Vibrations and diverging length scales near the unjamming transition.

By L. Silbert, Andrea J. Liu, Sidney R. Nagel. 2005

315 citations recorded by the source corpus.

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction phi is lowered towards the onset of unjamming at phi(c), the density of vibrational states approaches a nonzero value in the limit of zero frequency. For phi >phi(c), there is a crossover frequency, omega* below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with phi-phi(c). Characteristic length scales, determined from the dominant wave vector contributing to the eigenmode at omega*, diverge as power laws at the unjamming transition.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry, AI for Physical Sciences

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Citations in the corpus

The jamming transition as a paradigm to understand the loss landscape of deep neural networks (2018, background): “predict that the density of vibrational modes D( √ λ) displays a plateau up to vanishingly small λ, as observed numerically [35, 36] and sketched in Fig.”
Mean-field theory of hard sphere glasses and jamming (2008, methodology): “• An important result that attracted a lot of attention in the last years is the presence of an anomalous bunch of soft modes in jammed packings at ϕJ (Majmudar et al., 2007; O’Hern et al., 2003; Silbert et al., 2005; Wyart et al., 2005a).”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “Such a diverging length scale has been observed numerically in the vibrational eigenmodes and in the response to point perturbations (Ellenbroek et al., 2009, 2006; Silbert et al., 2005).”
Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, background): “We note that density of states (vibrational modes) in packings of soft spheres has been the subject of recent interest (Silbert et al., 2005; Wyart et al., 2005).”
A density-independent rigidity transition in biological tissues (2014, unknown): “tional spectrum of the dynamical matrix [36, 37].”
Universal spectrum of normal modes in low-temperature glasses (2015, methodology): “17 is fully consistent with the boson peak anomaly in the excitation spectrum of soft-sphere packings as known from simulations and scaling arguments (11, 12, 14, 23, 24, 40), confirming the superuniversal behavior of glassy systems close to jamming.”
Sum Rules for the Quasi-Static and Visco-Elastic Response of Disordered Solids at Zero Temperature (2004, background): “[64, 65, 66, 67] A divergence of the non-affine corrections to elasticity could thus arise around this point.”
Minimal model of active colloids highlights the role of mechanical interactions in controlling the emergent behavior of active matter (2015, background): “such low frequency modes have much lower energy barriers than high frequency modes [67].”
Measurement of growing dynamical length scales and prediction of the jamming transition in a granular material (2007, background): “Though very different, both types of systems seem to approach an unusual critical point where the growing lengthscale is purely dynamical, such that there is no macroscopic change in instantaneous structur”