Samuel S. Schoenholz, Carl P. Goodrich, Oleg Kogan, Andrea J. Liu, Sidney R. Nagel
At zero temperature and applied stress, an amorphous packing of spheres exhibits, as a function of packing fraction, a jamming transition where the system is sensitive to boundary conditions even in the thermodynamic limit. Upon further compression, the system should become insensitive to boundary conditions but only if it is sufficiently large. Here we explore the linear response to a large class of boundary perturbations in 2 and 3 dimensions. We consider each finite packing with periodic-boundary conditions as the basis of an infinite square or cubic lattice and study properties of vibrational modes at arbitrary wave vector. Our results can be understood in terms of competition between plane waves and the anomalous vibrational modes associated with the jamming transition; boundary perturbations become irrelevant for systems that are larger than a previously identified transverse length that diverges at the jamming transition.
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http://arxiv.org/abs/1301.6982
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