Phonon gap and localization lengths in floppy materials

By G. During, Edan Lerner, Matthieu Wyart. 2012

68 citations recorded by the source corpus.

Gels of semi-flexible polymers, network glasses made of low valence elements, softly compressed ellipsoid particles and dense suspensions under flow are examples of floppy materials. These systems present collective motions with almost no restoring force. To study theoretically and numerically the frequency-dependence of the response of these materials and the length scales that characterize their elasticity, we use a model of isotropic floppy elastic networks. We show that such networks present a phonon gap for frequencies smaller than a frequency ω* governed by coordination, and that the elastic response is characterized, and in some cases localized, on a length scale that diverges as the phonon gap vanishes (with a logarithmic correction in the two dimensional case). lc also characterizes velocity correlations under shear, whereas another length scale l* ∼ 1/ω* controls the effect of pinning boundaries on elasticity. We discuss the implications of our findings for suspension flows, and the correspondence between floppy materials and amorphous solids near unjamming, where lc and l* have also been identified but where their roles are not fully understood.

Subfields: Computer Vision and Pattern Recognition, Materials Chemistry, Mechanics of Materials, AI for Physical Sciences

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Citations in the corpus

Edwards Statistical Mechanics for Jammed Granular Matter (2016, methodology): “The length scale l∗ has been computed in (During et al., 2013; Wyart, 2010).”
A jamming transition from under- to over-parametrization affects loss landscape and generalization (2018, background): “In that case, we expect the landscape to be related to that of floppy spring networks, whose spectra are predicted in [11].”
Erratum: On variational arguments for vibrational modes near jamming (2016, background): “∼ 1/δz may seem to contradict effective medium results and numerics, which indicates that the length scale characterizing the decay of most of the amplitude of the response to a local strain is lc ∼ 1/ √ δz both for floppy [30] and jammed materials [5].”
Architecture and coevolution of allosteric materials (2016, methodology): “There, the elastic response becomes heterogeneous on all scales [15, 16].”