Gérald Gurtner

Physics, Networks and Agent-Based Models

Interlude: Random Networks — The “Delaunay” Network

You like periodic networks but they give you headaches when you look at them? Me too. Let’s have a look to another random network, the “Delaunay” network.

Delaunay.pngThis network is a bit special but it interesting to illustrate one important point about these networks. It is generated thanks to random uniform distribution of points on the plane. The points are then linked with a Delaunay triangulation. Since it is fully triangulated, the theory predicts that all the beams will deform through the stretching mode, not through bending. In the literature there is sometimes a confusion between material deforming exclusively through stretching (whose MIcroscopic deformation is affine) and optimal material (whose MAcroscopic deformation is affine). If it is rather straight-forward that the latter implies the former, the reverse is not true. This is an example: theory predicts that this is not an optimal material, and numerical simulations show that its elastic moduli are between 73% and 78% of the optimal ones.

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