of platinum in the electrode. Second, for a given platinum loading, the diffusion area is higher when the mass ratio of platinum to carbon nanotube decreases. This point indicates that the accessibility of platinum capped electrocatalyst is better in such cases. It is thus concluded that the oxygen diffusion area determination in porous electrode structures may be used to characterize the accessibility of the capped electrocatalysts for oxygen reduction. Even if this area is different in nature from the one calculated by Hydrogen Underpotential Deposition, we believe that its determination might be of interest for the characterization of porous electrodes structures in which the electrocatalyst is combined with a finely divided carbon support.