Bundling by volume exclusion in non-equilibrium spaghetti

In physical networks, like the brain or metamaterials, we often observe localbundles, corresponding to locally aligned link configurations. Here weintroduce a minimal model for bundle formation, modeling physical networks asnon-equilibrium packings of hard-core 3D elongated links. We show that growthis logarithmic in time, in stark contrast with the algebraic behavior of lowerdimensional random packing models. Equally important, we find that this slowkinetics is metastable, allowing us to analytically predict an algebraic growthdue to the spontaneous formation of bundles. Our results offer a mechanism forbundle formation resulting purely from volume exclusion, and provide abenchmark for bundling activation and growth during the assembly of physicalnetworks.