Jamming at zero temperature and zero applied stress: the epitome of disorder.

By C. O’Hern, L. Silbert, Andrea J. Liu, Sidney R. Nagel. 2003

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We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

Subfields: Computational Mechanics, Condensed Matter Physics, Materials Chemistry, Probabilistic & Bayesian Methods

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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): “Interestingly, this state of affairs is very similar to the jamming transition of particles, for which the noise in the data due to finite size effects is quite strong when quantities are expressed in terms of the density φ (analogous to P/N) but very small when quantities are expressed in terms of ”
Universal robotic gripper based on the jamming of granular material (2010, background): “While the concept of jamming has been used to explain the onset of rigidity in a wide range of amorphous systems from molecular glasses to macroscopic granular materials [22, 24, 26], the benefits of jamming for the assembly of materials with tunable behavior are just beginning to”
End-to-End Differentiable , Hardware Accelerated , Molecular Dynamics in Pure Python (2019, background): “The study of such disordered systems is often referred to as the study of “Jammed (O’hern et al., 2003)” solids.”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, methodology): “…are independent of polydispersity or dimensionality (van Hecke, 2010; Liu and Nagel, 2010; Majmudar et al., 2007; Makse et al., 2004, 1999, 2000; O’Hern et al., 2003, 2002; Zhang and Makse, 2005): • Pressure: p ∼ (φ− φc)α (38) • Static bulk modulus: B∞ ∼ (φ− φc)α−1 (39) • Static shear…”