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Contact detection for convex polygons/polyhedra has been a critical issue in discrete/discontinuous modelling, such as the discrete element method (DEM) and the discontinuous deformation analysis (DDA). The recently developed 3D contact theory for polyhedra in DDA depends on the so-called entrance block of two polyhedra and reduces the contact to evaluate the distance between the reference point to the corresponding entrance block, but effective implementation is still lacking.

In this paper, the equivalence of the entrance block and the Minkowski difference of two polyhedra is emphasised and two well-known Minkowski difference-based contact detection and overlap computation algorithms, GJK and expanding polytope algorithm (EPA), are chosen as the possible numerical approaches to the 3D contact theory for DDA, and also as alternatives for computing polyhedral contact features in DEM. The key algorithmic issues are outlined and their important features are highlighted.

Numerical examples indicate that the average number of updates required in GJK for polyhedral contact is around 6, and only 1 or 2 iterations are needed in EPA to find the overlap and all the relevant contact features when the overlap between polyhedra is small.

The equivalence of the entrance block in DDA and the Minkowski difference of two polyhedra is emphasised; GJK- and EPA-based contact algorithms are applied to convex polyhedra in DEM; energy conservation is guaranteed for the contact theory used; and numerical results demonstrate the effectiveness of the proposed methodologies.

The purpose of this paper is to investigate the role of gender in education, occupation and employment in Southern Europe and more specifically in Greece, Italy, Portugal and Spain. The goal is to provide measures that can trace gender differences with respect to their educational and employment features in these countries, explore whether these differences converge over time and compare the patterns observed in each country given their socio-economic similarities.

This paper uses raw data drawn from the European Social Survey (ESS) for the decade 2002-2012. It provides a method for quantifying gender differences in education, occupation and employment and their evolution over time based on distance measures.

The results reveal that gender distances in education have gradually subsided in these countries. However, occupational choices differ steadily over the years for all countries. The paper provides, therefore, solid evidence that equalizing the level of education between men and women during those years did not result in a decrease in the occupational distances between them. Moreover, based on the latest round the findings suggest that men and women are equally likely to having experienced unemployment within the last five years.

Further research could be done to include results based on raw data from the seventh round of the ESS. This may provide valuable information for Spain and Portugal who did participate in this round.

This research implies that more needs to be done to accelerate progress in order to achieve gender occupational equality in Southern Europe.

This paper draws attention to issues concerning gender differences in education, horizontal and vertical segregation and employment for which it provides distance measures and evidence of how they have evolved over time, based on raw data analysis from the ESS.