My main research interests are in geometry, but I also worked on the numerical simulation of granular media. How do these seemingly distant subjects relate to one another?
Numerical simulation of granular media consists in reproducing the evolution with time of an assembly of particles (typically sand, pebbles, rice...) on a computer. This requires, among other things, a physical model for the contacts and an algorithm to detect the occurrence of these contacts. The contact detection algorithm is the reason why geometry comes into play. The contact detection method implemented in the simulation code I contributed to develop uses weighted Delaunay triangulations, also sometimes called regular triangulations. This method was designed by Didier Müller in the twodimensional case [1] and JeanAlbert Ferrez for threedimensional spherical grains [2,3]. I extended the method and JeanAlbert Ferrez's code to handle nonspherical particle shapes: spheropolyhedra [4]. The convergence of the triangulationsbased contact detection method is conditioned to the connectedness of the flipgraph associated to a finite subset of the 3dimensional Euclidean space, a longstanding open problem in discrete geometry. Along these directions, I proved that the flipgraph of the (set of vertices of the) 4dimensional cube (also sometimes called tesseract), is connected. [1]Techniques informatiques efficaces pour la simulation de milieux granulaires par des méthodes déléments distincts
