Wear-quantification of textured geomembranes using digital imaging analysis

During the past decades there has been an increase in the use of geosynthetics in construction due to their versatility in providing a wide array of functions such as reinforcement, containment, separation, filtration and drainage. Often, geosynthetics are used in conjunction with other geosynthetics to accomplish these functions. However, geosynthetics create possible planes of weakness which can lead to failures. Textured geomembranes are widely used within landfill and mining industries due to their containment and shear strength properties, however, there are subjected to a wide array of loads and environments which are potentially hazardous, as such is of utmost importance to retain their integrity in order to avoid ecological disasters. The challenge is to understand how geomembranes resist damage, wear and which of these factors control the development of wear on textured geomembranes. Digital imaging techniques have been used in order to develop a protocol that describes the quantification of wear on textured structured geomembranes. Direct shear tests were performed to induce wear on the geomembrane textures (asperities) to analyse the wear mechanisms and study the factors that induce wear on the asperities. The research showed that normal stress and shear displacement have a major role in the development of wear on interfaces. However, the geometrical characteristics of the geomembrane asperities control the amount of wear the geomembrane can sustain without significant shear strength loss. These outcomes help to better understand the behaviour of interfaces which have as component geomembranes, leading to more robust designs. This study also proposed new asperity texture shapes by using Rapid Prototyping (RP) techniques, such as Selective Laser Sintering and Fused Filament Fabrication. Using RP techniques to create new textures for the geomembrane, could allow the creation of textures which have increased shear strength thresholds and better withstand wear, allowing for more advanced and economical designs

On the Distribution of Small Powers of a Primitive Root

AbstractLet Ng={gn:1⩽n⩽N}, where g is a primitive root modulo an odd prime p, and let fg(m, H) denote the number of elements of Ng that lie in the interval (m, m+H], where 1⩽m⩽p. H. Montgomery calculated the asymptotic size of the second moment of fg(m, H) about its mean for a certain range of the parameters N and H and asked to what extent this range could be increased if one were to average over all the primitive roots (modp). We address this question as well as the related one of averaging over the prime p

Surface feature detection and description with applications to mesh matching

In this paper we revisit local feature detectors/descriptors developed for 2D images and extend them to the more general framework of scalar fields defined on 2D manifolds. We provide methods and tools to detect and describe features on surfaces equiped with scalar functions, such as photometric information. This is motivated by the growing need for matching and tracking photometric surfaces over temporal sequences, due to recent advancements in multiple camera 3D reconstruction. We propose a 3D feature detector (MeshDOG) and a 3D feature descriptor (MeshHOG) for uniformly triangulated meshes, invariant to changes in rotation, translation, and scale. The descriptor is able to capture the local geometric and/or photometric properties in a succinct fashion. Moreover, the method is defined generically for any scalar function, e.g., local curvature. Results with matching rigid and non-rigid meshes demonstrate the interest of the proposed framework

On the Structure of the Irreducible Polynomials Over Local Fields

AbstractThe paper is concerned with the structure of irreducible polynomials in one variable over a local field (K, v). The main achievement is the definition of a system P(ƒ) of invariant factors for each monic irreducible polynomial ƒ ∈ K[X]. It is proved that these invariants are characteristic, i.e., by using invariants we may describe the set of irreducible polynomials over a local field

Tin dioxide sol-gel derived thin films deposited on porous silicon

Undoped and Sb-doped SnO2 sol¿gel derived thin films have been prepared for the first time from tin (IV) ethoxide precursor and SbCl3 in order to be utilised for gas sensing applications where porous silicon is used as a substrate. Transparent, crack-free and adherent layers were obtained on different types of substrates (Si, SiO2/Si). The evolution of the Sn¿O chemical bonds in the SnO2 during film consolidation treatments was monitored by infrared spectroscopy. By energy dispersive X-ray spectroscopy performed on the cross section of the porosified silicon coupled with transmission electron microscopy, the penetration of the SnO2 sol¿gel derived films in the nanometric pores of the porous silicon has been experimentally proved