We present a three-dimensional distinct element model (DEM) able to handle populations of spherocylinders. We report on granular crystallization occurring when vibrating mono-disperse assemblies of spherocylinders that faithfully reproduce the corresponding results of physical experiments from the literature.

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We address the weighted max-cut problem, or equivalently the problem of maximizing a quadratic form in n binary variables. If the underlying (symmetric) matrix is positive semidefinite of fixed rank d, then the problem can be reduced to searching the extreme points of a zonotope, thus becoming of polynomial complexity in O(n d−1 ). Reverse search is an efficient and practical means for enumerating the cells of a regular hyperplane arrangement, or equivalently, the extreme points of a zonotope. We present an enhanced version of reverse search of significantly reduced computational complexity that uses ray shooting and is well suited for parallel computation. Furthermore, a neighborhood zonotope edge following descent heuristic can be devised. We report preliminary computational experiments of a parallel implementation of our algorithms.

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We consider the school bus routing and scheduling problem, where transportation demand is known and bus scheduling can be planned in advance. We present a comprehensive methodology designed to support the decision of practitioners. We first propose a modeling framework where the focus is on optimizing the level of service for a given number of buses. Then, we describe an automatic procedure generating a solution to the problem. It first builds a feasible solution, which is subsequently improved using a heuristic. We analyze two important issues associated with this methodology. On the one hand, we analyze the performance of three types of heuristics both on real and synthetic data. We recommend the use of a simulated annealing technique exploring infeasible solutions, which performs slightly better than all others. More importantly, we find that the performance of all heuristics is not globally affected by the choice of the parameters. This is important from a practitioner viewpoint, as the fine tuning of algorithm parameters is not critical for its performance. On the other hand, we propose an interactive tool allowing the practitioner to visualize the proposed solution, to test its robustness, and to dynamically rebuild new solutions if the data of the original problem are modified.

We first describe the three-dimensional extension of the molecular-dynamics models for granular media simulations. We then discuss the known energy dissipation problem occurring when simulating dense granular media with the usual molecular-dynamics forces models. We finally propose a force model able to control the energy dissipation in the multiparticle contact situations typical to dense granular media, together with appropriate numerical results.

This paper introduces the notion of Voronoi diagrams and Delaunay triangulations generated by the vertices of a piecewise at, triangulated surface. Based on properties of such structures, a generalized ip algorithm to construct the Delaunay triangulation and Voronoi diagram is presented. An application to biological membrane growth modeling is then given. A Voronoi partition of the membrane into cells is maintained during the growth process, which is driven by the creation of new cells and by restitutive forces of the elastic membrane.

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