Effects of compression on the vibrational modes of marginally jammed solids.

By Matthieu Wyart, L. Silbert, Sidney R. Nagel, T. Witten. 2005

296 citations recorded by the source corpus.

Glasses have a large excess of low-frequency vibrational modes in comparison with most crystalline solids. We show that such a feature is a necessary consequence of the weak connectivity of the solid, and that the frequency of modes in excess is very sensitive to the pressure. We analyze, in particular, two systems whose density D(omega) of vibrational modes of angular frequency omega display scaling behaviors with the packing fraction: (i) simulations of jammed packings of particles interacting through finite-range, purely repulsive potentials, comprised of weakly compressed spheres at zero temperature and (ii) a system with the same network of contacts, but where the force between any particles in contact (and therefore the total pressure) is set to zero. We account in the two cases for the observed (a) convergence of D(omega) toward a nonzero constant as omega-->0, (b) appearance of a low-frequency cutoff omega*, and (c) power-law increase of omega* with compression. Differences between these two systems occur at a lower frequency. The density of states of the modified system displays an abrupt plateau that appears at omega*, below which we expect the system to behave as a normal, continuous, elastic body. In the unmodified system, the pressure lowers the frequency of the modes in excess. The requirement of stability despite the destabilizing effect of pressure yields a lower bound on the number of extra contact per particle deltaz:deltaz> or =p1/2, which generalizes the Maxwell criterion for rigidity when pressure is present. This scaling behavior is observed in the simulations. We finally discuss how the cooling procedure can affect the microscopic structure and the density of normal modes.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, 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): “[35] Matthieu Wyart, Leonardo E Silbert, Sidney R Nagel,”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “Equation (41) has been shown to be a bound for stability in (Wyart et al., 2005b) based on physical arguments and confirmed analytically in a replica calculation of the perceptron model of jamming (Franz et al., 2015).”
Mean-field theory of hard sphere glasses and jamming (2008, background): “• 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).”
Hyperuniform states of matter (2018, background): “Jammed packings have received considerable attention in the theoretical and experimental literature [38, 45–48, 199, 245, 247–257].”
Jammed hard-particle packings: From Kepler to Bernal and beyond (2010, background): “…2001; Gao et al., 2006; Liu and Nagel, 1998; Makse and Kurchan, 2002; O’Hern et al., 2003; Parisi and Zamponi, 2010; Silbert et al., 2002, 2005; Song et al., 2008; Wyart et al., 2005), which for a given packing procedure aims to understand typical configurations and their frequency of occurrence.”
Universal spectrum of normal modes in low-temperature glasses (2015, background): “Hence, above a typical frequency ωp ∼ e1=2 the density of states is flat, as found in soft spheres (12, 14).”
The role of local structure in dynamical arrest (2014, background): “Approaching φj from the high density side, a number of scaling laws emerge, and parallels may be drawn with the normal mode analysis discussed in section VE [566, 569].”
A jamming transition from under- to over-parametrization affects loss landscape and generalization (2018, background): “An opposite bound can be obtained by considerations of stability as for spheres [44], by imposing that in a stable minimum the Hessian must be positive definite.”
Erratum: On variational arguments for vibrational modes near jamming (2016, background): “In particular, there is a frequency scale ω∗ ∼ δz = z − zc beyond which the density of vibrational modes D(ω) displays a plateau [11, 20].”
Fractal free energy landscapes in structural glasses (2014, background): “Although κ = 3/2 was proposed in earlier studies [13, 14, 16, 49], the theory predicts a slightly smaller κ = 1.”