Jamming criticality revealed by removing localized buckling excitations.

By Patrick Charbonneau, E. Corwin, Giorgio Parisi, Francesco Zamponi. 2014

123 citations recorded by the source corpus.

Recent theoretical advances offer an exact, first-principles theory of jamming criticality in infinite dimension as well as universal scaling relations between critical exponents in all dimensions. For packings of frictionless spheres near the jamming transition, these advances predict that nontrivial power-law exponents characterize the critical distribution of (i) small interparticle gaps and (ii) weak contact forces, both of which are crucial for mechanical stability. The scaling of the interparticle gaps is known to be constant in all spatial dimensions d-including the physically relevant d=2 and 3, but the value of the weak force exponent remains the object of debate and confusion. Here, we resolve this ambiguity by numerical simulations. We construct isostatic jammed packings with extremely high accuracy, and introduce a simple criterion to separate the contribution of particles that give rise to localized buckling excitations, i.e., bucklers, from the others. This analysis reveals the remarkable dimensional robustness of mean-field marginality and its associated criticality.

Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, 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): “[62] Patrick Charbonneau, Eric I Corwin, Giorgio Parisi, and”
Universality of the SAT-UNSAT (jamming) threshold in non-convex continuous constraint satisfaction problems (2017, methodology): “(12) is precisely the modulus of the contact force associated to the particle pair 〈 i j 〉 , and the matrix encodes the network of contacts in the particle packing [ 10 ] .”
Edwards Statistical Mechanics for Jammed Granular Matter (2016, background): “…predict instead (DeGiuli et al., 2014b) D(ω) ∼ ωd−1 ω ω0 ω2/ω∗2 ω0 ω ω∗ constant ω ω∗ , (42) which is also exhibited by the perceptron model (Franz et al., 2015) and found in simulations of jammed soft spheres in dimensions 3–7 (Charbonneau et al., 2015a; Lerner et al., 2016; Mizuno et al., 2017).”