The onset of jamming as the sudden emergence of an infinite $k$-core cluster

Details The onset of jamming as the sudden emergence of an infinite $k$-core cluster The onset of jamming as the sudden emergence of an infinite $k$-core cluster

2004-10-25

arxiv.org/abs/cond-mat/0410595v2

Physics

Condensed Matter

Soft Condensed Matter

5 pages; new k-core with "force balance" model introduced replacing directed k-core model (where anisotropic scaling was not t

Scientific paper

A theory is constructed to describe the zero-temperature jamming transition as the density of repulsive soft spheres is increased. Local mechanical stability imposes a constraint on the minimum number of bonds per particle; we argue that this constraint suggests an analogy to $k$-core percolation. The latter model can be solved exactly on the Bethe lattice, and the resulting transition has a mixed first-order/continuous character. The exponents characterizing the continuous part appear to be the same as for the jamming transition. Finally, numerical simulations suggest that in finite dimensions the $k$-core transition can be discontinuous with a nontrivial diverging correlation length.

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